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1 Introduction

The detection of secondary electrons (SEs) has been the most widely used node of operation in scanning electron microscopy (SEM) since the middle of the last century, when a sensitive SE detector was developed by Everhart and Tornley [1]. The SE detection mode has a number of advantages, including a low lateral spread of the electron escape volume and a simple analytical shape of the dependence of SE yield on the angle of incidence, providing high resolution and easily interpretable SE images. Physical processes related to the electron emission from samples and its application for image formation in SEM have been extensively investigated and their detailed description has been published in books [2, 3] and reviews [4, 5].

SEs can be excited not only by electrons but also by any other primary particles (ions, atoms, electromagnetic quants) that are able to transfer a sufficient amount of their energy to electrons in solids. In scanning ion microscopy , SEs are excited by the focused beam of accelerated ions. By convention, an SE is assumed to have a kinetic energy less than 50 eV. This restriction was introduced to distinguish SEs from scattered electrons of the primary beam in SEMs operating with accelerating voltages above hundreds of volts. In scanning ion microscopes, all electrons excited by the ion beam are secondary.

SE emission is characterized by the number of SEs per primary particle, known as SE yield (SEY), and by SE energy distribution (SEED) . The angular dependence of the total SEY provides the main base of topography contrast formation in scanning electron or ion microscopy. The SEY value and the shape of the SEED depend on both the kind of excitation and on the material. Exact knowledge of the particular SEED parameters has been shown to be very useful for correct interpretation of SEM images [5] as well as for electron or ion assisted lithography [6].

In this chapter we present a brief review of available state-of-the-art results of the main properties of SEs excited in the helium ion microscope (HIM) and their use in diverse HIM imaging modes.

2 The Processes of Secondary Electron Generation in the Helium Ion Microscope

The process of SE emission can be divided into three consecutive processes: an instant energy transfer from primary particles to electrons in any point of the sample, transport of excited electrons to the surface and their escape through the surface barrier. The mechanisms of the last two processes are independent of the kind of exciting particle or of radiation and are related only to material properties. SE escape from the sample into the vacuum is limited by a barrier at the surface that is determined by the work function of the sample, whereas the transport is usually described as electron diffusion characterized by the electron mean free path (MFP) of a solid.

The energy transfer from primary particles to the electrons of the sample is a multistage process that includes many channels of initial energy dissipation. An important difference between electron-induced and ion-induced SE generation is that ion-induced generation can take two distinct forms: potential electron emission and kinetic electron emission.

Potential emission occurs when the potential energy released on neutralization of the incident ion can provide the energy required to free electrons from the solid [7]. This process has no lower energy threshold but is significant only when the primary ion is slow enough [8] that it corresponds to the kinetic energy of helium ions of few hundred eV [9]. In this case, the potential energy of an ion at the surface can be transferred to an Auger electron in the solid via a two-step process as illustrated in Fig. 5.1. The first step is the tunneling of an electron from the solid to the ion (marked 1 in Fig. 5.1) resulting in its neutralization. The second step is the excess energy transfer to another electron of the solid via the Auger process (marked 2 in Fig. 5.1). The maximum kinetic energy of SE in that case is I-2Ф, where I is the ionization potential of the primary ion and Ф is the work function of the material. The relatively high ionization potential of helium ions, 24.5 eV, makes the Auger mechanism of potential emission possible for the most materials, since in most cases the work function is less than 10 eV.

Fig. 5.1
figure 1

Schematic diagram illustrating the potential electron emission process. The ion is neutralized as the result of the tunneling of an electron from the solid (arrow 1). The energy I-2Ф (arrow 2) is transferred to another electron in the solid via the Auger process . I is the ionization potential of the primary ion and Ф is the work function of the material

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An additional mechanism of ion–electron interaction at low primary ion energies that might contribute to potential electron emission is potential plasmon excitation [10, 11]. Neutralization of the ion results in the appearance of a hole near the sample surface because of the loss of an electron. Surrounding electrons of the sample move to screen the hole, and oscillations of electron gas can be excited. A detailed review of plasmon excitation in ion–solid interaction can be found elsewhere (see [11] and references therein). Though the contribution of the potential electron emission mechanism to the total SEY in HIM working with accelerating voltages more than 20 kV seems to be insignificant, it should be noted for the following discussion of SEED shape that experimental observations of that mechanism serve as evidence for ion neutralization near the surface.

Kinetic energy transfer takes place when the energy of projectile particles is sufficient for them to penetrate into a solid. There are several mechanisms for the transfer of kinetic energy from projectile particles to the electrons in solids which can result in excitation of secondary electrons. Four of them are depicted in Fig. 5.2. They are direct binary ion–electron collisions, electron cascades generation, excitation by recoil atoms and plasmon excitation.

Fig. 5.2
figure 2

Schematic presentation of the processes of kinetic energy transfer from a projectile to the electrons in solids, resulting in kinetic electron emission: 1 direct binary ion–electron collisions, 2 Electron cascades generation, 3 Excitation by recoil atoms and 4 Plasmon excitation. Green, blue and red arrows show trajectories of the ions, electrons and recoils, respectively

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The resulting impact of all of the processes can be described by stopping power, that is, the rate (in eV/nm) of energy transfer from the primary particles to the sample per unit of the primary path. The instant rate of SE generation is proportional to the stopping power. For electrons the stopping power increases rapidly with increasing energy E reaching a maximum value of about 60 eV/nm at an energy on the order of hundreds of eVs and then falls away at about 1/E following Bethe’s law [3]. As a result, the mean free path (MFP) of the SEs (which are the electrons with energies below the stopping power maximum) decreases with their energy, providing behavior similar to SE escape depths in a range from a few to tens of nanometers. Accordingly, the latter values are defined as the values of the depth which are relevant to the ion–electron energy transfer for SE generation.

