Nano-optical Imaging and Spectroscopy of Single Semiconductor Quantum Constituents

Abstract

In this chapter, current progress in the instrumentation and measurements of aperture-based near-field scanning optical microscopy and its application to spectroscopic study of semiconductor nanostructures are described. The design and fabrication of the probe with regard to aperture quality and the efficiency of light propagation are carefully examined. The recent dramatic improvements in spatial resolution and optical throughput are demonstrated by single quantum dot spectroscopy.

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Introduction

The optical control of single electronic quantum states is the most fundamental and critical technique needed for the functioning of nano-optical devices and for the implementation of quantum-information processing. Semiconductor quantum dots (QDs), where electrons are confined in a nanoscale volume, are one of the promising candidates for a prototype of such quantum systems due to their atom-like density of states, long duration of coherence [1, 2] (narrow transition linewidth [3–5]), and strong interaction between confined carriers. So far, as a result of these specific properties in QDs, optical manipulations of single quantum states such as qubit rotations [6, 7], optically induced entanglement [8], and single-photon turnstile [9] are realized in well-characterized QD systems including interface QDs formed in a narrow quantum well and self-assembled QDs grown in Stranski–Krastanov mode.

Conventional far-field optical techniques are unsatisfactory for exploring and addressing these individual nanoscale systems in terms of spatial resolution, which is limited to half the wavelength of used light due to the diffraction limit. Probing systems with fixed apertures or with mesa structures is a useful solution for isolating single quantum constituents, but the imaging ability is sacrificed. Near-field scanning optical microscopy (NSOM), where single systems are observed through a small aperture at the end of a scanning probe, is a more powerful tool for locally accessing individual QDs and obtaining spatial information [10–12]. By achieving spatial resolution higher than 50 nm with reasonable sensitivity for spectroscopic measurements, we are able to explore internal structures of QDs; real-space mapping out of wave functions of electrons and holes (excitons) confined in the QDs.

The combination of femtosecond spectroscopy with NSOM offers new perspectives for the direct investigation of carrier dynamics [13, 14] and the local manipulation of electronic quantum states [15, 16] on the nanometer length scale. Time-resolved optical spectroscopy also provides a wealth of information on dynamic processes like the phase and energy relaxation of carriers. Real-space diffusion, trapping, and relaxation processes of photogenerated carriers in low-dimensional semiconductors are of interest from the viewpoint of fundamental physics as well as with regard to potential device applications. Moreover, coherent control of electronic excitation of the quantum-confined system is of great importance because of its possible application in quantum-information processing such as quantum computation, as described above.

In this chapter, current progress in the instrumentation and measurements of NSOM and its application to imaging spectroscopy of single quantum constituents are described. The most critical element in NSOM is an aperture probe, which is a tapered and metal-coated optical fiber. We examine the design and fabrication of the probe with regard to aperture quality and the efficiency of light propagation. The recent dramatic improvements in spatial resolution and optical throughput are illustrated by single quantum dot spectroscopy, which reveals the intrinsic nature of quantum-confined systems. Beyond such an application, real-space mapping of exciton wave functions confined in a quantum dot is also demonstrated.

General Description of NSOM

When a small object is illuminated, its fine structures with high spatial frequency generate a localized field that decays exponentially normal to the object. This evanescent field on the tiny substructure can be used as a local source of light illuminating and scanning a sample surface so close that the light interacts with the sample without diffracting. There are two methods by which a localized optical field suitable for NSOM can be generated. As illustrated in Fig. 10.1a, one method uses a small aperture at the apex of a tapered optical fiber coated with metal. Light sent down the fiber probe and through the aperture illuminates a small area on the sample surface. The fundamental spatial resolution of so-called aperture NSOM is determined by the diameter of the aperture, which ranges from 10 to 100 nm [10].

In the other method, called apertureless (or scattering) NSOM and illustrated in Fig. 10.1b, a strongly confined optical field is created by external illumination at the apex of a sharpened metal or dielectric tip [12]. Spatial resolution approaching the atomic scale is expected, and laboratory experiments have yielded resolutions ranging from 1 to 20 nm. A rather large (diffraction limited) laser spot focused on a tip apex frequently causes an intense background that reduces the signal-to-noise ratio. This contrasts with what is done in aperture NSOM, where the aperture serves as a localized light source without any background. The general applicability of the apertureless method to a wide range of samples is currently being investigated.

Fig. 10.1

Schematic illustration of (a) aperture NSOM and (b) apertureless (scattering) NSOM. (c) Schematic of standard NSOM setup with a local illumination and local collection configuration

The simplest setup for aperture NSOM, a configuration with local illumination and local collection of light through an aperture, is illustrated in Fig. 10.1c. The probe quality and the regulation system for tip-sample feedback are critical to NSOM performance, and most NSOMs use a method similar to that used in an atomic force microscope (AFM), called shear-force feedback, the regulation range of which is 0–20 nm. The light emitted by the aperture interacts with the sample locally. It can be absorbed, scattered, or phase-shifted, or it can excite fluorescence. Which of these occurs depends on the sample and produces contrast in the optical images. In any case, light emerging from the interaction volume must be collected as efficiently as possible. When the sample is prepared on a transparent substrate, signal light is frequently collected with an objective lens arranged in a transmission configuration.

