Scanning Electron Microscopy

Abstract

This chapter provides an overview of the concepts of scanning electron microscopy ( ) from a theoretical as well as practical operational perspective. The theory section begins with the basics of image formation followed by an explanation of the interaction of the electron beam with the sample. A description of the different types of electron guns is also included. The concepts involved with image formation from a rastered (or scanned) electron beam on a surface is explained along with the mechanisms of contrast generation from sample surface topography and sample composition. The different SEM detectors are also explained including a description of the practical application of detectors under various sample conditions. Numerous diagrams and figures in this chapter illustrate imaging geometries and possible SEM system configurations. Included in the chapter is an explanation of the various instrument operation parameters for different samples as well as a discussion of the effects of electron-beam accelerating voltages on sample imaging, contrast, and resolution.

More advanced topics are also included such as the use of beam deceleration and in-lens imaging and detectors. Analytical SEM techniques are also explained with the explanation of the use of energy-dispersive x-ray detectors (EDS) used to measure sample composition as well as provide compositional maps of a sample. Application of SEM to a variety of materials systems under varying conditions are discussed with multiple examples and illustrations given.

The earliest historical contribution to the idea of a scanning electron microscope (SEM) was probably made by H. Stintzing in a German patent application [5.1]. In his patent he proposed irradiating a sample with a narrowly collimated beam (light, x-ray, corpuscles) and moving the sample transversely to the beam. The magnitude of interaction between beam and sample was to be measured by a sufficiently sensitive recording device, to be amplified and then displayed on an electron tube. This idea aimed to determine the size of small particles not accessible to light microscopy. Howeve,r the method proposed was unable to generate a magnified image.

The first electron-beam scanner capable of producing an image of the surface of a bulk sample with the emitted secondary electrons ( ) was developed by H. Knoll [5.2]. In this instrument a focused electron beam was scanned across the sample surface by magnetic deflection line-by-line. The generated SE were converted into an electronic signal, which was amplified and then used to modulate the brightness of an electron tube. Both the electron beam of the scanner and of the display tube were scanned synchronously across the same distance by perpendicular pairs of deflection coils, thus the electron-beam scanner at that time possessed unit magnification. The contrast in the SE image was due to the varying yield of SE caused by the different local chemical composition of the sample surface. However, submicroscopic resolution with an SEM was first obtained by M. von Ardenne using the transmission mode (so-called scanning transmission electron microscope ( )) [5.3]. The early development of electron microscopy up to 1940 has been described extensively by E. Ruska [5.4]. While the development of SEM in Europe was interrupted by World War II, the idea of SEM was used by Zworykin, Hillier, and Snyder in the United States for the construction of such an instrument [5.5]. After World War II, experiments with scanning electron microscopes started in England and France. Since 1948 C.W. Oatley from the Engineering Laboratory of the University of Cambridge directed intensive development in that field, which led to the first commercial scanning electron microscope available in 1965. Pioneering work in the improvement of instrumentation (e. g., electron sources, electron optics, detectors, signal processing), the investigation of electron–specimen interaction, elucidation of fundamental contrast mechanisms, and development of methods for the preparation of samples were done in the 1960s and 1970s (for books, proceedings of SEM conferences, and reviews see [5.10, 5.11, 5.12, 5.13, 5.14, 5.15, 5.16, 5.6, 5.7, 5.8, 5.9]). At the same time the SEM was applied extensively in very different fields for imaging of surfaces, for the local crystallographic characterization of polycrystalline materials by electron backscattered diffraction ( ), and in combination with x-ray microanalytical equipment such as an energy-dispersive spectrometer ( ) or a wavelength-dispersive spectrometer ( ) for the local element analysis of specimens (for books or proceedings of SEM conferences see [5.14, 5.15, 5.17, 5.18, 5.19, 5.20, 5.21, 5.22, 5.23, 5.24, 5.25, 5.26, 5.27, 5.28]).

A significant improvement in SEM instrumentation was made by the development of the field-emission scanning electron microscope ( ) that became commercially available in the 1980s. In the FESEM instead of a thermionic gun a field-emission gun ( ) is used for electron-beam generation, which allows the formation of an electron probe with a diameter of about ${\mathrm{0.5}}\,{\mathrm{nm}}$. Together with further improvements in electron optics and electron detectors on the one hand and in specimen preparation on the other hand, high-resolution imaging by FESEM became feasible. Additionally, the FESEM enables specimens to be imaged at extremely low acceleration voltages, i. e., below ${\mathrm{1}}\,{\mathrm{kV}}$, also at high resolution, without sacrificing the traditional high kV and high current (analytical) performance. The operation of the FESEM at low acceleration voltages opens new avenues for interesting applications in the characterization of surfaces (for reviews of specific aspects of the instrumentation, image formation, and application of FESEM at conventional or low acceleration voltages, respectively, see [5.29, 5.30, 5.31, 5.32, 5.33, 5.34]).

A very interesting step forward in the instrumentation was the development of a so-called variable pressure ( ) or environmental scanning electron microscope ( ) pushed in the 1980s in particular by G.D. Danilatos. Investigations of specimens using secondary or backscattered electrons for imaging, in SEM and FESEM restricted to high vacuum, can be performed in the VP/ESEM in a low vacuum at a pressure of about $\mathrm{10}$ up to a few thousand Pa, often assisted by introduction of water vapor into the chamber during imaging. Obviously, this is of great interest for samples that consist of materials that may contain dirt or fluids, respectively, having a partial pressure in the low vacuum range mentioned. Typical examples are water- or oil-containing natural specimens. Moreover, electric insulators can be imaged without prior conductive coating by VP/ESEM in low vacuum without significant electric charging artifacts. The VP/ESEM (ESEM was originally developed by Electroscan, and in later years has been used as a trade name by FEI/Thermo) became commercially available in 1987 (for reviews of specific aspects of the instrumentation, image formation, and application of VP/ESEM see [5.35, 5.36, 5.37]). Currently all manufacturers offer some form of variable-pressure SEM, with the ability to image with both secondary and backscatter electrons.

Modern high-resolution FESEMs have at an electron energy of ${\mathrm{30}}\,{\mathrm{keV}}$ a specified resolution power in the SE mode in the range of $0.5{-}1\,{\mathrm{nm}}$, which corresponds to about the size of a small molecule. It marks the smallest size of a structure accessible on one hand. Working at the lowest magnification of an SEM on the other hand allows imaging of visible structures as large as about ${\mathrm{5}}\,{\mathrm{mm}}$, i. e., high-resolution SEMs cover a wide range of six orders of magnitude for the structural characterization of surfaces. A further advantage of the SEM is the simul taneous acquisition of different signals generated by the local interaction of the beam electrons with the specimen. Each of these signals, e. g., SE and backscattered electrons ( s), carries different information about the sample, thus an extensive multidimensional data set about an area of interest can be obtained by one scan line-by-line across this area. The recording time may vary from a few seconds only to about ${\mathrm{1}}\,{\mathrm{min}}$ depending on the strength of the signal and the signal-to-noise ratio ( ) required.

Scanning electron microscopy is now a well-established method for the characterization of surfaces in ultrahigh vacuum ( ), high vacuum ( ), and low vacuum ( ) in many different fields. Clearly, it is not possible to mention all of them, however, the main fields are certainly the materials (metals, alloys, ceramics, glasses) and surface sciences, semiconductor research and industry, life sciences, and miscellaneous sciences such as polymer and food research, mineralogy, geology, the oil industry, and archaeology.

In addition to scanning electron microscopy some other surface-sensitive methods such as atomic force microscopy, scanning tunneling microscopy, and photoelectron microscopy are described in this book. It is certainly of particular interest to see in detail how these surface-sensitive methods complement each other, what specific advantages they offer, and how they compare with SEM.

1 Conventional Scanning Electron Microscopy

The principle of a scanning electron microscope is shown schematically in Fig. 5.1. The two major parts are the microscope column and the electronics console. The microscope column consists of the electron gun (with the components cathode, Wehnelt cylinder, anode), one or two condenser lenses, two pairs of beam deflection coils (scan coils for $x$, $y$ deflection), the objective lens, and some apertures. In the specimen chamber at the lower end of the microscope column are located the specimen stage and the detectors for the different signals generated by the electron–specimen interaction, though the current FESEMs often feature some form of in-lens detectors. The microscope column and the specimen chamber are evacuated using a combination of prevacuum and high-vacuum pumps (usually turbomolecular pumps). The pressure in the specimen chamber typically amounts to about ${\mathrm{10^{-4}}}\,{\mathrm{Pa}}$, allowing the beam electrons to travel from the cathode to the specimen with little interaction with the residual gas molecules. The electronics console consists of the electric power supplies for the acceleration voltage (usual range about $0.5{-}30\,{\mathrm{kV}}$) as well as the condenser and objective lenses, the scan generator, and electronic amplifiers for the different signals acquired. Moreover, the console also houses one or more monitors (liquid crystal display (LCD)) for displaying the graphic user interface and live or recorded image, numerous knobs and a computer keyboard to control the electron beam, the signals selected, and the image recording. More recently, some SEMs forego the numerous knobs which are replaced by a mouse-controlled interactive program running on the personal computer (PC).

Fig. 5.1

Schematic drawing of a conventional SEM . The evacuated microscope column (inside the dashed frame) contains the electron gun, electromagnetic lenses, electromagnetic deflection coils, apertures, the specimen stage, and the detectors. The electronics console houses the power supplies for the acceleration voltage and the electromagnetic lenses, the scan generator, amplifiers for the signals, and monitors for display and recording of images. Modern SEMs are controlled by a PC. BSE: backscattered electrons; : cathodoluminescence; SE: secondary electrons; STEM: scanning transmission electron microscope signal; x-ray: x-ray signal

How does the SEM work? The beam electrons are emitted from the cathode and accelerated by a voltage of $0.5{-}30\,{\mathrm{kV}}$ between the cathode and anode forming a smallest beam cross section—the crossover—near the anode with a diameter of about $10{-}50\,{\mathrm{\upmu{}m}}$. This spot size is too large to produce a sharp image. Therefore, the crossover is demagnified by the lens system consisting of one or two condenser lenses and one objective lens and focused on the specimen surface. Most SEMs can produce an electron beam having a smallest spot size of about $5{-}10\,{\mathrm{nm}}$ and an electron probe current in the range of $E-12{-}E-10\,{\mathrm{A}}$, which is sufficient to form an image with a reasonable SNR. For higher probe currents required for some modes of operation the smallest probe spot size increases to ${\mathrm{100}}\,{\mathrm{nm}}$ or more. The objective lens has a variable relatively long focal length that allows a large working distance ( ; it corresponds to the distance between the specimen and lower pole piece) in the range of about $2{-}50\,{\mathrm{mm}}$. This ensures that the various signals generated by the impinging beam electrons (Fig. 5.2) in the small specimen interaction volume can be collected by detectors located lateral above the specimen with sufficient efficiency. Pairs of beam deflection coils located in front of the objective lens and controlled by a scan generator scan the electron probe line-by-line across a small area of the specimen. The detected signal is then collected and recorded through the graphic user interface on the computer monitor screen.

Fig. 5.2

Schematic drawing of signals for a thin sample generated by the impinging electrons

The signals may vary from one location to another as the electron–specimen interaction changes because of, e. g., topography and specimen composition. The magnification of the image is given by the ratio of the length of the scan on the monitor and the corresponding length of the scan on the specimen. For example, an increase in magnification can simply be achieved by decreasing the current of the deflection coils in the microscope column (i. e., lowering the length of the scan on the specimen) and keeping the image size on the monitor constant. It should be mentioned that the magnification also depends on the WD, however, modern SEMs compensate automatically for each WD, thus keeping the displayed magnification correct. Figure 5.3 shows a series of images recorded with increasing magnifications over a range of almost three orders of magnitude.

Fig. 5.3

Micrograph series of increasing magnification of a tick nymph, recorded at ${\mathrm{2}}\,{\mathrm{kV}}$ ($60\times$ to ${\mathrm{10000}}\times$). The specimen was air dried and sputter coated with gold

For crystal structure analysis (Sect. 5.5) basically two strategies exist: (1) The mode of beam deflection changes from scanning line-by-line to rocking of the electron beam when the probe is at rest on a chosen location and the angle of incidence is scanned within a selectable angular range to form an electron channeling pattern. (2) The electron backscattered diffraction pattern from the point of electron-beam impact is recorded by means of a position-sensitive detector and analyzed revealing information about the local crystal structure.

One of the greatest strengths of the SEM is the tremendous depth of focus, i. e., the range of heights of the specimen being simultaneously in focus (Fig. 5.3). Because of the small objective aperture diaphragm (about $30{-}100\,{\mathrm{\upmu{}m}}$) and the large WD the semiangle $\alpha_{\mathrm{p}}$ of the convergent impinging electron probe is in the order of ${\mathrm{10}}\,{\mathrm{mrad}}$ only. At magnifications that are comparable to those of light microscopy (e. g., $1000\times$) the SEM has a depth of focus that is about $\mathrm{100}$ times greater than that of an optical microscope, obviously because the semiangle of convergence is much larger in the latter case.

To take full advantage of all the information that SEM can provide, an understanding of its operation modes and the influence of electron-beam parameters on the image resolution, the image contrast, the signal strength, and the SNR as well as the electron–specimen interaction is mandatory. The remarkable success of scanning electron microscopy over several decades is mainly due to the tremendous depth of focus, the brilliant image contrast, and the relatively straightforward sample preparation for imaging of surfaces, and, in combination with x-ray microanalytical equipment, its capability of local quantitative element analysis of specimens.

1.1 Electron Guns, Electron Lenses, Detectors, and Stages

1.1.1 Electron Guns

The electron gun provides the SEM with an electron beam of adjustable current and energy. The most classic electron gun is the triode gun based on thermionic emission from a tungsten filament heated to about $T_{\mathrm{c}}={\mathrm{2700}}\,{\mathrm{K}}$ (Fig. 5.4). The filament has a diameter of about ${\mathrm{0.1}}\,{\mathrm{mm}}$ and is bent in the shape of a V hairpin to localize the emission area on the tip. The size of this area is around ${\mathrm{100}}\,{\mathrm{\upmu{}m}}\times{\mathrm{150}}\,{\mathrm{\upmu{}m}}$. By thermionic excitation the electrons overcome the work function $\phi$ of the tungsten tip and a current with the density $j_{\mathrm{c}}$ is emitted according to the Richardson law

$$j_{\mathrm{c}}=AT_{\mathrm{c}}^{2}\exp\left(-\frac{\phi}{k_{\mathrm{B}}T_{\mathrm{c}}}\right),$$

(5.1)

where $A$ represents a constant depending on the cathode material and $k_{\mathrm{B}}$ is the Boltzmann constant; $\phi={\mathrm{4.5}}\,{\mathrm{eV}}$ for tungsten. The density $j_{\mathrm{c}}$ depends strongly on the temperature: $j_{\mathrm{c}}$ is about ${\mathrm{1.8}}\,{\mathrm{A{\,}cm^{-2}}}$ for $T_{\mathrm{c}}={\mathrm{2700}}\,{\mathrm{K}}$ and about ${\mathrm{3}}\,{\mathrm{A{\,}cm^{-2}}}$ for $T_{\mathrm{c}}={\mathrm{2800}}\,{\mathrm{K}}$.

Fig. 5.4

Schematic drawing of the thermionic emission triode gun with a tungsten hairpin filament. The filament is heated by the applied voltage $U_{\mathrm{H}}$; $R_{\mathrm{W}}$, variable resistor to adjust the potential $U_{\mathrm{W}}$ between the Wehnelt cylinder and cathode; $U$, acceleration voltage. After [5.30]

The emitted electrons are accelerated from the filament at a high negative potential (e. g., ${\mathrm{-30}}\,{\mathrm{kV}}$) toward the anode at ground potential (${\mathrm{0}}\,{\mathrm{V}}$). Central holes in the Wehnelt cylinder and in the anode enable a fraction of the accelerated electrons (e. g., $E_{0}={\mathrm{30}}\,{\mathrm{keV}}$) to move toward the lenses in the microscope column. The emission current is typically in the order of ${\mathrm{100}}\,{\mathrm{\upmu{}A}}$ and can be controlled by the bias of the Wehnelt cylinder, which surrounds the filament. The negative Wehnelt bias is provided by a voltage drop caused by the emission current through the resistor $R_{\mathrm{W}}$. The electrostatic field distribution inside the triode gun has a focusing action to the emitted electrons generating a crossover that is located between the Wehnelt cylinder and the anode. This crossover can be characterized by the diameter $d_{0}$ and the semiangle $\alpha_{0}$ of the divergence. $d_{0}$ is usually in the order of ${\mathrm{50}}\,{\mathrm{\upmu{}m}}$. As we will see later the condenser and objective lenses produce a demagnified image of that crossover on the specimen surface representing the final electron probe (diameter $d_{\mathrm{p}}$).

An important parameter of an electron gun is its axial brightness $\beta$, which is defined as the beam current per area (equal to current density) into a solid angle $\uppi\alpha^{2}$ [5.38]

$$\beta=\frac{j}{\uppi\alpha^{2}}=\text{const}\;.$$

(5.2)

It is important to note that the brightness remains constant for all points along the electron optical axis from the cathode through the microscope column to the specimen. This means that the brightness of the final electron probe on the specimen surface is equal to the brightness of the gun regardless of apertures in the microscope column, i. e.,

$$\beta=\frac{4I_{0}}{\uppi^{2}{d_{0}}^{2}{\alpha_{0}}^{2}}=\frac{4I_{\mathrm{p}}}{\uppi^{2}{d_{\mathrm{p}}}^{2}{\alpha_{\mathrm{p}}}^{2}}\;,$$

(5.3)

where $I_{0}$ is the beam current at the crossover inside the electron gun. Equation (5.3) shows that the characteristic illumination parameters $I_{\mathrm{p}}$, $d_{\mathrm{p}}$, and $\alpha_{\mathrm{p}}$ cannot be changed independently. For example, an increase of $\beta$ for given $d_{\mathrm{p}}$ and $\alpha_{\mathrm{p}}$ clearly requires an increase of $I_{\mathrm{p}}$.

The work function of tungsten is relatively high. Lanthanum hexaboride ($\mathrm{LaB_{6}}$) has a significantly lower work function ($\phi={\mathrm{2.7}}\,{\mathrm{eV}}$) and can therefore emit greater current densities at lower temperature ($T_{\mathrm{c}}={\mathrm{1900}}\,{\mathrm{K}}$). At the same time the brightness of the electron probe is also increased since the maximum brightness of an electron gun [5.38] is given as

$$\beta=\frac{j_{\mathrm{c}}E_{0}}{\uppi kT_{\mathrm{c}}}$$

(5.4)

i. e., the brightness $\beta$ is inversely proportional to the temperature of the cathode. The $\mathrm{LaB_{6}}$ cathode consists of a small piece of an $\mathrm{LaB_{6}}$ single crystal with a tip radius typically of about ${\mathrm{1}}\,{\mathrm{\upmu{}m}}$. The single crystal is supported by a nonreactive material and is resistively heated. It seems worth mentioning that (1) in the cathode chamber the operation of an $\mathrm{LaB_{6}}$ requires a vacuum better than ${\mathrm{10^{-4}}}\,{\mathrm{Pa}}$ to avoid cathode contamination (tungsten cathode: about ${\mathrm{10^{-3}}}\,{\mathrm{Pa}}$) and (2) its alignment is critical.

Characteristic values of the triode gun with thermionic tungsten and the $\mathrm{LaB_{6}}$ cathode are summarized in Table 5.1.

Table 5.1 Characteristic parameters of different electron guns

1.1.2 Electron Lenses

As discussed in Sect. 5.1.1, Electron Guns, the electrons emerge from the electron gun as a divergent beam. Two or three electromagnetic lenses and apertures in the microscope column (Fig. 5.1) reconverge and focus the beam into a demagnified image of the first crossover generated by the gun. The final lens—the objective lens—focuses the beam into the smallest possible spot of $4{-}10\,{\mathrm{nm}}$ (thermionic source) on the sample surface, i. e., the total demagnification is about $5000\times$.

Rotationally symmetric electromagnetic lenses consist of a coil with $N\,I$ ampere windings inside an iron pole piece. Typically, $N\,I$ is in the order of ${\mathrm{10^{3}}}\,{\mathrm{A}}$ for the condenser and objective lenses. The iron pole piece has a small gap in its axial bore. The current in the coil generates a magnetic field carried by the iron, which also appears at the gap forming a bell-shaped stray field distribution on the optical axis with a radial and axial field component. Off-axis electrons move due to the Lorentz force along screw trajectories because the radial component of the field results in a rotation around the optical axis. Electrons emerging divergently from a point in front of the lens are focused in an image point behind the lens. The lenses of SEMs can usually be considered weak lenses (because the pole piece is not saturated). In this case, the principal planes of the lens coincide with its optical center and the formulas for thin light optical lenses can be used. In close analogy to light optics the strength of an electromagnetic lens can be characterized by its focal length $f$. Using the thin lens formulas we can write

$$\frac{1}{f}=\frac{1}{p}+\frac{1}{q}\;,$$

(5.5)

where $p$ is the distance from the object ($=$ crossover) and $q$ is the distance to the image. Both, $p$ and $q$ are related to the center of the lens. The magnification $M$ is given simply by

$$M=\frac{q}{p}\;,$$

(5.6)

where $M<1$ for $p> 2f$, i. e., a demagnified image of an object is obtained at these imaging conditions. Therefore, a strong demagnification of about $5000\times$ of the first crossover can be obtained for $p\gg 2f$ for each of the two or three lenses by successive demagnification of each intermediate crossover. In case of two condenser lenses they usually are combined and adjusted by one control only.

The pole pieces of condenser lenses are symmetrical, i. e., the diameters of the axial bores in the upper and lower half of the pole piece are identical. In contrast to that the pole piece of the objective lens is very asymmetric (1) to limit the magnetic field at the specimen level and (2) to house the beam deflections coils, the adjustable objective aperture, and the stigmator (not shown in Fig. 5.1). The asymmetric objective lens (called the pinhole or conical lens) adapts for the wide range of the WD of about $2{-}50\,{\mathrm{mm}}$ by an adjustable focal length. However, working at a large WD inevitably degrades the electron optical properties of the objective lens and enlarges the final spot size $d_{\mathrm{p}}$. For a detailed description of the electron optical properties of electromagnetic lenses and deflection coils the reader is referred to books about electron optics [5.40, 5.41, 5.42, 5.43].

All electromagnetic lenses involved in successive demagnification suffer from an imperfect rotational symmetry and aberrations, which degrade their electron optical performance. The effects of lens aberrations cannot be compensated. However, they can be minimized, which is most effective for the final—the objective—lens. Let us consider briefly the three significant effects:

• 1. Spherical aberration : The spherical aberration constant $C_{\mathrm{s}}$ causes an error disc of the diameter [5.44]

  $$d_{\mathrm{s}}=\frac{1}{2C_{\mathrm{s}}{\alpha_{\mathrm{p}}}^{3}}$$

  (5.7)

• 2. Chromatic aberration : The chromatic aberration caused mainly by the energy spread of the electrons from the gun is characterized by the constant $C_{\mathrm{c}}$ and causes an error disc of the diameter

  $$d_{\mathrm{c}}=C_{\mathrm{c}}\,\frac{\Updelta E}{E_{0}}\,\alpha_{\mathrm{p}}\;,$$

  (5.8)

  where $\Updelta E/E_{0}$ represents the relative energy spread of the beam electrons.

• 3. Diffraction : The diffraction of electrons on the objective aperture results in a further error disc—the Airy disc —of diameter

  $$d_{\mathrm{f}}=\frac{0.6\lambda}{\alpha_{\mathrm{p}}}\;,$$

  (5.9)

  where $\lambda$ is the wavelength of the electrons.

In a first approximation it is possible to superpose the squared diameters of the individual discs to estimate the effective electron probe diameter

$$d_{\text{pe}}^{2}={d_{\mathrm{p}}}^{2}+{d_{\mathrm{s}}}^{2}+{d_{\mathrm{c}}}^{2}+{d_{\mathrm{f}}}^{2}\;.$$

(5.10)

$d_{\mathrm{p}}^{2}$ is given by (5.3) as

$$d_{\mathrm{p}}^{2}=\left(\frac{4I_{\mathrm{p}}}{\uppi^{2}\beta}\right)\alpha_{\mathrm{p}}^{-2}\;.$$

More precise, but at the same time more complicated relations for the effective probe diameter were derived by Barth and Kruit [5.45] and Kolarik and Lenc [5.46].

Under the conditions normally used in conventional SEM (i. e., $E_{0}=5{-}30\,{\mathrm{keV}}$) the chromatic aberration as well as the effect of the diffraction are relatively small compared to the remaining contributions and can be neglected [5.38]. The optimum aperture $\alpha_{\text{opt}}$, which allows the smallest effective electron probe diameter $d_{\text{min}}$, can be obtained by the first derivative $\partial d_{\text{pe}}/\partial\alpha_{\mathrm{p}}=0$ and is given as

$$\alpha_{\text{opt}}=\left(\frac{4}{3}\right)^{1/8}\left[\dfrac{\left(\frac{4I_{\mathrm{p}}}{\uppi^{2}\beta}\right)^{1/2}}{C_{\mathrm{s}}}\right]^{1/4}.$$

(5.11)

By using the approach mentioned above, i. e., $d_{\text{pe}}^{2}=d_{\mathrm{p}}^{2}+d_{\mathrm{s}}^{2}$, and (5.3), (5.7a,b), and (5.11a,b), the minimum effective electron probe diameter is

$$d_{\mathrm{p},\min}=\left(\frac{4}{3}\right)^{3/8}\left[\left(\frac{4I_{\mathrm{p}}}{\uppi^{2}\beta}\right)^{3/2}{C}_{\mathrm{s}}\right]^{1/4}.$$

(5.12)

It is obvious that $d_{\mathrm{p},\min}$ increases as $I_{\mathrm{p}}$ increases or $\beta$ decreases. Both, $I_{\mathrm{p}}$ and $\beta$ are parameters depending on the performance of the electron gun (5.3). $C_{\mathrm{s}}$ is a parameter characterizing the performance of the objective lens and should be as small as possible. As previously mentioned, the operation of the SEM at a large WD inevitably degrades the electron optical properties of the objective lens, i. e., $C_{\mathrm{s}}$ increases as the WD increases. Just to provide a rough idea about values for $d_{\mathrm{p},\min}$ and $\alpha_{\text{opt}}$ at usual electron energies ($5{-}30\,{\mathrm{keV}}$), a moderate WD and a probe current $I_{\mathrm{p}}$ of about ${\mathrm{10^{-11}}}\,{\mathrm{A}}$, which gives a sufficient $\mathrm{S}/\mathrm{N}$ ratio, $d_{\mathrm{p},\min}$ typically amounts to approximately ${\mathrm{5}}\,{\mathrm{nm}}$ and $\alpha_{\text{opt}}$ to $5{-}10\,{\mathrm{mrad}}$.

It is also of interest to know the maximum probe current $I_{\mathrm{p},\max}$ under these conditions. Using (5.12) and (5.3) one obtains

$$I_{\mathrm{p},\max}=\frac{3\uppi^{2}}{16}\beta C_{\mathrm{s}}^{-2/3}{d_{\mathrm{p},\min}}^{8/3}\;.$$

(5.13)

Interestingly, it becomes obvious from (5.13) that including the effect of the spherical aberration, $I_{\mathrm{p}}$ is now proportional to $d_{\mathrm{p}}^{8/3}$ instead of $d_{\mathrm{p}}^{2}$ as before (5.3).

The electron probe current in an SEM equipped with a thermionic gun can be increased several orders of magnitude above ${\mathrm{10^{-11}}}\,{\mathrm{A}}$ as required, e. g., for microanalytical studies (Sect. 5.4). It is clear from the considerations above that an increase in the probe current inevitably increases the probe size. A rough estimate for $\mathrm{30}$-$\mathrm{keV}$ electrons shows that an increase of $I_{\mathrm{p}}$ to ${\mathrm{10^{-9}}}\,{\mathrm{A}}$ requires a probe size of about ${\mathrm{60}}\,{\mathrm{nm}}$. However, because of the electron–specimen interaction the lateral resolution of x-ray microanalysis is limited to about ${\mathrm{1}}\,{\mathrm{\upmu{}m}}$ for thick samples. Therefore, a probe diameter of ${\mathrm{100}}\,{\mathrm{nm}}$ or even several hundred nanometers can be tolerated without disadvantage for x-ray microanalysis in this case.

When considering the effective electron probe diameter the chromatic aberration of the objective lens could be neglected for energies $> {\mathrm{10}}\,{\mathrm{keV}}$. Because $d_{\mathrm{c}}$ is inversely proportional to $E_{0}$ (5.8) there is a significant increase for energies below ${\mathrm{10}}\,{\mathrm{keV}}$, in particular for the low-voltage range below ${\mathrm{5}}\,{\mathrm{keV}}$. For example, for $\mathrm{1}$-$\mathrm{keV}$ electrons the diameter of the chromatic error disc increases by a factor of $\mathrm{30}$ compared to ${\mathrm{30}}\,{\mathrm{keV}}$! When using a thermionic cathode with a tungsten filament and a probe current of about ${\mathrm{10^{-11}}}\,{\mathrm{A}}$ the energy spread is about ${\mathrm{2}}\,{\mathrm{eV}}$ (Table 5.1) and $d_{\mathrm{c}}$ contributes dominantly to the enlargement of the probe diameter (5.10). Therefore, the thermionic source is inappropriate for imaging in the low-voltage range. As we shall see in Sect. 5.2, field-emission guns with a one order of magnitude smaller energy spread and about five orders of magnitude larger brightness are very well suited for low-voltage SEM ( ).