For the helium ions, however, the stopping power stays relatively low until the energy reaches about 5 keV, then increases steadily to reach a maximum value of about 700 eV/nm at an energy of about 800–1000 keV before starting to fall. These distinctly different behaviors might appear to suggest that electrons and helium ions interact with the target in completely different ways, but this conclusion is incorrect because comparing ions and electrons on the basis of their energy is not appropriate. In fact, the interaction of swift particles with a solid depends on their velocity but not on their energy, since according to momentum and energy conservation laws the maximum momentum transfer from any particle to an electron cannot exceed the value 2 mv, where m is the electron rest mass and v is the velocity of the projectile.

The latter value for a helium ion as a function of energy can be calculated as:

$$v_{He + } (cm/s) = 2.196 \times 10^{7} \,\sqrt {E(keV)}$$
(5.1)

which corresponds to approximately 1 % of the velocity of an electron of the same energy.

Figure 5.3 shows the normalized stopping power dependence of helium ions and electrons in chromium as a function of incident particle velocity calculated in the paper by Ramachandra et al. [9]. The helium data were obtained from the SRIM routines of Ziegler et al. [12] and include both nuclear and electronic contributions; the corresponding incident electron stopping profile was taken from previous experimental data [13].

Fig. 5.3
figure 3

Normalized stopping power (SE yield) dependence of helium ions and electrons as a function of incident particle velocity in chromium replotted using the data calculated in [9]. Arrows show helium ion and electron velocities corresponding to usual accelerating voltage values of about 20 kV either in HIM or in SEM

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Both particles are seen from the Fig. 5.3 to show rather similar behavior and each reaches its peak value close to the same velocity of about 6 * 108 cm/s. The shape of the curve for ions is not identical to the shape of the curve for electrons. It is important to note that the SEY for helium exceeds that for electrons at velocities below the maximum. The energies of He ions in HIM (from 10 to 45 keV) correspond to velocities on the left-hand side of the stopping power maximum, while for electrons in SEM their energies (from 0.5 to 30 keV) represent velocities that fall on the right-hand side of the stopping power peak. Thus, increasing the energy of the helium beam in HIM increases the stopping power, leading to an increase in SE production, while increasing the energy of the electron beam results in a fall in stopping power , i.e. in a reduction of SE emission.

The stopping power of He ions is an order of magnitude higher than that of electrons, which corresponds to a higher number of secondary electrons (i.e. to a higher SEY) in HIM. The available experimental data collected during past decades [8, 14, 15,] and obtained recently [16] show that SEY values increase with the ion energy within the energy ranges of interest, and above energies of 5–20 keV (depending on the element) can well exceed unity. SEY values measured in HIM at 20 kV were found to be between 2 and 5 for different metals and reached 7.9 for platinum [17]. Several methods of SEY calculations have been developed using analytical approaches [18–20] as well as Monte Carlo simulations [9, 21, 22]. The results of two SEY calculation routines developed independently by Ramachandra et al. [9] and Inai et al. [22] are in good agreement.

3 SE Energy Distribution in HIM

SEY discussed in the previous section is a value independent of the SE energy value which counts the total number of SEs produced by an ion. Secondary electron energy distribution (SEED) describes the number of secondary electrons as a function of their energy. Generally, this function is non-monotonic and can be characterized by its shape and maximum value. The integral of SEED over the energy gives the total SEY. For electron excitation the shape of SEED is known to be essentially independent of the energy of the primary electron beam [4]. It is characterized by most probable energy, Emax, and the full width at half maximum (HW). Both Emax and HW depend on the surface material of the specimen, so HW is smaller for insulators than for metals [4]. Among numerous papers devoted to theoretical explanations or simulations of SEED shape, the most commonly accepted and used one is the result of Chung and Everhart [23], which suggested a simple equation for SEED as follows:

$$\frac{dN}{dE} = K\frac{E}{{(E +\Phi )^{4} }}$$
(5.2)

where K is a constant dependent on SEY value, E is the kinetic energy of emitted SE and Φ is a material work function . Equation (5.2) predicts that the SEED maximum corresponds to an SE energy of one-third of the material work function.

SEED in the helium ion microscope was experimentally investigated in [24, 25] by the retarding potential method with a hemispherical analyzer that was also used for SEED measurements in conventional SEM. Black open and closed dots in Fig. 5.4 represent the results of such measurements for molybdenum in SEM and in HIM, respectively. The dashed line in Fig. 5.4 was calculated theoretically with (5.2) of Chung and Everhart taking the known work function value for Mo. One can see that experimental data of SEED shape in SEM can be well-fitted with the theory whereas the data for HIM cannot, because the maximum of SEED in HIM is situated at somewhat lower energy than that in SEM and the high energy tail of SEED for HIM decays more rapidly with the energy than that for SE.

Fig. 5.4
figure 4

Energy distribution of secondary electrons for Mo excited in SEM (black closed dots) and in HIM (open dots) working at acceleration voltages of 30 kV and of 32 kV, respectively. Dashed and solid lines represent the theoretical shapes of SEED for SEM and for HIM according to (5.2) and (5.10), respectively

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SEED measurements in HIM performed on different metals confirmed the general trend which was well established for electron excitation, that the SEED peak position energy follows the changes of the material work function value (see Fig. 5.5).

Fig. 5.5
figure 5

Secondary electron energy distribution measured in HIM for three metals [25]. Inset shows the dependence of SEED maximum position on the metal work function

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To describe the shape of SEED in HIM, a modified Chung-Everhart model was suggested in [25] that used the same formalism to describe the transport of excited electrons to the surface and their escape through the surface barrier, but introduced another function for the description of the energy transfer from primary ion to secondary electron. The number of secondary electrons excited per unit energy in the energy interval between E and E + dE at a depth of z from the surface is designated as S(E, z).