Design, Fabrication, and Evaluation of NSOM Aperture Probes

Basic Process of Aperture Probe Fabrication

Great efforts have been devoted to the fabrication of the aperture probe, which is the heart of NSOM. Since the quality of the probe determines the spatial resolution and sensitivity of the measurements, tip fabrication remains of major interest in the development of NSOM. The fabrication of fiber-based optical probes can be divided into the three main steps illustrated in Fig. 10.2: (a) the creation of a tapered structure with a sharp apex, (b) the coating with a metal (Al, Au, Ag) to obtain an entirely opaque film on the probe, and (c) the formation of a small aperture at the apex.

Fig. 10.2

Fabrication of an aperture NSOM probe: creation of the taper structure, metallization of an exterior surface, and formation of the aperture at the apex. The inset shows scanning electron micrographs of 50- and 70-nm apertures made by the impact method

There are two methods used to make tapered optical fibers with a sharp tip and reasonable cone angle. One is the heating-and-pulling method, where the fiber is locally heated using a CO₂ laser and is subsequently pulled apart [17]. The other method, based on chemical etching in a hydrofluoric acid (HF) solution, is a more easily reproducible production and can be used to make many probes at the same time [18, 19]. To realize the ideal taper structures of the sort that will be discussed below, the chemical-etching method is advantageous because the taper angle can be adjusted by changing the composition of a buffered HF solution. Another important advantage of the chemical-etching method is the excellent stability of the polarization state of the probe. When the heating-and-pulling method is used, in contrast, temporal fluctuation of polarization occurs due to the relaxation of strain induced by the production process.

The technique most often used to form a small aperture is based on the geometrical shadowing method used in the evaporation of metal. Since the metal is evaporated at an angle from behind, the coating rate at the apex is much slower than that on the sides. The evaporated metal film generally has a grainy texture, resulting in an irregularly shaped aperture with asymmetric polarization behavior. The grains also increase the distance between the aperture and the sample, not only degrading resolution, but also reducing the intensity of the local excitation. A method for making a high-definition aperture probe by milling and polishing using a focused ion beam has been developed [20], as has a simple method based on the mechanical impact of the tip on a suitable surface [21]. In both methods, the resulting probe has a flat end and a well-defined circular aperture. Furthermore, the impact method assures that the aperture plane is strictly parallel to the sample surface, which is important in minimizing the distance between the aperture and the sample surface.

Tapered Structure and Optical Throughput

Improvement of the optical transmission efficiency (throughput) and collection efficiency of aperture probes is the most important issue to be addressed for the application of NSOM in the spectroscopic studies of nanostructures. In addition to contributing to the high sensitivity of NSOM measurements, optical probes with high throughput will open up attractive new areas of research, such as nonlinear processes and optical manufacturing on the nanometer scale. It is therefore of great importance to understand the limitations and possibilities of aperture probes with respect to light transmission.

The tapered region of the aperture probe operates as a metal–clad optical waveguide. The mode structure in a metallic waveguide is completely different from that in an unperturbed fiber and is characterized by the cutoff diameter and absorption coefficient of the cladding metal. Theoretical and systematic experimental studies have confirmed that the transmission efficiency of the propagating mode decreases in the region where the core diameter is smaller than half the wavelength of the light in the core (Fig. 10.3) [22]. The power that is actually delivered to the aperture depends on the distance between the aperture plane and the plane in which the probe diameter is equal to the cutoff diameter, which distance is determined by the cone angle of the taper. We therefore proposed a double-tapered structure with a large cone angle [22]. This structure is easily realized using a multistep chemical-etching technique, as will be described below. With this technique, the transmission efficiency is much improved by two orders of magnitude as compared to the single-tapered probe with a small cone angle [21, 22].

Fig. 10.3

Mode propagation in a tapered optical fiber probe coated with a perfect conductor at a wavelength of 633 nm

Simulation-Based Design of a Tapered Structure

Further optimization of the tapered structure is needed to achieve much higher probe efficiency. However, it is very time-consuming to assess many structure parameters, such as the cone angle and taper length, by trial and error. Numerical analysis is a more reasonable way to attain an optimized structure efficiently and to understand the electromagnetic field distribution in a tapered waveguide including the vicinity of the aperture. Computational calculation by the finite-difference time-domain (FDTD) method is the most popular and promising method available for this purpose, because it can be easily applied to actual three-dimensional problems [23]. Although there have been many simulations focusing on the electric field distribution in the vicinity of the aperture to examine the spatial resolution of NSOM, no calculations have been reported that deal with the light propagation in the tapered region in terms of the sensitivity of the probe. Here, using the three-dimensional FDTD method, we demonstrate the high collection efficiency of double-tapered probes including guiding optical fibers, as compared with single-tapered probes [24]. We also describe in detail the dependence of the collection efficiency on the cone angle and taper length.

Figure 10.4 illustrates the cross-sectional view of the FDTD geometry of the three-dimensional problem, which reproduces the experimental situation of single quantum-dot imaging. A fiber probe with a double- or single-tapered structure collects luminescence (λ = 1 μm) from a quantum dot buried 3λ ∕ 40 beneath the semiconductor (GaAs; n = 3. 5) surface. We assume that the source of luminescence is a point-like dipole current linearly polarized along the x direction. The radiation caught by the aperture with a diameter of λ ∕ 5 propagates in the tapered region clad with a perfectly conducting metal and then is guided to the optical fiber waveguide. The refractive indices of the core and cladding of the fiber are 1. 487 and 1. 450, respectively. The intensity of the collected signal, I _coll, is evaluated by two-dimensionally integrating the electric field intensity in the core area of the optical fiber. The simulation box consists of a 120 ×120 ×360 grid in the x, y, and z directions; the space increment is λ ∕ 40. We run the simulation employing Mur’s boundary condition.