In the context of the objective lens the existence of a stigmator was mentioned, which usually is located near the pole-piece gap. Because of imperfect rotational symmetry of the pole-piece bores, magnetic inhomogeneities of the pole piece, or some charging effects in the bore or at the objective aperture, the magnetic field in the objective lens becomes asymmetric. This causes different focal lengths in the sagittal and meridional planes, which leads to low image quality degraded by astigmatism. The astigmatism can be compensated for by adding a cylinder lens adjustable in its strength and azimuth. The effect of a cylinder lens is realized by the stigmator consisting of a pair of quadrupole lenses.

1.1.3 Detectors and Detection Strategies

Electron detectors specifically collect the signals emerging from the specimen as a result of electron–specimen interaction. The efficiency of the signal collection depends on the type of the detector, its performance, and its detection geometry, i. e., its position related to location of the signal emitting area. For an understanding of the recorded signals, knowledge of the influence of these parameters is critical.

1.1.3.1 Detectors

To detect electrons in SEM three different principles are commonly used. One principle is based on the conversion of signal electrons to photons by a scintillation material. Then, the photons are converted into an electric signal by a photomultiplier, which is proportional to the number of electrons impinging on the scintillator. The second principle is based on the conversion of electrons to electron–hole pairs by a semiconductor, which can be separated before recombination causing an external charge-collection current. This current is proportional to the number of electrons impinging on the semiconductor. While the principle of scintillation detection is used for secondary, backscattered, and transmitted electrons (in case of thin specimens), the semiconductor detector is mostly used for backscattered electrons only. Finally, the third principle is based on the electron channel multiplier tube, which converts the signal electrons by direct impact at its input to secondary electrons and multiplies them inside the tube. The output signal is proportional to the number of impinging signal electrons.

Besides of electrons the electron–specimen interaction can also produce electromagnetic radiation, namely cathodoluminescence ( ) and x-rays (Fig. 5.2). Cathodoluminescence shows a close analogy to optical fluorescence light microscopy ( ) where light emission is stimulated by irradiation with ultraviolet light (photoluminescence ). In principle, for the detection of emitted light, which has a wavelength in the range of about $0.3{-}1.2\,{\mathrm{\upmu{}m}}$, a photomultiplier is very well suited (see above) and therefore most often used. However, the commonly low intensity of the CL signal requires, for a sufficient $\mathrm{S}/\mathrm{N}$ ratio, a high collection efficiency of the emitted light. Table 5.2 presents the most common detector types for SE, BSE, and CL. The detectors for x-rays will be described in Sect. 5.4 of this chapter.

Table 5.2 Most common electron detectors for SEM

1.1.3.1.1 Scintillation Detector

The scintillation detector for SE—the Everhart–Thornley (ET ) detector  [5.47]—is shown schematically in Fig. 5.5. The generated SE are collected by a positively biased collector grid, then they pass the grid and are accelerated by about ${\mathrm{10}}\,{\mathrm{kV}}$ to the conductive coated scintillator. The scintillation material converts electrons to photons, which are guided by a metal-coated quartz glass to the photocathode of a photomultiplier where photoelectrons are generated and amplified by a factor of about $\mathrm{10^{6}}$. Usually the electronic signal at the output of the photomultiplier is further amplified. Several scintillator materials, such as plastic scintillators, lithium-activated glass, P-47 powder, or yttrium-aluminum-garnet ( ) and yttrium-aluminum-perovskite ( ) single crystals, are in use, which differ in their performance (for details see [5.38, 5.50, 5.51, 5.56, 5.57, 5.58]).

Fig. 5.5

Schematic drawing of Everhart–Thornley detector (scintillator–photomultiplier combination) for recording secondary electrons (SE). (BSE: backscattered electrons; PE: primary electrons; PM: photomultiplier; $h\nu$: energy of photons)

When the collector grid of the ET detector is negatively biased by $<{\mathrm{-50}}\,{\mathrm{V}}$ SE are not collected. In this case only the BSE can reach the scintillator on almost straight trajectories because of their higher energies. The detected fraction of BSE is very low because of the small solid angle of collection, i. e., small angular collection efficiency ( ). However, for an efficient detection of BSE the solid angle of collection of BSE detectors is significantly larger by using a larger scintillator and at the same time a shorter distance to the specimen. The BSE detector does not require the collector grid used for the SE (Fig. 5.5).

1.1.3.1.2 Semiconductor Detector

The semiconductor detector—often denoted as a solid-state detector —generates from an impinging electron with the energy $E$ a mean number of electron–hole pairs given by

$$n_{\mathrm{m}}=\frac{E}{E_{\text{exm}}}\;,$$

(5.14)

where $E_{\text{exm}}={\mathrm{3.6}}\,{\mathrm{eV}}$ is the mean energy per excitation in silicon [5.59]. The electron–hole pairs can be separated before recombination, in this way generating an external charge-collection current, which is proportional to the number of impinging electrons. Because of the energy dependence of $n_{\mathrm{m}}$ the BSE with higher energy contribute with a larger weight to the signal than the BSE having low energies. The semiconductor detector can be used only for the direct detection of BSE because impinging SE are absorbed in its thin electrical conductive layer. However, a special detector design for accelerating the SE to energies above ${\mathrm{10}}\,{\mathrm{keV}}$ also allows for detection of SE [5.48].

1.1.3.1.3 Microchannel Plate Detector

A microchannel plate (MCP) consists of a large number of parallel very small electron-multiplier tubes (diameter about $10{-}20\,{\mathrm{\upmu{}m}}$, length of a few millimeters) covering an area of about ${\mathrm{25}}\,{\mathrm{mm}}$ in diameter [5.49]. Thus this detector is thin and, when placed between objective pole piece and specimen, enlarges the work distance by only about ${\mathrm{3.5}}\,{\mathrm{mm}}$. The MCP detector system is efficient at both high and low accelerating voltages, and is capable of both secondary electron and backscattered electron detection. The MCP becomes of increasing interest for studies with low currents and in low-voltage scanning electron microscopy [5.60]. However, as yet the MCP detector is not as common as the other detector types described above.

1.1.3.1.4 Cathodoluminescence Detectors

In the few cases of strongly luminescent specimens a lens or a concave mirror is sufficient for light collection [5.61]. As mentioned above, mostly the intensity of the CL signal is low, thus a high collection efficiency of the emitted light is indispensable. This requires a solid angle of collection as large as possible, an optimum transfer of the collected light to a monochromator or directly to the photomultiplier, and a photomultiplier with a high quantum efficiency in the spectral range of the CL [5.62]. Commercial CL collector and imaging systems allow for investigations with a wavelength from less than $\mathrm{200}$ to about ${\mathrm{1800}}\,{\mathrm{nm}}$ in the imaging and spectroscopy mode. The following are the most commonly used collection systems:

• 1. Parabolic or elliptic mirrors. The light-emitting area of the specimen is located at the focus of the mirror and is formed into a parallel beam for a parabolic mirror [5.54] or focused to a slit of a spectrometer for an elliptic mirror [5.63]. The solid angle of collection is in the order of $\uppi$ sr but SE detection with an ET detector is still feasible.

• 2. Rotational ellipsoidal mirror. The light-emitting area of the specimen is located at one focus of the half of the ellipsoid of rotation [5.64]. The emitted light is focused to a light pipe or to the focal point of an optical microscope objective at the second focal point of the ellipsoid. Although the ellipsoidal mirror has the largest collection angle, the effective collection angle is limited by the acceptance angle of the light pipe or the optical microscope objective, respectively, to about ${\mathrm{0.75}}\uppi\,\text{sr}$. The limitation by the acceptance angle can be avoided by placing a parabolic mirror below the second focal point of the ellipsoid [5.65]. Very recently Rau et al [5.66] proposed an ellipsoidal confocal system collecting the emitted light, which enables CL microtomography in SEM. In principle, the proposed system allows for CL studies at high resolution, which is well below the size of the light-emitting volume.

• 3. Optical microscope objective. The CL of an optically transparent specimen can be studied by an optical microscope objective positioned below the specimen. The collection angle of this setup amounts to about ${\mathrm{1.4}}\uppi\,\text{sr}$ [5.67].

1.1.3.2 Detection Strategies

Generally, the detectors for the various signals can be combined and each of them should have an optimum position to make the best use of the electron–specimen interaction. As a matter of fact, the space for detectors is limited in particular with a short WD or with an in-lens position of the specimen for higher resolution.

A conventional SEM commonly is equipped with an ET detector located laterally above the specimen and a BSE detector (for different types see Table 5.2) located centrally above the specimen (top position). Additional ports at the specimen chamber of the SEM enable additional detectors to be installed. Because of geometry limitations, not all of the installed detectors may be used simultaneously. However, there are retractable detectors (e. g., BSE detectors) available, which can be kept in the retracted position when not needed (providing space for another detector or allowing for a shorter WD) and can readily be moved into working position if required for signal recording. Numerous multidetector systems have been proposed for BSE and SE (for reviews see [5.38, 5.68]). In the top position, e. g., two semiannular semiconductor detectors [5.69, 5.70] allow for separation of topographic and material contrast; with a four-quadrant semiconductor detector [5.71, 5.72, 5.73] the surface profile can be reconstructed and the distinction between elements with different atomic numbers is improved. Even a six-segment semiconductor detector is of interest [5.74].

For high-resolution and LVSEM the working distance should be as short as possible (say below ${\mathrm{5}}\,{\mathrm{mm}}$) because both the focal length and the aberrations of the objective lens increase with the WD (see also Sects. 5.1.1, Electron Lenses and 5.2). In contrast to the asymmetric objective lens (large focal length) where the region above the specimen is a magnetic field free space, the specimen is immersed in the field of the objective lens with a short focal length. In this case the specimen is very close to the lower objective pole piece or is placed directly inside the pole-piece gap (as in a transmission electron microscope ( ); see Chaps. 1–4). For the latter lens type—the specimen has an in-lens position and is limited in size to a few millimeter only—the collection of SE takes advantage of the fact that they can spiral upward in the magnetic field of the objective lens because of their axial velocity component. The SE have to be deflected off the axis to be recorded by an ET detector located laterally above the lens (Fig. 5.6).

Fig. 5.6

Schematic drawing of the magnetic through-the-lens detection of secondary electrons (SE) for the in-lens position of the specimen. After [5.30]

The separation of the downward-moving beam electrons and the upward-moving secondary electrons can be done most efficiently by an $\boldsymbol{E}\times\boldsymbol{B}$ system, which employs crossed electric and magnetic fields. The forces of these fields compensate each other for the beam electrons, but add for the opposite moving secondary electrons. This magnetic through-the-lens detection (for review see [5.75]) of SE has several advantages:

• 1. SE can be separated from BSE, which may not reach the detector because their higher kinetic energy causes different trajectories

• 2. Very high collection efficiency for real SE emerging from the specimen and a suppression of SE created on the walls of the system by BSE

• 3. Improved collection efficiency from inside a porous specimen (in particular cavities or holes facing the electron beam) [5.76]

• 4. Loss of directionality in the image because the SE are detected irrespective of the direction of emission (in contrast to the lateral position of the ET detector; Fig. 5.7a,ba).

Fig. 5.7a,b

Secondary (a) and backscattered electron (b) micrograph of a $\mathrm{1}$-$\mathrm{mm}$ steel ball. The arrow in (b) indicates the direction of the backscattered electron (negatively biased ETD) and the secondary electron detector

It seems worth mentioning that a real through-the-lens detection system was incorporated in one of the early SEMs [5.5]. The magnetic through-the-lens detection of SE was established by Koike et al [5.77] using a TEM with scanning attachment.

Another type of in-lens detection of SE and BSE is used in the electrostatic detector objective lens [5.78, 5.79, 5.80]. The detector is of the annular type and possesses a high collection efficiency of SE of about ${\mathrm{75}}\%$. Replacing the annular detector by a combination of two semiannular detectors A and B (Fig. 5.8) could be used to illustrate the topographic or material contrast, respectively [5.30]. Similarly, in-lens annular-type detection of SE and BSE is also used in combined or hybrid magnetic-electrostatic objective lenses [5.81]. Both types of lens are advantageous for low-voltage SEM (Sect. 5.2.2) because they provide excellent image resolution at low electron energies.

Fig. 5.8

Schematic drawing of the in-lens detection of secondary electrons (SE) with the electrostatic detector–objective lens

1.1.4 Specimen Stages and Attached Equipment

A conventional SEM is equipped with a specimen stage. The stage commonly can be loaded with the specimen via a specimen-exchange airlock chamber without breaking the high vacuum in the specimen chamber. The stage allows $x,y,z$ movements, rotation around $360^{\circ}$, and tilting (the tilting range depends on the type of the stage, e. g., $\mathrm{-15}$ to $+90^{\circ}$) of the specimen. The movements, rotation, and tilt are usually motorized in modern scanning electron microscopes. The specimen stage is eucentric if the observation point does not vary during tilting and rotation. However, some stages have this property only for tilting (semieucentric specimen stage) or do not have it (goniometric specimen stage). If the specimen stage is eucentric or semieucentric, the WD and therefore the magnification do not change during $x,y$ movement or movement along the tilt axis, respectively. Usually, the specimen is at ground potential (${\mathrm{0}}\,{\mathrm{V}}$). However, the wiring allows also the recording of the specimen current or absorbed current, as well as application of specimen bias for charge neutralization and improvement of resolution. It is obvious that the higher the electron optical performance of the SEM the better the quality of the specimen stage in terms of mechanical and thermal stability.

The manufacturers of SEMs as well as small companies supplying special attachments offer optionally specimen stages for specific investigations. For example, there are commercial hot stages available for in situ surface investigations at elevated temperatures. Depending on the type of heating device, it is possible to reach specimen temperatures up to about ${\mathrm{1370}}\,{\mathrm{K}}$ with a maximum heating rate of about ${\mathrm{200}}\,{\mathrm{K{\,}min^{-1}}}$. A hot specimen stage in an environmental scanning electron microscope (Sect. 5.3) is, among other things, very useful in studying the surface modifications caused by chemical reactions due to the exposure of samples to gases. For specific in situ heating experiments, e. g., local heating with rapid thermal loads, irradiation heating by a high-power laser coupled to an SEM can be used [5.25, 5.82].

Mainly for investigations of organic materials and, in particular, of biological specimens, cold stages are of great interest for low-temperature studies. At low temperature the electron-beam damage of the sample due to electron–specimen interaction is smaller than at room temperature [5.83, 5.84, 5.85, 5.86, 5.87] and specimens can be investigated in the frozen-hydrated stage [5.88, 5.89, 5.90]. However, cold stages are also of significant interest for materials science to investigate the low-temperature behavior of materials such as changes in mechanical properties or variations in electrical conductivity. In most cases liquid nitrogen or liquid helium is used as the cooling medium. In particular the temperature range around ${\mathrm{4}}\,{\mathrm{K}}$ and below down to about ${\mathrm{1.5}}\,{\mathrm{K}}$ allows for the investigation of typical low-temperature phenomena such as superconductivity and low-temperature devices used in cryoelectronics. Furthermore, experiments can be performed in which the temperature range of liquid He is required by the measuring principle, e. g., the ballistic phonon signal represents an example. Here the small specimen volume locally heated by the electron beam acts as a source of phonons, which propagate ballistically (i. e., without scattering) to the opposite side of the crystal where the photon detector is located. Both, the specimen and the detector have to be kept in the temperature range of liquid He. The SEM at very low temperatures was reviewed by Huebener [5.91].

The Peltier cryo stage is also typically used in conjunction with VP/ESEM—the specimen needs to be cooled down below room temperature to maintain a solid(ice)/vapor (ice sublimation) environment at a reasonable pressure (for example at ${\mathrm{0}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$ and $> {\mathrm{533}}\,{\mathrm{Pa}}$ there is still liquid water).

Further, deformation stages are used in materials science to study static and dynamic specimen deformation-related phenomena in situ [5.25]. In more detail, different types of sample deformation such as tension and compression, unidirectional bending, bending fatigue, materials machining (e. g., study of the microscopic mechanisms of abrasive wear), and microhardness testing can be performed with a microhardness tester mounted on the stages in the SEM specimen chamber. This allows for very precise positioning of the indentations generated with a very low force and their subsequent viewing/measuring. In combination with a surface displacement transducer for the detection of acoustic emission signals, the quantitative acoustic emission due to crack coalescence can be measured [5.92]. There are also stages in different laboratories that combine, e. g., deformation and heating capabilities.

With high-precision stages based on laser interferometer technology, a new field of applications is opened up in the area of SEM/FIB-based e-beam lithography, metrology, and semiconductor failure analysis. The fine positioning of the stage is made with piezoelements, which, according to the manufacturer's specification, allow a positioning reproducibility of better than ${\mathrm{50}}\,{\mathrm{nm}}$.

To obtain ultralow-magnification SEM images an SEM equipped with a motor drive specimen stage fully controlled with a personal computer (PC) has been utilized [5.93]. This motor drive stage works as a mechanical scanning device. To produce ultralow-magnification SEM images, a combination of the mechanical scanning, electronic scanning, and digital image processing techniques is used. This is a time-saving method for ultralow magnification and wide-area observation.

The stage in the SEM specimen chamber can integrate not only tools such as a microhardness tester but also other types of high-resolution microscopes, e. g., a scanning tunneling [5.94, 5.95, 5.96], scanning force [5.97], or scanning near-field optical microscope [5.98], thus combining two different microscopic techniques with their specific advantages in one hybrid microscope.

As mentioned in the previous section, the specimen for in-lens SEMs must be small because it has to be placed in the gap of the objective lens. This requires specimen stages and holders almost identical to the ones used in TEM (side-entry sample exchange system). The specimen is mounted in a specimen holder, which commonly allows for tilting the specimen around one axis by $\pm 30^{\circ}$ or $\pm 40^{\circ}$. Optionally, there are, for example, double-tilt specimen holders with two tilt axes as well as hot and cold/cryoholders available. The specimen holders also normally allow the use of support grids ${\mathrm{3}}\,{\mathrm{mm}}$ in diameter, which is of interest for studies in transmission mode.

1.1.5 Special Topics

1.1.5.1 Digital Image Recording

Modern SEMs allow recording of multichannel (e. g., SE and BSE) digital images, which are stored pixel by pixel (pixel: picture element) in a PC. Digital images usually have a square size of ${\mathrm{512}}\times{\mathrm{512}}$, ${\mathrm{1024}}\times{\mathrm{1024}}$ pixels or larger [5.99]. However, rectangular image formats are also in use, e. g., ${\mathrm{3000}}\times{\mathrm{2000}}$ pixels. For each pixel the analog signal arriving from the detector is integrated during the pixel time. The value obtained represents the pixel intensity, which is digitized by an analog-to-digital-converter () usually into a range of $\mathrm{8}$ or ${\mathrm{16}}\,{\mathrm{bit}}$. In practice, a sufficient lateral and signal resolution can be obtained with ${\mathrm{1024}}\times{\mathrm{1024}}$ pixels and ${\mathrm{8}}\,{\mathrm{bit}}$, respectively, which requires a storage capacity over ${\mathrm{10^{7}}}\,{\mathrm{bit}}$, i. e., ${\mathrm{1}}\,{\mathrm{MB}}$. Twice the number of pixels in the $x$- and $y$-direction requires a 4-fold storage capacity, i. e., ${\mathrm{4}}\,{\mathrm{MB}}$. For final storage, the digital images can be transferred from the PC via fast data transfer to external mass storage devices or cloud computers.

1.1.5.2 Specimen Tilting and Stereo Imaging

Specimen stages allow the sample to be tilted, which is of interest for several special applications such as stereo imaging, reconstruction of the topography, three-dimensional () morphometry, and possibly contrast enhancement. In the case of a flat object aligned normal to the beam, i. e., the tilt angle $\Theta$ amounts to $0^{\circ}$, there is no distortion of the projected shape of structures. For example, circular holes in a flat specimen appear circular in the image (Fig. 5.9a-ea). After tilting the flat object (the tilt axis has a horizontal direction in the micrograph) two effects become obvious in the image (especially visible at high tilt angles, e. g., $\Theta=45^{\circ}$) (Fig. 5.9a-eb): (1) the circular holes have an elliptic shape with an axis ratio of approximately $\mathrm{0.7}$, i. e., the shape is distorted, and (2) the upper and lower rim of the upper and lower hole appears unsharp whereas the rim of the central hole appears sharp.

Fig. 5.9a-e

Effect of tilt compensation and dynamic focusing in the SEM. Secondary electron micrographs of the holes in a flat aluminum specimen. (a) Tilt angle $\Theta=0^{\circ}$. (b) Tilting $\Theta=45^{\circ}$ around the horizontal axis (the focus of the beam is located in the center of the micrograph). (c) Tilt compensation is ON. (d) Tilt compensation and dynamic focusing are ON. The visible wall of the bore of the holes proves that the specimen is still tilted. (e) Schematic illustration of the effects caused by tilting the sample. The position of the optimum focus plane, the depth of focus $D$, and the height range $\Updelta z$ ($\Updelta z> D$) are shown for a constant focus of the beam (solid lines). In that case, only a central region along the tilt axis is within the depth of focus (i. e., sharp image) whereas the lower and the upper range are outside $D$ (unsharp region of the image). In the case of the dynamic focus, three positions of the beam (dashed lines) are drawn indicating that the whole scan range will be in focus, thus being imaged sharply

The first effect is caused by the fact that because of the tilt the scanned range on the specimen surface perpendicular to the tilt axis is enlarged by a factor $1/(\cos\Theta)$ (Fig. 5.9a-ee). That corresponds to a reduced magnification

$$M^{\prime}=M\cos\Theta$$

(5.15)

in the direction of the short axis whereas along the tilt axis the magnification $M$ is not affected. The effect can be fully compensated by enlarging the reduced magnification by $1/(\cos\Theta)$, which restores the magnification $M$ (Fig. 5.9a-ec,e). The tilt compensation can be performed directly by electronic means (hardware, the unit is called tilt compensation) during scanning or posterior by digital image processing on condition that the directions of the tilt axis and the tilt angle are known.

The second effect is caused by the fact that because of the tilt the height range of the tilted specimen extends the depth of focus, thus the image is not sharp in regions outside the depth of focus. This effect can be compensated by dynamic focusing  [5.100], i. e., by adjusting the strength of the objective lens as a function of the scan position perpendicular to the tilt axis. This adjustment brings the optimum focus position in coincidence with the surface at all working distances in the scanned range (Fig. 5.9a-ed and e). Both effects mentioned can be compensated completely only for planar specimens and a known tilt angle.

The SEM forms in imaging mode a two-dimensional () image of a three-dimensional specimen with each of the signals generated by electron–specimen interaction (Fig. 5.2). Although these images contain a wealth of information about the specimen, there is no solid information about the third dimension, which is parallel to the optical axis. Stereo imaging is one possibility to obtain information about the third dimension. It takes advantage of the fact that depth perception is obtained when viewing an object from two separate directions. In an SEM stereo imaging is performed by taking two images—the stereo pair—at two different tilt angles of the specimen. A good stereo effect is obtained when the angles differ form each other by about $6^{\circ}$. A significantly larger difference in $\Theta$ overemphasizes the stereo effect whereas a smaller difference in $\Theta$ shows a softened stereo effect. Usually, a stereo pair is viewed through a stereo viewer. A simple version of a stereo viewer consists of two short focal lenses on a stand at the correct distance from the stereo pair. There are more sophisticated versions with lens–mirror combinations, which allow for a larger field of view. For each type of viewer it is mandatory to place and to align both images precisely to obtain correct depth perception. Figure 5.10a,b shows a stereo pair of SEM micrographs.

Fig. 5.10a,b

Stereopair of rust ($\mathrm{Fe_{2}O_{3}}$) crystals imaged at ${\mathrm{5}}\,{\mathrm{kV}}$ (a) and (b) the resulting stereo (green/red) combined image. The difference in the tilt angles of the micrographs is $6^{\circ}$

A further method for viewing the stereo images is the anaglyph technique [5.101], which can now readily be performed by PC (Fig. 5.56a-d). In this technique both images are superimposed in different colors. A red–green stereo anaglyph coding can be obtained readily by freeware, e. g., ImageJ (NIH); or commercially available software, e. g., MountainMaps (Digital Surf, France). This allows for a quick and simple qualitative assessment. The mixed colored image has to be viewed by colored glasses. However, the stereo pair can also be used to calculate the height difference $\Updelta h$ between two image points 1 and 2 by measuring the parallax $p_{x}$ given as

$$p_{x}=\left(x_{2}^{\mathrm{l}}-x_{1}^{\mathrm{l}}\right)-\left(x_{2}^{\mathrm{r}}-x_{1}^{\mathrm{r}}\right)$$

(5.16)

and

$$\Updelta h=\frac{p_{\mathrm{x}}}{2M\sin(\Theta_{\mathrm{r}}-\Theta_{\mathrm{l}})}\;,$$

(5.17)

where $(x_{2}^{\mathrm{l}}-x_{1}^{\mathrm{l}})$ corresponds to the distance between the two points in the left and $(x_{2}^{\mathrm{r}}-x_{1}^{\mathrm{r}})$ to the distance between the two points in the right image. $\Theta_{\mathrm{r}}$ and $\Theta_{\mathrm{l}}$ correspond to the tilt angle of the specimen used for the right and left image, respectively. Equation (5.17) holds for magnifications $M> {\mathrm{100}}$, i. e., in case of parallel projection. The successful application of the latter two formulas requires (1) distinct surface structures to measure $p_{x}$ with sufficient accuracy, and (2) the magnification and the tilt angle must be known exactly. On the basis of the relations (5.16) and (5.17) and data analysis software quantitative dimensional and angular measurements, the reconstruction of the specimen topography and three-dimensional morphometry can be achieved. The latter is very useful to analyze microstructures such as blood capillaries, which have diameters in the range of a few micrometers [5.102, 5.103, 5.104]. Using the image pair imported for anaglyph generation, a point of reference has to be selected in one of the images that would also be clearly visible in the second image. The software uses this reference point to define a small region and then uses correlation to accurately align the images. Once aligned, the parallax difference allowed generation of a new ${\mathrm{8}}\,{\mathrm{bit}}$ grayscale image in which depth differences are encoded as different gray values. Quantitative measurements, e. g., the volume of depressions, can be performed using the same piece of software.

1.1.5.3 Magnification Calibration

The actual magnification of the SEM is indicated numerically and by a scale bar on the monitor with a precision of about $\pm{\mathrm{2}}\%$. However, if exact measurements have to be made (Sect. 5.1.1, Specimen Tilting and Stereo Imaging), the magnification should be verified using an external standard. Calibrated gratings with known spacings are commercially available from different suppliers of electron microscopy accessories (e. g., Agar Scientific, http://www.agarscientific.com). For a magnification range up to about ${\mathrm{100000}}\,\times$ crossed gratings with spacings of $\mathrm{1200}$ and $\mathrm{2160}$ lines per mm (Fig. 5.11a,b) are recommended.

Fig. 5.11a,b

SE micrograph of a standard TEM mesh grid at low (a) and medium (b) magnification at ${\mathrm{15}}\,{\mathrm{kV}}$

Latex spheres of defined diameter (different diameters in the range from about $\mathrm{0.1}$ to ${\mathrm{1}}\,{\mathrm{\upmu{}m}}$ are commercially available) can also be used. However, the size of the latex spheres varies to some extent (e. g., small diameter, ${\mathrm{0.112}}\,{\mathrm{\upmu{}m}}$; standard deviation, ${\mathrm{10^{-3}}}\,{\mathrm{\upmu{}m}}$; large diameter, ${\mathrm{1.036}}\,{\mathrm{\upmu{}m}}$; standard deviation, ${\mathrm{16.1\times 10^{-3}}}\,{\mathrm{\upmu{}m}}$). Moreover, the latex spheres are sensitive to electron radiation, thus their size may change caused by electron dose-induced damages. To calibrate the magnification range above ${\mathrm{100000}}\,\times$ negatively stained catalase (periodic lattice spacings: $\mathrm{8.75}$ and ${\mathrm{6.85}}\,{\mathrm{nm}}$) can be used as standard (preferentially in the STEM mode).

1.2 Electron–Specimen Interaction and Signal Generation

As the beam electrons enter the specimen, they interact with the atoms of the specimen. This interaction either results in elastic or inelastic scattering of the impinging electrons.