Following Chung and Everhard, S(E, z) SEED can be obtained by integrating the product S(E, z) P(E, θ, z) over all possible θ and z, where P(E, θ, z) is the probability for secondary electrons to reach the surface moving in the direction θ with the normal:

$$P(E,\theta ,z) = \exp \left\{ { - \left. {\frac{z}{\lambda (E)\cos \theta }} \right\}} \right.$$
(5.3)

Here λ (E) is the electron MFP in the solid. SEs can escape the surface if their energy exceeds a critical value of Ecr = Ef + Φ, measured from the bottom of the conduction band. Ef is the Fermi energy, and the relationship \(\theta < \arccos (p_{cr} /p)\) is used, where p is a momentum of electron and \(p_{cr} = \sqrt {2mE_{cr} }\) [23].

Using the fact that most SEs have energy at most 5–7 eV above the Fermi level, one can estimate the electron MFP to be between 1 and 5 nm according to the results of [26]. According to SRIM calculations [12], helium ion stopping power for most metals remains constant within the first 50 nm from the surface, being as low as about 100–300 eV/nm. Accordingly, the helium ion energy losses at the maximum depth of SE escape are not more than 5% of the initial ion energy and can be considered to be constant within the electron MFP, making the number of secondary electrons excited per unit energy independent of the depth, i.e. S(E,z) = S(E). Under these assumptions, SEED is given by the same expression as that obtained in [23]:

$$\frac{dN}{dE} = \frac{S(E)\lambda (E)}{4}\left[ {1 + \left( {\frac{{E_{f} +\Phi }}{E}} \right)} \right]$$
(5.4)

where E is measured from the bottom of the conduction band .

Since the transport mechanism of excited electrons to the surface is independent of the kind of excitation, the common expression for MFP obtained in [26] can be used:

$$\lambda (E)\sim \frac{E}{{(E - E_{f} )^{2} }}$$
(5.5)

Inserting (5.5) in (5.4) and denoting SE energy in a vacuum as Ese = E – Ef − Φ, one obtains:

$$\frac{dN}{dE}\sim S(E_{se} )\frac{{E_{se} }}{{(E_{se} +\Phi )^{2} }}$$
(5.6)

Energy distribution for excited electrons inside the solid S(E) depends on excitation mechanisms.

Chung and Everhart used the equation calculated by Baroody [27] for electrons to describe S(E):

$$S(E)\sim \frac{1}{{(E_{se} +\Phi )^{2} }}$$
(5.7)

which resulted in the dependence (5.2).

Because an explicit form S(E) for excitation of SEs by helium ions in HIM similar to (5.7) is not known, it was suggested in [25] to retrieve the shape of S(E) function S(E) from SEED experimental data. Since MFP of SE does not depend on the excitation mechanism, the function S(E) can be calculated as:

$$S(E)\sim \frac{dN}{dE}\frac{{(E_{se} +\Phi )^{2} }}{{E_{se} }}$$
(5.8)

The S(E) dependence calculated from experimental data [25] is presented in Fig. 5.6 on a double logarithmic scale where energy is measured from the Fermi level.

Fig. 5.6
figure 6

Energy distribution for electrons excited by helium ions inside three metals in HIM at 32 kV [25]

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One can see from Fig. 5.6 that, for all three metals, the dependences show a linear behavior in double logarithmic scale, reflecting a power dependence of:

$$S(E)\sim \frac{1}{{(E_{se} +\Phi )^{a} }}$$
(5.9)

where a = 3.3 ± 1 irrespective of material [25].

Thus, for SEED:

$$\frac{dN}{dE}\sim \frac{{E_{se} }}{{(E_{se} +\Phi )^{5.3} }}$$
(5.10)

Solid lines in Fig. 5.5 represent the theoretical shape of SEED for SEM according to (5.2) and for HIM according to (5.10) with b = 5.3. A good correspondence between the experimental data and the approximated formulas is evident.

The suggested phenomenological model describing the shape of the SEED for metals can be useful in different applications due to its explicit and simple analytic form.

The difference in the shape of the energy distribution for excited electrons inside a solid and the energy distribution for ions might be explained qualitatively by the distinguishing mechanism of ion–electron interaction. In fact, Monte Carlo simulation of SEED in the case of HIM performed by Ohya et al. [21] showed that SEED for HIM was narrower than SEED for SEM, which is in qualitative agreement with experimental results described before. However, direct comparison of SEED calculated in [21] with experimental data of [25] presented in one plot (Fig. 5.7) shows two noticeable discrepancies.

Fig. 5.7
figure 7

Comparison of experimental SEED [25] (dots) and simulation results from [21] (solid line)

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Firstly, the experimentally obtained SEED is narrower than the calculated one, and secondly, calculated SEED decreases to zero at 10 eV, whereas experimentally obtained SEED has a tail up to 15 eV.

The authors of [21] performed their calculations in the framework of a kinetic ion–electron emission model that included the processes of binary ion–electron collisions, of excitation of electrons by recoiled atoms and of electron cascades. But other ion–electron interaction processes, such as potential emission or Auger neutralization discussed above, were not taken into account, since in the ranges of ion energy in HIM, the kinetic emission is commonly understood to dominate [8].

Meanwhile, for the investigated materials, the work function values are about 5 eV, which gives an energy release in the Auger process of helium neutralization at the surface of about 15 eV, so the released energy is enough to excite SE. Thus, the tail of SEED extending up to 15 eV is expected.