Fig. 10.4

Cross-sectional view of the FDTD geometry of the three-dimensional NSOM model

To demonstrate the performance of the double-tapered probe, we performed calculations for three types of probes, as shown in Fig. 10.5, where the spatial distribution of the electric field intensity is shown on a logarithmic scale. In Fig. 10.5a, b, I _coll is compared for probes with $\theta = 2{8}^{\circ }$ and $\theta = 9{0}^{\circ }$. The I _coll ratio is estimated to be 1:32. Such a distinct improvement in I _coll can be attributed to the difference in the length of the cutoff region. By making the cone angle large and shortening the cutoff region, we can direct much of the radiation power towards the tapered region. Figure 10.5c shows the calculation result in the case of a double-tapered probe whose cone angle is the same as in Fig. 10.5b. The neck diameter D is assumed to be λ, which is threefold the cutoff diameter of the cylindrical waveguide clad with a perfectly conducting metal. I _coll of Fig. 10.5c is found to be three times greater than I _coll in Fig. 10.5b. The radiation pattern in Fig. 10.5c clearly illustrates that the second tapered region modifies the wave front of the propagating light to match the guiding mode of the optical fiber, while the spherical-wave-like propagation in Fig. 10.5b cannot be coupled to the guiding mode so efficiently. To summarize, the collection efficiency of the double-tapered probe in Fig. 10.5c is greater by two orders than that of the conventional single-tapered probe in Fig. 10.5a.

Fig. 10.5

Calculated distribution of the electric field intensity for three types of probes. (a) Single-tapered probe with a cone angle $\theta = 2{8}^{\circ }$, (b) single-tapered probe with $\theta = 9{0}^{\circ }$, and (c) double-tapered probe with $\theta = 9{0}^{\circ }$ and neck diameter D = λ

Although we have demonstrated the advantage of a double-tapered probe, its performance is also dependent on various structure parameters. In Fig. 10.6a, b, the values of I _coll as a function of cone angle θ and neck diameter D, respectively, are plotted. The enhancement of I _coll with the increase in θ is easy to understand. I _coll will increase monotonously as θ approaches $18{0}^{\circ }$. In the case of a realistic metal aperture, however, a large θ will cause diminished spatial resolution due to the finite skin depth of the metal. The optimum value of θ should be chosen by balancing the collection efficiency with the spatial resolution. As depicted in Fig. 10.6b, the dependence of I _coll on D is found to be more complicated and seems to be less essential. One significant result is that a neck diameter D as small as 3d _c ∕ 2 is preferable compared with a diameter of 3d _c to attain high efficiency in coupling to the guiding mode of the optical fiber.

Fig. 10.6

Plots of the intensity of collected light as a function of (a) cone angle θ and (b) neck diameter D

Fabrication of a Double-Tapered Aperture Probe

We used a chemical-etching process with buffered HF solution to fabricate the double-tapered probe. Since the details of probe fabrication with selective etching are described in Ref. [18], we describe the process only briefly here. The cone angle θ can be controlled by the buffering condition of the etching solution, which is adjusted by the volume ratio X of NH₄F maintaining the proportion of HF to H₂O at 1:1. Here, the composition of the solution is expressed as X:1:1. A two-step etching process is employed to make a double-tapered probe, as shown in Fig. 10.7a. In the first step, using a solution with a composition of X = 1. 8, a short tip with a large cone angle of $15{0}^{\circ }$ is fabricated. Second, the guiding region is obtained with a solution of X = 10. As shown in the scanning electron micrograph of Fig. 10.7b, the resultant cone angle is approximately $9{0}^{\circ }$. The neck diameter D can be controlled by the etching time in the second step.

The next step for metal coating and aperture formation is summarized in Fig. 10.8a. The entire exterior surface of the etched probe was metal-coated with an Au film 200 nm in thickness using a sputtering coating method. A small aperture was created by pounding the metal-coated probe on a sapphire substrate or on the sample itself and squeezing the Au off to the side. Figure 10.8b shows a scanning electron micrograph of the 70-nm aperture, taken after conducting photoluminescence (PL) imaging several times. Not only a smooth and flat end face but also a round and well-defined aperture was obtained in this fabrication process. As mentioned above, the aperture plane is parallel to the sample surface to minimize the distance between the aperture and the sample surface. The size of the aperture can be selected by carefully monitoring the intensity of light transmitting from the apex, since the throughput of the probe is strictly dependent on the aperture diameter. Such controllability in aperture formation is demonstrated in the scanning electron micrographs of ultrasmall apertures in Fig. 10.9.

Fig. 10.7

(a) Two-step chemical etching for the fabrication of a double-tapered fiber probe. (b) Scanning electron micrograph of a double-tapered probe

Fig. 10.8

(a) Process for coating the tapered probe with metal and formation of an aperture. (b) Scanning electron micrograph of the aperture with a diameter of 70 nm

Fig. 10.9

Scanning electron micrographs of (a) an entirely metal-coated probe and an apertured probe with aperture diameters of (b) 15 nm, (c) 30 nm, and (d) 50 nm

Evaluation of Transmission Efficiency and Collection Efficiency

To evaluate the transmission efficiency of aperture probes, researchers often measure the light power emitted by the aperture in the far-field region. However, in many experimental situations, the instantaneous electric fields are dominant in the interaction between light and matter. Thus, the far-field transmission coefficient (the ratio of the far-field light power emitted by the aperture to the power coupled into the fiber) does not reflect the field enhancement in the near-field region. However, in comparing probes with the same aperture diameter in terms of the transmission efficiency in tapered regions, the far-field transmission coefficient can be valuable information.