The elastic scattering of the electron is caused by its interaction with the electrical field of the positively charged nucleus and results only in a deflection of the beam electron, i. e., after the scattering event the electron trajectory has a different direction than before scattering. There is almost no loss of kinetic energy of the electron scattered elastically. For scanning electron microscopy it is necessary to know the elastic electron scattering through large angles between $\mathrm{0}$ and $180^{\circ}$. The scattering can be described quantitatively by the scattering cross section $\sigma$ . The exact elastic scattering cross sections for large-angle scattering are the Mott cross sections $\sigma_{\mathrm{M},\text{el}}$, which, in contrast to Rutherford scattering , consider the electron spin and spin-orbit coupling during scattering (for details see [5.105, 5.106, 5.38]). The easy to calculate unscreened differential Rutherford cross section $\mathrm{d}\sigma_{\mathrm{R},\text{el}}/\mathrm{d}\Omega$ are given as [5.38]

$$\frac{\mathrm{d}\sigma_{\mathrm{R},\text{el}}}{\mathrm{d}\Omega}=\dfrac{{e}^{4}Z^{2}}{\left[4(4\uppi\varepsilon_{0})^{2}m^{2}v^{4}\sin^{4}\left(\frac{\varphi}{2}\right)\right]}\;,$$

(5.18)

where $\mathrm{d}\Omega$ is the cone of the solid angle, $e$ is the electric charge ($e={\mathrm{1.602\times 10^{-19}}}\,{\mathrm{C}}$) and $m$ the mass of the electron, $v$ is the velocity of the electron, $Z$ is the atomic number, $\varepsilon_{0}$ is the dielectric constant ($\varepsilon_{0}={\mathrm{8.85\times 10^{-12}}}\,{\mathrm{C{\,}V^{-1}{\,}m^{-1}}}$), and $\varphi$ is the scattering angle. The comparison of the differential Mott cross sections $\mathrm{d}\sigma_{\mathrm{M},\text{el}}/\mathrm{d}\Omega$ [5.107] with the unscreened differential Rutherford cross sections $\mathrm{d}\sigma_{\mathrm{R},\text{el}}/\text{d}\Omega$ for electron energies between $\mathrm{1}$ and ${\mathrm{100}}\,{\mathrm{keV}}$ shows that there are strong deviations of the Rutherford cross section, particularly for high $Z$. Mott cross sections for electron energies below ${\mathrm{1}}\,{\mathrm{keV}}$ (energy range ${\mathrm{20}}\,{\mathrm{eV}}$ to ${\mathrm{20}}\,{\mathrm{keV}}$) were calculated by Czyżewski et al [5.108] (see also http://web.utk.edu/~srcutk/Mott/mott.htm). There is very reasonable agreement between both cross sections for low atomic numbers and electron energies above ${\mathrm{5}}\,{\mathrm{keV}}$. However, for low $Z$ and energies below ${\mathrm{5}}\,{\mathrm{keV}}$, the Rutherford cross sections are larger than the Mott cross sections for scattering angles below $70{-}80^{\circ}$ and are smaller than the Mott cross sections for scattering angles above $70{-}80^{\circ}$. The probability for elastic scattering is approximately proportional to $Z^{2}$ and inversely proportional to $E^{2}$ (with $E=mv^{2}/2$), i. e., the scattering cross section strongly increases with the atomic number and decreases for increasing electron energy $E$. The total elastic scattering cross section $\sigma_{\text{el}}$ can be obtained by integration

$$\sigma_{\text{el}}=2\uppi\int_{0}^{\uppi}\left(\frac{\mathrm{d}\sigma_{\text{el}}}{\mathrm{d}\Omega}\right)\sin\varphi\,\mathrm{d}\varphi\;.$$

(5.19)

$\sigma_{\text{el}}$ can be used to calculate the mean free path for elastic scattering $\Lambda_{\text{el}}$, i. e., the free path between two consecutive elastic scattering events in a specimen consisting of many atoms, which is given as

$$\Lambda_{\text{el}}=\frac{1}{N\sigma_{\text{el}}}\;.$$

(5.20)

$N$ represents the number of atoms per unit volume and can be calculated simply by

$$N=\frac{N_{\mathrm{A}}\rho}{A}\;,$$

(5.21)

where $\rho$ is the density, $N_{\mathrm{A}}$ is Avogadro's number ($N_{\mathrm{A}}={\mathrm{6.0221\times 10^{23}}}\,{\mathrm{mol^{-1}}}$), and $A$ is the atomic weight ($\mathrm{g{\,}mol^{-1}}$). Much more detailed data of elastic electron-scattering cross sections were recently published [5.109].

As we shall see later, the mean free path is an important quantity for describing plural (mean number of collisions $<{\mathrm{25}}$) and multiple electron scattering (mean number of collisions $> {\mathrm{25}}\pm{\mathrm{5}}$).

The inelastic scattering of the electron is caused by its interaction with the electrical field of the electrons in the solid, i. e., either with the electrons in the valence or conduction band and with atomic electrons of inner shells, respectively. After an inelastic scattering event the electron trajectory has a slightly different direction than before scattering (typically the inelastic scattering angles are of the order of a few milliradians only) and less kinetic energy. If the lost energy was transferred to electrons in the valence or conduction band then the excitation of plasmons (a plasmon is a longitudinal charge-density wave of the valence or conduction electrons) or inter- and intraband transitions may occur. Both the energy of plasmons and the energy differences of inter- and intraband transitions are in the order of about $5{-}50\,{\mathrm{eV}}$. The physics of the latter processes is reviewed by Raether [5.110]. If the lost energy was transferred to atomic electrons of inner shells then, for example, K-, L-, or M-shell ionization may occur. In this case the energy loss typically is higher than ${\mathrm{50}}\,{\mathrm{eV}}$. The differential inelastic electron-scattering cross section with a free electron (which is an approximation for an electron in the valence or conduction band) is given [5.38] as

$$\frac{\mathrm{d}\sigma_{\text{in}}}{\mathrm{d}W}=\frac{\uppi{e}^{4}}{\left[(4\uppi\varepsilon_{0})^{2}EW^{2}\right]}\;,$$

(5.22)

where $W$ is the energy loss. The equation shows that the differential inelastic scattering cross section is inversely proportional to electron energy $E$ and to $W^{2}$ and that small energy losses occur with a larger probability. In a more complex approach for the differential inelastic scattering cross section the energy loss function $\mathfrak{Im}(-1/\varepsilon)$ is used taking the dielectric properties of the material into account [5.111]. An impinging electron can be inelastically scattered passing the atom even in a distance of a few nanometers, thus the inelastic scattering is delocalized to a certain extent [5.112, 5.113, 5.114, 5.115, 5.116].

In the case of inner shell excitation the electron interaction is localized to an electron shell. The corresponding inelastic scattering, also called ionization cross section, is the probability of bringing a scattering atom to a given excited state through an inelastic process. The related cross sections are typically at least two orders of magnitude smaller than those for the electrons in the valence or conduction band. Calculations of the ionization cross sections of the K-, L-, and M-shell have been published [5.117, 5.118, 5.119].

The total inelastic scattering cross section $\sigma_{\text{in}}$ can be obtained by integration

$$\sigma_{\text{in}}=2\uppi\int_{0}^{\uppi}\left(\frac{\mathrm{d}\sigma_{\text{in}}}{\mathrm{d}\Omega}\right)\sin\varphi\mathrm{d}\varphi\;.$$

(5.23)

The mean free path for inelastic scattering $\Lambda_{\text{in}}$ is given analogous to (5.20) as

$$\Lambda_{\text{in}}=\frac{1}{N\sigma_{\text{in}}}$$

(5.24)

(for detailed data and calculation of the electron inelastic mean free path see Powell and Jablonski [5.120]).

The total scattering cross section then is given as

$$\sigma=\sigma_{\text{el}}+\sigma_{\text{in}}\;.$$

(5.25)

In bulk specimens multiple scattering of the impinging electrons takes place. Mainly the multiple elastic scattering causes a successive broadening of their angular distribution and can, after numerous scattering events, result in beam electrons leaving the specimen. The beam electrons, which leave the specimen, are designated as backscattered electrons and carry an important class of information about the local specimen volume through which they have been passing. Multiple inelastic scattering along the electron trajectories results in a slowing down and the beam electron can come to a standstill if it cannot leave the specimen as BSE. The majority of beam electrons are scattered both elastically as well as inelastically. Therefore, the majority of BSE have energies smaller than $E_{0}$ (Fig. 5.12). The broadening of the angular distribution can be calculated analytically using the autoconvolution of the single scattering distribution expanded in terms of Legendre polynomials [5.121].

Fig. 5.12

Schematic energy distribution of electrons emitted $n_{\text{el}}$ from a surface as a result of its bombardment with fast electrons with energy $E_{0}$

Another method to treat multiple scattering is the simulation of the successive scattering events by Monte Carlo calculations for about $E3{-}E5$ electron trajectories (Fig. 5.13; for Monte Carlo simulations of electron scattering see [5.105, 5.122, 5.123, 5.124, 5.125, 5.126, 5.127, 5.128, 5.129]).

Fig. 5.13

Monte Carlo simulation of the trajectories of $\mathrm{100}$ electrons for carbon (atomic number $Z={\mathrm{6}}$) and gold ($Z={\mathrm{79}}$) for electron energies $E_{0}={\mathrm{30}}$, $\mathrm{5}$, and ${\mathrm{1}}\,{\mathrm{keV}}$. For simulation of the electron trajectories the Monte Carlo program MOCASIM [5.126] was used. Note the different scales across three orders of magnitude indicated by bars and the variation of the shape of the local volume where electron scattering takes place. That local volume is usually denominated as the excitation volume

In this method, the most important scattering parameters, such as scattering angle, mean free electron path, and energy loss, are simulated for each individual scattering event along the trajectory by a computer using random numbers and probability functions of the scattering parameters. The energy loss along the trajectory (in units of $\mathrm{eV{\,}cm^{-1}}$) can be described by the Bethe continuous-slowing-down approximation [5.130]

$$\frac{\mathrm{d}E}{\mathrm{d}s}=-{\mathrm{7.8\times 10^{10}}}\left(\frac{\mathrm{Z}\rho}{AE}\right)\ln\left(1.166\frac{E}{J}\right),$$

(5.26)

where $\rho$ is the density ($\mathrm{g{\,}cm^{-3}}$), $E$ the electron energy (eV), and $J$ the mean ionization potential in eV [5.131] given by

$$J=9.76Z+58.8Z^{-0.19}\;.$$

(5.27)

The limitations of the Bethe expression at low electron energy can be overcome by using an energy-dependent value $J^{*}$ for the mean ionization potential [5.132]

$$J^{*}=\dfrac{J}{\left(\frac{1+kJ}{E}\right)}$$

(5.28)

where $k$ varies between $\mathrm{0.77}$ (carbon) and $\mathrm{0.85}$ (gold). The total traveling distance of a beam electron in the specimen—the Bethe range $R_{\mathrm{B}}$—can be obtained by integration over the energy range from $E_{0}$ to a small threshold energy and extrapolation to $E=0$.

The practical electron range $R$ (Fig. 5.14) obtained by fitting experimental data of specimens with different $Z$ over a wide energy range is given by the power law

$$R=aE_{0}^{n}\;,$$

(5.29)

where $n$ is in the range of about $1.3{-}1.7$ and the parameter $a$ depends on the material [5.38]. Characteristic values for $R$, $\sigma_{\text{el}}$, $\sigma_{\text{in}}$, $\Lambda_{\text{el}}$, and $I_{\text{in}}$ are shown in Table 5.3. It shows that independent of the electron energy the electron range for carbon is about one order of magnitude larger than for gold. The decrease of the electron energy from $\mathrm{30}$ to ${\mathrm{1}}\,{\mathrm{keV}}$, i. e., a factor of $\mathrm{30}$, reduces the electron range by a significantly higher factor of roughly $\mathrm{300}$.

Fig. 5.14

Schematic illustration of the generation of secondary electrons SE1 and SE2, backscattered electrons BSE1 and BSE2, Auger electrons: , cathodoluminescence CL, and x-rays in a bulky specimen. $t_{\text{SE}}$ and $t_{\text{BSE}}$ indicate the escape depth for SE and BSE, respectively. $R$ is the electron range

Table 5.3 Characteristic values for $R$, $\sigma_{\text{el}}$, $\sigma_{\text{in}}$, $\Lambda_{\text{el}}$, and $\Lambda_{\text{in}}$

The mean free path lengths indicate after which traveling distance on average elastic and inelastic collisions will occur. For example, in a thin organic specimen having a thickness of $50{-}100\,{\mathrm{nm}}$ only a few collisions on average will take place with ${\mathrm{30}}\,{\mathrm{keV}}$ electrons but about seven times more with ${\mathrm{5}}\,{\mathrm{keV}}$ electrons. Specimens, which have thicknesses of about $t\leq{\mathrm{10}}[\Lambda_{\text{el}}\Lambda_{\text{in}}/(\Lambda_{\text{el}}+\Lambda_{\text{in}})]$ can also be imaged in the transmission mode (Figs. 5.1 and 5.2) using unscattered, elastically or inelastically scattered electrons, respectively. The angular and energy distribution of the scattered electrons can be calculated by Monte Carlo simulations if the elemental composition and the density of the specimen are known [5.133, 5.134].

The inelastic electron-scattering events in the specimen cause secondary electrons, Auger electrons, cathodoluminescence, and x-rays, which carry a wealth of local information about the topography, the electronic structure, and the composition of the specimen. The signals, resulting from inelastic electron scattering, can also be calculated by Monte Carlo simulations.

1.2.1 Secondary Electrons

The energy spectrum of the electrons emitted from a specimen irradiated with fast electrons consists of secondary electrons, backscattered electrons, and Auger electrons (Fig. 5.12). The SE show a peak at low energies with a most probable energy of $2{-}5\,{\mathrm{eV}}$. By definition the maximum energy of SE amounts to ${\mathrm{50}}\,{\mathrm{eV}}$. Secondary electrons are generated by inelastic scattering of the beam electrons along their trajectories within the specimen (Fig. 5.14). The physics of secondary electron emission is reviewed by Kollath [5.135] and Dekker [5.136] but is beyond the scope of this chapter. Because of the low energy of the SE only those SE are observable that are generated within the escape depth from the surface. The actual escape depth of SE for pure elements varies with their atomic number [5.137]. A general rule for their escape depth is $t_{\text{SE}}=5\Lambda_{\text{SE}}$ [5.138], where $\Lambda_{\text{SE}}$ is the mean free path of the SE. $t_{\text{SE}}$ amounts to about ${\mathrm{5}}\,{\mathrm{nm}}$ for metals and up to about ${\mathrm{75}}\,{\mathrm{nm}}$ for insulators [5.139]. The angular distribution of SE follows Lambert's law , i. e., is a $\cos\zeta$ distribution, where $\zeta$ represents the SE emission angle relative to the surface normal [5.140, 5.141]. The angular distribution of the SE is not important for the image contrast in SEM because the extraction field of the ET detector normally collects the emitted SE. The situation, however, is different in case of magnetic through-the-lens detection where no electric extraction field is applied (Fig. 5.6).

Figure 5.15 shows schematically the SE yield $\delta$ versus the energy of the beam electrons, which is the number of SE produced by one beam electron. $\delta$ increases with $E_{0}$, reaches its maximum $\delta^{\mathrm{m}}$ at $E_{0,\mathrm{m}}$, and then decreases with further increasing $E_{0}$. Typical values for metals are ${\mathrm{0.35}}\leq\delta^{\mathrm{m}}\leq{\mathrm{1.6}}$ and ${\mathrm{100}}\,{\mathrm{eV}}\leq E_{0,\mathrm{m}}\leq{\mathrm{800}}\,{\mathrm{eV}}$ and for insulators ${\mathrm{1.0}}\leq\delta^{\mathrm{m}}\leq{\mathrm{10}}$ and ${\mathrm{300}}\,{\mathrm{eV}}\leq E_{0,\mathrm{m}}\leq{\mathrm{2000}}\,{\mathrm{eV}}$ [5.139]. For $E_{0}\gg E_{0,\mathrm{m}}$, $\delta$ is proportional to $E_{0}^{-0.8}$ [5.142], which indicates that $\delta$ is significantly smaller at $\mathrm{30}$ than at ${\mathrm{5}}\,{\mathrm{keV}}$. Both parameters, $\delta^{\mathrm{m}}$ at $E_{0,\mathrm{m}}$ depend on the ionization energy of the surface atoms [5.143]. Figure 5.16 shows the SE yield $\delta$ versus the energy $E_{0}$ for the element copper.

Fig. 5.15

Schematic representation of the SE yield $\delta$ versus the energy $E_{0}$ of beam electrons

Fig. 5.16

SE yield $\delta$, BSE yield $\eta$, and $\delta+\eta$ versus the energy $E_{0}$ for polycrystalline copper at $\theta=0^{\circ}$. (Data from [5.144])

There is no monotonic relation between $\delta$ and the atomic number as shown in Fig. 5.17. However, published data of $\delta$ scatter which indicates that the specimen surface conditions and the quality of the vacuum can significantly affect the secondary yield [5.145].

Fig. 5.17

SE yield $\delta$ and BSE yield $\eta$ versus atomic number $Z$ at $E_{0}={\mathrm{30}}\,{\mathrm{keV}}$ and $\theta=0^{\circ}$. (Data from [5.146, 5.147])

Secondary electrons generated by the incident beam electrons are designated SE1 [5.142]. The SE1 carry local information about the small cylindrical volume that is given approximately by the cross section of the beam $(\uppi/4)d_{\text{pe}}^{2}$ and the escape depth $t_{\text{SE}}$. For a beam diameter about $\leq{\mathrm{1}}\,{\mathrm{nm}}$ the SE1 deliver high-resolution information. Those beam electrons, which are multiply scattered and emerge from the specimen as BSE, also generate secondary electrons within the escape depth. These secondary electrons are designated SE2 [5.142]. Their origin is far from the point of incidence of the beam caused by the spatial distribution of BSE. Changes of the amount of SE2 correlate with corresponding changes of BSE, thus SE2 carry information about the volume from which the BSE originate. The size of the volume depends on the electron range $R$ and is much larger than the excitation volume of the SE1 for electron energies $E_{0}> {\mathrm{1}}\,{\mathrm{keV}}$ (Fig. 5.14 and Table 5.3); thus SE2 deliver low-resolution information. The SE yield $\delta$ consists of the contributions of SE1 and SE2 given as

$$\delta=\delta_{\text{SE1}}+\eta\delta_{\text{SE2}}\;,$$

(5.30)

where $\eta$ is the BSE coefficient and $\delta_{\text{SE2}}$ the SE2 yield, i. e., the number of SE2 generated per BSE. For $E_{\mathrm{0,m}}<E_{0}<{\mathrm{5}}\,{\mathrm{kV}}$ the ratio $\delta_{\text{SE2}}/\delta_{\text{SE1}}$ amounts to about $\mathrm{4}$ and for $E_{0}\geq{\mathrm{10}}\,{\mathrm{kV}}$ about 2 [5.138]. For an increasing angle of incidence $\theta$, this ratio decreases [5.148].

The SE yield increases with increasing angle of incidence $\theta$ according to (Fig. 5.18)

$$\delta(\theta)=\frac{\delta_{0}}{\cos\theta};\quad\delta_{0}=\delta(\theta=0)\;.$$

(5.31)

This relation is valid for a specimen with a mean atomic number, for $E_{0}\geq{\mathrm{5}}\,{\mathrm{keV}}$, and $\theta$ up to a few degrees below $90^{\circ}$. The increase of $\delta$ with $\theta$ is greater for specimens with a low atomic number and smaller for samples with high $Z$ [5.13]. For crystalline objects, the increase of $\delta$ with $\theta$ is superimposed by electron channeling and crystalline orientation contrast (Sect. 5.1.3). The distinct dependence of the SE yield on $\theta$ provides the basis for the topographic contrast in secondary electron micrographs.

Fig. 5.18

Normalized SE yield $\delta^{*}$ and BSE yield $\eta^{*}$ versus the angle of incidence $\theta$ of the electron beam. $\delta^{*}=\delta(\theta)/\delta_{0}$, $\eta^{*}=\eta(\theta)/\eta_{0}$. $\eta$ was calculated for gold and copper according to (5.34)

1.2.2 Backscattered Electrons

The majority of BSE is due to multiple scattering of the beam electrons within the specimen (Fig. 5.14). The energy spectrum of the backscattered electrons is shown schematically in Fig. 5.12. By definition the energy of BSE is in the range ${\mathrm{50}}\,{\mathrm{eV}}<E_{\text{BSE}}\leq E_{0}$. The BSE spectrum has a small peak consisting of elastically scattered electrons at $E_{0}$ (this peak is not visible in Fig. 5.12). Toward energies lower than $E_{0}$ there is a broad peak, which covers the range down to about ${\mathrm{0.7}}E_{0}$ for high atomic numbers and further down to about ${\mathrm{0.4}}E_{0}$ for low atomic numbers. The majority of BSE are within this broad peak. For high atomic number elements such as gold, the maximum of the distinct peak is at about ${\mathrm{0.9}}E_{0}$, whereas for low atomic numbers, e. g., carbon, the maximum of the less distinct peak is located at about $(0.5{-}0.6)E_{0}$. The cumulative fraction of ${\mathrm{50}}\%$ of BSE is reached for carbon at $E_{\text{BSE}}/E_{0}={\mathrm{0.55}}$ and for gold at $\mathrm{0.84}$, respectively [5.28]. It seems worth mentioning that the energy distribution of BSE is shifted toward higher energy if the angle of incident electrons is larger than $70^{\circ}$ [5.9].

As shown in Fig. 5.14, the BSE can originate either from the small area directly irradiated by the electron beam—they are denoted as BSE1—or after multiple elastic and inelastic scattering events from a significantly larger circular area around the beam impact point, which are designated BSE2. The lateral distribution of BSE2 has been calculated by Monte Carlo simulation for different materials [5.149, 5.150]. It shows that the BSE-emitting surface area increases with electron energy $E_{0}$. For a given energy $E_{0}$ the size of the BSE-emitting area increases with descending atomic number. As with SE1, the BSE1 carry local information about the small volume and deliver high-resolution information for a beam diameter of about $\leq{\mathrm{1}}\,{\mathrm{nm}}$. As a consequence of lateral spreading the BSE2 carry information about a much larger region, thus fine structural details on the scale of the beam diameter cannot be resolved.

Figure 5.14 also shows that the beam electrons travel in a small subsurface volume before they return to the surface to escape as BSE2. The escape depth of BSE is much larger than $t_{\text{SE}}$ and depends on—in contrast to $t_{\text{SE}}$—the electron energy $E_{0}$. Experimental data for different materials show that $t_{\text{BSE}}$ amounts to about half of the electron range $R$ [5.142, 5.151].

Knowledge of the angular distribution of BSE is of great importance for understanding and optimization of BSE detection geometry. For normal beam incidence the angular distribution can be approximated by a $\cos\zeta$ distribution [5.142], where $\zeta$ represents the BSE emission angle relative to the surface normal. Because of the fact that the emitted BSE move on nearly straight trajectories, the angular detector position has a strong influence on the collection efficiency of the detector. For non-normal beam incidence the distribution is asymmetric and a reflection-like emission maximum is observed. The angular distribution consists for large angles of incidence $\theta$ of cosine distribution approximately directed to $-\theta$ and a superimposed fraction at smaller emission angles [5.142].

The BSE coefficient $\eta$ is defined by

$$\eta=\frac{n_{\text{BSE}}}{n_{\mathrm{b}}}\;,$$

(5.32)

where $n_{\text{BSE}}$ is the number of BSE and $n_{\mathrm{b}}$ is the number of incident electrons. $\eta$ is approximately independent of the electron energy $E_{0}$ in the range of about $10{-}30\,{\mathrm{keV}}$. For low atomic numbers and beam energies below ${\mathrm{5}}\,{\mathrm{keV}}$ $\eta$ increases as $E_{0}$ decreases, whereas for medium and high atomic numbers $\eta$ decreases with $E_{0}$ (Fig. 5.16) [5.152]. However, at low energies $\eta$ depends in a complex manner on the atomic number [5.145, 5.146].

The BSE coefficient monotonically increases with the atomic number as shown for ${\mathrm{30}}\,{\mathrm{keV}}$ in Fig. 5.17. Because of the approximate independence of the electron energy $E_{0}$, the graph of the BSE coefficient is valid for beam energy ranging from $\mathrm{30}$ down to about ${\mathrm{5}}\,{\mathrm{keV}}$. The graph of $\eta$ versus $Z$ can be approximated by a polynomial [5.153]

$$\begin{aligned}\displaystyle\eta(Z)&\displaystyle={\mathrm{0.0254}}+{\mathrm{0.016}}\,Z-{\mathrm{1.86\times 10^{-4}}}Z^{2}\\ \displaystyle&\displaystyle\quad\,+{\mathrm{8.31\times 10^{-7}}}Z^{3}\;.\end{aligned}$$

(5.33)

For energies below ${\mathrm{5}}\,{\mathrm{keV}}$ the dependence of $\eta$ on $Z$ is more complicated (for details see [5.154, 5.155, 5.156, 5.34]). The distinct dependence of the BSE coefficient on the atomic number $Z$ provides the basis for the atomic number contrast (Sect. 5.1.3).

Like the SE yield, the backscattering coefficient also increases monotonically with increasing angle of incidence $\theta$ according to [5.157]

$$\eta(\theta)=(1+\cos\theta)^{-9/{\sqrt{Z}}}\;.$$

(5.34)

Figure 5.18 shows the graphs $\eta(\theta)$ versus $\theta$ for Cu ($Z=29$) and Au ($Z=79$). The graphs indicate the strong influence of the atomic number, in particular for $\theta> 50^{\circ}$. The monotonic increase of $\eta$ with $\theta$ provides the basis for the topographic contrast in BSE micrographs. For the sake of completeness it should be mentioned that Drescher et al [5.142] derived from experimental data at ${\mathrm{25}}\,{\mathrm{keV}}$ an analytical expression for $\eta(\theta,Z)$ other than the one given by (5.34).

The backscattering coefficient of a single crystal depends sensitively on the direction of the incident electrons related to the crystal lattice [5.151, 5.158]. This dependence is caused by the regular three-dimensional arrangement of the atoms in the lattice, whose atomic density depends on the direction. The backscattering coefficient is lower along directions of low atomic density, which permits a fraction of the incident electrons to penetrate deeper than in amorphous material before being scattered. Those electrons have a reduced probability of returning to the specimen surface and leaving the sample as BSE. The maximum relative variation of the backscattering coefficient is in the order of ${\mathrm{5}}\%$.

1.2.3 Transmitted Electrons

When the thickness of a specimen approaches the electron range $R$ or becomes even smaller than $R$, an increasing fraction of beam electrons is transmitted. Specimens that are sufficiently thin (typically less than ${\mathrm{100}}\,{\mathrm{nm}}$), or particles mounted onto a thin electron-transparent film supported by a metallic mesh grid commonly used in TEM and STEM can then be imaged in transmission mode in the SEM. To improve the stability of the ${\mathrm{5}}\,{\mathrm{nm}}$-thick carbon film, the film is placed onto a holey thick carbon film supported by a mesh grid. In contrast to a solid support, a ${\mathrm{5}}\,{\mathrm{nm}}$-thick carbon film contributes only insignificantly to the SE and BSE signal, thus particles deposited onto a thin support film can be imaged in the normal manner using SE and BSE, respectively, providing complimentary information from several different detectors. An example of STEM imaging is shown in Fig. 5.19a-c. The figure demonstrates the same specimen (zeolite decorated with nanoparticles) that was imaged using SE, BSE, and STEM modes.

Fig. 5.19a-c

Comparison of (a) SE (${\mathrm{1}}\,{\mathrm{kV}}$); (b) BSE (${\mathrm{1}}\,{\mathrm{kV}}$); and (c) STEM-in-SEM (${\mathrm{30}}\,{\mathrm{kV}}$) images of mesoporous silica loaded with Pd nanoparticles

As a result of electron–specimen interaction the transmitted electrons can be unscattered or elastically or inelastically scattered (Fig. 5.20). Because of their characteristic angular and energy distribution, the transmitted electrons can be separated by placing suitable detectors below the specimen. Frequently, a rather simple and inexpensive device for observing an STEM image [5.159]—sometimes called poor man's STEM in SEM detector—is used. The transmitted electrons are passing through an angle-limiting aperture, strike a tilted gold-coated surface, and thus create a high SE and BSE signal, which can then be collected by a conventional ET detector. The angle-limiting aperture cuts off the transmitted, scattered electrons. In this case the poor man's STEM in SEM detector acquires those electrons, which represent the bright-field signal. The poor man's STEM in SEM detector just cuts the transmitted scattered electrons without making use of their inherent information. Both the elastically and the inelastically scattered electrons are signals, which very sensitively depend on the mass thickness $\rho t$ if the specimen thickness $t\leq[\Lambda_{\text{el}}\Lambda_{\text{in}}/(\Lambda_{\text{el}}+\Lambda_{\text{in}})]$ [5.133, 5.160] (Fig. 5.19a-c) can be used.

Fig. 5.20

Fraction of transmitted electrons scattered into an angular range of $25{-}300\,{\mathrm{mrad}}$ for carbon ($\rho={\mathrm{2}}\,{\mathrm{g{\,}cm^{-3}}}$; solid line) and protein ($\rho={\mathrm{1.35}}\,{\mathrm{g{\,}cm^{-3}}}$; dashed line). Parameters: $E_{0}={\mathrm{30}}\,{\mathrm{keV}}$, $\alpha_{\mathrm{p}}={\mathrm{10}}\,{\mathrm{mrad}}$. The graphs show an increasing fraction of scattered and a decreasing fraction of unscattered electrons with increasing thickness. (Calculation according to [5.134])

Another important application of STEM-in-SEM imaging is the measurement of the physical probe size of the SEM using a thin carbon film (thickness below ${\mathrm{10}}\,{\mathrm{nm}}$, preferably containing nanoparticles of gold or gold-palladium for better contrast). In this case, the broadening of the electron beam in the film is negligible and so the resolution of the STEM image is equal to the probe diameter. The image resolution can be determined either by analysis of the diffractogram (power spectrum) of the STEM micrograph [5.161, 5.162, 5.38] or by cross-correlation function analysis [5.163] of the phase noise in the bright-field STEM image of the carbon film. The latter directly yields the probe diameter of the SEM [5.162].

Combining the SE and BSE detectors above as well as the bright-field and dark-field detectors below the specimen, its surface as well as its internal structure can be observed simultaneously in the SEM.