In addition, such a processes can result in neutralization of helium ions even before entering the solid. Recent experiments of the impact of voltage bias on the spectra of backscattered ions in HIM [28] confirmed the existence of this neutralization process. This serves as an indirect confirmation of the presence of a potential emission mechanism at the surface of the metals in HIM. In addition, when neutral atoms penetrate into the solid they can also excite secondary electrons. Neutral atoms were shown to generate SEs, though with a lower mean energy than that of ions [29]. Thus, the fact that the experimentally observed SEED shape is narrower and shifted towards lower energies than that calculated based on a kinetic emission model [21] can also be explained as a result of ion neutralization.

Though potential emission and excitation of SE by neutrals are minor processes in ion–electron interaction, their contribution to SEED shape should be taken into account in future accurate calculations.

4 Imaging with SE

4.1 Topographic Yield

The most important application of SE imaging—revealing surface topography —is made possible because of the variation of SEY with the angle of incidence of the incoming beam to the surface. For electron irradiation, the SEY at some angle of incidence can be approximately related to the yield at normal incidence by the secant law [4]. This is valid for primary particles of sufficiently high energy when the electronic stopping power along the particle trajectory of SE generation is constant and there are no angular changes in the particle scattering or in the recoil atoms.

The topographic yield behavior in HIM was calculated in [9, 21, 22, 30] using somewhat different algorithms of Monte Carlo simulations. Earlier experimental data for some elements in the helium ion energy ranges of interest are also available [31, 32]. It has been shown that the shape of the angular dependence of the ion-induced SE yield varies with the ion primary energy and with the material atomic number and exactly follows the secant law only for light elements. Thus, special attention to the SE topography treatment is required to retrieve reliable data for metrological measurements of heavy elements in HIM.

4.2 SE2/SE1 Ratio

Secondary electrons can be excited by primary ions as well as by backscattered ions (BSI) . The ratio of SE excited by BSI is known as SE2. The presence of SE2 is the one of the main factors limiting the spatial resolution of SEM and HIM, because SE2 escapes from the region defined by the width of the interaction volume. In general, the SE2/SE1 ratio depends on the specimen material and on the ion energy. When energy of the primary ions increases, BSI energy also increases. As pointed out in the Sect. 5.2 of this chapter, the stopping power of the ions in HIM increases with energy, so the number of SE2 excited by BSI increases similarly to the number of SE1. At the same time, according to SRIM calculations the number of BSI decreases with the primary ion energy [12]. As a result of the two competitive processes, the energy dependence of SE2/SE1 ratio exhibits a maximum in the range from 10 to 100 keV [9]. According to numerical simulations, the value of this ratio for light elements is far below a unit, but for gold and heavier elements it can exceed one [9]. The latter fact seems to be in contradiction with the suggested energy dependence of SEY, because the energy of backscattered ions is less than the energy of primary ions and backscattering ion yield never exceeds unity. It can be explained due to particular trajectories of BSI (see Fig. 5.8). The number of SE2 per unit path of BSI is less than number of SE1 per unit path of primary ions, but the total length of BSI paths in the SE generation layer is longer due to deviation of those directions from normal. Thus, the number of SE2 which can escape from the sample (red arrows in Fig. 5.8) increases due to the distortion of the trajectories of backscattered ions.

Fig. 5.8
figure 8

Schematic of the trajectories of helium ions (green lines) and secondary electrons in solids. Blue and red arrows correspond to SE1 and SE2, respectively

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In general, SE1 and SE2 might have different energy distributions. An attempt to investigate this difference experimentally was performed by V. Mikhailovskii et al. [42]. SEED was measured from thin Pt films of different thicknesses deposited on a silicon substrate. The thickness of the Pt film was varied from 5 to 160 nm, which according to SRIM calculations [12] corresponds to the variation of backscattered ion yield by an order of magnitude. Experimentally, the measured SEED shape was found to be identical for films of different thicknesses within the measurement error indicating that SEED shape for SE2 does not significantly differ from that for SE1.

4.3 SE3

In addition to SE1 excited by primary ions and SE2 excited by BSI, the third kind of SE, SE3 , is generated by the ions backscattered from the sample that reach the chamber walls. Some amount of the BSI can immediately reach the SE detector window, but their contribution to the SE detector signal cannot be separated from the signal of SE3, and is formally included in the latter. Thus, the total signal from the ET detector, S, is proportional to the sum:

$$S = S_{SE1} + S_{SE2} + S_{SE3} = f_{1} (\gamma_{1} + \gamma_{2} \eta ) + f_{3} \gamma_{3} \eta$$
(5.11)

where γ1, γ2 and γ3 are the SEY of SE1, SE2 and SE3, respectively; η is the backscattering ion (BSI) yield of the sample; and f 1 and f 3 are the collection efficiency of SE1, SE2 and of SE3 with the detector; γ1 and γ2 are dependent on the material, while γ3 is not defined by the chamber material.

The SE detector collection efficiencies f 1, f 3 are largely defined, and can be varied, by the potential difference between the particular point of SE sources and ET detector, as well as, in part, by the local electric field configuration of the SE emitted surface.

Experimental measurements of the SE3 ratio were performed in [33] by means of the retarding field method, utilizing the fact that at sufficiently high retarding potential, the collection efficiency f 1 can be eliminated, since SEs generated by the sample (SE1 and SE2) come to be blocked, as schematically depicted in Fig. 5.9.

Fig. 5.9
figure 9

Schematic diagram of an SE3 detection set-up. Semi-spherical grid electrode 1 is installed above the positively biased specimen 2. Secondary electrons emitted from the specimen (blue arrows in Fig. 5.9) are attracted to the sample and do not reach the detector 3. Backscattered ions (green arrows in Fig. 5.9) can escape through the grid electrode due to their energy, and reach chamber walls and objective lens polar piece 4. Excited SE3 are detected with an ET detector whose signal is proportional to the number of backscattered ions

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According to (5.11), the contribution of SE3 to the detected signal depends on both BSI and SE yields of materials and increases with the atomic number of elements.