In Fig. 10.10 the transmission coefficient is plotted against the aperture diameter for conventional single-tapered probes and for double-tapered probes with cone angles of $6{0}^{\circ }$ and $9{0}^{\circ }$. As a light source for the measurement, we used a He–Ne laser (λ = 633 nm). It is clear that the transmission efficiency of the double-tapered structure with a large cone angle is improved by two orders of magnitude greater than that of the single-tapered probe with a small cone angle. In the case of a 100-nm aperture, the transmission coefficient is as large as 10^{− 2}. The reduction of the throughput with a decrease of aperture diameter is not so severe as predicted by Bethe’s theory, where the throughput must be proportional to d ⁻⁶ (d: aperture diameter) [25]. Thus, we obtain reasonable illumination intensity even in the case of a 10- to 30-nm aperture.

Fig. 10.10

Plots of the transmission coefficient of an aperture probe as a function of aperture diameter for single-tapered and double-tapered probes with cone angles of 60$^{\circ }$ and 90$^{\circ }$. A He–Ne laser with a wavelength of 633 nm was used for this measurement

In addition to a high throughput for efficient illumination of light, superior collection of the locally emitted signal is critical for the observation of opaque materials such as semiconductors. We checked the collection efficiency of a 70-nm aperture probe quantitatively by collecting PL from an InGaAs QD buried 70 nm beneath the surface. We compared the PL intensity collected by the aperture probe with that collected simultaneously by an objective with a numerical aperture of 0. 8 (Fig. 10.11 inset). In Fig. 10.11, the PL signal intensities are plotted as a function of distance between the aperture and the sample surface. Within 15 nm of the surface, the amount of light collected by the aperture probe increases rapidly and reaches a value as great as the amount collected by an objective with a numerical aperture of 0. 8. This suggests that fabrication of the flat-ended probe makes a considerable contribution to the efficient interaction of the aperture and evanescent field in the vicinity of the sample.

Fig. 10.11

Comparison of collection efficiency of an objective (open circles) and a probe with a 70-nm aperture (closed circles). Photoluminescence intensities collected from a single quantum dot are plotted as a function of distance between the aperture and the surface

The overall throughput (or collection efficiency) of light is determined by various factors such as the wavelength of propagating light and the corresponding dielectric constant of the cladding metal, as well as by the structure of unperturbed fiber. The FDTD simulation of light propagation is a useful and efficient way to obtain the information needed to make an optimized structure.

Evaluation of Spatial Resolution with Single Quantum Dots

Fluorescence imaging of point-like emission sources is the most straightforward and reliable method for evaluating the spatial resolution of a probe. In particular, semiconductor quantum dots are most suitable in terms of their sizes, quantum efficiency, and optical stability. We evaluated the spatial resolution for various aperture diameters by PL imaging of single InAs self-assembled QDs [26]. The typical lateral size and height of the dots were 22 and 3 nm, respectively. The thickness of the GaAs cap layer, which determines the achievable spatial resolution, is of critical importance. While a thinner cap layer contributes to the higher resolution, it also causes the degradation of the optical quality of the QDs [4, 27]. We used the QD sample with a cap layer of 20-nm thickness, taking into account the balance between the achievable spatial resolution and the optical quality.

By illuminating the sample with diode laser light (λ = 685 nm) through the aperture, we generated most of the carriers in a barrier layer surrounding the QDs. After diffusing in the barrier layer, the carriers were captured in the confined states of QDs. The PL signal from a single QD was collected by the same aperture. All of the measurements were performed at 9 K in a cryostat. The tapered structure, defined by a cone angle ($\theta = 9{0}^{\circ }$) and a neck diameter (D = 1 μm), was optimized from the viewpoint of both the optical throughput and the spatial resolution, based on the results of FDTD simulation.

Fig. 10.12

Low-temperature near-field PL images of InAs QDs, obtained by using the probes with aperture diameters of (a) 135 nm, (b) 75 nm, and (c) 30 nm, respectively. (d) Cross-sectional PL intensity profiles of the spots indicated by the arrows

Figure 10.12a–c show the low-temperature PL images of InAs QDs obtained (center photon energy E = 1. 33 eV, ΔE = 60 meV) by the apertures with diameters of 135, 75, and 30 nm, respectively. The individual bright spots correspond to the PL signal from single QDs. The size of each spot becomes smaller with a decrease of the aperture diameter employed. To evaluate the spatial resolution in Fig. 10.12c, we plotted the cross-sectional profiles of PL signal intensity for the spots indicated by arrows in Fig. 10.12d. Full width at half maximum (FWHM) of the PL signal profile was 37 ± 2 nm. Taking into account the size of QD (22 nm), we estimated the spatial resolution of this measurement to be about 30 nm, which corresponds to λ ∕ 30. In the illumination–collection mode operation of NSOM, the small aperture plays roles in both excitation and collection of the PL signal. In the case of carrier generation in the barrier layer, however, the excitation process does not contribute to such a high spatial resolution due to the carrier diffusion in several hundreds nanometers. We conclude that high resolution could be achieved solely by the collection process of the PL signal.