1.2.4 Cathodoluminescence

Cathodoluminescence (CL) is the emission of light generated by the electron bombardment of semiconductors and insulators ([5.164]; Fig. 5.14). Those materials have an electronic band structure characterized by a filled valence band and an empty conduction band separated by an energy gap $\Updelta E_{\text{CV}}=E_{\mathrm{C}}-E_{\mathrm{V}}$. Electrons from the valence band can interact inelastically with a beam electron and can be excited to an unoccupied state in the conduction band. The excess energy of the excited electron will be lost by a cascade of nonradiative phonon and electron excitations. Most of the recombination processes of excited electrons with holes in the valence band are nonradiative processes, which elevate the sample temperature. There are different radiative processes, which take place in inorganic materials, semiconductors, and organic molecules.

In inorganic materials intrinsic and extrinsic transitions can take place. The intrinsic emission is due to direct recombination of electron–hole pairs. Extrinsic emission is caused by the recombination of trapped electrons and holes at the donor and acceptor level, respectively. The trapping increases the probability of recombination. The extrinsically emitted photons have a lower energy than intrinsically emitted photons.

In semiconductors the radiative recombination can be due to the direct collision of an electron with a hole with the emission of a phonon. Depending on the nature of the band structure of the material, the recombination can be either direct or indirect. In the latter case, the recombination must occur by simultaneous emission of a photon. Indirect recombination is less likely than direct recombination. If the material contains impurities, the process of recombination via impurity level becomes important. The modification of CL efficiency as a function of the purity and the perfection of the material is the most important aspect of the use of this method in scanning electron microscopy. It is because of such modifications that a contrast is generated (for details see [5.165, 5.166]). It was shown in some cases that the sensitivity of CL analyses can be at least $\mathrm{10^{4}}$ times higher than that obtainable by x-ray microanalysis, i. e., an impurity concentration as low as ${\mathrm{10^{14}}}\,{\mathrm{cm^{-3}}}$ [5.167].

In organic materials the excitation is inside an individual molecule. Electrons go from a ground state to a singlet state at least two states above. Then the deexcitation to the ground state is radiationless up to the singlet state directly above the ground level and from this state the deexcitation can be either radiationless or radiative with decay times larger than ${\mathrm{10^{-7}}}\,{\mathrm{s}}$ (fluorescence). The CL spectra depend on the chemical structure of the molecule [5.168, 5.169]. Cathodoluminescence of organic matter also can be caused by selective staining with luminescent molecules (fluorochromes). Typical fluorochromes are, e. g., fluoresceine, fluoresceine isothiocyanate ( ), and acridine orange.

Independent of the material the light generated by CL inside the specimen has to pass the surface according to the Snell law  [5.170]. The critical angle $\theta_{\mathrm{t}}$ of total internal reflection is given as

$$\sin\theta_{\mathrm{t}}=\frac{n_{1}}{n}\;,$$

(5.35)

where $n_{1}={\mathrm{1}}$ (vacuum) and $n$ is the refractive index of the specimen ($1<n<5$). As shown by (5.35) the fraction of emitted light is significantly reduced by total internal reflection for $n> 2$ (semiconductors).

1.2.5 X-Rays

The x-ray spectrum is considered to be that part of the electromagnetic spectrum that covers the wavelengths $\lambda_{\mathrm{X}}$ from approximately $\mathrm{0.01}$ to ${\mathrm{10}}\,{\mathrm{nm}}$. The energy of x-rays is given as

$$E_{\mathrm{X}}=h\nu=\frac{hc}{\lambda_{\mathrm{X}}}\;,$$

(5.36)

where $h={\mathrm{6.6256\times 10^{-34}}}\,{\mathrm{J{\,}s}}$ is Planck's constant, $c={\mathrm{2.99793\times 10^{8}}}\,{\mathrm{m{\,}s^{-1}}}$ is the speed of light, and $\nu$ is the frequency of x-rays. The x-rays are generated by deceleration of electrons (x-ray continuum or Bremsstrahlung) or by electron transition from a filled higher state to a vacancy in a lower electron shell (characteristic x-ray lines) (Fig. 5.21).

The x-ray continuum is made up of a continuous distribution of intensity as a function of energy whereas the characteristic spectrum represents a series of peaks of variable intensity at discrete element-specific energies. As the electron energy increases the intensity of the continuous spectrum also increases and the maximum of the distribution is shifted toward higher energies. The general appearance of the continuous spectrum is independent of the atomic number of the specimen, however, the absolute intensity values are dependent on the atomic number. The maximum possible energy $E_{\mathrm{X}}$ is given by the electron energy $E_{0}$, which corresponds to instantaneous stopping of an electron at a single collision (Duane–Hunt limit) . According to Kramers [5.171] the intensity of the continuous spectrum $I_{\mathrm{C}}$ emitted in an energy interval with the width $\mathrm{d}E_{\mathrm{X}}$ is given as

$$I_{\mathrm{C}}(E_{\mathrm{X}})\mathrm{d}E_{\mathrm{X}}=\frac{kZ(E_{0}-E_{X})}{E_{\mathrm{X}}}\,\mathrm{d}E_{\mathrm{X}}\;.$$

(5.37)

$k$ represents the Kramers constant, which varies slightly with the atomic number [5.38]. A detailed treatment of the continuous x-ray emission is given by Stephenson [5.172].

Fig. 5.21

Schematic representation of the x-ray spectrum emitted from a specimen bombarded with fast electrons

The characteristic x-ray spectrum consisting of peaks at discrete energies is superimposed on the continuous x-ray spectrum (Fig. 5.21). Their positions are independent of the energy of the incident electrons. The peaks occur only if the corresponding atomic energy level is excited. The generation of characteristic x-rays consists of three different steps. First, a beam electron interacts with an inner shell electron of an atom and ejects this inner shell electron leaving that atom in an excited state, i. e., with a vacancy on the electron shell. Second, subsequently the excited atom relaxes to the ground state by transition of an electron from an outer to an inner shell vacancy. The energy difference $\Updelta E_{\text{ch}}$ between the involved shells is characteristic for the atomic number. Third, this element-specific energy difference is expressed either by the emission of an electron of an outer shell with a characteristic energy (Auger electron) or by the emission of a characteristic x-ray with energy $E_{\mathrm{X}}=\Updelta E_{\text{ch}}$. The fraction of characteristic x-rays emitted when an electron transition occurs is given by the fluorescence yield $\omega$. This quantity increases with the atomic number and depends on the inner electron shell involved (Fig. 5.22). The complement, $1-\omega$, represents the Auger electron yield , which gives the corresponding fraction of Auger electrons produced. The fluorescence yield for the different shells and subshells can be calculated (for details see [5.173]).

Fig. 5.22

Dependence of the x-ray fluorescence yield $\omega$ and its complement ($1-\omega$) of the K-, L-, and M-shell from the atomic number $Z$. The complement ($1-\omega$) corresponds to the Auger electron yield

Moseley studied the line spectra in detail and found that the general appearance of the x-ray spectrum is the same for all elements. The energy of a characteristic x-ray line depends on the atomic shells involved in the transition resulting in the emission of this line. The x-ray lines can be classified in series according to the shell where the ionization took place, e. g., K-, L-, M-shell, etc. The quantum energies of a series are given by Moseley's law

$$E_{\mathrm{X}}=A(Z-B)^{2}\;,$$

(5.38)

where $A$ and $B$ are parameters that depend on the series to which the line belongs. The characteristic x-ray energy $E_{\mathrm{X}}$ is denoted by symbols that identify the transition that produced it. The first letter, e. g., K, L, identifies the original excited level, whereas the second letter, e. g., $\alpha$, $\beta$, designates the type of transition occurring. For example, $\mathrm{K}_{\alpha}$ denotes the excitation energy between the K- and L-shell, whereas $\mathrm{K}_{\beta}$ denotes the excitation energy between the K- and M-shell. Transitions between subshells are designated by a number, e. g., a transition from the subshell $\mathrm{L}_{\mathrm{III}}$ to K is denoted as $\mathrm{K}_{\alpha 1}$ and from the subshell $\mathrm{L}_{\mathrm{II}}$ to K is denoted as $\mathrm{K}_{\alpha 2}$, respectively. The transition from the subshell $\mathrm{L}_{\mathrm{I}}$ to K is forbidden. The characteristic x-ray energies and x-ray atomic energy levels for the K-, L-, and M-shells are listed in tables [5.174, 5.175]. Fortunately, the atomic energy levels are not strongly influenced by the type and strength of the chemical bonds. However, chemical effects on x-ray emission are observed for transitions from the valence electron states, which are involved in chemical bonds. In such cases, the narrow lines show changes of their shape and their position (energy shift $<{\mathrm{1}}\,{\mathrm{eV}}$) as well [5.176].

1.2.6 Auger Electrons

As mentioned in Sect. 5.1.2, X-Rays when an excited atom relaxes to the ground state by transition of an electron from an outer to an inner shell the energy difference $\Updelta E_{\text{ch}}$ between the involved shells can be expressed by the emission of an electron of an outer shell with a characteristic energy $E_{\text{AE}}$. The emission is due to the Auger effect [5.177, 5.178] and the emitted electron is designated as an Auger electron ( ). Its energy E${}_{\mathrm{AE}}$ is given by

$$E_{\text{AE}}=\Updelta E_{\text{ch}}-E_{\text{ionr}}\;,$$

(5.39)

where the term $E_{\text{ionr}}$ contains the ionization energy of the AE-emitting outer shell and also considers relaxation effects. The shape and the position of the AE peaks are influenced by the type and strength of the chemical bonds [5.179]. The AE peaks have an energy width of a few electronvolts and are superimposed on the low-energy range of the BSE spectrum up to energies of about ${\mathrm{2.5}}\,{\mathrm{keV}}$ (Fig. 5.12). The identification of the AE peaks on the BSE background [5.180] can be improved by differentiation of the electron energy spectrum.

The Auger electrons are generated within the excitation volume (Fig. 5.14). Because of their low energies only AE with a short pathway to the specimen surface can escape. However, energy losses caused by inelastic scattering on the pathway to the surface remove AE from the AE peaks. The decrease of the AE peak is proportional to $\exp(-x/\Lambda_{\text{AE}}$), where $x$ denotes the length of the path inside the specimen and $\Lambda_{\text{AE}}$ the mean free path of the AE. Depending on their energy and the atomic number of the specimen the mean free path $\Lambda_{\text{AE}}$ can have values in the range of about ${\mathrm{0.4}}\,{\mathrm{nm}}$ to a few nanometers [5.181, 5.182]. If AEs are inelastically scattered on their path to the surface, then they cannot be identified as an AE in the BSE background. Therefore, only atoms within a depth of about $\Lambda_{\text{AE}}$ can contribute to the AE peaks. Since Auger electrons yield information on element concentrations very near the surface, the specimen must be in an ultrahigh vacuum environment and special sample preparations are required (e. g., ion sputtering in situ, cleavage in situ) to obtain clean surfaces.

Because the AE yield of the K-shell $1-\omega_{\mathrm{K}}$ is much larger than $\omega_{\mathrm{K}}$ for light elements (Fig. 5.22) AE spectroscopy is advantageous for elements with atomic number $Z=4$ ($\omega_{\mathrm{K}}={\mathrm{4.5\times 10^{-4}}}$) up to $Z\approx{\mathrm{30}}$ ($\omega_{\mathrm{K}}={\mathrm{4.8\times 10^{-1}}}$) [5.183]. Similar to SE, which are also emitted only from a very thin surface layer, the AE can be generated directly by the beam electrons and by BSE within a larger circular area around the beam impact point (Fig. 5.14). Like the SE yield, which increases with increasing angle of incidence $\theta$ according to $\delta(\theta)=\delta_{0}/\cos\theta$ (5.31), the integral AE peak intensity is proportional to $1/\cos\theta$ [5.184, 5.185, 5.38].

Recent developments in scanning Auger microscopy and AE spectroscopy are described by Jacka [5.186].

1.2.7 Others

The incident electron beam bombards the specimen with electrons thereby introducing a negative electric charge. A certain amount of negative electric charge is leaving the specimen as secondary ($I_{\text{SE}}$), backscattered ($I_{\text{BSE}}$), and Auger electrons ($I_{\text{AE}}$). To avoid an accumulation of charges a specimen current $I_{\text{sp}}$ must flow from the specimen to the ground. The conservation equation for the electric charge is

$$I_{\mathrm{p}}=I_{\mathrm{SE}}+I_{\mathrm{BSE}}+I_{\mathrm{AE}}+I_{\mathrm{sp}}\;,$$

(5.40)

where $I_{\mathrm{p}}$ is the probe current. The specimen current changes the sign when $I_{\mathrm{SE}}+I_{\mathrm{BSE}}+I_{\mathrm{AE}}> I_{\mathrm{p}}$. Because $I_{\mathrm{SE}}+I_{\mathrm{BSE}}\gg I_{\mathrm{AE}}$ this means basically that $\delta+\eta> 1$ (Fig. 5.16). $I_{\mathrm{sp}}$ depends on the angle of beam incidence $\theta$ and the electron energy $E_{0}$ as expected from $\delta(\theta,E_{0})$ and $\eta(\theta,E_{0})$ [5.38]. The resolution of specimen current images is comparable to that of BSE images. One advantage of the specimen current mode is that the contrast is independent of the detector position. A critical review of this mode was published by Newbury [5.187].

1.3 Contrast Formation and Resolution

Since the image formation is due to the image signal fluctuation $\Updelta S$ from one point to another point, the contrast $C$ is designated as in television to be

$$C=\frac{S-S_{\mathrm{av}}}{S}=\frac{\Updelta S}{S}\;.$$

(5.41)

$S_{\mathrm{av}}$ is the average value of the signal and $S$ represents the signal of the considered point ($S> S_{\mathrm{av}}$, i. e., $C$ is always positive). The signal fluctuation may be caused by local differences in the specimen topography, composition, lattice orientation, surface potential, magnetic or electric domains, and electrical conductivity. The minimum contrast is obtained if $S=S_{\mathrm{av}}$, whereas the maximum contrast is obtained for $S_{\mathrm{sv}}=0$. This is the case, e. g., when the signal $S$ from a feature is surrounded by a background with $S_{\mathrm{av}}=0$. The contrast will be visible if $C$ exceeds the threshold value of about $\mathrm{5\times 10^{-2}}$.

According to the point-resolution criterion two image points separated by some horizontal distance (i. e., within the $x$–$y$ plane perpendicular to the optical axis) are resolved when the minimum intensity between them is ${\mathrm{75}}\%$ or less of the maximum intensity. Because of the inherent noise of each signal of the SEM characterized by its signal-to-noise ratio ( ) the drop to ${\mathrm{75}}\%$ of the maximum intensity will not be reliably defined at the minimum distance. Consequently, at low SNR two image points can be resolved only if their distance is larger than the minimum distance reliably defined for noiseless signals.

As opposed to the light or transmission electron microscope the resolution of the SEM cannot be defined by Rayleigh's criterion . The resolution obtained in the SEM image depends in a complex manner on the electron-beam diameter, the electron energy, the electron–specimen interaction, the selected signal, the detection, as well as the electronic amplification and electronic processing. An object point corresponds to the size of a small local excitation volume (Figs. 5.13 and 5.14) designated as the spatial detection limit from which a sufficient signal can be obtained. Obviously, the point resolution cannot be less than the spatial detection limit. It becomes clear from Fig. 5.14 that the spatial resolution of an SEM is different for each signal since the size of the signal-emitting volume as well as the signal intensity depends on the type of signal selected.

The important quality parameters such as spatial resolution, astigmatism, and SNR of SEM images, as well as drift and other instabilities that occur during imaging, can be determined most reliably and objectively by Fourier analysis of the recorded micrographs [5.161, 5.38]. However, such determinations are problematic, since, unlike TEM resolution specimens, there is no single type of sample that will give completely unambiguous results, especially in the current microscope environment, where the resolution is measured in angstroms for high-end systems (typical resolution quoted for an FESEM hovers around $8{-}10\,{\mathrm{\AA{}}}$). Other measurement procedures involve measuring the separation gap between two particles or via a line profile through a defined sharp edge structure. These techniques are subjective in nature. Defining the edge of a particle will be different from one person to the next based on how that person interprets the edge of a particle. When using the line profile method, the distance for the signal transition is considered to be related to probe diameter. While the traditional convention and measurement have been done at the 84th and 16th percentile of the transition ($1\sigma$ value), different SEM manufacturers have reported values at 75th/25th and 65th/35th percentile. This leads to lower reported values of resolution even from the same edge profile in an image.

Another layer of complexity is added with digital image acquisition in today's SEMs. The pixel resolution of the final image has an impact on the smallest features that can be resolved, meaning that the resolution measurement is intimately linked to the pixel size. Consider an image taken at ${\mathrm{100000}}\,\times$ with a field of view of ${\mathrm{1.28}}\,{\mathrm{\upmu{}m}}$. If the image pixel resolution is ${\mathrm{1280}}\times{\mathrm{960}}$, then we have a pixel length of ${\mathrm{1}}\,{\mathrm{nm/pixel}}$. To distinguish a probe diameter of ${\mathrm{3}}\,{\mathrm{nm}}$ would require image information that could be observed across only $\mathrm{3}$ pixels. Taking the same image with an increased pixel density of ${\mathrm{2560}}\times{\mathrm{1920}}$ would mean that the same information could be observed across $\mathrm{6}$ pixels.

Clearly, resolution specifications cannot be compared easily today between different manufacturers, so far as there is no standardized methodology and specimen.

1.3.1 Topographic Contrast

Presumably the SEM is most frequently used to visualize the topography of three-dimensional objects. The specimen topography gives rise to a marked topographic contrast obtained in secondary and backscattered images. This contrast has a complex origin and is formed in SE images by the following mechanisms:

• 1. Dependence of the SE yield $\delta$ on the angle of incidence $\theta$ of the electron beam at the local surface element (5.31). The tilt angle of the local surface elements is given by the topography of the sample.

• 2. Dependence of the detected signal on the angular orientation of the local surface element related to the ET detector (Sect. 5.1.1, Detectors and Detection Strategies). SE generated behind local elevations, in holes, in fissures, or in cavities reach the ET detector incomplete. This causes a more or less pronounced shadow contrast (Fig. 5.7a,ba).

• 3. Increase of the SE signal when diffusely scattered electrons pass through an increased surface area. This is the case at edges or at protruding surface features, which are smaller than the excitation volume. Electron diffusion leads to overbrightening of edges and small surface protrusions in the micrograph and is known as an edge effect.

• 4. Charging artifacts with objects of low electric conductivity.

Contributions (1) to (3) are illustrated by SE micrographs of different specimens shown in Figs. 5.23a-da and 5.24a-da as well as schematically by profiles of the topography and the related SE signals in Fig. 5.25a-d. In these figures the direction to the ET detector is indicated. The ball in Fig. 5.23a-da shows a contrast, which is mainly due to the varying angle $\theta$ of beam incidence across the ball ((1) above) and the angular orientation of the local surface elements related to the Everhart–Thornley detector ((2) above). The collection efficiency of the ETD is significantly higher for surface elements facing the detector than for those on the back (shadow region). Whereas the intensity of emitted secondary electrons of the ball reveals radial symmetry, the effect of detection geometry causes the nonradial symmetric image intensity distribution of the ball (Fig. 5.25a-da–c). The rim of the ball is bright in the SE image because of the enhanced SE emission due to an incidence angle $\theta\approx 90^{\circ}$ and the effect of diffusely scattered electrons passing through an increased surface area ((3) above). The radius of the ball is larger than the electron range $R$ (Fig. 5.14) therefore the latter effect occurs just near the rim of the ball. If the mean radius of ball-like particles becomes comparable or smaller than the electron range, diffusely scattered electrons generate more SE over the whole particle surface, thus the SE emission typically is distinctly enhanced (small particles are marked by small arrowheads in Figs. 5.23a-da and 5.24a-da). If the shadow contrast is visible in the image and the direction toward the ETD is known then elevations and depressions clearly can be readily identified (Fig. 5.23a-da). Another way to distinguish elevations and depressions is to record and to analyze SE stereopairs.

The SE micrograph of large crystal-like particles (Fig. 5.24a-da) basically shows the same contrast mechanisms as discussed above but with a more complex structured sample than the ball. The individual flat surface planes of the crystal-like particles occur with almost constant brightness because of the constant angle of beam incidence and the constant detection geometry (provided that there is no shadow effect from other large particles). Some surface planes possess fissures of different size, which typically appear rather dark because just a minor fraction of the generated SE can escape from inside the fissures. In such cases SE can be extracted either by a positively biased grid in front of the specimen [5.188] or by a superimposed magnetic field in which the SE follow spiral trajectories around the lines of magnetic flux until they reach the collecting field of the ETD [5.76].

Fig. 5.23a-d

Secondary (a) and backscattered electron micrographs (b–d) of a steel ball recorded at ${\mathrm{30}}\,{\mathrm{kV}}$ and normal beam incidence. The arrow in (a) indicates the direction of the laterally located ET detector. The BSE micrographs shown in (c,d) were acquired using a four-quadrant semiconductor detector mounted below the objective pole piece, which records BSE over a large solid angle. The steel ball is mounted on carbon (marked by C), which is supported by aluminum (marked by Al). The small arrows in (a) indicate small particles with enhanced SE emission (bright blobs in the SE image). Elevations (E) and depressions (D) are also marked by small arrows

Fig. 5.24a-d

Secondary (a) and backscatter (b–d) electron micrographs of table salt crystals coated with gold recorded at ${\mathrm{10}}\,{\mathrm{kV}}$. The arrow in (a) indicates the direction of the ET detector. (b) Shows an image recorded with ET detector with collector cage at ${\mathrm{-100}}\,{\mathrm{V}}$; (c) is a backscatter image recorded with a 3-segment solid-state detector (A+B chips), showing mainly compositional contrast; (d) is a backscatter image recorded with a 3-segment solid-state detector (C-chip only), showing mainly topography

Fig. 5.25a-d

Schematic specimen surface profile of an assumed topography having elementally shaped elevations and a depression (a). Those elemental shapes are present in the samples shown in Figs. 5.23a-d and 5.24a-d. The size of the excitation volume of the electron beam is drawn in relation to the local topographic structures. The amount $n_{\mathrm{SE}}$ of locally emitted SE is shown qualitatively in (b) and the corresponding SE signal $S_{\mathrm{SE}}$ in (c). The BSE signal $S_{\mathrm{BSE}}$ collected by the negatively biased ET detector is schematically presented by the graph in (d). ETD, Everhart–Thornley detector

It should be mentioned that the laterally located ETD also registers those BSE, which are within the small solid angle of collection defined by the scintillator area and the specimen–scintillator distance. The BSE contribute in the order of $10{-}20\%$ to the SE signal [5.38] and are the same as those collected by the negatively biased ET detector. Furthermore, BSE that are not intercepted by the detector strike the pole piece of the objective lens and the walls of the specimen chamber. These stray BSE generate so-called SE3 emitted from the interior surfaces of the specimen chamber. The SE3 carry BSE information and form a significant fraction of the SE signal for specimens with an intermediate and high atomic number [5.189].

The contrast in BSE images is formed by the following mechanisms:

• 1. Dependence of the BSE coefficient $\eta$ on the angle of incidence $\theta$ of the electron beam at the local surface element (5.34).

• 2. Dependence of the detected signal on the angular orientation of the local surface element related to the BSE detector (Sect. 5.1.1, Detectors and Detection Strategies). BSE emitted behind local elevations, in holes, or in cavities, which do not reach the BSE detector on nearly straight trajectories, are not acquired. This causes a pronounced shadow contrast (Fig. 5.7a,bb).

• 3. Increase of the BSE signal when diffusely scattered electrons pass through an increased surface area. This is the case at edges or at protruding surface features, which are smaller than the excitation volume.

The BSE leave the specimen on almost straight trajectories and only those within the solid angle of collection of the BSE detector can be recorded. Thus, dedicated BSE detectors have a large solid angle of collection to record a significant fraction of the BSE and to generate a signal with a sufficient SNR. The larger the solid angle of collection the less pronounced the shadow effects.

Contributions (1) to (3) mentioned above are illustrated by BSE micrographs from two specimens used for SE imaging and are shown in Figs. 5.23a-db,c and 5.24a-db and c as well as schematically by profiles of the topography and the related BSE signals in Fig. 5.25a-d. Two different types of BSE images are shown: the highly directional image recorded with the negatively biased ETD (Figs. 5.23a-db and 5.24a-db) and the top-view image recorded with the four-quadrant semiconductor detector mounted below the objective pole piece (Figs. 5.23a-dc and 5.24a-dc). The ball in Fig. 5.23a-db shows a contrast, which is mainly due to the varying angle $\theta$ of beam incidence across the ball ((1) above) and the angular position of the local surface elements related to the negatively biased ETD ((2) above). A pronounced sharp shadow occurs at the back of the ball and behind the ball (shadowed oblong area of the support). Whereas the intensity of the BSE of the ball reveals radial symmetry, the effect of detection geometry causes the nonradial symmetric image intensity distribution of the ball (Fig. 5.25a-da,d). The fade contour of the ball at its back is due to BSE redirected toward the negatively biased ETD by scattering on some interior surfaces of the specimen chamber. The pronounced directional shadow contrast in the image allows for unambiguous identification of elevations and depressions (Fig. 5.23a-db). Moreover, if the detection geometry of the BSE is known, the length of the shadow can be used in some cases to obtain a rough estimate of the height of elevations or depth of depressions.

The BSE micrograph of the ball recorded with the four-quadrant semiconductor detector (Fig. 5.23a-dc) shows an almost radial symmetric image intensity distribution. It is obvious that the increase of the BSE coefficient $\eta$ with the increasing angle of incidence $\theta$ (Fig. 5.18) toward the rim of the ball is superimposed by the stronger counteracting effect of the directed asymmetric distribution, for a large $\theta$ reflection-like angular distribution of BSE for non-normal beam incidence (Sect. 5.1.2, Backscattered Electrons). The shadow-like hem along the contour of the elevations reflects the fact that BSE emitted from the lower surrounding areas toward elevations can be absorbed or redirected; thus those BSE do not reach the BSE detector. In the case of depressions there is also a shadow-like hem but it is located inside the contour of the depression. A comparison of the different types of BSE images in Fig. 5.23a-db,c clearly shows that the topography of the sample is pronounced in Fig. 5.23a-db while—as we shall see later—the atomic number contrast is pronounced in Fig. 5.23a-dc.

The BSE micrographs of large crystal-like particles (Fig. 5.24a-db,c) basically show the same contrast mechanisms as discussed previously (no orientation anisotropy of the electron backscattering and SE emission [5.158, 5.190] is involved). Figure 5.24a-db recorded with the negatively biased ETD shows large shadowed regions (containing almost no information) and some highlighted individual flat surface planes of the crystal-like particles that occur with almost constant brightness because of the constant angle of beam incidence of the constant detection geometry. Figure 5.24a-db demonstrates that the detection geometry used for recording was not at an optimum. The micrograph obtained with the four-quadrant semiconductor detector is shown in Fig. 5.24a-dc, which depicts exactly the same area as Fig. 5.24a-db. Because of the large solid angle of collection of this BSE detector the effects mentioned above in (1) and (2) do generate just small differences in the image intensity of differently oriented surface planes of the crystal-like particles. The effect of shadowing is not substantial in that micrograph. The increase of the BSE signal at edges, at surface steps, and small protruding particles ((3) above) located on the flat surface planes due to enhanced BSE emission is significant. The fissures on some surface planes of the crystal-like particles (Fig. 5.24a-da) occur in the BSE micrograph also as rather dark features because just a minor fraction of the BSE can escape from inside the fissures.

Fig. 5.26a-d

BSE micrographs of a steel ball on carbon (Fig. 5.23a-d) each recorded with another individual quadrant of the four-quadrant semiconductor detector. (a) ($-x$)-quadrant, (b) ($+y$)-quadrant, (c) ($-y$)-quadrant, (d) ($+x$)-quadrant. The micrographs were recorded at ${\mathrm{30}}\,{\mathrm{kV}}$ and normal beam incidence. The angular position of the four-quadrant semiconductor detector is rotated clockwise against the $x$–$y$ coordinates of the images by $34^{\circ}$. Shadows of the surface step of the feature at the bottom left of each image help to identify the position of the active quadrant visually

The SEM micrographs are closely analogous to viewing a macroscopic specimen by eye. In the light optical analogy the specimen is illuminated with light from the side of the detector and viewed from the position of the electron beam [5.191, 5.68]. When a rather diffuse illumination is used then all surface elements are illuminated but those directed to the light source are highlighted. This corresponds to the situation for the positively biased ETD. The light optical analogy shows a pronounced shadow contrast if a directional light source illuminates the specimen surface from a suitable direction. This situation closely resembles BSE images recorded with a positively biased ETD. The strong light optical analogy very likely explains the fact that SEM micrographs of objects with a distinct topography can be readily interpreted even without extensive knowledge of the physics behind the imaging process.