When comparing SE3 generation in SEM and HIM, one should note that variation in BSE yield with atomic number does not exceed a factor of 5 (it is typically from 0.1 to 0.5), whereas BSI yield can vary in significantly wider ranges, from 0.01 to 0.2. In addition, BSI yield in crystalline materials is affected more strongly by the channeling than that for electrons. As a result, the SE3 ratio can vary more strongly in HIM than in SEM, depending on the element and on the crystalline orientation.

The dependence of the ET detector signal on the retarding grid potential for two heavy polycrystalline metals is presented in Fig. 5.10.

Fig. 5.10
figure 10

Dependence of ET detector signal on retarding bias for Pt and Mo from [33]

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One can see from Fig. 5.10 that with the increase of the electron retarding potential, the SE signal measured by the ET detector tends to a constant value that is as high as about 10% of the total signal for both metals, despite one being twice the other in atomic mass and a corresponding difference in BSI yield. The nearly equal ratios of SE3 signals for Pt and Mo to the total SE signal can be explained by the similar character of the yield changes for BSI and for SE1 (but not of SE2) with the element atomic number resulting in a nearly constant value of the yield’s ratio. This assumption is valid until the product of the BSI yield and of the sum of SE and SE2 yields is less than that for SE1, as follows from:

$$\frac{{S_{SE3} }}{S} = \frac{{\gamma_{3} \eta }}{{\gamma_{1} (Z) + \gamma_{2} (Z)\eta + \gamma_{3} \eta }} = \frac{{\gamma_{3} }}{{\gamma_{1} (Z)/\eta + \gamma_{2} (Z) + \gamma_{3} }} \approx \frac{{\gamma_{3} }}{{\gamma_{1} (Z)/\eta }}$$
(5.12)

It seems to be that 10% is a roughly universal ratio value of SE3 signals in HIM for many materials.

A large ratio of SE3 signal to the total detected SE signal requires a careful interpretation of SE images. The impact of SE3 on imaging with the ET detector was demonstrated in [33] on a polycrystalline molybdenum sample. The result is presented in Fig. 5.11. An examination of the images of the same sample region obtained in HIM with the detection of all SEs, with the detection of SE3 (SEs with energies above 50 eV) and direct BSI detection with the standard HIM MCP detector reveals a striking resemblance.

Fig. 5.11
figure 11

HIM images of Mo with different detectors [30]: a MCP detector; b, c ET detector with 50 V or 0 V retarding potential on the retarding grid sphere, respectively. Field of view is 10 × 10 µm

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The SE3 (Fig. 5.11b) and MCP (Fig. 5.11a) images are practically identical, confirming that the origin of SEs with energies above 50 eV was indeed caused the BSI converted to SEs in the HIM stainless steel chamber beyond the retarding grid sphere. It was pointed out in [33] that the SE3 image exhibited an even better signal-to-noise ratio than the one obtained with MCP detector. Besides, the fact of high efficiency BSI-to-SE conversion by metals can be and was already used for the development of additional operation modes for HIM that will be discussed below.

Dark–bright contrasts on BSI images of the polished metal surface in Fig. 5.11 are believed to be due to the effect of ion channeling on the grain of different crystal orientations. Similar features can be also recognized on the SE image in Fig. 5.11c, indicating that the image obtained with the ET detector in the usual way is a composition of morphological and material contrasts. The contribution of SE3 to the SE image is expected to decrease with a decrease of atomic number and becomes negligible for Z < 10.

4.4 Material Characterization by SE Contrast Measurements with Energy Filtering

As shown above, the energy distribution of the SEs produced by the interaction of helium ions with a material can be described by an analytical function that depends mainly on two material parameters: its total ion-induced SEY and its work function . The value of the work function can be retrieved from fitting the experimentally obtained function shape with only one adjustable parameter. Unfortunately, the procedure of SEED data acquisition is time consuming and requires a rather big sample area with uniform properties to avoid carbon contamination during multiple scans with different retarding potential values. The common approach to characterize material properties microscopically is to evaluate the SE image contrast between two closely spaced sample regions with different values of surface potentials, as used in SEM [5, 34, 35] and recently, as well, in HIM [33, 36, 37]. SE contrast investigations in SEM have shown that SE energy filtration could increase the sensitivity and the precision of the potential measurements (for a recent review see [5]).

The explicit form describing the SEED shape (5.10) and the possibility of measuring SE3 contrast independently allow us to obtain analytical descriptions of the SE contrast changes between two materials [33] as a function of retarding grid potential, of material work function and of SEY. The energy-filtered SE signal under the application of retarding grid potential V can be calculated by the integration of:

$$S(\Phi ,\gamma ,V) = \int\limits_{{eV +\Delta \,\Phi }}^{\infty } {\frac{dN}{dE}} dE$$
(5.13)

where \(\frac{dN}{dE}\) is SEED normalized to the total SEY, \(\Delta \,\Phi =\Phi _{r} -\Phi\) , Φ, Φ r —material and retarding grid work function. SEED normalization factor can be calculated as the number of ions N i multiplied by the total SEY γ:

$$N_{i} \gamma = c\int\limits_{0}^{\infty } {\frac{E}{{(E +\Phi )^{a} }}dE}$$
(5.14)

where a = 5.3 in HIM for metals [25], but may have another value for insulators or semiconductors (note that in SEM a = 2 for metals [23] and a = 1 for insulators [38]).