Fig. 10.13

PL spot diameter as a function of aperture size. The aperture size of 0 nm means that the probe does not have a physical aperture (entirely metal-coated probe)

We carried out the same measurements as described above for other probes and evaluated PL spot size as a function of aperture diameter, as shown in Fig. 10.13. The aperture size of 0 nm means that there is no physical aperture at the apex, which was obtained by stopping the pounding procedure just before opening the aperture. In spite of the lack of physical aperture, we could detect reasonable intensity of the PL signal and image with a resolution of 75 nm. Except for the 0-nm aperture, the spatial resolution is monotonously enhanced with a decrease of the aperture diameter. The spatial resolution is almost equal to the aperture diameter, whose behavior is also reproduced well by the FDTD simulation.

Super-resolution in Single Molecule Detection

NSOM fluorescence measurements are the simplest and most informative method because they provide high-contrast imaging of nanostructures, revealing the chemical composition and molecular structure as well as the defects and dopants in semiconductors. High-resolution optical imaging of biological samples with fluorescence labels is also a promising field of application. NSOM has the potential to create images of the distribution of such labels down to the level of single fluorophores. Furthermore, the presence of the probe (metal aperture) alters the fluorescence lifetime and emission pattern, making it possible to control radiation in the immediate vicinity of the probe (i.e., locally within the nanoenvironment).

Although NSOM offers attractive possibilities with regard to the detection of single molecules, the current spatial resolution of 100 nm is not sufficient for application to actual biological samples. Imaging with a very small aperture ( < 30 nm) has often been impossible because the transmission efficiency decreases drastically with aperture diameter. Moreover, even a small grain on the aperture plane is problematic because the consequent increase of the aperture–sample distance reduces the spatial resolution. As mentioned in the previous section, however, the development of tailored probes with a high-quality aperture has solved this problem.

We have made fluorescence images of single dye molecules by using an aperture significantly smaller than that usually employed [28]. Cy5.5 dye molecules were dispersed on a quartz substrate and illuminated by He–Ne laser light through an aperture made of gold. The fluorescence from a single molecule was collected by the same aperture or by an objective in transmission configuration. Figure 10.14a shows a typical fluorescence image of individual molecules, and Fig. 10.14b is magnified views of some of the bright spots in Fig. 10.14a. The diameter of each spot was estimated to be 30 nm, which corresponds to the aperture diameter produced by using the impact method. Steplike digital bleaching, which occurred at the moment indicated by the arrow, confirms that we actually observed single molecules. The highest resolution we achieved by using an aperture with a diameter of approximately 10 nm is shown in Fig. 10.15. The diameter of the fluorescence spot was as small as 10 nm.

Fig. 10.14

(a) Typical near-field fluorescence image of single dye molecules. (b) Magnified view of one of the bright spots in part (a). Irreversible photobleaching occurred at the moment indicated by the arrow

Fig. 10.15

(a) One of the highest-resolution images obtained by using a 10-nm aperture. (b) and (c) Magnified view of two of the bright spots in part (a)

The spatial resolution of 10 nm achieved in the experiment is inconsistent with conventional NSOM resolution; the optical spot generated at the aperture should be larger than the physical aperture diameter because of the finite penetration of light into the coated metal. When we use a gold-coated probe with a cone angle of $9{0}^{\circ }$, the spatial resolution (spot size) should be limited to 30 nm at λ = 633 nm even in the case of a 10-nm aperture. To examine this discrepancy, we used FDTD calculation to take into account a realistic situation, including the complex dielectric function of the gold film. Figure 10.16a shows the model for calculation. The radiation (λ = 633 nm) from a point dipole current, oscillating in the x direction, propagates in the tapered region, and then a small light spot is created by the aperture. The cone angle is $9{0}^{\circ }$, and the aperture diameter is 10 nm. The simulation box is 500 nm × 500 nm × 425 nm in the x, y, and z directions, respectively, and the space increment is 2. 5 nm. Figure 10.16b shows the cross-sectional profile of the electric field intensity along the x direction 5 nm below the aperture. The twin-peak structure comes from the enhancement of the electric field at the edge of the aperture. The spot size, which is defined as a full width at half maximum of the profile, is estimated to be 16 nm. In Fig. 10.17, calculated spot sizes are plotted as a function of the aperture diameter. While we could expect to achieve 10-nm resolution from this simulation, a contribution of another mechanism, such as energy transfer from an excited molecule to the metal aperture, is also possible [29]. When the molecule is beneath the metal coating, the energy transfer shortens the fluorescence decay time and thus reduces emission intensity dramatically. On the other hand, no energy is transferred when the molecule is below the aperture hollow. Because the interaction distance in the process of energy transfer is only a few nanometers, we expect to reach a spatial resolution of less than 10 nm.

Fig. 10.16

(a) Simulation model for a gold-coated probe with a 10-nm aperture. (b) Cross-sectional profile of the electric field intensity along the x direction 5 nm below the aperture

Fig. 10.17

Plot of calculated spot sizes (spatial resolution) as a function of the aperture diameter

Single Quantum-Dot Spectroscopy

With the recent progress in the nanostructuring of semiconductor materials and in the applications of these nanostructured materials in optoelectronics, near-field optical microscopy and spectroscopy have become important tools for determining the local optical properties of these structures. In single quantum-dot spectroscopy, NSOM provides access to individual QDs, an ensemble of which exhibits inhomogeneous broadening due to the wide intra-ensemble distribution of sizes and strains [4, 5, 30–35]. NSOM can thus elucidate the nature of QDs, including the narrow optical transition arising from the atom-like discrete density of states and the line broadening due to the interaction with phonons and/or carriers.