As briefly mentioned in Sect. 5.1.1, Detection Strategies, the topographic and the material contrast can be pronounced or suppressed, respectively, by a combination of the signals of two oppositely placed detectors, $A$ and $B$. Two BSE semiconductor detectors were first used by Kimoto et al [5.69] and they showed that the sum $A+B$ results in material and the difference $A-B$ in topographic contrast. Volbert and Reimer [5.192] used a BSE/SE converter system and two opposite ET detectors for that kind of contrast separation in the SEM. The four-quadrant semiconductor detector used for recording Figs. 5.23a-dc and 5.24a-dc allows for signal mixing of the four signals acquired simultaneously. Figures 5.23a-dc and 5.24a-dc represent the sum of the four signals ($S_{\mathrm{Q1}},\ldots,S_{\mathrm{Q4}}$), thus both micrographs show a pronounced material contrast. By addition of the signals of two adjacent quadrants at a time (i. e., $S_{\mathrm{Q1}}+S_{\mathrm{Q2}}=A$; $S_{\mathrm{Q3}}+S_{\mathrm{Q4}}=B$) the effect of two semiannular detectors $A$ and $B$ is obtained. The difference image $A-B$ shows a pronounced topographic contrast (Fig. 5.23a-dd). The directionality in Fig. 5.23a-dd can be varied readily by using a different combination of the individual signals of the quadrants, e. g., $A=S_{\mathrm{Q2}}+S_{\mathrm{Q3}}$ and $B=S_{\mathrm{Q1}}+S_{\mathrm{Q4}}$. Difference SE and BSE images recorded at exactly defined detection geometry allow for the reconstruction of the surface topography [5.68, 5.71, 5.72, 5.73]; see also Sect. 5.1.1, Detection Strategies and Specimen Tilting and Stereo Imaging. However, special care is required for the reconstruction of the surface topography using BSE images because of artifacts in the reconstructed image [5.68]. To demonstrate the effect of directionality for four different detections Fig. 5.26a-d shows four individual BSE micrographs each recorded with another quadrant of the semiconductor detector. The individual BSE images contain superimposed topographic and compositional contrast components.

1.3.2 Material Contrast

The material or compositional contrast arises from local differences in chemical composition of the object investigated. As shown in Fig. 5.17, the SE yield $\delta$ increases weakly with increasing atomic number but the increase is significantly less than that of the BSE coefficient $\eta$. Experimental values of $\delta$ (see, e. g., the data collection by Joy [5.145]) scatter strongly around a mean curve. The increase of $\delta(Z)$ with $Z$ is mainly due to SE (5.30) generated by emitted BSE near the specimen surface (SE2). At electron energies larger than ${\mathrm{5}}\,{\mathrm{keV}}$ the SE images usually show the same compositional contrast as the corresponding BSE image. This situation is illustrated in Fig. 5.23a-da–c where at normal beam incidence carbon ($Z={\mathrm{6}}$) is darker than aluminum ($Z={\mathrm{13}}$) in both the SE and BSE image. Table 5.4 gives some numerical values for the compositional contrast for carbon, aluminum, and iron calculated with the related BSE coefficients for normal beam incidence, which qualitatively agrees with the contrasts obtained in Fig. 5.23a-dc. At accelerating voltages below ${\mathrm{5}}\,{\mathrm{kV}}$, the interpretation of the observed contrast gets quite complicated, and often times there is a reversal of BSE contrast [5.34, 5.68].

Table 5.4 Compositional contrast calculated according to (5.33) for normal beam incidence $\theta=0$ for the elements C, Al, and Fe

1.3.3 Other Contrasts

1.3.3.1 Voltage Contrast

The secondary electron image intensity varies if the potential of the specimen is positively or negatively biased with respect to the ground. In principle, a positively biased surface area shows decreased image intensity because low-energy SE are attracted back to the specimen by the electric field. Conversely, a negatively biased surface area shows enhanced image intensity because all SE are repulsed from the specimen. This voltage-dependent variation in contrast is designated as voltage contrast and dates back to the late 1950s [5.193, 5.194, 5.195]. Strictly speaking all emitted electrons are influenced to some extent by the potential of the sample, but only the SE and, in principle, the Auger electrons can be used for voltage contrast studies [5.196]. The use of Auger electrons is more difficult than that of SE because of the very low yield of AE and the ultrahigh vacuum requirements of AE analysis.

The voltage contrast depends on the energy of the beam electrons and on the properties of the specimen, being most pronounced in the low electron energy region where the SE yield is highest (Fig. 5.12). Biasing the specimen positively or negatively by a few volts not only affects the amount of emitted SE but also their trajectories. This is caused by the fact that the majority of the SE have energies of a few electron volts in contrast to BSE and Auger electrons. The effect of specimen voltage on the SE trajectories is rather complex because it depends on the SE detection geometry, the sample position in the specimen chamber, the properties of the sample, and the operation conditions of the SEM. However, voltage contrast is a valuable tool for the investigation of a wide range of simple faults in microelectronic devices or studies of the potential distribution at grain boundaries obtained on the cross section of varistors at applied low DV voltage and their breakdown behavior at elevated voltage [5.197]. The voltage contrast is also used to characterize the surface charge distribution of ferroelectrics [5.198, 5.199, 5.200] and piezoelectrics [5.201].

Voltage contrast measurements can also be performed in a dynamic mode on semiconductor devices by pulsing the electron beam (called electron stroboscopy [5.202]) synchronously with the device signal as shown by Plows and Nixon [5.203]. This dynamic mode allows for quantitative voltage contrast measurements on semiconductor devices at high-frequency operation conditions known as electron-beam testing widely used by the electronics industry for the development, fault diagnosis, and debugging of innovative integrated circuits. High-frequency electron stroboscopy requires high-speed electrostatic beam-blanking systems with subnanosecond time resolution. For very high-frequency electron stroboscopy in the gigahertz range a special transverse–longitudinal combination gate system [5.204] or microwave structure-based beam-blanking techniques have been employed [5.205]. A comprehensive treatment of the fundamentals of voltage contrast and stroboscopy has been published by Davidson [5.206] and the state of the art of voltage contrast has been reviewed by Girard [5.207]. Furthermore, improvements of voltage contrast detectors as well as of detection strategies are discussed in detail by Dubbeldam [5.208]. Voltage contrast is now of a mature age, but the extension to future microelectronics also presupposes an extension in the domain of in situ testing methods and techniques.

1.3.3.2 Electron Beam-Induced Current

The electron beam generates a variety of signals emitted from the specimen as shown in Figs. 5.2 and 5.14. In semiconductors the primary electrons generate electron–hole pairs or minority carriers within the excitation volume. The mean number of electron–hole pairs is given by $E_{0}/E_{\mathrm{exm}}$ (5.14), where $E_{\mathrm{exm}}$ is the mean energy per electron–hole pair-forming event. For example, $E_{\mathrm{exm}}$ amounts to ${\mathrm{3.6}}\,{\mathrm{eV}}$ for Si and ${\mathrm{2.84}}\,{\mathrm{eV}}$ for Ge, i. e., one ${\mathrm{10}}\,{\mathrm{keV}}$ electron generates on average approximately $\mathrm{2.7\times 10^{3}}$ electron–hole pairs in Si and $\mathrm{3.5\times 10^{3}}$ in Ge [5.209]. The charge-collection ( ) signal is detected between two electric contacts; one of these contacts collects the electrons and the other one collects the holes. If electromotive forces caused by electron voltaic effects are generated by the beam electrons in the specimen then a charge-collection current $I_{\mathrm{CC}}$ designated as an electron beam-induced current ( ) flows through the ohmic contacts. If no electron voltaic effects occur, the beam electrons cause local $\beta$-conductivity, where the separation of charge carriers results in an electron beam-induced voltage ( ). The most important type of signal of the two charge-collecting modes is EBIC. A detailed treatment of the basic physical mechanisms and applications of the charge-collection mode is given by Holt [5.210, 5.211], Deamy [5.212], Reimer [5.38], Shea et al [5.213], Alexander [5.214], and Yakimov [5.215].

EBIC can be observed in SEM simply by connecting a high-gain large-bandwidth amplifier across the specimen using the amplified EBIC signal as a video signal. The input impedance of the amplifier must be very low relative to that of the specimen to measure the true EBIC. For usual electron probe currents of some nanoamperes the charge collection currents are in the order of microamperes since for many materials the mean energy per electron–hole pair is between approximately $\mathrm{1}$ and ${\mathrm{13}}\,{\mathrm{eV}}$ [5.211]. In contrast to EBIC, for the measurement of the true EBIV an amplifier with a very high input resistance is necessary.

The resolution obtained in the charge-collecting modes depends on the size of the excitation volume within the specimen, which readily can be extracted from Monte Carlo simulation data (Sect. 5.1.2). For the CC mode, a depth and a lateral resolution have to be defined. The depth–dose function, which represents the energy loss per unit depth in the electron-beam direction, determines the depth resolution. The lateral–dose function, which represents the energy loss per unit distance perpendicular to the electron-beam direction, determines the lateral resolution. There are also empirical [5.216] and semiempirical expressions [5.217] as well as several analytical models [5.218, 5.219] for the depth–dose and for the lateral–dose function as well [5.218, 5.219].

Electron-beam chopping and time-resolved EBIC can enhance the accuracy of measurements in several cases, e. g., for the estimation of the depth of the p-n junction parallel to the surface [5.220] or allows for quantitative analysis of electrical properties of defects in semiconductors [5.221] and interesting applications for the failure analysis of (very-large-scale integration) circuits [5.222].

1.3.3.3 Crystal Orientation Contrast

As previously mentioned, the backscattering coefficient $\eta$ of a single crystal varies with the direction of the incident beam electrons related to the crystallographic orientation (Sect. 5.1.2). This effect is caused by the variation of the atomic density, which the incident electrons encounter when penetrating into the crystal. In certain crystallographic directions the beam electrons penetrate more deeply. Those directions represent channels for the incident electrons. Changing the direction of the incident electrons relative to the crystallographic orientation causes the so-called crystal orientation or channeling contrast of the BSE image, which amounts to a maximum of approximately ${\mathrm{5}}\%$. Scanning at low magnification both moves the electron probe and changes the angle of incidence across the field, thereby generating an electron channeling pattern ( ). At higher magnification the angle of beam incidence varies insignificantly across the small scanned field and channeling contrast is obtained in polycrystalline samples from small grains with different crystal orientations (Fig. 5.27). The information depth of the crystal orientation contrast is in the order of a few nanometers only [5.38] and therefore the contrast is very sensitive to distortions of the crystal at the surface. The channeling contrast reaches the maximum at energies between $\mathrm{10}$ and ${\mathrm{20}}\,{\mathrm{keV}}$ [5.158, 5.223].

An orientation anisotropy also occurs for the secondary yield [5.158], which gives rise to an SE orientation contrast.

Fig. 5.27

Cross section of a polycrystalline sample having grains with different crystal lattice orientation relative to the electron beam

1.3.3.4 Magnetic Contrasts

Basically, two different types of magnetic contrast can arise from the interaction of the emitted electrons with the magnetic field of small domains of the specimen.

1.3.3.4.1 Type-1 Magnetic Contrast

Secondary electrons are deflected after emission by an external magnetic field, thus generating a magnetic contrast [5.224]. External magnetic fields can exist in natural or synthetic engineered ferromagnetic materials such as magnetic tape, magnetic cards, and computer disks. The fringe fields near the surface are highly inhomogeneous and the SE trajectories are affected by the Lorentz force, which is proportional to $\boldsymbol{v}\times\boldsymbol{B}$ where $\boldsymbol{v}$ is the velocity vector of the SE and $\boldsymbol{B}$ the magnetic field. The most probable velocity corresponds to the electron energy of a few electronvolts (Sect. 5.1.2, Secondary Electrons). The acting Lorentz force deflects the trajectories of the SE and the resulting effect can be approximated to a tilt of Lambert's angular SE emission characteristics of the SE (Sect. 5.1.2, Secondary Electrons; [5.38]). Figure 5.28 illustrates this effect for two domains in the specimen having oppositely directed external magnetic fields. To observe type-1 magnetic contrast in the case of weak magnetic fields an ETD with a high angular sensitivity, a two-detector system [5.224, 5.225] or digital image processing [5.226, 5.227] has been employed. For the type-1 magnetic contrast low beam electron energies are favorable because of the enhanced SE yield and therefore an increased signal-to-noise ratio (SNR). The actual problems related to the complicated mechanism of type-1 magnetic contrast and its relatively low resolution were discussed by Szmaja [5.226].

Fig. 5.28

Scheme of type-1 magnetic contrast formation between two domains having oppositely directed external magnetic fields. The dashed lines indicate the SE trajectories for the most probable SE energy to the positively biased Everhart–Thornley detector (ETD) without a magnetic field and the solid lines the trajectories with magnetic fields. The effect of the magnetic force $F_{\mathrm{m}}$ on the SE tilts the trajectories by a small angle toward or away from the ETD, respectively

1.3.3.4.2 Type-2 Magnetic Contrast

This type of contrast arises from the deflection of backscattered electrons by the internal magnetic field within the specimen [5.228, 5.229]. Depending on the direction of the magnetic field inside the sample, the BSE are bent toward or away from the surface between consecutive scattering events, i. e., the BSE coefficient is increased in domains where trajectories are bent toward the surface and decrease when bending the BSE trajectories in an opposite direction. To observe a sufficient type-2 magnetic contrast the beam electrons need an energy of at least ${\mathrm{30}}\,{\mathrm{keV}}$ and a relatively high beam current [5.230]. The BSE signal modulation due to magnetic fields inside the specimen is typically less than ${\mathrm{1}}\%$ of the collected current and unwanted topographic contrasts can be reduced in comparison with this magnetic contrast by a lock-in technique [5.230, 5.231].

1.4 Specimen Preparation

The specimen preparation procedures required for optimum results of scanning electron microscopic investigations are of crucial importance. The dedicated preparation of the specimen under study is an essential prerequisite for the reliability of the experimental data obtained and has a significance comparable to the performance of the SEM used for the investigation. Unfortunately, the importance of specimen preparation is often underestimated. In principle, the preparation required depends significantly on the properties of the specimen to be investigated as well as on the type of SEM study, i. e., whether imaging of the surface or of cross sections of the sample (Sects. 5.1.2, 5.1.3, and 5.4), crystallographic characterization by electron diffraction techniques (Sect. 5.5), or x-ray microanalytical investigations (Sect. 5.4) are considered. Bearing in mind the variety of specimens having unknown properties on the one hand and the multitude of possible investigation techniques on the other hand, it is obvious that the choice of the most promising preparation procedures can be a rather complex matter. Although the preparation techniques are described in a variety of books [5.10, 5.23, 5.232, 5.233, 5.234, 5.235, 5.236, 5.237, 5.238, 5.239, 5.240, 5.241], collections of methods [5.242, 5.243] with updates, and publications, the successful preparation still also depends in many cases on experience and skillful hands.

It is beyond the scope of this chapter to discuss the wide field of preparation techniques. Therefore, a brief rather general outline of specimen preparation with reference to specific literature will be given. Figure 5.29 schematically outlines some important preparation procedures used for inorganic and organic materials. As a general rule, a successful investigation by SEM requires specimens, which have clean surfaces, sufficient electrical conductivity, are not wet or oily, and possess a certain radiation stability, to resist electron irradiation during imaging. Another critical parameter is a conductive pathway that needs to be created between the specimen and the holder, otherwise the specimen will exhibit significant instability under the electron beam (such a pathway could be achieved by using conductive paint or tape). An exception of this rule is allowed only for SEMs working at ambient pressure (say at low vacuum; Sect. 5.3), which permits direct imaging of dirty, wet, or oily samples, although radiation damage occurs with radiation-sensitive specimens. The goal of an ideal preparation consists in making specimens accessible for high-vacuum SEM studies without changing the relevant properties under investigation.

Fig. 5.29

Schematic drawing of important preparation procedures for SEM used for inorganic and organic materials with and without water. AD , air drying; , critical point drying; FD , freeze drying; , focused ion beam; , ion beam slope cutting

Many inorganic samples with sufficient electrical conductivity, such as metals, alloys, or semiconductors, can be imaged directly with little or no specimen preparation (Fig. 5.29). This is one very useful feature of scanning electron microscopy. In some cases a surface treatment may be required, e. g., to clean the specimen surface with an appropriate solvent, possibly in an ultrasonic cleaner, and with low-energy reactive gas plasma for the removal of hydrocarbon contamination [5.244]. The cleanings are suitable to prepare electrically conductive specimens for surface imaging in SEM. In the case of nonconductive samples, such as ceramics, minerals, or glass, a conductive coating [5.245] with a thin metal film (e. g., gold, platinum, tungsten, chromium) or a mixed conductive film (e. g., gold/palladium, platinum/carbon, platinum/iridium/carbon) is required for good-quality imaging. For x-ray microanalysis carbon coating is preferred because of its minimum effect on the x-ray spectrum. The coating can be performed by evaporation [5.232, 5.243, 5.246, 5.247], by diode sputtering [5.248], or by planar magnetron sputtering [5.249, 5.250]. High-quality conductive thin-film coating for high-resolution SEM (Sect. 5.2) can be performed in an oil-free high vacuum by both evaporation, using e. g., tungsten, tantalum/tungsten, platinum/carbon, or platinum/iridium/carbon, and rotary shadowing methods [5.247, 5.251, 5.252, 5.253] as well as by ion beam and by Penning sputtering with, e. g., chromium, tantalum, and niobium [5.254].

For the study of microstructural features (Sect. 5.5) and for microanalytical investigations (Sect. 5.4) a flat surface is required, therefore rough specimen surfaces have to be flattened by careful grinding and subsequent polishing according to standard metallographic methods [5.255]. To remove mechanical deformations caused by grinding and mechanical polishing, a final treatment with electrochemical polishing or ion beam polishing may be necessary. In case of polycrystalline and heterogeneous material, selective etching by ion bombardment may be used, which generates a surface profile caused by locally different sputtering yields, thus giving rise to topographic contrast of grains and the individual materials [5.256, 5.257].

Often, specimens need to be characterized and analyzed both above and below the surface, e. g., if the subsurface composition of the material, process diagnosis, failure analysis, in situ testing, or three-dimensional reconstruction of the spatial microstructure is required. Flat cross sections through the specimen can be obtained by ultramicrotomy ([5.258, 5.259, 5.260]; the block face can be used for SEM imaging), broad ion beam cutting [5.261, 5.262, 5.263], an FIB technique [5.264, 5.265, 5.266, 5.267, 5.268], or by a combination of an FIB system with a field-emission SEM (SEM/FIB), which allows the precise positioning of the cross section and, most importantly, realtime high-resolution SEM imaging of the cutting process, which enables, among other things, the examination of the spatial structure [5.269, 5.270, 5.271, 5.272, 5.273, 5.274]. An example for two perpendicular vertical cross sections into an integrated circuit is shown in Fig. 5.30a,b. The combined SEM/FIB additionally can be equipped with analytical techniques such as energy-dispersive x-ray spectroscopy and electron backscatter diffraction allowing for three-dimensional elemental and structural analysis of the interior of the specimen.

Fig. 5.30a,b

Integrated circuit with two perpendicular vertical cross sections into the interior. FIB sectioning was performed with the CrossBeam^® tool from Carl Zeiss NTS. The secondary electron images using the EDT were obtained by the field-emission SEM (a) at ${\mathrm{3}}\,{\mathrm{kV}}$ and by the FIB system (b) at ${\mathrm{5}}\,{\mathrm{kV}}$. Both micrographs reveal the site-specific internal structure of the integrated circuit, although some features occur with different contrast caused by different mechanisms of SE generation by electrons (a) and ions (b). (Courtesy of Carl Zeiss NTS, Oberkochen, Germany)

The other class of samples consists of organic material, which usually has an insufficient electrical conductivity for scanning electron microscopy. Although biological specimens contain water—the water content ranges in human tissues from approximately $\mathrm{4}$ to ${\mathrm{99}}\%$ [5.275]—many other organic materials do not, e. g., numerous polymers. The preparation strategies to be applied to specimens with and without water differ (Fig. 5.29), although there are also some similarities between them.

The surface treatment of organic specimens without water, such as cleaning, grinding, polishing, and etching by dissolution, chemical attack, or ion bombardment, has many similarities to the surface treatment of inorganic materials. A detailed discussion of and the recipes for specific preparation procedures for polymers are given in the chapter Specimen preparation methods in the book by Sawyer and Grubb [5.32]. Analogous to nonconductive inorganic materials, conductive coating with a thin metal film (e. g., gold, platinum, tungsten, chromium) or a mixed conductive film (e. g., gold/palladium, platinum/carbon, platinum/iridium/carbon) is required for good-quality imaging. If the subsurface structure of the material has to be studied, flat cross sections usually are prepared by ultramicrotomy or cryo-ultramicrotomy, depending on the cutting behavior of the specimen under study. In principle, cutting with ions and imaging and analysis with electrons by using a combined FIB/SEM tool is possible also with polymers. It was recently shown that ion milling is possible, e. g., with rubber ([5.276]; also Fig. 5.31) and with polymer material (Fig. 5.32).

Most of the organic specimens that contain water are biological samples. A small fraction of water-containing specimens is nonbiological, e. g., hydrogels. The water-containing specimens cannot be investigated in the wet state in the SEM in high vacuum without some additional preparation steps. In principle, three different preparation strategies exist to make wet specimens accessible to SEM investigations:

• 1. Withdrawal of the water

• 2. Replacement of the water by some vacuum-resistant material such as resins or freeze substitution [5.277, 5.278] of the ice of the rapidly frozen specimen by some organic solvent

• 3. Rapid freezing of the water.

Irrespective of the preparation strategy used the native spatial structure of the specimen should be maintained. Air drying, which is the most simple method of drying, is not suitable for drying soft specimens because the surface tension induces remarkable forces during the process of air drying, deforming the specimen irreversibly [5.279, 5.280]. Figure 5.29 shows different paths, which can be used, even though the degree of structural preservation depends on the preparation procedures applied. The different preparation procedures have been described in detail [5.236, 5.240, 5.243, 5.279, 5.281, 5.282, 5.283]. Among the different preparation methods rapid freezing is the method of choice for preparing biological specimens in a defined physiological state [5.240]. In the case of chemical fixation, which may create artifacts [5.283], the water of the sample has to be withdrawn or replaced afterward. If the surface structure of the specimen has to be studied, then the specimen surface has to be coated with a thin conductive film prior to SEM investigation. If the interior of the specimen has to be studied, the sample has to be opened by sectioning with the ultramicrotome or possibly FIB and subsequently coated. In the case of physical fixation, i. e., rapid freezing, the specimen has to be opened by freeze fracturing (for a review see [5.284, 5.285]), cryosectioning, or now possibly by ion milling the frozen-hydrated sample (ion milling in ice is possible [5.272]). After short partial freeze drying (also called freeze etching), the fracture face or block face has to be properly coated by a conductive film and then can be directly analyzed in the cryo-SEM [5.285, 5.286, 5.287, 5.288]. Another possible path is complete freeze-drying and subsequent conductive coating of the sample, which then can be analyzed at room temperature in the SEM.

Fig. 5.31

Secondary electron micrograph (through-the-lens detection) of a site-specific FIB cross-sectioned abrasive wear particle of a tyre supported onto carbon. The FIB sectioning and imaging at ${\mathrm{5}}\,{\mathrm{kV}}$ was performed with the CrossBeam^® tool combining a focused ion beam system with a field-emission SEM [5.270]. The cross section reveals the interior features of the rubber particle. (Courtesy of Carl Zeiss NTS, Oberkochen, Germany)

Fig. 5.32

SE micrograph showing cross section of acrylonitrile butadiene styrene (ABS ) polymer produced using JEOL JIB-4600F SEM-FIB. Image is taken using ${\mathrm{5}}\,{\mathrm{kV}}$

1.5 Radiation Damage and Contamination

The inelastic electron–specimen interaction inevitably damages the irradiated specimen and can induce contamination at the specimen surface. Although radiation damage, in particular of organic specimens, has been extensively investigated for thin films in transmission electron microscopy, comparatively little has been systematically studied for irradiation-sensitive samples in SEM. This may be due to the fact that the interpretation of radiation damage in TEM is easier because of the uniform ionization density through thin specimens. In bulk specimens, however, the ionization density is a function of the depth (for a detailed treatment of the depth–dose function see [5.289]) and a layer below the surface at the maximum ionization density will be damaged faster than others within the electron range $R$ (Figs. 5.13 and 5.14). According to the Bethe stopping power in (5.26), the damage will be proportional to $1/E$ ln(${\mathrm{1.166}}E/J$). Table 5.5 gives values of the stopping power for carbon and protein for electron energies from $\mathrm{0.1}$ to ${\mathrm{30}}\,{\mathrm{keV}}$, which show the increase of the stopping power with decreasing electron energy. It is commonly assumed that the shape of the depth—dose curve is not a function of either the primary electron energy or the material when normalized to the electron range [5.289]. That means that the layer with the maximum ionization density approaches the surface as the electron energy decreases.

Table 5.5 Mean ionization potential $J$ ((5.27) and (5.28), respectively) and the Bethe stopping power $\mathrm{d}E/\mathrm{d}s$ (5.26) for carbon and protein at different electron energies

In organics, the radiation breaks chemical bonds due to the transfer of typically tens of electron volts to an electron at the site of the interaction of many intra- and intermolecular bonds, which generates free radicals [5.290, 5.291, 5.292]. Many excited species will very rapidly recombine in $E-9{-}E-8\,{\mathrm{s}}$ and will reform the original chemical structure dissipating the absorbed energy as heat. Some recombinations will form new structures, breaking chemical bonds and forming others. If the material was initially crystalline, defects will form and gradually it will become amorphous. In addition to these structural changes the generated free radicals will rapidly diffuse to and across the surface or can evaporate, i. e., loss of mass and composition change will occur [5.160, 5.191, 5.293, 5.294, 5.295, 5.296, 5.84, 5.85]. Bubbles may form at high dose rates when volatile products are trapped. Not only the beam electrons damage the organic sample but also fast secondary electrons $(E_{\mathrm{SE}}> {\mathrm{50}}\,{\mathrm{eV}})$ can produce damage outside the directly irradiated specimen area [5.297]. Furthermore, beam-induced electrostatic charging and heating can also damage organic samples. Conductive coating of the organic specimen, as suggested for inorganic materials by Strane et al [5.298], can keep trapped free radicals as well as reduce beam-induced temperature rise or electrostatic charging [5.299]. Lowering of the temperature of the specimen is a further measure to reduce the sensitivity of an organic specimen to structural damage and mass loss. However, the reduction factor depends considerably on the material of the specimen.

The radiation damage mechanisms in semiconductors are different from those described above. As mentioned in Sect. 5.1.1, Detectors and Sect. 5.1.3, Electron Beam-Induced Current, the incident electrons generate electron–hole pairs, which will be trapped in the silicon oxide layer due to their decreased mobility. This can generate space charges, which in turn can affect the electronic properties of the semiconductor.

Beam-induced contamination is mass gain, which occurs when hydrocarbon molecules on the specimen surface are polymerized by the beam electrons. The polymerized molecules have a low surface mobility, i. e., the amount of polymerized molecules increases in the surface region where polymerization takes place. There are two main sources for hydrocarbon contamination: (1) gaseous hydrocarbons arising from oil pumps, vacuum grease, and possibly O-rings, and (2) residual hydrocarbons on the specimen. Several countermeasures exist to reduce the contamination to a tolerable level [5.300, 5.301, 5.302]. The amount of gaseous hydrocarbons is substantially reduced when the SEM is operated with an oil-free pumping system and a so-called cold finger (liquid nitrogen cooled copper plate) located above the specimen. Further, the contamination rate falls more rapidly as the specimen temperature is lowered, and below ${\mathrm{-20}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$ contamination is difficult to measure [5.301]. This is caused by the reduced diffusion of hydrocarbons on the specimen. In some cases, preirradiation of a large surface area with the electron beam is helpful, which immobilizes (polymerizes) hydrocarbons around the field of view to be imaged. Finally, specimens are mostly exposed to the atmosphere before transfer into the specimen chamber. Weakly bound molecules (e. g., hydrocarbons) can be completely eliminated by gently heating the sample in the specimen exchange chamber (low vacuum) to $40{-}50\,{\mathrm{{}^{\circ}\mathrm{C}}}$ for several minutes by a spot lamp [5.303]. A detailed topical review on the radiation damage and contamination in electron microscopy is given by Egerton et al [5.87].

1.6 Applications

Scanning electron microscopy is an indispensable tool for investigations of a tremendous variety of specimens from very different fields such as materials science, mineralogy, geology, semiconductor research, microelectronics, industry, polymer research, ecology, archeology, art, and life sciences. Although the investigations are not restricted just to imaging of surface structures, the majority of SEM studies apply the imaging modes. As mentioned previously, considerable additional information about the local elemental composition, electronic and magnetic properties, crystal structure, etc. can be acquired when the SEM is combined with supplementary equipment such as electron and x-ray spectrometers to take advantage of the energy spectra of the emitted electrons and x-rays. Table 5.6 surveys the information, which can be obtained from inorganic and organic specimens not containing water. Further, in situ scanning electron microscopy allows for different specific specimen treatments in the specimen chamber [5.25], which serves as a microlaboratory, and the simultaneous observation of the specimen response (Table 5.7).

Table 5.6 SEM applications on specimens from materials science, mineralogy, geology, polymer science, semiconductors, and microelectronics (state-of-the-art preparation and image analysis techniques are required to take full advantage of the capabilities of SEM)

Table 5.7 In situ treatments in SEM and available information about specimens from materials science

The advancement of nanoscale science and technology demands the manipulation of nano-objects at the molecular level and ultimately the manufacture of things via a bottom-up approach. For instance, a four-nanoprobe system can be installed inside a field-emission SEM, which may be used for gripping, moving, and manipulating nano-objects, e. g., carbon nanotubes, setting up electric contacts for electronic measurements, tailoring the structure of the nano-object by cutting, etc. and for making nanostructures [5.304]. The SEM in this setup allows for visualization of the four nanoprobes operating inside the specimen chamber as well as the process of formation of microstructures.