That gives the final expression for SEED:

$$\frac{dN}{dE} = N_{i} \gamma (a - 1)(a - 2)\Phi ^{a - 2} \frac{E}{{(E +\Phi )^{a} }}$$
(5.15)

and the final expression for SE signal generated by the specimen:

$$S(\Phi ,\gamma ,V) = N{}_{i}\gamma \left( {\Phi ^{a - 2} \frac{{(a - 1)(eV +\Delta \,\Phi ) +\Phi }}{{(eV +\Phi _{r} )^{a - 1} }} \cdot\Theta (eV +\Delta \,\Phi ) +\Theta ( - eV -\Delta \,\Phi )} \right)$$
(5.16)

where \(\Theta (eV +\Delta \,\Phi )\) is the Heaviside function that is used to take into account that \(\frac{dN}{dE} = 0\) for E < 0.

The detected SE signal also contains the contribution of SE3 that is proportional to the number of backscattered ions that should be added to the SE signal (5.16) for further calculations:

$$S(\Phi \;,\gamma \;,\eta \;,V) = S(\Phi ,\gamma ,V) + N_{i} \eta k$$
(5.17)

where η is the backscattered ions yield of the sample and k is the SE3 excitation and collection efficiency that depends on detection geometry and the materials that the chamber is made of.

The SE contrast between two different materials with work functions Ф 1 , Ф 2 , SE yields γ 1 and γ 2 , and BSI yields η1 and η2 is defined as:

$$C = \frac{{S(\Phi _{1} ,\gamma {}_{1},\eta_{1} ,V) - S(\Phi _{2} ,\gamma {}_{2},\eta_{2} ,V)}}{{S(\Phi _{1} ,\gamma {}_{1},\eta_{1} ,V)}}$$
(5.18)

The shape of the SE contrast dependence on the retarding grid potential calculated according to (5.18) for γ 1  > γ 2 , Ф 1  > Ф 2 is shown in Fig. 5.12. In the absence of SE3 electrons generated by BSI from the sample, the SE contrast is due to SE1 electrons. It monotonically increases with the applied grid voltage and saturates at the value defined by the ratio of SEY and work function . At low retarding bias voltages, SE contrast behavior is similar to the SE1 contrast (solid line). In the presence of SE3, depending on the backscattered ion yield values and the ratio between the materials, two kind of the behavior might be distinguished. If η 2 /η 1  > γ 2 /γ 1 (Ф 2 /Ф 1 ) a−2, then the contrast can reach a higher value than for SE1 (dashed line in Fig. 5.12), otherwise a non-monotonic contrast behavior can be observed (dotted line in Fig. 5.12).

Fig. 5.12
figure 12

SE contrast between two different materials (γ 1  > γ 2 , Ф 1  > Ф 2 ) as a function of retarding potential calculated with (5.18) for three cases: η 1  = η 2  = 0 , SE1 contrast calculated with (1.16)—solid line; η 2 /η 1  < γ 2 /γ 1 (Ф 2 /Ф 1 ) a−2—dotted line, η 2 /η 1  > γ 2 /γ 1 (Ф 2 /Ф 1 ) a−2—dashed line

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The comparison of the experimentally determined dependence of the detected SE contrast between Pt and Mo polycrystalline samples vs. retarding potential with the theoretically calculated dependence was presented in [33] and is shown in Fig. 5.13. The ratio of SE3 and SE total yields were obtained from measurements with the applied bias voltage of 50 V and 0 V, respectively.

Fig. 5.13
figure 13

Relative contrast between Pt and Mo from [33], dots—experiment, solid line—fitting with (1.18)

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Good agreement with experimental data was demonstrated and work function values Ф Pt  = 4.9 eV and Ф Mo  = 4.5 eV obtained from fitting with (5.17) (solid line in Fig. 5.14) coincide well with handbook values.

Fig. 5.14
figure 14

HIM SE images of Pt film on Mo taken with 0 V (left) or with 10 V (right) retarding potential on the retarding grid. Field of view of each is 22.5 × 45 µm

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Energy-filtered images of Pt film (bottom part of the figure) on polycrystalline Mo (top part of the figure) are shown in Fig. 5.14. It is evident that the relative contrast between Pt and Mo is enhanced when a retarding bias of 10 V is applied. In addition, under the bias within the area of polycrystalline Mo, the contrast of different grains becomes more pronounced. This enhancement results from the ion channeling effect which decreases the number of BSI and consequently decreases the number of SE3. In the case of Pt film, grain size is much smaller than that of Mo, so a channeling contrast is not observed. It should be noted that relative contrast values between Pt and Mo plotted in Fig. 5.13 were obtained by averaging the signal over the large area of the sample.

5 Imaging Utilizing a High SE Yield in HIM: Ion-to-SE Conversion

A high helium ion-induced SEY from a heavy metal surface provides the possibility to effectively convert BSI to SE, and that in combination with conventional SE detectors can be used for developing new operating modes in HIM. The idea of utilizing such a conversion was described for the first time for backscattered electrons in SEM by Reimer [39]. Obviously, not only backscattered ions can be detected by means of conversion to secondary electrons but so can any ions scattered by the sample or transmitted through it. Recently, two new HIM imaging techniques were realized by using ion-to-electron conversion.

5.1 Scanning Transmission Ion Microscopy (STIM) with SE Detector

The sketch of the scanning transmission ion microscope that was recently proposed and realized by A. Hall [40] is depicted in Fig. 15.

Thin sample 1 is installed inside the shield 2 with an aperture 5 under the sample. The surface under the aperture 3 is covered with a material having a high secondary electron yield (for instance, platinum) and tilted towards the ET detector 4 to increase the number of SE and detection efficiency. Transmitted ions (green ray in Fig. 5.15) come through the aperture and excite SEs from the surface (right arrows in Fig. 5.15). The number of this SE is proportional to the number of transmitted ions. Secondary electrons excited from the sample are stopped with the shield around the sample. A retarding field can be applied between the sample and the shield to improve the efficiency of the shield.