Homogeneous Linewidth and Carrier–Phonon Interaction

The electronic and optical quality of semiconductor QDs has been improved remarkably by using the Stranski–Krastanov growth mode. Owing to the atom-like density of states caused by the three-dimensional nanoscale confinement, the improvement of laser device performance such as ultralow threshold current and ultrahigh gain characteristics is theoretically predicted. Not only in terms of the device applications but also because of its fundamental physics, the QD is an interesting system due to its novel electronic and optical properties. The linewidth of PL or the absorption spectrum is one of the most fundamental and important parameters of these properties. There are intrinsic and extrinsic mechanisms responsible for the spectral broadening in semiconductor QDs. The former is homogeneous linewidth broadening, which is determined by the dephasing processes in electronic systems. The electron–phonon interactions, lifetime broadening, and carrier–carrier interactions are considered to cause the homogeneous broadening. The latter is inhomogeneous linewidth broadening due to the fluctuation in size, shape, and strain distribution of QD ensembles. Such inhomogeneity leads to variation in the optical transition energy from dot to dot and prevents us from understanding its intrinsic properties.

From the viewpoint of device applications, the homogeneous linewidth at room temperature is of great interest. The several mechanisms for linewidth broadening at high temperature such as carrier–carrier interaction [36] and carrier–phonon interaction [37] have been investigated by theoretical consideration. Compared with cryogenic measurement, however, single-QD PL spectroscopy at room temperature is technically more difficult, since the PL intensity decreases by a few orders due to the escape of carriers to the nonradiative recombination paths and/or thermal excitation to the barrier layer. For that reason, researchers have not yet reported the detailed experimental results of homogeneous linewidth broadening or the comparison between the experimental and the theoretical calculation results at high temperature.

In our single-QD PL spectroscopy study performed over a wide temperature range from 10 to 300 K, we observed that the spectral homogeneous linewidth increases with temperature, and it finally reaches a level greater than 10 meV at 300 K. We also found a correlation between the homogeneous linewidth and the inter-level spacing energy. These measured properties can be explained by theoretical calculations considering the electron–longitudinal optical (LO) phonon and electron–longitudinal acoustic (LA) phonon interactions [38].

The samples investigated in this study were In_{0. 5}Ga_{0. 5}As self-assembled QDs grown on GaAs (100) substrate fabricated by gas source molecular beam epitaxy [39]. The substrate was not rotated during growth of the QDs to create a gradient in the QD density. There were 70-nm thick cap layers covering the QDs. In order to achieve isolation of a single QD, we measured the region over the wafer where the density of the QDs was from 10⁸ to 10⁹ cm^{− 2}. The typical lateral size and height of the dots were 32 ± 6 and 8 ± 2 nm, respectively, as measured by means of an atomic force microscope.

The QD sample on the scanning stage was illuminated with a laser diode (λ = 687 nm) through an aperture of the fiber probe under shear-force feedback control. The PL measurements were performed in the illumination and collection hybrid mode to prevent a decrease in spatial resolution due to carrier diffusion. The collected PL signal was sent into a monochromator equipped with a cooled charge-coupled device (CCD). The spectral resolution of this measurement was about 1. 5 meV. The NSOM head was mounted in a temperature-controlled cryostat.

Figure 10.18a shows the ground-state emission of single QDs under weak excitation conditions at various temperatures. The excitation power density was kept at a sufficiently low level, where the average number of photoexcited electron–hole pairs (excitons) is less than one in the dot. Under these excitation conditions, the additional PL linewidth broadening due to carrier–carrier interaction does not occur [40, 41]. As shown in Fig. 10.18a, the PL spectrum is sharp at 8 K and the full width of half maximum (FWHM) of the spectrum is 1. 5 meV, which is restricted by the spectral resolution in our instrumental response. The real PL linewidth is thought to be much narrower than 1. 5 meV, as reported by other groups. The PL spectrum slightly broadens at 96 K, and the line shape can be reproduced by the Lorentzian function indicated by the fitting line. The FWHM of the PL spectrum, which corresponds to the homogeneous linewidth, is about 4 meV. With a further increase in temperature up to 250 K, the PL linewidth reaches approximately 10 meV. To demonstrate the linewidth variation from dot to dot, we measured the PL spectra of three different QDs at 250 K, as shown in Fig. 10.18b. The FWHM varies from 8. 5 to 11 meV, and this type of variation of the spectral linewidths has also been reported [42].

Fig. 10.18

(a) PL spectra of InGaAs single QDs under low excitation conditions at various temperatures. Smooth lines correspond to the Lorentzian function. (b) PL spectra of three different QDs at 250 K

Figure 10.19 shows the temperature dependence of the PL linewidths of single QDs from 8 to 300 K. We measured the PL spectra of several different QDs at various temperatures and plotted the experimental PL linewidths as open circles. Below 60 K, the PL linewidths are less than 1. 5 meV. With an increase in temperature, the PL linewidth gradually broadens and finally becomes larger than 10 meV at 300 K. We compared this experimental finding with the results obtained by theoretical calculation. Our theoretical approach is fundamentally based upon the Kadanoff–Baym–Keldysh nonequilibrium Green’s function technique [43]. The carriers interacting with phonons have a finite lifetime and violate a unique relation between the carrier energy and its wave vector. The spectral function is used to describe the relationship between them. To simplify the discussion, we consider only the lowest energy levels of the confined electron and the hole inside the quantum box. The LO phonon and LA phonon are assumed to be confined in the QD as well as the electron and the hole. We have plotted the calculation results in Fig. 10.21 as the solid squares and solid triangles, which correspond to the results considering both electron–LO and electron–LA phonon interactions and only the electron–LO phonon interaction, respectively. As a matter of course, the increase in the theoretical curves with temperature is coming from the temperature dependence of the phonon numbers. In view of the fairly good agreement between the experimental findings and the results obtained by theoretical calculation, we believe that the homogeneous linewidths measured in this study are governed by the interactions between carriers and phonons. In addition, we found that the interaction with LO phonons dominated the homogeneous linewidth in the high-temperature region.