Less spectacular, but nevertheless important, are applications of scanning electron microscopy to image macroscopic samples in the millimeter range at very low magnification (about ${\mathrm{10}}\,\times$ to ${\mathrm{100}}\,\times$), which cannot be seen clearly by the eye or by the light microscope for some reasons. Two examples from very different fields are shown in Figs. 5.33a,b and 5.34a,b taking advantage of the large depth of focus as well as distinct topographic and material contrast.

Fig. 5.33a,b

BSE micrograph (a) showing the microstructure of the material used to paint the white reflecting road demarcation lines; some of the light-reflecting glass spheres are missing (depressions in the paint surface). Overlay EDS map of various constituents is shown as well (b)—Ti (blue), Ca (green), and Si (red). For safety reasons protruding sharp-edge particles are embedded in the material to generate high friction between the tires and the white lines

Fig. 5.34a,b

Secondary (a) and backscatter (b) images of metal fracture recorded at ${\mathrm{20}}\,{\mathrm{kV}}$. The contrast in the SE image shows the overall surface morphology, whereas the BSE image highlights the location of the high $Z$ material (white patches)

Working in the low-magnification range, the depth of focus limit in the SEM (Sect. 5.1.1, Specimen Tilting and Stereo Imaging) can be overcome by recording stacks of through-focus images (as in conventional and confocal optical microscopy), which are digitally postprocessed to generate an all-in-focus image [5.305]. The application of the technique is advantageous when BSE imaging of spongy specimens is required, as demonstrated with examples from the study of human osteoporotic bone [5.305].

In life sciences, application of SEM mainly for morphological studies is also widespread and started when commercial SEMs became available in the late 1960s [5.306]. However, in life sciences SEM is used less than TEM. Table 5.8 provides a survey of the specimens and information that can be obtained by SEM. Engineered biomaterials and tissues are becoming increasingly important in biomedical practice and it has become clear that cellular responses to materials depend on structural properties of the material at both the micrometer and nanometer scale. SEM is one of several methods for controlling material properties on both of these scales and thus it is increasingly used to study those materials.

Table 5.8 SEM applications on specimens from life sciences (state-of-the-art preparation and image analysis techniques are required to take full advantage of the capabilities of SEM)

Scanning electron microscopy can be used for comparative morphological studies of tissues as demonstrated by the application in cardiovascular surgery to detect endothelial damage caused by skeletonization [5.307]. In cardiovascular surgery, the radial artery is increasingly used for myocardial revascularization because of its presumed advantageous long-term patency rates. The vessel can be harvested as a pedicle or skeletonized. The SEM reveals the endothelial morphology (Fig. 5.35a,b), and thus allows comparison of the skeletonization technique with pedicle preparation using either an ultrasonic scalpel or scissors.

Fig. 5.35a,b

Secondary electron micrograph of the cross-sectioned radial artery at low magnification (a) and of the endothelial cells at medium magnification (b). The vessel was critical point dried and sputter coated with gold

Figure 5.36 shows additional examples of SEM imaging of various biological specimens—from immune-labeled cells, to pathology of brain and kidney and even viruses.

Fig. 5.36

(a) ${\mathrm{10}}\,{\mathrm{nm}}$ Au-labeled cell (BSE image, ${\mathrm{10}}\,{\mathrm{kV}}$); (b) mouse brain thin section (through-the-lens BSE image at ${\mathrm{2}}\,{\mathrm{kV}}$, inverted); (c) T4 bacteriophage (STEM-in-SEM image, ${\mathrm{30}}\,{\mathrm{kV}}$); (d) kidney thin section (STEM-in-SEM image, ${\mathrm{30}}\,{\mathrm{kV}}$)

Microtechnology and microelectromechanical systems ( ) are additional fields in which SEM is used as a tool for monitoring processes, detecting defects, or measuring sizes and distances, e. g., in micromachines and micromechanical or micromachining processes [5.308, 5.309, 5.310, 5.311].

The acquisition of quantitative data about the third dimension (stereo, 3-D) of surfaces and interior specimen structures was previously mentioned (Sect. 5.1.4). In general, this requires digital image analysis, specific instrumentation for the SEM (e. g., specimen stage, detectors), and special specimen preparation (e. g., ultramicrotome, IBSC, FIB). For example, techniques such as array tomography [5.312] and serial block-face SEM [5.313] have become prominent avenues for tomographic information collection for biological specimens using SEM.

2 Field-Emission Scanning Electron Microscopy

The diameter of the electron beam at the specimen surface sets a fundamental lower limit to the signal localization and, therefore, also to the resolution, which can potentially be obtained. As discussed in Sect. 5.1.2 and shown in Figs. 5.13 and 5.14, the SE and BSE are emitted from a surface area, which commonly is much larger than the beam diameter at the specimen surface. The large emitting area is caused by multiple elastic and inelastic electron-scattering events within the excitation volume, whose size depends on the specimen composition and energy of the beam electrons. Only the SE1 and BSE1 generated as the beam enters the specimen carry local information, while the SE2 and BSE2 carry information about the larger region surrounding the point of beam entrance (Fig. 5.14). High-resolution information can be obtained from SE1 and BSE1 generated by an electron probe with a diameter at the specimen surface of about ${\mathrm{1}}\,{\mathrm{nm}}$ or even less. A probe of that small size can be achieved by using field-emission electron sources, electromagnetic lenses with low aberration coefficients (5.7), (5.8), and (5.10), and both highly stabilized acceleration voltage (5.8) and objective lens current. High-resolution scanning electron microscopy at conventional acceleration voltages—that is $5{-}30\,{\mathrm{kV}}$—will be treated in Sect. 5.2.1. Alternatively, high-resolution information, in principle, can also be achieved when the excitation volume is reduced to a size similar to the SE1 and BSE1 emitting area by using low-energy beam electrons. By definition, electrons below ${\mathrm{5}}\,{\mathrm{keV}}$ are considered low-energy beam electrons and, consequently, scanning electron microscopy at low energies is called scanning low-energy electron microscopy or low (acceleration)-voltage scanning electron microscopy ( ). This type of scanning electron microscopy will be treated in Sect. 5.2.2. However, the majority of commercial high-resolution SEMs are capable of operation at both conventional energies, i. e., from $\mathrm{5}$ to usually ${\mathrm{30}}\,{\mathrm{keV}}$, and at low energies, i. e., below ${\mathrm{5}}\,{\mathrm{keV}}$ down to usually ${\mathrm{0.1}}\,{\mathrm{keV}}$ (current models of FESEM can go down to ${\mathrm{10}}\,{\mathrm{eV}}$).

2.1 High-Resolution Scanning Electron Microscopy

2.1.1 Electron Guns

Two different types of electron guns are currently available as sources for high-resolution SEM: the cold field-emission gun ( ) and the so-called Schottky emission cathode ( ). The characteristic parameters of the different electron guns are listed in Table 5.1.

Schottky emission cathodes are of the $\text{ZrO}/\mathrm{W}(100)$ type—also called $\text{ZrO}/\mathrm{W}(100)$ thermal field emitter ( )—and have a tip radius of $\approx 0.1{-}0.5\,{\mathrm{\upmu{}m}}$ [5.314]. The work function of the TFE is lowered to about ${\mathrm{2.8}}\,{\mathrm{eV}}$. In operation the SEC is heated to about $1000{-}1500\,{\mathrm{K}}$ and electrons are extracted by a high electric field, which lowers the potential barrier (Schottky effect) . The SEC brightness is about three orders of magnitude higher and the energy spread of the emitted electrons is about a factor of 2 lower than those for the thermionic W-cathode. Presently, the SEC in commercial high-resolution SEM is used more frequently than the CFEG.

The CFEG usually consists of a very sharp [100] or [321] oriented tungsten single crystal and two anodes in front, which extract (first anode) and accelerate or decelerate (second anode) the electrons by the electric field to a final energy $E_{0}=eU$ (Fig. 5.37). Caused by the small tip radius $r$, which is in the range of $\mathrm{10}$ to about ${\mathrm{50}}\,{\mathrm{nm}}$, the electric field strength amounts to at least ${\mathrm{10^{8}}}\,{\mathrm{V{\,}cm^{-1}}}$ with an extraction voltage of approximately $4{-}5\,{\mathrm{kV}}$ applied between the first anode and the tip. Because of the high field strength at the tip the width of the potential barrier is significantly reduced and field emission takes place. The field-emission current density $j_{\mathrm{c}}$ is described by the Fowler–Nordheim equation

$$j_{\mathrm{c}}=\frac{c_{1}|E|^{2}}{\phi}\exp\left(-\frac{c_{2}\phi^{3/2}}{|E|}\right),$$

(5.42)

where $|E|\approx U_{1}/r$, $c_{1}$ and $c_{2}$ depend weakly on $|E|$, and $\phi$ is the work function of tungsten. The density $j_{\mathrm{c}}$ depends strongly on $|E|$, and $E$ can be varied by $U_{1}$. The cold FEG (CFEG) is operated at room temperature and generates a current density of typically ${\mathrm{2\times 10^{5}}}\,{\mathrm{A{\,}cm^{-2}}}$. However, after several hours of work adsorbed gas layers have to be removed by short heating to about ${\mathrm{2500}}\,{\mathrm{K}}$ (flashing), otherwise the emission current becomes very unstable. The distinct advantage of the cold FEG is the low-energy spread ($0.2{-}0.3\,{\mathrm{eV}}$).

Fig. 5.37

Schematic drawing of the field-emission gun with an electrolytically polished sharp monocrystalline tungsten tip. $U$, acceleration voltage; $U_{1}$, extraction voltage. (After [5.30])

Field-emission guns require ultrahigh vacuum in the order of $E-8{-}E-9\,{\mathrm{Pa}}$ in the gun chamber, which is generated by ion-getter pumps. This means that SEMs equipped with an FEG need a sophisticated and consequently cost-intensive vacuum system.

2.1.2 Electron Lenses

Electron lenses are used to demagnify the virtual source size, which amounts to $3{-}5\,{\mathrm{nm}}$ for the cold FEG, and about $20{-}30\,{\mathrm{nm}}$ for the Schottky emitter. To obtain an electron-beam diameter of about ${\mathrm{1}}\,{\mathrm{nm}}$ or less a demagnification of only $10{-}100\times$ is required in contrast to up to about ${\mathrm{5000}}\times$ for the thermionic emission triode gun (Sect. 5.1.2, Electron Lenses). To achieve the smallest effective electron probe diameter, the spherical and the chromatic aberration constants have to be as small as possible ((5.7), (5.8), and (5.10)). In the conventional SEM usually large working distances ranging from about $\mathrm{10}$ to ${\mathrm{40}}\,{\mathrm{mm}}$ are used. Typical values of the spherical aberration constant $C_{\mathrm{s}}$ are $10{-}20\,{\mathrm{mm}}$. Since $C_{\mathrm{s}}$ increases strongly with increasing WD ($C_{\mathrm{s}}\approx\text{WD}^{3}$) sufficiently small values of $C_{\mathrm{s}}\approx 1{-}2\,{\mathrm{mm}}$ can be achieved only with very short WD, i. e., the focus of the electron beam has to be inside (so-called in-lens type) or very close to the objective lens (frequently called semi-in-lens with a snorkel-type conical objective lens [5.315]). The chromatic aberration constant $C_{\mathrm{c}}$ corresponds approximately to the focal length of the objective lens for large WD, i. e., also the chromatic aberration is strongly lowered at a very short WD. The shortest WD of the in-lens-type SEM is about ${\mathrm{2.5}}\,{\mathrm{mm}}$ in order to secure a specimen traverse in the $x$- and $y$-direction perpendicular to the optical axis as well as specimen tilt angles up to a maximum of $|\pm 15^{\circ}|$. Larger tilt angles obviously require a larger work distance. To obtain the minimum effective electron probe diameter under these conditions, the optimum aperture $\alpha_{\mathrm{opt}}$ has to be used (5.11). Presently, the highest resolution obtained with the in-lens-type FESEM at ${\mathrm{30}}\,{\mathrm{keV}}$ using a test sample amounts to ${\mathrm{0.4}}\,{\mathrm{nm}}$ [5.316].

In addition, hybrid lens design SEM columns have become quite popular in recent years. Such column design typically features some form of a combination electrostatic-electromagnetic objective lens to provide the user with utmost versatility in terms of the types of samples that can be imaged and analyzed. For further review of these designs, please see Bell and Erdman [5.34].

2.1.3 Detectors and Detection Geometries

The detectors used in field-emission scanning electron microscopes (FESEM) have been described in Sect. 5.1.1, Detectors. The detection geometry depends on the particular type of FESEM. The instruments using the conventional specimen position outside the objective lens (out-lens), i. e., the WD is in the range of about $5{-}30\,{\mathrm{mm}}$, are commonly equipped with an ET detector located laterally above the specimen and a BSE detector located centrally above the specimen. The semi-in-lens or electrostatic/electromagnetic combination lens instruments, where the specimen is outside but immersed in the field of the objective lens, usually have both the detector arrangement of the out-lens-type SEM and the through-the-lens detection, thus combining the advantages of both detection geometries. The in-lens-type SEM is restricted to through-the-lens detection (Sect. 5.1.1, Detection Strategies).

2.1.4 Specimen Stages

The purpose of the specimen stage in high-resolution scanning electron microscopes is of course the same as in conventional SEM, i. e., the stage has to allow for precise backlash-free movement, tilting, and possibly rotation of the sample during the investigation. As for conventional SEM, there are optionally special specimen stages available that allow investigations of the specimen at elevated temperature, during different types of mechanical deformation, at positive or negative bias, and last at low temperature. Independent of the special type of specimen stage, a higher stability in terms of mechanical vibrations as well as mechanical or thermal drift is required to avoid any deterioration of the performance of the high-resolution SEM. The in-lens-type SEMs use side-entry specimen holders, which are almost identical to the ones used in TEMs (Sect. 5.1.1, Specimen Stages and Attached Equipment). However, the limited space available in this type of SEM places some restrictions on the specimen stage for the ultimate resolution of in-lens-type FESEM.

2.1.5 Contrast Formation and Resolution

At high beam energy, e. g., ${\mathrm{30}}\,{\mathrm{keV}}$, the lateral extension of the excitation volume in the specimen is for carbon approximately ${\mathrm{10}}\,{\mathrm{\upmu{}m}}$ and for a high atomic number element such as gold about ${\mathrm{1}}\,{\mathrm{\upmu{}m}}$ (Fig. 5.13). Secondary and backscattered electrons are emitted from a surface area of the specimen, which corresponds in size to about the lateral extension of the excitation volume (Fig. 5.14). As discussed in Sect. 5.1.2, Secondary Electrons and Backscattered Electrons the SE2 and BSE2 represent the majority of the SE and BSE, respectively, whereas the SE1 and BSE1, both carrying high-resolution information, represent the minority. Assuming for simplicity an electron-beam diameter of ${\mathrm{1}}\,{\mathrm{nm}}$, the ratio of the lateral size of the excitation volume and the beam diameter amounts to approximately $\mathrm{10^{4}}$ for carbon and $\mathrm{10^{3}}$ for gold. By choosing the magnification such that the field of view at the specimen surface approaches the lateral size of the excitation volume, i. e., related to a $\mathrm{100}$-$\mathrm{nm}$ image size about ${\mathrm{10000}}\,\times$ for carbon and ${\mathrm{100000}}\,\times$ for gold, both the SE2 and the BSE2 contributions will change in response to the features of the field of view on the size scale of the excitation volume. In contrast to this the SE1 and BSE1 contributions will change in response to the features of the field of view approximately on a size scale of the electron-beam diameter. That means that in the course of scanning the electron beam across the field of view, the SE2/BSE2 contribution only insignificantly varies from pixel to pixel whereas the SE1/BSE1 contribution depends sensitively on local features as small as the beam diameter. With a further increase of magnification the field of view becomes significantly smaller than the lateral size of the excitation volume, consequently the SE2/BSE2 contribution is almost constant over the image. The changes in the total SE/BSE signal are almost exclusively due to the SE1/BSE1 component and correspond to the changes in the very tiny volume where SE1/BSE1 are generated. Figure 5.38a,b shows an example of a high-resolution SE micrograph recorded from a test sample at a magnification of ${\mathrm{500000}}\,\times$. The distinct changes in image intensity reflect the variation of the SE1 component, which is due to the large differences in the atomic number between the carbon and the Au–Pd particles. This type of test sample is usually used to demonstrate the performance of SEMs.

Fig. 5.38a,b

Secondary electron micrographs of Au nanoparticles on Carbon support resolution standard recorded at ${\mathrm{1}}\,{\mathrm{kV}}$ (a) and ${\mathrm{15}}\,{\mathrm{kV}}$ (b) using a Schottky FESEM, JEOL JSM-7200F. The micrographs were recorded using a through-the-lens electron detector. Note the minimal change in resolution while changing accelerating voltage

The low SE yield of low atomic number specimens (Fig. 5.17) such as soft biological objects and polymers limits the resolution because of the poor SNR. However, the SNR can be improved significantly by coating the specimen surface with an ultrathin very fine-grain metal film [5.317] by Penning sputtering or by evaporation in oil-free high vacuum (Sect. 5.1.4). The thickness of such films can be as small as ${\mathrm{1}}\,{\mathrm{nm}}$ and, as we shall see later, such ultrathin films do not mask fine surface structures. In addition to improving the SNR the ultrathin coating plays an important role in contrast formation and the image resolution obtainable. As mentioned earlier, the SE1 arise from the area directly irradiated by the electron beam and its immediate vicinity caused by the delocalization of the inelastic scattering in the order of a very few nanometers (Sect. 5.1.2). In the case of the specimen coated with an ultrathin metal film the SE1 generation is confined almost exclusively to the film. Figure 5.39a,ba shows schematically the cross section of an object coated with a continuous metal film of constant thickness. As the electron beam is scanned across the object the projected film thickness will vary between the nominal film thickness and the maximum, which is several times greater than the nominal thickness. As shown by Monte Carlo calculations the SE1 yield increases very quickly with the thickness of the metal film [5.318]. For example, the Monte Carlo calculations by Joy [5.318] reveal for chromium and $\mathrm{20}$-$\mathrm{keV}$ electrons that half of the maximum SE1 yield is reached for a thickness of $1{-}1.5\,{\mathrm{nm}}$ only. The dependence of the SE1 yield versus the thickness of a coating film is shown schematically in Fig. 5.39a,bb. It indicates that the increase of the SE1 yield with the thickness slows down at twice the thickness at half of the maximum SE1 yield, i. e., the continuous film should be as thin as possible. Monte Carlo calculations of the SE1 yield for some of the metals suitable for preparing ultrathin very fine-grain metal films show a monotonic increase with the atomic number [5.155]; thus some further improvement of the SNR may be expected with high atomic number metals.

Fig. 5.39a,b

Schematic cross section of a specimen coated with an ultrathin continuous metal layer of constant thickness (a). The projected mass thickness of the metal layer varies as the electron beam is scanned across the specimen. (b) Graph of the SE1 yield versus the thickness of the coating film

The ultrathin very fine-grain metal film on the sample surface also improves the BSE1 component significantly, thus improving the SNR in high-magnification BSE micrographs. The BSE1 are very important for high-resolution SEM because the elastic electron scattering is strongly localized. The intensity of the BSE1 component increases with the projected film thickness, i. e., increases with the number of atomic scattering centers. Since the BSE coefficient strongly increases with the atomic number (Fig. 5.17), the BSE1 component of the metal film is significantly larger than the contribution from the coated low-atomic number specimen. The same is also true for small metal clusters or small particles at the specimen surface, e. g., such as colloidal gold down to a minimum diameter of ${\mathrm{0.8}}\,{\mathrm{nm}}$ [5.319], which can be identified unambiguously in the high-resolution BSE micrograph.

2.1.6 Selected Applications

Since the achievable resolution is the main difference between the high-resolution field-emission SEM and the conventional SEM, it is obvious that the high-resolution SEM ( ) can readily handle almost all of the applications mentioned in Sect. 5.1.6. Because vacuum conditions in FESEMs are more strict concerning the pressure in the specimen chamber (at least one order of magnitude less than in conventional high-vacuum scanning electron microscopy ( )) as well as the content of gaseous hydrocarbons and hydrocarbons at the specimen, some specimens may not meet the requirements for cleanness and very low partial pressure. However, if high-resolution FESEM is applied instead of CSEM, more information about the specimen will be obtained due to the higher resolution as soon as the magnification used exceeds approximately ${\mathrm{10000}}\,\times$ to ${\mathrm{20000}}\,\times$. That means that lateral resolutions requiring magnifications clearly beyond about ${\mathrm{20000}}\,\times$ belong to the dedicated domain of high-resolution SEM.

The following few applications selected from an almost unlimited quantity should demonstrate the strength of HRSEM in several fields of research. It is clearly beyond the scope of this section to discuss in this context specific details about the specimens and imaging techniques.

Figure 5.40a-ca shows the secondary electron micrograph of a regular protein surface layer of a bacterial cell envelope. The specimen was unidirectional shadowed with an ultrathin tungsten layer leaving an uncoated region behind the latex bead. Comparison of the regular structure of the HPI layer in the coated and the uncoated region shows that the contrast in the uncoated area is significantly lower than in the coated region, though the resolution of structural details is very similar as verified by the related power spectra. This example also demonstrates that coating with the ultrathin very fine-grain metal film does not mask fine structural features. In principle, a similar resolution can also be obtained with nonregular organic specimens, however, it remains more difficult to quantify unambiguously the resolution obtained.

Fig. 5.40a-c

Secondary electron micrograph of a regular protein surface layer (hexagonally packed intermediate ( ) layer [5.320]) of Deinococcus radiodurans recorded with an in-lens FESEM at ${\mathrm{30}}\,{\mathrm{kV}}$ (a). The specimen was unidirectional shadowed (see arrow) at an elevation angle of $45^{\circ}$ with a ${\mathrm{0.7}}\,{\mathrm{nm}}$-thick tungsten layer leaving an uncoated region behind the latex bead. The power spectra of a coated (b) and an uncoated (c) region of the HPI layer reveal the resolution obtained (outermost diffraction spots are indicated and the corresponding reciprocal values of resolution are given). The contrast in the uncoated region is about $15{-}20\%$ of that from the coated region. Reprinted with permission from [5.321], micrographs kindly provided by R. Wepf

An extremely important application of HRSEM, as yet unrivaled by other surface imaging techniques, is the localization of molecules on surfaces by immunolabeling techniques (for reviews see [5.234, 5.322, 5.323, 5.324, 5.325]). The use of HRSEM for immunoelectron microscopy started more than 20 years ago [5.326, 5.327, 5.328, 5.329, 5.330, 5.331, 5.332]. Since then efforts have been made to optimize the technique of immunoscanning electron microscopy in terms of localization precision, contrast, and SNR [5.319, 5.333, 5.334, 5.335]. While the colloidal gold can be localized directly in the BSE image, the precision of the indirect localization of the antigen depends on the type of labeling and the size of the colloidal gold and ranges from less than $\mathrm{5}$ to about ${\mathrm{10}}\,{\mathrm{nm}}$ [5.336, 5.337]. Figure 5.41a,bb demonstrates the unambiguous detection of immunogold-labeled proteins on cells (specimen was coated with a thin layer of carbon prior to imaging). However, for more than a decade immunoscanning electron microscopy has been established as a trusted technique and, with the commercial availability of high-quality gold probes (available in sizes ranging from $\mathrm{1}$ to ${\mathrm{40}}\,{\mathrm{nm}}$), is used in many electron microscopic laboratories for various studies [5.338, 5.339, 5.340, 5.341, 5.342, 5.343].

Fig. 5.41a,b

Secondary electron (a) and backscatter electron (b) micrographs of immunogold-labeled cells

The interior structure of biological specimens is accessible by HRSEM, if samples are rapidly frozen and opened by cryofracturing or cryoultramicrotomy. After partial freeze-drying and double-layer coating of the block face, the specimen can be directly analyzed in the cryo-SEM [5.286, 5.287, 5.344]. Figure 5.42 shows for comparison a cross section of yeast cells prepared via argon ion polishing with subsequent etching by a low-voltage ion beam. Particles and structures as small as ${\mathrm{25}}\,{\mathrm{nm}}$ can be visualized clearly.

Fig. 5.42

Secondary electron images of yeast cell cross sections taken with an ET detector at ${\mathrm{3}}\,{\mathrm{kV}}$. The sample was prepared from a freeze-dried specimen using a broad-beam argon ion polisher (IB-19530 CP, JEOL Ltd)

Both strengths of the HRSEM, namely the high resolution and the high depth of focus, are required to resolve surface structures at the nanometer scale on randomly oriented tilted surfaces. One typical example are submicrometer-sized crystalline zeolite particles as shown in Fig. 5.43a,b. The HRSEM is the tool most suited to characterize the habit of the individual particles as well as to visualize the fine surface structure such as growth steps of terraces [5.345]. The current resolution of the FESEM allows observation of nanopore arrangement in zeolites, and make a determination about zeolite reactivity and functionality in catalytic processes (blocked pores, surface step structure, etc.).

Fig. 5.43a,b

Secondary electron micrographs of zeolites Y (a) and ZSM-5 (b) imaged with a through-the-lens detector in Schottky FESEM using a ${\mathrm{0.8}}\,{\mathrm{kV}}$ landing voltage, uncoated

HRSEM is also a very valuable tool for the evaluation of mechanical properties of structural materials. For example, most structural materials are strengthened by fine particles of second phases usually having diameters less than ${\mathrm{500}}\,{\mathrm{nm}}$. The strengthening effect is primarily governed by the mean size, the size distribution, and the volume fraction of the particles. Both HRSEM and allow for the precise determination of the mean size, size distribution, and volume fraction of the particles as demonstrated by Fruhstorfer et al [5.346]. Figure 5.44a-d shows the SEM micrograph (Fig. 5.44a-da) and the AFM topograph (Fig. 5.44a-dc) of the electrolytically polished surface of the superalloy NIMONIC PE16 with the protruding caps of the second-phase particles. In contrast to AFM, where corrections were necessary to take into account the exact tip radius, corrections for the very small electron probe diameter are not urgently required in HRSEM. The size distribution function and mean radius of the second-phase particles calculated from HRSEM (Fig. 5.44a-db) and AFM (Fig. 5.44a-dd) data are in excellent agreement with those gained earlier by TEM [5.347]. The distinct advantages of HRSEM in this application are that micrographs are readily recorded and the data can be processed without additional correction procedures.

Fig. 5.44a-d

Surface of electrolytically polished superalloy NIMONIC PE16. Secondary electron micrograph recorded with an in-lens FESEM at ${\mathrm{10}}\,{\mathrm{kV}}$ (a) and AFM topograph (c). The related distribution functions $g$ of the true radii $\rho$ are shown for the HRSEM in (b) and for the AFM in (d). Reprinted with permission from Taylor Francis Ltd from [5.346], www.tandfonline.com

The characterization of porous materials such as porous silicon or porous aluminum oxide gains increasing attention because of important potential applications [5.348, 5.349, 5.350, 5.351, 5.352, 5.353]. Among others, HRSEM is an indispensable tool for structural characterization of porous materials taking advantage of the large depth of focus and the high resolution obtainable. Figure 5.45a,b shows high-resolution SE and BSE micrographs of the surface and cross section of porous aluminum oxide, which exhibits a network with randomly distributed, but almost perfectly aligned cylindrical pores perpendicular to the substrate. The simultaneous imaging of the surface and the cross section reveals information about the three-dimensional specimen structure. Under the conditions given the SE mode yields higher resolution than the BSE mode.

Fig. 5.45a,b

High-resolution micrograph of the surface (a) and cross section (b) of porous aluminum oxide membrane recorded using FESEM. The images were acquired at $\mathrm{0.2}$ and ${\mathrm{1.2}}\,{\mathrm{kV}}$, respectively, the specimen was imaged uncoated

However, the BSE mode is of significant importance if greater information depth and material differentiation are required. Figure 5.46a,b shows SE and BSE micrographs of temperature-sensitive hydrogels, based on poly(vinylmethyl ether) (PVME), with ferromagnetic properties due to incorporated nickel particles used as a ferromagnetic filler. The contrast in the SE micrograph (Fig. 5.46a,ba) is mainly caused by the very thin membrane-like PVME, which envelops the nickel particles, whereas the BSE image (Fig. 5.46a,bb) has a strong material contrast component due to the nickel particles underneath the PVME membrane. This new class of hydrogels is of great interest for delivery of materials at the micro- and nanometer scale.

Fig. 5.46a,b

High-resolution micrographs of poly(vinylmethyl ether) (PVME ) hydrogel with ferromagnetic properties filled with submicrometer nickel particles in the swollen state. The hydrogel was rapidly frozen, freeze dried, and rotary shadowed with an ultrathin layer of platinum/carbon. The SE (a) and BSE (b) micrograph were recorded with an in-lens FESEM at ${\mathrm{10}}\,{\mathrm{kV}}$, (specimen kindly provided by Dr. K.-F. Arndt, Institut für Physikalische Chemie und Elektrochemie, Technische Universität Dresden, Dresden, Germany)

As mentioned in Sect. 5.1.2, Transmitted Electrons, the high-resolution in-lens FESEM equipped with an annular dark-field detector is capable of mass measurements on thin specimens [5.354, 5.355] at a resolution approaching that of a dedicated STEM [5.134, 5.356, 5.357]. Mass measurement of molecules and molecular assemblies are of great importance in biophysics and structural biology (for a review see [5.358]).