Fig. 5.15
figure 15

Schematic diagram of scanning transmission ion microscope. See text for detailed description of the comprising elements

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The working principle of STIM is similar to STEM. The incident well-collimated ion beam goes through the thin sample without noticeable energy losses but changes the initial ion directions due to elastic scattering in the foil. The output aperture 5 limits spatial angle of the detected transmitted ions and, together with I-to-SE convertor 3, works as a bright field detector. This method of STIM detection was used for the imaging and for the in situ thickness definition of silicon nitride membranes [40]. It was shown that STIM was extremely sensitive for the thin film thickness measurements. The minimum thickness for silicon nitride that could be detected with STIM was about 5 nm, which corresponds to a surface density of 1.5 × 10−6 gcm−2.

5.2 Reflection Ion Microscopy

Another method utilizing conversion of scattered ions to secondary electrons that was introduced recently is scanning reflection ion microscopy (RIM) [41]. Reflection microscopy is a method that uses low angle scattered particles to form an image of a surface. The best results from reflection microscopy can be obtained in an ideal case of a strictly parallel incident beam. One of the main features of the HIM is a narrow beam convergence angle of about 0.5 mrad that is ten times less than the optimal beam convergence angle in SEM. That makes HIM very suitable for scanning reflection microscopy.

The RIM scheme suggested in [41] is depicted in Fig. 5.16.

Fig. 5.16
figure 16

Scheme of detection of reflected ions in the helium ion microscope [41]: 1—sample, 2—Pt-coated surface, 3—secondary electron detector, 4—SE grounded shield, 5—SE3 shield, 6—slit diaphragm

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Similarly to the case of STIM, reflected ions come through the aperture 6 and excite secondary electrons which, in turn, are detected with the ET detector 3. Platinum-coated surface 2 is used for RI-to-SE conversion. SE excited from the sample 1 and SE3 are stopped with the shields 4 and 5.

Numerous examples of STIM applications were presented in [41]. It was shown that imaging using an incident ion beam at low grazing angles is insensitive to the atomic number or to the density as well as to the resistivity of materials, and RIM contrast is determined by surface morphology only. In particular, it was shown [41] that RIM can be used for imaging of an insulating surface without charge compensation, as demonstrated by the RIM image of a mica surface (Fig. 5.17).

Fig. 5.17
figure 17

RIM image of a cleaved mica surface

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The reason for the insensitivity of RIM to surface charging is not exactly known. One can speculate that some amount of reflected ions neutralize during interaction with the sample surface, so reflected neutrals are not affected by the electric field of the charged surface. At the same time, the probability of neutralization at a charged insulating surface is less than that of a conductive surface because of the low concentration of electrons.

A simple theory of RIM image formation was developed that, in particular, enables us to quantify surface step heights from experimental data. Below is a short version of this theory. The incident beam is considered as an infinitely narrow one. Figure 5.18 represents the paths of incident and reflected ion beams in RIM and the designations in the figure caption are used in the following calculations.

Fig. 5.18
figure 18

Schematic diagram of incident and reflected ion paths from [41]. α is the angle between the specimen holder plane and a local detail of the specimen surface, \(\Theta _{0}\) is the grazing angle between the incident beam and the specimen plane, \(\Theta _{1}\) is the angle between the incident beam and a local detail of the specimen surface (\(\Theta _{1} =\Theta _{0} + \alpha\)), \(\Theta _{2}\) is the angle between the reflected beam and the specimen plane, \(\Delta {\kern 1pt}\Theta\) is the angular aperture of RI detection, \(\delta\Theta\) is the half width of the angular divergence of RI

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In RIM, the reflection coefficient, or reflected ion yield (RIY) , is defined as the number of reflected ions per incident ion, which depends on the incident and reflected angles, and will be notated as \(\eta (\Theta _{1} ,\Theta _{2} )\). Note that BSI yield is just RIY at the fixed angles of 90°. It was shown [41] that the RI signal, which is the number of SE per second measured by the ET detector, is determined by RIY, and its angular dependence, the angular distribution of the reflected ions and the angular aperture of the diaphragm can be expressed as follows:

$$S(\alpha ) = \frac{{N_{I} \gamma_{0} }}{2}\int\limits_{{\Theta _{0} - \frac{{\Delta \,\Theta }}{2}}}^{{\Theta _{0} + \frac{{\Delta \,\Theta }}{2}}} {\eta (\Theta _{0} + \alpha ,\,\Theta _{2} )\sin \,\Theta _{2} d\Theta _{2} }$$
(5.19)

where \(N_{I}\) is the number of primary ions per second, \(\gamma_{0} (\Theta _{2} )\)—secondary electron yield for a Pt-coated surface.

The dependence \(\eta (\Theta _{1} )\) for different materials as obtained [41] by Monte Carlo simulation with SRIM software [12] is presented in Fig. 5.19.

Fig. 5.19
figure 19

Dependence of reflection coefficient of 35 keV He+ on the grazing angle for different materials calculated in [41] by Monte Carlo simulation with SRIM software [12]

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As can be seen from Fig. 5.19, the RIY is a monotonic decreasing function of the grazing angle that tends to constant values and depends on the material atomic number when the grazing angle approaches 90°. In contrast, when \(\Theta _{1}\) approaches zero the RIY tends to unity independent of the material. This is because nearly all of the incident ions pass over the specimen surface.

When the sample surface is sufficiently smooth, i.e. the angular deviations of the reflected ions are so small that all of the reflected ions pass through the output diaphragm aperture and are collected with the ET detector, RI contrast is determined by the angular dependence of the reflection coefficient only. Under these conditions, the expression for the RI signal can be simplified as:

$$S(\Theta _{1} ) = N_{I} \gamma_{0} \eta_{0} (\Theta _{1} )$$
(5.20)

where \(\eta_{0} (\Theta _{1} )\) is the RI reflection coefficient as a function of the grazing angle.