Fig. 10.19

Experimental and theoretical results for homogeneous linewidths as a function of temperature. Solid squares and solid triangles correspond to the calculated results considering both electron–LO phonon and electron–LA phonon interactions and only the electron–LO phonon interaction, respectively. The dotted line represents the spectral resolution in our measurement

Next, to understand why the homogeneous linewidths vary from dot to dot, we performed careful measurement of the homogeneous linewidths of many QDs at room temperature. To address the individual QD, we introduce the inter-level spacing energy (ΔE), which reflects the size of the QD. Figure 10.20a shows the excitation power dependence of the PL spectra of a single QD. The peak intensity of each spectrum is normalized by the excitation power. Under weak excitation conditions, a single peak is observed at 1. 158 eV (E ₁), which originates from the recombination of the ground state. When the excitation power is higher than 10 μW, another PL peak appears at the higher energy of 1. 205 eV (E ₂). From the threshold-like PL behavior as a function of excitation power, it is evident that this emission line of E ₂ is associated with the first excited state. Figure 10.20b shows a plot of the PL spectrum at intermediate excitation power. Here, we define the inter-level spacing energy (ΔE) as the energy difference between the ground state and the first excited state ( = E ₂ − E ₁).

Fig. 10.20

(a) PL spectra of a single QD at various excitation powers ranging between 3 and 20 μW at 300 K. The vertical axis is normalized by the excitation intensity. (b) PL spectra of a single QD under intermediate excitation conditions, where several electron–hole pairs are excited in a QD. Inter-level spacing energy (ΔE) is defined as the energy difference between the ground-state emission energy (E ₁) and the first excited state energy (E ₂)

Fig. 10.21

Experimental (open circles) and theoretical (closed squares) results for homogeneous linewidth as a function of inter-level spacing energy (ΔE) at 300 K. Contributions from electron–LO phonon and electron–LA phonon interactions are also plotted separately

Figure 10.21 shows the homogeneous linewidths as a function of ΔE, where the experimental data are plotted with open circles. The linewidths tend to increase with ΔE. Here, the absolute values and large variation (25–45 meV) of ΔE are considered to be reasonable as determined by comparing these findings with the results obtained by theoretical calculation taking into account the averaged QD size and its distribution, respectively. Based upon Green’s function theory mentioned above, the homogeneous linewidths are computed for QDs of different size. The closed squares in Fig. 10.21 denote the calculated results considering the interactions with LO and LA phonons. The theoretical calculation results quantitatively reproduce the experimental results, indicating that the magnitude of electron–phonon interaction depends on the ΔE (size of QDs). That is, in the case of a smaller quantum dot, the overlap integral of the carrier and phonon eigenfunctions becomes larger, which leads to a more strongly coupled electron–phonon system. In Fig. 10.21, the contributions from LO– and LA–phonon interactions are also plotted separately. We can see that the ΔE dependence of the LA phonon contribution is slightly larger than that of the LO phonon contribution, which is due to the fact that the deformation potential includes the spatial derivative of the lattice displacement.

As for GaAs/Al_{0. 3}Ga_{0. 7}As quantum well structures, Gammon et al. have reported the well-width dependence of the homogeneous linewidth [44]. According to their experimental and theoretical results, the linewidth has a weak dependence on the quantum well width. On the contrary, our experimental and theoretical results demonstrate that the strength of the electron–phonon interaction largely varies depending on the spatial confinement in a given QD. Such a size-dependent electron–phonon interaction implies that the QD would have a novel character with a strongly coupled electron–phonon mode.

Homogeneous Linewidth and Carrier–Carrier Interaction

Phenomena occurring under highly excited conditions have been one of the most significant topics that have been frequently studied in bulk, quantum well (QW), and quantum wire (QWR) systems [45–48]. In semiconductors occupied by many carriers, the carrier–carrier interaction appears as a consequence of a change of self-energy. Changes of the real and the imaginary part of a self-energy induce the shrinkage of a fundamental bandgap (band-gap renormalization) and an increase of the damping rate, respectively [45]. The experimental results show that the band-gap renormalization is reduced in accordance with the reduction of a dimensionality from bulk to QWR [48].

As mentioned in the previous subsection, the most essential problem in preventing the realization of ideal QD devices is the several kinds of inhomogeneity of QD such as size, shape, and strain. However, the homogeneity of QD size is drastically improved when growth conditions are optimized. In this case, the narrow inhomogeneous broadening of 20 meV in the optical spectrum has been realized [49], and the performance of the QD lasers has been much improved. If the inhomogeneous broadening can be suppressed enough, the intrinsic homogeneous linewidth becomes one of the restrictive parameters with respect to attaining the maximum gain. In the operation of a QD laser at room temperature, many carriers are injected in and around the QDs, and the carrier–carrier interaction affects the homogeneous linewidth. Several scattering mechanisms via carrier–carrier interaction have been discussed, and the dephasing rate (linewidth) has been estimated by several theoretical calculations [37]. So far, however, the detailed experimental results involving carrier–carrier interaction in QDs at room temperature have not been reported.