Finally, nanotechnology and nanoelectromechanical systems ( s) are additional fields in which HRSEM is used as a tool for monitoring processes, detecting defects, or measuring sizes and distances, e. g., in nanodevices, which will contain nanotubes, nanoparticles, nanowires, and other particles [5.309, 5.359, 5.360].

2.2 Low- and Very-Low-Voltage Scanning Electron Microscopy

Scanning electron microscopy with electron energies below ${\mathrm{5}}\,{\mathrm{keV}}$ is usually designated as scanning low-energy electron microscopy ( ) or, related to the acceleration voltage, LVSEM. The energy of ${\mathrm{5}}\,{\mathrm{keV}}$ can be considered as a threshold energy because the monotonic dependence of the BSE coefficient on the atomic number breaks below this (Sect. 5.1.2, Backscattered Electrons). A second prominent energy threshold is at about ${\mathrm{50}}\,{\mathrm{eV}}$, which corresponds to the electron energy with minimum inelastic mean free path of electrons in matter [5.182]. Therefore, scanning microscopy with electron energies below ${\mathrm{50}}\,{\mathrm{eV}}$ is designated as scanning very low-energy electron microscopy [5.33] or, related to the acceleration voltage in the scanning mode, very low-voltage scanning electron microscopy ( ). An excellent review on the latest developments in low-voltage electron microscopy was presented by Bell and Erdman [5.34].

What is the motivation for low electron energy operation in SEM? What are the advantages expected at low energies and what are the inherent disadvantages?

Clearly, almost all of the advantages for working at low energy derive directly from the energy dependence of the electron–specimen interaction (Sect. 5.1.2). The advantages include the following:

• 1. The penetration depth of the impinging electrons decreases with decreasing energy due to the reduced electron range $R$ (5.29), i. e., the excitation volume in the specimen shrinks (Fig. 5.13) and the volume emitting SE2 and BSE2 approaches the volume emitting SE1 and BSE1 (Fig. 5.14). As a result the edge effect, i. e., overbrightening of edges, is strongly reduced or even suppressed completely.

• 2. The SE yield $\delta$ increases because of the reduced electron range and the SE are generated near the surface, where they can escape (Fig. 5.15). As a result, the SNR of the SE signal increases with decreasing energy as low as $E_{0,\mathrm{m}}$.

• 3. As the SE yield increases, the total amount of emitted electrons approaches unity (Fig. 5.16). Because of the conservation of electric charge (5.40) the amount of incoming and emitted charges is balanced and, consequently, the specimen current equals zero. That means that at this particular electron energy $E_{2}$ no electric conductivity of the specimen is required. Ideally, imaging of electric insulators without conductive coating becomes possible. For normal incidence, $E_{2}$ is within the range $0.5{-}5\,{\mathrm{keV}}$ for most of the materials. $E_{2}$ increases with the increasing angle of beam incidence $\theta$ according to

  $$E_{2}(\theta)=\frac{E_{2}(0)}{\cos^{2}\theta}\;,$$

  (5.43)

  where $E_{2}(0)=E_{2}(\theta=0)$ [5.361], i. e., increases as $\theta$ increases.

• 4. As mentioned above, the monotonic dependence of the BSE coefficient on the atomic number breaks below ${\mathrm{5}}\,{\mathrm{keV}}$ [5.152, 5.362]. This behavior enables the material contrast in the BSE image to be finetuned by choosing the most suitable electron energy [5.363].

• 5. There is a reduced depth of specimen radiation damage (Sect. 5.1.5). At very low electron energies, say less than ${\mathrm{30}}\,{\mathrm{eV}}$, the elastic scattering dominates and radiation damage becomes negligible [5.33].

The problems and disadvantages inherent to microscopy at low electron energy concern both the instrumentation and the specimen and include the following:

• 1. Reduced resolution due to chromatic aberration and diffraction ((5.8)–(5.10)).

• 2. Stronger sensitivity of the electron beam to electromagnetic stray fields.

• 3. Special detector strategies required for SE and BSE.

• 4. Enhanced contamination rate, which can be counteracted by ultrahigh vacuum or an anticontamination device.

• 5. Reduced topographic contrast in SE and BSE micrographs. For electron energies below ${\mathrm{5}}\,{\mathrm{keV}}$, the increase of SE yield $\delta(\theta)$ with increasing $\theta$ (5.31) drops way down to ${\mathrm{0.5}}\,{\mathrm{keV}}$ as shown for different metals experimentally and by Monte Carlo simulation [5.364, 5.365]. Similarly, the backscattering coefficient $\eta(\theta)$ shows less increase with $\theta$ than given by (5.34), which is more pronounced at low electron energies [5.305].

• 6. Reduced material contrast, because the differences of the backscattering coefficient between low and high atomic number material become smaller [5.152, 5.366, 5.367].

2.2.1 Electron Lenses

Modern commercial field-emission scanning electron microscopes can operate usually from $\mathrm{30}$ down to ${\mathrm{0.5}}\,{\mathrm{keV}}$ or even ${\mathrm{0.01}}\,{\mathrm{keV}}$, i. e., an energy range that covers conventional electron energies and most of the low-energy region. Improved computer-aided methods enable electron optical systems to be designed such that they have high performance within the whole energy range mentioned above. Compared with the old-fashioned thermionic gun scanning electron microscopes the aberration coefficients of the objective lens were improved dramatically for modern field-emission instruments commercially available: $C_{\mathrm{s}}$ was reduced by a factor of about $\mathrm{30}$ down to $C_{\mathrm{s}}={\mathrm{1.6}}\,{\mathrm{mm}}$ [5.368], and $C_{\mathrm{c}}$ was reduced by a factor of about $\mathrm{10}$. With the ultrahigh-resolution objective lens, the CFEG, improved electrical and mechanical stability, as well as strongly reduced specimen contamination rate, the resolution obtained with test specimens amounts presently to ${\mathrm{0.5}}\,{\mathrm{nm}}$ (at ${\mathrm{30}}\,{\mathrm{keV}}$) and ${\mathrm{0.7}}\,{\mathrm{nm}}$ (at ${\mathrm{1}}\,{\mathrm{keV}}$). Those values are exemplary for the high performance of commercial FESEM over an energy range from $\mathrm{1}$ to ${\mathrm{30}}\,{\mathrm{keV}}$, though obtained with special test specimens. More recently, a commercial FESEM equipped with a spherical and chromatic aberration corrector has been developed, consisting of four sets of a $\mathrm{12}$-pole component that corrects the spherical and chromatic aberration simultaneously [5.369]. Another development has been the development of a monochromator for FESEM [5.370].

Electrostatic as well as combined magnetic and electrostatic lenses in LVSEM are a very interesting alternative to the magnetic lenses mentioned above. Microscopes equipped with this type of objective lens permit nonconstant beam energy along the column, i. e., the beam electrons pass the column with high energy and are decelerated to low energy in the immersion electrostatic lens. First, the magnitude of the aberrations of immersion electrostatic lenses corresponds to the high energy at the entrance side. A more detailed treatment of the estimation of electrostatic lenses is beyond the scope of this section [5.371, 5.372]. Second, the high electron energy in the column is advantageous because the gun brightness increases with electron energy ((5.4) and (5.42)) and electromagnetic stray fields result in less deterioration of the electron beam at high energy. The combined magnetic–electrostatic objective lens [5.81] has aberration coefficients as low as $C_{\mathrm{s}}={\mathrm{3.7}}\,{\mathrm{mm}}$ and $C_{\mathrm{c}}={\mathrm{1.8}}\,{\mathrm{mm}}$.

Very low landing energies of the electrons can be realized with a retarding-field SEM. There are several retarding-field configurations described in the literature but basically in all of them the specimen is connected to the adjustable bias supply $U_{\text{sp}}$ [5.373, 5.374, 5.375, 5.5, 5.79, 5.80]. The landing energy of the beam electrons is simply given by the difference $E_{0}-eU_{\text{sp}}$. Using retarding-field SEM, landing energies of a few electronvolts are achievable and recently micrographs with reflected electrons even at ${\mathrm{0.5}}\,{\mathrm{eV}}$ were obtained [5.363].

With the availability of magnetic materials having high coercive force permanent rare-earth-metal magnets have attracted attention as replacements for magnetic lens coils [5.376]. Khursheed et al [5.377] proposed a portable SEM column design, which makes use of permanent magnets. The column of this miniature SEM amounts to a height of less than ${\mathrm{12}}\,{\mathrm{cm}}$ and is designed to be modular, so that it can fit onto different specimen chamber types, and can also be readily replaced. Focusing of the electron beam onto the specimen can be achieved by varying the specimen height or by an outer magnetic slip ring on the objective lens, which controls the strength of the magnetic field on the axis. Scanning of the beam is performed by deflection coils, which are located above and within the permanent magnet objective lens. A high-resolution miniature SEM with a total height of less than ${\mathrm{5.5}}\,{\mathrm{cm}}$, proposed by Khursheed [5.378], uses a permanent magnet objective lens that lies outside the vacuum with spherical and chromatic aberration coefficients (parameters: $E_{0}={\mathrm{1}}\,{\mathrm{keV}}$, $\text{WD}={\mathrm{7.5}}\,{\mathrm{mm}}$) of $\mathrm{0.36}$ and ${\mathrm{0.6}}\,{\mathrm{mm}}$, respectively. These aberration coefficients are about an order of magnitude smaller than those for conventional SEMs with comparable working distance conditions.

Miniaturization of the SEM column has advantages such as microlenses with small aberration coefficients, reducing the influence of electromagnetic stray fields and of the electron–electron interaction, improving the mechanical stability, and reducing the demands on space for the microscope. Chang et al [5.379] proposed a miniaturized electron optical system consisting of a field-emission microsource and an electrostatic microlens for probe forming with performance exceeding that of a conventional system over a wide range of potentials ($0.1{-}10\,{\mathrm{kV}}$) and working distances (up to ${\mathrm{10}}\,{\mathrm{mm}}$). Liu et al [5.380] proposed another design that has a column length of only ${\mathrm{3.5}}\,{\mathrm{mm}}$ and can be operated over a wide retarding range of potentials ($0.1{-}10\,{\mathrm{kV}}$). The instrument has an optimized design (microeinzel lens followed by a retarding region) to minimize the primary beam diameter and to maximize secondary electron collection (approximately ${\mathrm{50}}\%$ of SE are collected).

2.2.2 Detectors and Detection Strategies

As mentioned previously, modern commercial FESEMs can operate usually from $\mathrm{30}$ down to ${\mathrm{0.1}}\,{\mathrm{keV}}$ or even ${\mathrm{0.01}}\,{\mathrm{keV}}$; the commonly used detectors and detection strategies of these instruments were discussed in Sects. 5.1.1 and 5.2.1, Detectors and Detection Geometries. It is clear from Fig. 5.12 that the lower the energy $E_{0}$ of the beam electrons the lower the energy difference between the secondary and backscattered electrons. The lower the difference of the different signal electrons the more difficult is their separation. At very low electron landing energies SE and BSE are almost indistinguishable, thus the total emission is detected. The majority of FESEMs nowadays feature some form of in-lens or through-the-lens detection system that has an ability to separate and collect SE, BSE, or a mixture of both types of signals. The instruments are also typically equipped with a dedicated BSE detector (retractable type). The BSE detectors are often multisegmented solid-state-type detectors that are highly sensitive and work at essentially any accelerating voltage, from ultralow to high kV. For an in-depth review of the current detector technology on FESEM, please see [5.34].

2.2.3 Contrast Formation

The contrast formation in LVSEM and VLVSEM is controlled by the electron–specimen interaction at the electron energy used, the specific signal considered, the detector, and the detection geometry. However, the contrast formation at low energies is much more complex than for electron energies ranging from $\mathrm{5}$ to ${\mathrm{30}}\,{\mathrm{keV}}$. A variety or reasons accounts for this complexity. For example, the BSE coefficient is for a given material almost constant and the SE yield depends just weakly on the electron energy for $E_{0}\geq{\mathrm{5}}\,{\mathrm{keV}}$. In contrast to this, the monotonic increase of the BSE coefficient with rising atomic number breaks below ${\mathrm{5}}\,{\mathrm{keV}}$ as previously mentioned and, additionally, the BSE coefficient becomes dependent on the electron energy for many chemical elements. Furthermore, the signals obtained at low electron energies are affected more strongly on electron beam-induced contamination or other thin layers on the surface, which is caused by the strongly reduced electron range.

Nevertheless, the main types of contrast, such as topographic, compositional, voltage, electron channeling, crystal orientation, and type-1 and type-2 magnetic and mass-thickness contrast, are also observed in LVSEM, although it is in many respects different from that obtained at conventional energies. There are also several observations that evidently show some chemical or electronic contrast, i. e., contrast that does not result from an increase in the mean atomic number of the specimen [5.381, 5.382, 5.383]. Although these effects may also be visible at conventional energies they are most readily observed at low energies where the SE yield is higher.

The thickness contrast described in Sect. 5.2.1, Contrast Formation and Resolution, also plays an important role in LVSEM of electric insulators. Though direct imaging of electrical insulators without electric charge-up should be feasible at electron energy $E_{2}$, where incoming and emitted charges are balanced, in practice it often does not work for various reasons. Therefore, coating the specimen surface with an ultrathin very fine-grain metal film [5.317] by Penning sputtering or by evaporation in oil-free high vacuum is often done. As in high-resolution SEM with conventional beam energies, the film plays an important role in contrast formation, in image resolution obtainable, and in the improvement of the SNR. The image contrast of coated specimens essentially depends on the projected film thickness, which will vary between the nominal film thickness and the maximum film thickness, which is several times greater than the nominal thickness in tilted regions (Fig. 5.39a,ba). Monte Carlo calculations of the SE yield of a film of chromium at ${\mathrm{2}}\,{\mathrm{keV}}$ also prove for low electron energy a monotonic increase with film thickness [5.364].

2.2.4 Selected Applications

The application of LVSEM and VLVSEM logically seems likely in cases in which SEM at conventional acceleration voltages obviously would fail, e. g., the investigation of uncoated insulating materials and radiation-sensitive semiconductors. Another compelling reason is the necessity of a reduced electron range, e. g., with specimens having one or more very thin surface layers and samples possessing a spongy- or foam-like fine structure. SEM studies of these types of specimens aim at information restricted to the surface-near zone. With ever-decreasing device dimension and film thickness this issue becomes more and more crucial. There are also not compelling, but still justifiable reasons, which may aim at optimum imaging conditions at low electron energy, or LVSEM may be part of a series of increasing or decreasing electron energies over a wide energy range as used for depth profiling. Finally, there are also applications of LVSEM that may also work at conventional energies but are most readily obtained at low energies.

The LVSEM is widely applied to semiconductor structures relating to an examination of their geometry, critical dimensions, and local voltages or currents, which may be either biased or induced by the electron beam. One example of an integrated circuit was previously shown in Fig. 5.30a,b. Figure 5.47a,b shows the cross-fractured semiconductor structure with Schottky barrier on tungsten contacts. A nanostructured two-dimensional lattice of $\mathrm{100}$-$\mathrm{nm}$-spaced inverted square pyramids in silicon used as standard for scanning probe microscopy is shown in Fig. 5.48a-c. Imaging of the uncoated lattice is necessary to avoid modifications of the standard by thin film coating, thus LVSEM is most appropriate.

Fig. 5.47a,b

Secondary (a) and backscatter (b) electron images of a cross section of an IC semiconductor device. The image was recorded using an in-lens detector with energy filtering grid in Schottky FESEM. The image was taken using ${\mathrm{5}}\,{\mathrm{kV}}$ accelerating voltage

Fig. 5.48a-c

Secondary electron micrographs of an uncoated $\mathrm{100}$-$\mathrm{nm}$ calibration standard made from silicon for scanning probe microscopy (NANO WORLD, Neuchatel, Switzerland) recorded with an in-lens field-emission SEM at ${\mathrm{3}}\,{\mathrm{kV}}$. The calibration standard consists of a two-dimensional lattice (lattice constant $={\mathrm{100}}\,{\mathrm{nm}}$) of inverted pyramids shown at different magnifications (a,b). (c) Structural details of a large pyramidal pit

Another challenging application for LVSEM is the quantitative characterization of the geometry and radius of very sharp tips for atomic force microscopy, which are necessary for many quantitative measurements with the AFM [5.346, 5.384, 5.385]. Figure 5.49a,b shows two extremely sharp commercial tips. The tip radius at the very end amounts typically to $2{-}3\,{\mathrm{nm}}$, thus only SE1 contribute to the signal. An optimum quality of SE imaging in terms of sharpness, contrast, and SNR can be obtained with electron energies ranging from about $\mathrm{3}$ to ${\mathrm{10}}\,{\mathrm{keV}}$. It seems worth mentioning that very sharp tips are interesting samples with which to study experimentally the delocalization of the secondary electrons.

Fig. 5.49a,b

Secondary electron micrographs of uncoated SuperSharpSilicon AFM Probe silicon cantilevers for noncontact/tapping mode (NANOWORLD, Neuchatel/Switzerland) in atomic force microscopy recorded with an in-lens field-emission SEM at ${\mathrm{3}}\,{\mathrm{kV}}$ (a) and at ${\mathrm{10}}\,{\mathrm{kV}}$ (b). The tip radius of both tips amounts to about $2{-}3\,{\mathrm{nm}}$

The characterization of organic mono- and multilayers on solids is especially valuable in technology development, such as bio- and chemosensors, since detailed information on the film surface and its morphology is obtained. Figures 5.50a,b–5.53a-d demonstrate with different mono- and multilayered ultrathin uncoated and coated organic films how direct information about the film thickness, step heights of the film, and differences in the chemistry and molecular packing density can be obtained. As shown by Fig. 5.50a,ba, upward and downward steps with height differences of a few nanometers can be readily identified on a tilted sample coated with an ultrathin conductive film. Whereas the step of constant height reveals in an in-lens SEM a constant intensity at normal electron-beam incidence, tilting causes an asymmetry such that steps can face upward or downward, which leads to an increase or decrease of their image intensities, respectively. Uncoated organic layers on solids usually reduce the SE yield as shown in Fig. 5.50a,bb. As demonstrated in Fig. 5.51a,b by a comparison of an SE micrograph with an AFM topograph of the same area, the SE intensity decreases with increasing thickness of the organic layer [5.386]. The monotonic dependence of SE intensity and the thickness of the organic film enables its thickness to be mapped without destruction of the film. The influence of organic film thickness on the SE yield vanishes after ultrathin coating of the organic film as proven by Fig. 5.50a,ba.

Fig. 5.50a,b

Secondary electron micrographs of a phospholipid/protein film (dipalmitoylphosphatidylcholine (DPPC ) : dipalmitoylphosphatidylglycerol (DPPG ) (ratio $=4:1$)/pulmonary surfactant protein C (SP-C; ${\mathrm{0.4}}\,{\mathrm{mol\%}}$)) supported by a silicon wafer. The organic film has terrace-like regions of different thickness (height differences between terraces are between $\mathrm{5.5}$ and ${\mathrm{6.5}}\,{\mathrm{nm}}$ [5.387]. Micrographs were recorded with an in-lens FESEM at ${\mathrm{2}}\,{\mathrm{keV}}$ from the ultrathin platinum/carbon-coated film (tilted $40^{\circ}$ around the horizontal axis) (a) and at ${\mathrm{1.8}}\,{\mathrm{keV}}$ from the uncoated film (b). (Specimens kindly provided by Dr. H.-J. Galla and Dr. M. Siebert, Institut für Biochemie, University of Münster, Münster, Germany)

Fig. 5.51a,b

Secondary electron micrograph (a) and AFM topography (b) of the same area of an uncoated phospholipid/protein film (dipalmitoylphosphatidylcholine (DPPC) : dipalmitoylphosphatidylglycerol (DPPG) (ratio $=4:1$)/pulmonary surfactant protein C (SP-C; ${\mathrm{0.4}}\,{\mathrm{mol\%}}$)) supported by a silicon wafer. The organic film has terrace-like regions of different thickness (height differences between terraces are between $\mathrm{5.5}$ and ${\mathrm{6.5}}\,{\mathrm{nm}}$ [5.387]). The micrograph was recorded with an in-lens FESEM at ${\mathrm{2}}\,{\mathrm{keV}}$. The scale in between (a) and (b) represents the coding of brightness relative to the height used in the topograph (b). (Specimens kindly provided by Dr. H.-J. Galla and Dr. M. Siebert, Institut für Biochemie, University of Münster, Münster, Germany)

Figure 5.52a,ba demonstrates that the SE yield also depends on the chemical nature of the molecules assembling an organic film. For example, differences in the terminal group of molecules obviously cause a significant difference in the SE yield, which creates a sufficient chemical contrast in the micrograph. This chemical contrast vanishes after ultrathin coating of the organic film (Fig. 5.52a,bb). Finally, Fig. 5.53a-d shows that the SE yield is sensitive to the molecular packing density of the organic film, i. e., the number of organic molecules per area [5.388].

Fig. 5.52a,b

Secondary electron micrographs of a patterned self-assembled thiol monolayer on polycrystalline gold recorded at ${\mathrm{2}}\,{\mathrm{keV}}$ with the in-lens FESEM. (a) Uncoated monolayer. The circular domains consist of –$\mathrm{(CH_{2})_{15}CH_{3}}$ molecules (hydrophobic), which are surrounded by –$\mathrm{S(CH_{2})_{12}OH}$ molecules (hydrophilic). The contrast is due to the different end groups rather than to the small difference in chain length. (b) Monolayer coated with an ultrathin platinum/carbon film. (Specimen kindly provided by Dr. G. Bar, Freiburger Materialforschungszentrum, Freiburg, Germany)

Fig. 5.53a-d

Secondary electron micrographs (a,b) and AFM topographs (c,d) of the same area of a 1,2-dipalmitoyl-sn-glycero-3-phosphothioethanol (DPPTE) monolayer on a silicon wafer having domains with densely (liquid condensed (LC ) phase) and loosely (liquid expanded (LE) phase) packed molecules. The specimen was masked by a TEM finder grid and then coated with an ultrathin platinum/carbon film to obtain neighboring coated and uncoated areas on the specimen (for details see [5.388]). The SE micrographs were recorded with an in-lens FESEM at ${\mathrm{5}}\,{\mathrm{keV}}$. The brighter regions of the SE micrograph (b) correlate with the elevated domains (LC phase) in the AFM topograph (d), whereas the darker regions correlate with the LE phase. In contrast to the SE micrograph (a) the height differences in coated areas of the film, which are related to its molecular packing density, are still visible in the AFM topograph (c). Reprinted with permission from [5.388]. Copyright 2001 American Chemical Society

It is easy to understand that the BSE signal is not sensitive to the film thickness and differences in the chemistry and molecular packing density, because the backscattering of thin low atomic number films is negligible compared with those of the substrate having a significantly higher atomic number.

Figures 5.54a-d and 5.55a-e show secondary electron micrographs of an uncoated glass micropipette and a microtome glass knife, which are almost free of electric charging. However, at higher magnifications the typical signs of charging occur.

Fig. 5.54a-d

Secondary electron micrograph series of increasing magnification of an uncoated glass micropipette recorded at ${\mathrm{2}}\,{\mathrm{kV}}$ with an out-lens FESEM. The uppermost part of the tip of the micropipette is within the depth of focus. The lower part is out of focus

Fig. 5.55a-e

Scheme and SE micrographs of an uncoated microtome glass knife recorded at ${\mathrm{1}}\,{\mathrm{kV}}$ with an out-lens FESEM. The arrows in (a) indicate the two directions of the electron beam related to the glass knife, which were used for imaging. (b,c) The electron beam has a shallow angle against the cutting edge. Only the uppermost part of the cutting edge is within the depth of focus. (d,e) The electron beam impinges perpendicularly onto the cutting edge. The different mean brightness of the clearance angle side and backside of the knife is due to the effect of the detection geometry of the ET detector

The characterization of sponge-like microstructures, such as hydrogels and microgels, is a further challenging application of LVSEM, where a large depth of focus, high resolution, and low penetration power (i. e., small electron range) of the electron beam are required. Figure 5.56a-d shows a stereopair of highly magnified SE micrographs of a hydrogel. The optimum imaging quality of fine structural details well below ${\mathrm{10}}\,{\mathrm{nm}}$ was obtained with electron energies around ${\mathrm{2}}\,{\mathrm{keV}}$.

Fig. 5.56a-d

Stereo pair of SE micrographs (a,b) of the hydrogel poly-($N$-isopropylacrylamide) (PNIPAAm ) in the swollen state recorded at ${\mathrm{2}}\,{\mathrm{keV}}$ with the in-lens FESEM. The specimen was rapidly frozen, freeze dried, and ultrathin rotary shadowed with platinum/carbon. (c) Red–green stereo anaglyph prepared from (a,b). The tilt axis has a vertical direction. (d) Red–green stereo anaglyph in a bird's-eye view

Figures 5.57 and 5.58a,b show a set of secondary electron micrographs recorded from biological samples at low magnification with different electron energies. The micrographs demonstrate to what extent the contrast and information depth vary with the electron energy in a range from $\mathrm{0.4}$ to ${\mathrm{30}}\,{\mathrm{keV}}$, which corresponds to about the accessible energy range of commercial FESEMs. As yet, not all of the contributing contrast mechanisms are fully understood, thus the interpretation of micrographs recorded at a specific selected energy requires great care.

Fig. 5.57

Secondary electron micrograph series of increasing electron energies from $\mathrm{0.5}$ to ${\mathrm{30}}\,{\mathrm{keV}}$ from a keratinocyte. The micrographs are recorded with an in-lens FESEM. The image contrast varies significantly with the electron energy. Inhomogeneities in the leading edge of the keratinocyte, which has a thickness of about $200{-}400\,{\mathrm{nm}}$, are most clearly visible at ${\mathrm{2}}\,{\mathrm{keV}}$. (Micrographs kindly provided by Dr. R. Wepf, Beiersdorf AG, Hamburg, Germany)

Fig. 5.58a,b

Secondary electron micrograph pair of the cuticula of a leaf recorded at electron energies of $\mathrm{0.4}$ (a) and ${\mathrm{30}}\,{\mathrm{keV}}$ (b) with an in-lens SEM. The low-energy image contains information only from the surface whereas the $\mathrm{30}$-$\mathrm{keV}$ image also reveals information about structural features below the surface, e. g., new spores, which are not visible in (a). Courtesy of R. Wepf

Finally, LVSEM is also a promising and efficient alternative to conventional approaches for micromorphological and microstructural characterization of polymers [5.32, 5.389, 5.390, 5.391].

3 Scanning Electron Microscopy at Elevated Pressure

The scanning electron microscopic investigation of specimens must meet several requirements, which were mentioned in previous sections. To sum it up, it can be said that specimens:

• 1. Have to be compatible with the low pressure in the specimen chamber ($\approx{\mathrm{10^{-3}}}\,{\mathrm{Pa}}$ in conventional SEM and $E-5{-}E-4\,{\mathrm{Pa}}$ in field-emission SEM)

• 2. Have to be clean, i. e., the region of interest has to give free access to the primary beam

• 3. Need sufficient electrical conductivity

• 4. Need to be resistant to some extent to electron radiation

• 5. Have to provide a sufficient contrast.

In a narrower sense, only metals, alloys, and metallic compounds fulfill those requirements. Numerous preparation procedures mentioned in Sect. 5.1.4 were developed in the past and are still in the process of improvement, to provide a sufficient electrical conductivity to nonconductive specimens, to remove the water in samples, and to replace it or to rapidly freeze it in a structure-conserving manner. Nevertheless, there was and still is enormous interest in investigating specimens in their genuine state.

Thirty years ago Robinson [5.392] proposed examining any uncoated insulating specimen in the SEM at high accelerating voltages in the specimen chamber, which had been modified to contain a small residual water vapor environment. It appeared that the presence of the water vapor sufficiently reduced the resistance of the insulator so that no charging effects were detected in backscattered electron micrographs. Danilatos [5.393] developed an atmospheric scanning electron microscope ( ), which later was called an environmental scanning electron microscope (ESEM^®) [5.394] and is now a registered trademark. To enable the investigation of water and water-containing specimens in their native state at stationary conditions a minimum pressure of water vapor of about ${\mathrm{612}}\,{\mathrm{Pa}}$ is required at ${\mathrm{0}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$ (Fig. 5.59). Stationary conditions in the specimen chamber of the SEM can be accomplished by controlling the water vapor pressure $p$ in close vicinity of the specimen as well as the specimen temperature $T$ such that the $p$–$T$ values always correspond to points on the solid $p$–$T$ graph in Fig. 5.59. For example, at ${\mathrm{20}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$ a water vapor pressure as large as about ${\mathrm{2330}}\,{\mathrm{Pa}}$ is required for stationary conditions. $p$–$T$ values below the solid graph, e. g., ${\mathrm{300}}\,{\mathrm{Pa}}$ at ${\mathrm{0}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$ (Fig. 5.59), correspond to a relative humidity of less than ${\mathrm{100}}\%$, thus representing nonstationary conditions.

Fig. 5.59

Phase diagram of water. Solid line: ${\mathrm{100}}\%$ relative humidity (saturated vapor conditions); dashed line: ${\mathrm{50}}\%$ relative humidity. (Data from [5.395])

How can stationary conditions be reached during imaging of a wet sample in the specimen chamber of an SEM? Figure 5.60 shows the cross section of the ESEM, which permits investigations at pressures sufficient for stationary conditions. Basically, the electron beam propagates in the column as in a conventional SEM until it reaches the final aperture. Then, since the pressure increases gradually as the electrons proceed toward the specimen, the electrons undergo significant scattering on gas molecules until they reach the specimen surface.