In the case of a rough surface, where the angle between the incident beam and local points on the surface varies across a wide range, some part of the RI are stopped by the diaphragm or by the elements of the specimen surface (shadowing effect). An example of such a situation is presented in Fig. 5.20, where the SE and RI signal profiles taken across the eminence of a square bar shape of a height of 20 nm are shown.

Fig. 5.20
figure 20

a—signal profiles of secondary electrons (dashed line) and of reflected ions (solid line) across the silicon dioxide bar on silicon substrate measured as schematically shown in (b); red arrows mark the positions of upward (u) and downward (d) steps

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The edges of the bar are marked with arrows: the upward step and the edge of the downward step are marked with “u” and “d” correspondingly. The comparison of the SE profile (dashed line in Fig. 5.20a) and RI profile (solid line in Fig. 5.20a) reveal that the dark area in the RI image of the upward step was broader than the dark area in the SE image of the same step. The width of the bright area in the RI image of the downward step was found to be equal to the width of this area in the SE image.

A detailed calculation of the RI contrast at the upward and downward surface steps was presented in [41]. The shadowing effect and a finite aperture size result in dark areas on the image. These dark areas appear in the regions of a sample where \(\alpha > \frac{{\delta\Theta }}{2} + \frac{{{\Delta \varTheta }}}{4}\). It was shown that the height of the surface step could be calculated from the width of dark contrast in the RI image and the half width of the slit aperture as follows:

$$h = \frac{d}{{\cos\Theta _{0} + \frac{{\sin\Theta _{0} }}{{tg(\Theta _{0} +\Delta \,\Theta )}}}}$$
(5.21)

where d—is the width of the dark contrast.

The shadowing contrast formation mechanism describes the RI signal from particular parts of the sample which faced towards the incident ion beam. In the opposite case the primary beam does not hit the surface immediately and, accordingly, no RI signal can be obtained from the scattered ions, except in the vicinity of knobs with sharp edges where the ion transmission may contribute to the image contrast formation. The idea of transmission contrast formation is described in [41]. The reflection coefficient of the primary beam from the upper surface is denoted as \(\eta^{*} (\Theta _{1} ,\Theta _{2} )\). The asterisk is used to emphasize that the reflection coefficient near the step edge differs from the reflection coefficient of the thick sample surface. Near the step edge, some part of the incident beam penetrates through it with the probability \(\rho (\Theta _{1} ,\Theta _{3} )\) and hits the substrate at an angle \(\Theta _{3}\) that is assumed to be close to the angle of incidence, i.e. \(\Theta _{3} \approx\Theta _{1}\). The transmitted ions are reflected from the substrate with reflection coefficient \(\eta (\Theta _{3} ,\Theta _{2} )\). Using these designations, the total reflection coefficient can be written as:

$$\eta_{edge} (\Theta _{1} ,\Theta _{2} ) = \eta^{*} (\Theta _{1} ,\Theta _{2} ) + \rho (\Theta _{1} ,\Theta _{3} )\eta (\Theta _{3} ,\Theta _{2} )$$
(5.22)

Figure 5.21 shows dependence of reflection and transmission coefficients as functions of the distance from the rectangular step edge along the top surface from [41]. The ion transmission probability (dotted line in Fig. 5.21) decreases from unity when the ion beam is just at the step edge. On the other side, the ratio of the ions reflected from the upper surface (dashed line in Fig. 5.21) increases with the distance from step edge. The total reflection coefficient calculated with (5.22) (solid line in Fig. 5.21) exhibits a maximum at a distance of about 50 nm from the edge of the step, giving the bright contrast in the RI-image. The step height must be higher than \(h > x_{\hbox{min} } \tan\Theta _{1}\) to observe edge contrast.

Fig. 5.21
figure 21

Dependence of coefficients on the distance from the edge of the step: reflection coefficient from upper surface (dashed line), ion transmission probability (dotted line) and total reflection coefficient calculated with (5.10) (solid line) (angle of incidence is 10°) [41]

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The RI image formation mechanisms described above originate from ion scattering by the specimen relief and do not consider a possible impact of the surface potential produced by the interaction of the ions with the sample. Positive charging makes it impossible to use SE detection for imaging at both normal and at glancing ion incidence, but RI detection can be successfully used in this case. Generally, the angle of incidence changes due to the surface charging, so it should be taken into account for the metrology of the surface relief. As for accurate calculation of the step height from shadowing contrasts, it should be noted that the dependence of the width of a shadow on the angle of incidence according to (5.21) is rather weak for the experimental parameters used in RIM. In fact, a variation of the angle of incidence from 0° to 10° results in relative variation of the width of a shadow within few percentage points and does not affect the accuracy of the measurements.

6 Summary

Secondary electron generation is a very important process under both electron and helium ion bombardment, as their detection is the main imaging operation mode in SEM and HIM. In this chapter it was shown that there are several distinguishing features of that process in HIM caused by particular properties of ion–electron interaction in solids, such as a high total SE generation yield that might significantly exceed unity, a narrow SEED, and a low ratio of SE generated by backscattered ions, at least for the elements with atomic number less than that of gold. The properties give rise to enhanced potential contrast sensitivity, enabling easy conversion of incident helium ion fluxes into electron current that has been used to characterize samples in transmission and reflection ion microscopy.

The number of examples of the application of these properties is not very large, to date. In addition, there is a lack of experimental data about SEED in many materials, including semiconductors and insulators. There are also many issues that are due to be solved in the future, such as a theory of SE generation which could satisfactorily explain the shape of the SEED in HIM, quantitative understanding of neutralization processes of the ions of the energy ranges of interest and many others. Obviously it will take time…