Fig. 5.60

Schematic cross section of the first commercial electroscan environmental SEM (ESEM^®) showing the vacuum and pumping system. Two pressure-limiting apertures separate the electron optical column from the specimen chamber. Differential pumping of the stage above and between the two pressure-limiting apertures ensures the separation of high vacuum in the column from low vacuum in the specimen chamber. The differential pumping of two stages and optimum arrangement of the pressure-limiting apertures can work successfully to achieve pressures up to ${\mathrm{10^{5}}}\,{\mathrm{Pa}}$ in the specimen chamber. After [5.396]

The electron–gas interaction is discussed in detail by Danilatos [5.35]. According to this study the average number of scattering events per electron $n$ can be approximated by

$$n=\frac{\sigma_{\mathrm{g}}p_{\mathrm{g}}L}{k_{\mathrm{B}}T}\;,$$

(5.44)

where $\sigma_{\mathrm{g}}$ represents the total scattering cross section of the gas molecule for electrons, $L$ is the electron path length in gas, and $k_{\mathrm{B}}$ is the Boltzmann constant. These approximations hold for $\Lambda\gg L$, where $\Lambda$ represents the mean free path of a beam electron in the gas. According to (5.44) the average number of collisions increases linearly with the gas pressure $p_{\mathrm{g}}$ and the path length in the specimen chamber. Furthermore, $n$ depends via the scattering cross section on the type of gas molecules and on the temperature. When the beam electrons start to be scattered by the gas molecules, the fraction of scattered electrons is removed from the focused beam and hit the specimen somewhere in a large area around the point of incidence of the focused beam. The scattered electrons form a skirt around the focused beam, which has a radius of ${\mathrm{100}}\,{\mathrm{\upmu{}m}}$ for a pathlength of ${\mathrm{5}}\,{\mathrm{mm}}$ (conditions: $E_{0}={\mathrm{10}}\,{\mathrm{keV}}$, water vapor pressure $={\mathrm{10^{3}}}\,{\mathrm{Pa}}$) [5.35]. Using a phosphor imaging plate, the distribution of unscattered beam electrons and the scattered skirt electrons was directly imaged by exposure to the electron beam for a specified time [5.397]. Related to the electron-beam intensity within ${\mathrm{25}}\,{\mathrm{\upmu{}m}}$, the skirt intensity as a function of the distance from the center drops to ${\mathrm{15}}\%$ at ${\mathrm{100}}\,{\mathrm{\upmu{}m}}$, ${\mathrm{5}}\%$ at ${\mathrm{200}}\,{\mathrm{\upmu{}m}}$, and ${\mathrm{1}}\%$ at ${\mathrm{500}}\,{\mathrm{\upmu{}m}}$ (conditions: $E_{0}={\mathrm{20}}\,{\mathrm{keV}}$, water vapor pressure $={\mathrm{266}}\,{\mathrm{Pa}}$, $l={\mathrm{10}}\,{\mathrm{mm}}$) [5.397]. The signals generated by the electrons of the skirt originate from a large area, which contributes to the background, whereas the unscattered beam remains focused to a small spot on the specimen surface, although its intensity is reduced by the fraction of electrons removed by scattering. The resolution obtainable depends on the beam diameter and the size of the interaction volume in the specimen, which is analogous to the situation in conventional and high-resolution SEM, i. e., the resolving power of ESEM can be maintained in the presence of gas.

The detection of BSE, CL, and x-rays is to a great extent analogous to the detection in a conventional SEM, because these signals can penetrate the gas sufficiently [5.37, 5.398, 5.399]. However, the situation is completely different for the detection of SE. The conventional Everhart–Thornley detector would break down at elevated pressure in the specimen chamber. However, the gas itself can be used as an amplifier in a fashion similar to that used in ionization chambers and gas proportional counters. An attractive positive voltage on a detector will make all the secondary electrons drift toward it. If the attractive field is sufficiently large, each drifting electron will be accelerated, thus gaining enough energy to cause ionization of gas molecules, which can create more than one electron. This process repeating itself results in a significant avalanche amplification of the secondary electron current, which arrives at the central electrode of the environmental secondary electron detector (ESD ) [5.35]. The avalanche amplification works best only in a limited pressure range and can amplify the SE signal up to three orders of magnitude [5.400]. Too high pressure in the specimen chamber makes the mean free path of the electrons very small and a high electric field between specimen and detector is required to accelerate them sufficiently. Too low pressure in the chamber results in a large mean free electron path, i. e., only a few ionization events take place along the electron path from the specimen to the detector, thus the avalanche amplification factor is low. The new generation of ESD, the gaseous secondary electron detector ( ), which consists of a ${\mathrm{3}}\,{\mathrm{mm}}$ diameter metallic ring placed above the specimen, provides better discrimination against parasitic electron signals. Both the ESD and GSED are patented and are available only in the ESEM [5.37].

However, the ionization of gas molecules creates not only electrons but also ions and gaseous scintillation. The latter can be used to make images [5.399], i. e., in that case the imaging gas acts as a detector. This principle is used in the patented variable pressure secondary electron ( ) detector. Nonconductive samples attract positive gas ions to their surface as negative charge accumulates from the electron beam, thus effectively suppressing or at least strongly reducing charging artifacts [5.37, 5.401, 5.402, 5.403, 5.404, 5.405]. The gas ions can affect or even reverse the contrast in the GSED image under specific conditions, e. g., at specimen regions of enhanced electron emission, where the rate of electron–ion pairs increases [5.400]. The highly mobile electrons generated by electron–gas interaction are removed from the gas by rapid sweeping to the GSED, which in turn causes an increased concentration of positive ions during image acquisition due to different electric field-induced drift velocities of negative and positive charge carriers in the imaging gas [5.406].

However, imaging of wet, soft specimens can be hampered by the effect of surface tension [5.279], which may flatten and hereby deform the specimen. Obviously, this is a misleading situation demonstrating that environmental conditions do not necessarily guarantee structural preservation.

As mentioned above, about ${\mathrm{612}}\,{\mathrm{Pa}}$ is the crucial minimum pressure for wet specimens. In addition to the ESEM, which enables imaging with SE at pressures up to about ${\mathrm{6500}}\,{\mathrm{Pa}}$, numerous variable pressure scanning electron microscopy ( ), high-pressure SEM, and low vacuum scanning electron microscopy (sometimes the abbreviation is used, which cannot be distinguished from the low-voltage SEM) became commercially available. The water vapor pressure in the specimen chamber of those SEM is typically at maximum ${\mathrm{300}}\,{\mathrm{Pa}}$, i. e., below the crucial value of ${\mathrm{612}}\,{\mathrm{Pa}}$, which is not sufficient for imaging of wet specimens at stationary conditions. To separate the specimen pressure of maximum ${\mathrm{300}}\,{\mathrm{Pa}}$ from the high vacuum in the column only one pressure-limiting aperture is sufficient. For imaging at pressures in the range from $\mathrm{250}$ to ${\mathrm{300}}\,{\mathrm{Pa}}$ backscattered electrons are utilized.

The workaround has been demonstrated by Thiberge et al [5.408] for scanning electron microscopy of cells and tissues under fully hydrated atmospheric conditions utilizing a small chamber with a polyimide membrane (${\mathrm{145}}\,{\mathrm{nm}}$ in thickness) that is transparent to beam and backscattered electrons. The membrane protects the fully hydrated sample from the vacuum. BSE imaging at acceleration voltages in the range of $12{-}30\,{\mathrm{kV}}$ revealed structures inside cultured cells and colloidal gold particles having diameters of $\mathrm{20}$ and ${\mathrm{40}}\,{\mathrm{nm}}$, respectively. Another interesting experimental setup is the habitat chamber designed to keep living cells under fully hydrated atmospheric conditions as long as possible and to reduce the exposure time to the lower pressure in the ESEM below ${\mathrm{2}}\,{\mathrm{min}}$ [5.409].

Scanning electron microscopy at elevated pressure is increasingly used in very different fields. Apart from variations in the pressure and chamber gas a heating stage (maximum temperature about ${\mathrm{1500}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$) allows changes in the specimen temperature. For example, chemical reactions such as corrosion of metals, electrolyte–solid interactions, alloy formation, and the degradation of the space shuttle ceramic shields by increasing oxygen partial pressures at high temperatures are possible with micrometer resolution. The onset of chemical reactions that depend on various parameters can by studied in detail. Insulators, including oil and oily specimens, can be directly imaged. Water can also be imaged directly in the ESEM, which allows studies of wetting and drying surfaces [5.410, 5.411, 5.412] and direct visualization of the dynamic behavior of a water meniscus [5.407, 5.413].

Figure 5.61a-e shows an example of dynamic studies of a water meniscus between the scanning tunneling tip and a support when the tip is moved across the sample. The wetting of the tip indicates a hydrophilic surface, whereas Fig. 5.62 clearly indicates a hydrophobic tip surface.

Fig. 5.61a-e

Time-resolved sequence of secondary electron images recorded with an ESEM^®-E3 (ElectroScan Corp., Wilmington, MA). The water meniscus between the hydrophilic tungsten tip (normal electron-beam incidence) and the $\text{Pt}/\mathrm{C}$-coated mica (incidence angle of $85^{\circ}$) is clearly visible (a–d). Because of locally decreasing relative humidity the meniscus becomes gradually smaller until it snaps off (e). The absence of the meniscus leads to a significant change of shape of the water bead below the tip (d,e). Some water drops are located on the sample in front of and behind the tip. The sequence was recorded within ${\mathrm{11}}\,{\mathrm{s}}$ and each image was acquired within about ${\mathrm{2}}\,{\mathrm{s}}$. Experimental conditions: $E_{0}={\mathrm{30}}\,{\mathrm{keV}}$, $I_{\mathrm{p}}={\mathrm{200}}\,{\mathrm{pA}}$, $p_{\mathrm{g}}={\mathrm{1.2}}\,{\mathrm{kPa}}$. Reprinted from [5.407], with the permission of AIP Publishing

ESEM studies of the wettability alteration due to aging in crude oil/brine/rock systems that are initially water wet are of significant importance in the petroleum industry in understanding the water condensation behavior on freshly exposed core chips. Surface active compounds are rapidly removed from the migrating petroleum, thus changing the wettability and subsequently allowing larger hydrophobic molecules to sorb [5.414, 5.415, 5.416]. Furthermore, the ESEM is a powerful tool with which study the influence of salt, alcohol, and alkali on the interfacial activity of novel polymeric surfactants that exhibit excellent surface activity due to their unique structure [5.417].

Environmental scanning electron microscopy has disseminated rapidly among scientific and engineering disciplines. Applications range widely over diverse technologies such as pharmaceutical formulations, personal care and household products, paper fibers and coatings, cement-based materials, boron particle combustion, hydrogen sulfide corrosion of Ni-Fe, micromechanical fabrication, stone preservation, and biodeterioration. In spite of the broad applications, numerous contrast phenomena are not fully understood as yet. In addition, ESEM investigations of polymeric and biological specimens, which are known from conventional electron microscopy to be highly irradiation sensitive, are more difficult because water acts as a source of small, highly mobile free radicals, which accelerate specimen degradation [5.418, 5.419].

Fig. 5.62

Secondary electron image recorded with an ESEM-E3 (ElectroScan Corp., Wilmington, MA) from a hydrophobic tungsten tip (normal electron-beam incidence) and a water bead on $\text{Pt}/\mathrm{C}$-coated mica (incidence angle of $85^{\circ}$). The shape of the deformed water surface in the submicrometer vicinity of the tip clearly indicates its hydrophobic surface. The spherical object (black) at the right of the tip in the back is probably a polystyrene sphere and any resemblance is purely coincidental. Reprinted from [5.407], with the permission of AIP Publishing

4 Microanalysis in Scanning Electron Microscopy

The generation of x-rays due to electron–specimen interactions was discussed in Sect. 5.1.2, X-Rays. The characteristic x-rays emitted from the specimen carry information about its local element composition, which is utilized as a powerful microanalytical tool combining SEM with EDX and WDX spectrometers. X-ray microanalysis is by far the most widely used method combined with SEM, which enables in various modes qualitative and quantitative element analysis from a point or area of interest as well as mapping of the distribution of various elements simultaneously with SE and BSE imaging. The size of the interaction volume emitting x-rays is significantly larger than the ones for AE, SE, and BSE because of the weaker absorption of x-rays inside the specimen (Fig. 5.14) and the secondary emission by x-ray fluorescence outside the electron interaction volume. The secondary x-ray emission volume is much larger than that for primary x-ray emission since x-rays are more penetrating than electrons having the same energy. For electron-excited x-ray spectrometry performed on thick specimens in the SEM, the range $R_{\Updelta 1}$ for x-ray excitation in $\mathrm{\upmu{}m}$ is given according to Kanaya and Kayama [5.420] by

$$R=\left(\frac{0.0276\,A}{\rho\mathrm{Z}^{0.89}}\right)\left({E_{0}}^{1.67}-{E_{\mathrm{X}}}^{1.67}\right)\;,$$

(5.45)

where $A$ is the atomic weight ($\mathrm{g{\,}mol^{-1}}$), $\rho$ is the density ($\mathrm{g{\,}cm^{-3}}$), $Z$ is the atomic number, $E_{0}$ is the incident electron energy (keV), and $E_{\mathrm{X}}$ is the x-ray energy (keV).

For reliable quantitative x-ray microanalytical studies, x-ray absorption, x-ray fluorescence, and the fraction of backscattered electrons, all of which depend on the composition of the specimen, have to be taken into account and are performed by the so-called ZAF correction . Z stands for atomic number, which affects the penetration of incident electrons into the material, A for absorption of x-rays in the specimen on the path to the detector, and F for fluorescence caused by other x-rays generated in the specimen.

Three different types of detectors can be used to measure the emitted x-ray intensity as a function of the energy or wavelength. In an EDX system, as described there are now two different types of detectors available, an SiLi detector and a silicon drift detector ( ) (Fig. 5.63a,b). The x-rays enter the detector and create electron–hole pairs that cause a pulse of current to flow through the detector circuit. The number of pairs produced by each x-ray photon is proportional to its energy (Sect. 5.1.1, Detectors and Detection Strategies).

Fig. 5.63

(a) Scheme of Si (Li) x-ray diode coupled to a field-effect transistor ( ) with a resistive feedback loop ($R_{\mathrm{F}}$, $C_{\mathrm{F}}$). The shape of the output signal is shown in the output voltage versus time diagram. Typically, this principle is used in energy-dispersive x-ray ( ) detectors. (b) Silicon drift detector, showing small anode size. Courtesy of PNSensor

SDDs have a small-sized anode with respect to their active area. The x-ray generates charged carriers (i. e., holes and electrons) that are directed along these electric field lines to the dramatically smaller anode at the center of the detector. Since the capacitance of the device is proportional to the anode size, a very small anode leads to a drastically lower device capacitance. Having a very small anode helps achieve better resolution at shorter shaping times (higher count rates) owing to the fact that the electronic noise at short shaping times varies in proportion to capacitance squared, especially at low energies where the SNR is much less. If the noise is small enough, it is possible to operate the device at temperatures ($\approx{\mathrm{-20}}\,{\mathrm{{}^{\circ}\mathrm{C}}}$) that are readily achievable with a Peltier device. This avoids the use of LN2 cooling as in SiLi detectors.

In a WDX spectrometer (Fig. 5.64) the x-rays fall on a bent crystal and are reflected only if they satisfy Bragg's law. The crystal bending is such that it focuses x-rays of one specific wavelength onto a proportional counter and rotates to scan the wavelength detected. Some important features of both types of x-ray spectrometer are listed in Table 5.9. However, since instrumentation and analysis of data in x-ray microanalysis are usually considered a separate discipline, no further details are discussed in this section [5.27, 5.28, 5.421, 5.422, 5.423, 5.43].

Fig. 5.64

Principle of a wavelength-dispersive x-ray ( ) spectrometer. Generated x-rays that hit the analyzing crystal are focused and because of Bragg reflection directed to a slit in front of the proportional counter lying on a Rowland circle with radius $r_{\mathrm{f}}$. The lattice planes of the crystal are bent to a radius of $2r_{\mathrm{f}}$

A selected application of the very powerful combination of SEM imaging, x-ray microanalysis, and element mapping—the latter was invented almost exactly 50 years ago by Cosslett and Duncumb [5.424]—is illustrated in Fig. 5.65a-h. The selected specimen is a Cr-Fe alloy with an Si phase, which has a locally varying composition as clearly indicated by the energy-dispersive spectra in Fig. 5.65a-ha,b recorded at different locations (Fig. 5.65a-hc).

Fig. 5.65a-h

X-ray microanalysis of a Cr-Fe-alloy with an Si phase. The EDX spectra (a,b) were recorded with the Bruker Flash^® 3001 from locations 1 and 2 marked in the SE micrograph of the specimen (c). The positions of the characteristic x-ray energies for the various elements emerging in the spectra are indicated by thin lines, which are labeled with the chemical symbol of the corresponding chemical element. The elements iron, chromium, and vanadium occur with one $\mathrm{K}_{\alpha}$ peak each in the energy range from $\mathrm{4.95}$ to ${\mathrm{6.40}}\,{\mathrm{keV}}$ and with one less intense $\mathrm{L}_{\alpha}$ peak each in the energy range from $\mathrm{0.51}$ to ${\mathrm{0.71}}\,{\mathrm{keV}}$. Elemental distribution maps of Fe (d), Cr (e), Si (f), and Ti (g) were recorded using the $\mathrm{K}_{\alpha}$ lines. (h) Mixed micrograph obtained by superimposition of the SE image and the maps of the distribution of Fe, Cr, Si, and Ti within the field of view. Experimental conditions: SEM, LEO 438VP. For recording spectra: $E_{0}={\mathrm{20}}\,{\mathrm{keV}}$; count rate, $\approx{\mathrm{3\times 10^{3}}}\,{\mathrm{cps}}$; acquisition time, ${\mathrm{300}}\,{\mathrm{s}}$. For recording maps: $E_{0}={\mathrm{25}}\,{\mathrm{keV}}$; count rate $\approx{\mathrm{1.5\times 10^{5}}}\,{\mathrm{cps}}$; acquisition time ${\mathrm{600}}\,{\mathrm{s}}$. Kindly provided by Bruker Nano GmbH (formerly Röntec GmbH), Berlin, Germany

The area under each characteristic peak represents the amount of x-ray counts, which is—after subtraction of the Bremsstrahlung background below the peak and ZAF correction—a direct quantitative measure of the number of atoms of the specific element belonging to that peak. However, a simple visual inspection of the spectra shows, e. g., that the location 1 (Fig. 5.65a-ha) contains significantly more chromium and less iron than location 2 (Fig. 5.65a-hb). In addition, a strong silicon peak emerges in the spectrum of location 2 not present in the spectrum of 1 (Fig. 5.65a-ha). The element distribution maps of four important chemical elements in the specimen, namely iron, chromium, silicon, and titanium, are shown in Fig. 5.65a-hd–g. Comparing the information given by the four element distribution maps on the one hand and the two spectra on the other hand immediately makes clear why the titanium peak does not emerge in the spectra and the chromium peak is dominant at location 1 but not at 2. By means of simple image-processing procedures the SE micrograph (Fig. 5.65a-hc) and the element distribution maps (Fig. 5.65a-hd–g) can be superimposed in one image (Fig. 5.65a-hh) presenting information for five individual images.

The most powerful tool in electron-beam microanalysis is the ability to depict the elemental compositional heterogeneity of matter with micrometer to nanometer lateral resolution. Many developments have occurred over the intervening years to advance this critical method (see detector performance comparison in Table 5.9). Further, computer-controlled SEM in connection with image processing and EDX spectrometry enables the unattended and automated determination of both the geometric parameters and the chemical composition of thousands of individual particles down to a size of $50{-}100\,{\mathrm{nm}}$ [5.34, 5.430]. Consequently, correlations between particle size, chemical composition, the number of different compounds, and their contribution to the overall concentration can be established. Problems may arise in connection with specimen preparation, optimization of the image contrast, the sometimes nonhomogeneous composition of particles, shadowing of the x-rays in the case of large particles, and the lack of a rigorous ZAF correction procedure for particles of arbitrary shape.

Table 5.9 Characteristic features of energy-dispersive x-ray (EDX) and wavelength-dispersive x-ray (WDX) detectors${}^{\mathrm{a}}$. Modern SDD EDS is capable of an energy resolution of down to ${\mathrm{121}}\,{\mathrm{eV}}$ at Mn $\mathrm{K}_{\alpha}$ and a maximum output count rate of ${\mathrm{400}}\,{\mathrm{cps}}$ per detector, amounting to ${\mathrm{1.6}}\,{\mathrm{Mcps}}$ for a BrukerFlatQUAD detector^b,c

Another increasingly important application is multilayer analysis, i. e., the nondestructive measurement of the thickness and composition of thin films both unsupported and on substrates, which can be performed with high accuracy down to a thickness of ${\mathrm{2}}\,{\mathrm{nm}}$ by a combination SEM and EDX [5.431, 5.432, 5.433]. For this purpose the ratio between the x-ray intensity of the film and the intensity of the same element of a bulk standard is used.

Low-voltage scanning electron microscopy ($E_{0}<{\mathrm{5}}\,{\mathrm{keV}}$) offers both high spatial resolution and a significantly reduced x-ray generation depth. This enables the composition of thin layers on substrates to be determined without the need to use a dedicated thin film analysis program. The analysis of small phases down to a size of ${\mathrm{50}}\,{\mathrm{nm}}$ is also possible [5.434, 5.435]. In principle elements of higher atomic number can be identified using L- and M-shell x-rays, but these are somewhat more complicated than the rather simple K-shell x-ray emissions.

5 Crystal Structure Analysis by Electron Backscatter Diffraction

In crystalline specimens electrons are diffracted at lattice planes according to Bragg's law given as

$$2d\sin\vartheta=n\lambda\;,$$

(5.46)

where $d$ is the lattice-plane spacing, $\vartheta$ is Bragg's angle, and $\lambda$ is the electron wavelength. Bragg's law requires that the incident and emergent angles should be equal $\vartheta$. As previously mentioned, the backscattering coefficient sensitively depends on the tilt of the incident electron beam relative to the lattice and Bragg position. Changing the tilt of the incident beam relative to the lattice, e. g., by rocking the electron beam or tilting the specimen, affects the backscattering coefficient, which results in an electron channeling pattern ( ). To obtain from an ECP information about the crystal structure, e. g., the crystal orientation and the lattice-plane spacings, a so-called panorama diagram recorded by successively tilting the specimen over a large angular range is required [5.43, 5.436, 5.437]. However, establishing a panorama diagram is a somewhat difficult task.

Another way of obtaining information about the crystal structure of the specimen is the use of electron diffraction effects associated with the scattered electrons. As described in Sect. 5.1.2, the beam electrons are scattered elastically and inelastically due to the electron–specimen interaction, thus scattered beam electrons travel within the excitation volume in all directions (Fig. 5.13). This scattering process can be considered as a small electron source inside the crystalline specimen emitting electrons in all directions as shown in Fig. 5.66. These electrons may be diffracted at sets of parallel lattice planes according to Bragg's law (5.46) as first observed by Venables and Harland [5.438]. Figure 5.66 illustrates that the electrons emitted from one point and diffracted at lattice planes will form pairs of cones centered with respect to the normal vector of these lattice planes. The opening angle of the cones is $180^{\circ}-2\vartheta$ and the angle between them is $2\vartheta$. Since the Bragg angle is in the order of $1^{\circ}$ for $15{-}30\,{\mathrm{keV}}$ electrons and lattice-plane spacings of $0.2{-}0.3\,{\mathrm{nm}}$, the intersections of the cones with a flat observation screen positioned at a distance much larger than $d$ (usually $2{-}4\,{\mathrm{cm}}$ from the point of beam–specimen intersection) and tangential to the propagation sphere of the scattered electrons are almost straight and parallel pairs of lines. They are called Kikuchi lines. The angle between parallel pairs of Kikuchi lines is $2\vartheta$. The whole EBSD pattern with the Kikuchi lines reveals local information about the crystalline structure within the individual excitation volume. A detailed treatment of EBSD, which is beyond the scope of this section, is given by Wilkinson and Hirsch [5.439]. Nevertheless, it is worth mentioning that the relationship between EBSD and the previously introduced ECP is characterized by the reciprocity of their ray diagrams [5.38].

Fig. 5.66

Scheme of the formation of one pair of cones from diffraction of scattered electrons at one set of parallel lattice planes

The recording of the EBSD pattern, which originally was performed by exposure of a photographic film, is now done by position-sensitive detectors such as a scintillation window with a CCD camera attached. To allow the diffracted electrons to escape from the specimen its surface is usually tilted approximately $60^{\circ}$ or $70^{\circ}$ toward the screen. The EBSD patterns are digitally acquired by computer, which also controls the positioning of the beam. In the case of automated crystal orientation mapping, the computer scans the electron beam stepwise across the specimen and controls the dynamic focusing of the beam (Fig. 5.9a-ee and Sect. 5.1.1, Specimen Tilting and Stereo Imaging). Since special software algorithms for the automated detection and indexing of Kikuchi lines in EBSD patterns were introduced by Krieger-Lassen et al [5.440], Adams et al [5.441] developed a new scanning technique called orientation imaging microscopy ( ). In OIM, which is also called automated crystal orientation mapping, the EBSD pattern from each individual point at the specimen surface radiated by the electron beam is recorded and analyzed.

In the past decade, EBSD has become a powerful tool for crystallographic analysis such as the determination of the orientation of individual crystallites of polycrystalline materials in the SEM, phase identification, and characterization of grain boundaries, which is illustrated by the following examples. Figure 5.67a-c shows two different EBSD patterns from an as-cast niobium sample recorded with high (Fig. 5.67a-ca) and low resolution (Fig. 5.67a-cb), respectively [5.442], at a stationary beam position. Figure 5.67a-cc shows the colored pairs of Kikuchi lines generated by automatic indexing and overlayed to the EBSD monitored in Fig. 5.67a-ca.

Fig. 5.67a-c

ESBD patterns from an as-cast niobium specimen. (a) High-resolution EBSD pattern with background subtraction. Exposure time, ${\mathrm{7}}\,{\mathrm{s}}$. (b) Raw data EBSD pattern for high-speed mapping. Exposure time, ${\mathrm{15}}\,{\mathrm{ms}}$. EBSD patterns are recorded with a JSM-6500F thermal FESEM. (c) EBSD pattern from (a) with pairs of Kikuchi lines generated by automatic indexing. Images courtesy of JEOL USA

Figure 5.68a-ca shows an SE micrograph of polycrystalline austenite with the related color-coded orientation map of polycrystalline austenite monitored in Fig. 5.68a-cb [5.443]. The spatial resolution obtained amounts to about ${\mathrm{50}}\,{\mathrm{nm}}$ (at $E_{0}={\mathrm{15}}\,{\mathrm{keV}}$), i. e., smaller grains or precipitates cannot be detected in the orientation map. The map shown in Fig. 5.68a-cc provides information about the grain boundary character and the orientation variations inside of each grain. The latter is shown for an individual grain in more detail in Fig. 5.69.

Fig. 5.68a-c

Secondary electron micrograph of austenite (a) with rough (1), relatively smooth (2), and smooth (3) surface areas. (b) Orientation map of (a) measured by automated crystal orientation mapping and grayscale coded for the crystal direction parallel to the normal direction (ND ) of the sheet. Hatched areas correspond to austenite grains. (c) The boundary character between $\upgamma$- and $\upalpha$-grains, different orientation components ($(001)\parallel\text{ND}$, red; all others blue) and the orientation variations inside of each grain (color shading; b: bainite). The micrograph and the maps are recorded with a JSM-6500F thermal FESEM. Note: the extension toward the top and bottom of the measured area in (b,c) is larger than the area marked in (a). (Reprinted from [5.443], with permission from Elsevier)

Fig. 5.69

Orientation map of one grain from the microstructure in Fig. 5.68a-ca. Grayscale code: angular deviation of every mapping point to one orientation in the center of the grain. Bainite appears in conjunction with a steep orientation gradient in ferrite. The white line marks the maximum extension of austenite at the austenization temperature. f: ferrite; a: austenite (hatched); b: bainite. Reprinted from [5.443], with permission from Elsevier

The OIM developed into a powerful technique providing a wealth of information about the type and distribution of different phases, the size, shape, and defects of grains, the type of grain boundaries, the local crystal orientation, and the preferential orientation (texture). To take full advantage of this new imaging technique in terms of spatial and orientation accuracy the thermal field-emission SEM providing a high beam current is most suitable. Furthermore, the SEM needs a very high mechanical and electronic stability because EBSD measurements require very long recording time, e. g., up to ${\mathrm{12}}\,{\mathrm{h}}$ for very large orientation maps [5.442]. Finally, the preparation of specimens is a very delicate task since EBSD is a very surface-sensitive technique with an information depth of less than ${\mathrm{10}}\,{\mathrm{nm}}$ up to a few tens of nanometers. Thus, the surface-near zone must be free of any deformation and, in addition, the surface has to be rather smooth because any surface relief may affect data acquisition.

The application of OIM is not restricted to metals and alloys. Crystalline materials such as semiconductors [5.444], ceramics [5.445, 5.446], and minerals [5.447, 5.448] can be investigated. A new avenue for EBSD introduced in the last few years is called , or transmission Kikuchi diffraction [5.449]. The technique effectively used ultrathin, TEM-like specimens to achieve on the order of $10{-}20\,{\mathrm{nm}}$ resolution crystallographic analysis inside the SEM. TKD requires a slightly different holder to accommodate an ultrathin specimen imaged and analyzed using transmitted electrons in SEM.