In this subsection, we described a single-QD PL spectroscopy in high excitation conditions at room temperature. We concentrated on the characteristic excitation power-dependent shift and broadening of ground-state emission. These behaviors have been discussed while taking into consideration the carrier–carrier interaction in QDs.

Fig. 10.22

(a) PL spectra of a single QD at various excitation densities ranging from 0. 3 to 7. 1 kW/cm². (b) Excitation power dependence of integrated PL intensity at ground-state emission (I _g: closed circles) and at the first excited state (I _exc: open circles). Inset shows the PL intensity ratio (I _g/I _exc) as a function of excitation density. The excitation power density at which the PL intensity ratio exhibits a critical increase is defined as I ₀

Figure 10.22a shows the excitation power dependence of PL spectra in a single QD and WL at 300 K. In the weak excitation condition, a single PL line originating from the recombination of an electron and hole pair in the lowest energy level (ground state: E ₁) is observed at 1. 222 eV. With an increase of the excitation power density, additional lines associated with excited states (E ₂, E ₃) appear and grow up at 1. 252 and 1. 280 eV. The shape of each spectrum is well reproduced by a sum of Lorentzian functions. The precise values of the transition energy and the linewidth are determined from the fitting results. The additional broadening and spectral redshift of the ground-state emission are observed at several kW/cm². Such behaviors have been commonly observed in 20 QDs, which we have investigated.

Figure 10.22b shows the integrated PL intensities of both the ground state and the first excited state as a function of excitation power densities. The PL intensity of the ground state (I _g: closed circles) grows linearly as a function of excitation power density and reaches saturation at approximately 1. 5 kW/cm². The nonlinear power dependence of the PL intensity indicates that the nonradiative recombination process is dominant at room temperature [50]. The PL intensity of the first excited state (I _exc: open squares) increases more rapidly than I _g above 0. 5 kW/cm². The inset of Fig. 10.22b shows the excitation power dependence of the ratio of the emission intensity from the first excited state to that from the ground state ( = I _exc/I _g), which reflects the degree of a carrier population in the first excited state. The PL intensity ratio is constant below 0. 5 kW/cm². The finite population in the first excited state at the lowest excitation condition is well understood by the thermal carrier excitation at 300 K. The ratio exhibits critical increases above 0. 5 kW/cm² because additional carriers occupy the first excited state due to the strong excitation. Hereafter, we define the power density where the PL intensity ratio critically changes as I ₀.

To study the many-body effect in the QD, we have plotted the spectral energy shift of the ground state (E ₁) and the first excited state emission (E ₂) of the QD and WL as a function excitation power in Fig. 10.23. Both E ₁ and E ₂ shift to the lower energy side with an increase in excitation density [51]. As the PL peak energy of the WL and GaAs barrier layer (not shown) does not change, the redshift of E ₁ and E ₂ cannot be explained by simple band-gap shrinkage of the barrier layer; rather, it is caused by the band-gap renormalization of the QD itself due to the Coulomb interaction between carriers. When the excited carrier density is 2 ×10¹⁷ cm^{− 3}, the value of band-gap renormalization is evaluated to be 8 meV, which is in good agreement with the theoretical predictions [52, 53].

Fig. 10.23

Energy shifts of the ground-state emission (E ₁) and the first excited state (E ₂) of QD as a function of excitation power density. The PL peak energy of WL as a function of power density is also plotted

Next, we examined additional broadening by evaluating the linewidth of the ground-state emission. Figure 10.24 shows a dependence of the emission linewidth (A: closed squares) on the excitation power density. Results of two different QDs (B: open circles, C: open squares) are also plotted. The linewidth remains constant below I ₀. In this regime, the broadening is well explained by the dephasing process due to the interaction between electron (carrier) and phonon, which has already been discussed in detail [38]. At higher excitation, the linewidth increases with the excitation power. Through the investigation of many QDs, we found that the values of I ₀ were scattered from QD to QD, and we also found that additional broadening always starts to occur at I ₀, that is, when the carriers are populated in the excited state of QD. The strong dependence of this broadening on the excitation power implies that the interaction between carriers, such as the Auger scattering process, would lead to an increased dephasing rate. We should consider two types of Auger scattering process in the QD system grown in the S–K mode. One is the scattering process that takes place between confined carriers in the QD and free carriers in two-dimensional (2D) WL. The other is the intra-QD process, in which carriers in the QD interact each other.

Fig. 10.24

Linewidth of the ground-state emission (E ₁) as a function of excitation power density for three different QDs

We will discuss which processes are dominant in terms of causing the excitation power-dependent broadening in the QD system. First, we consider the scattering process between confined carriers in a QD and free carriers in a 2D WL. A theoretical calculation predicts that the exchange process between a carrier in the QD and a free carrier in the WL causes a broadening of several meV at high carrier density and that the value of broadening is determined by the carrier density in the WL. However, this mechanism should be ruled out because the broadening behavior in the experiment differs from QD to QD (Through the 2D mapping of PL intensity, we confirmed that the carrier density in WL was uniform in the observation area).

Next, we consider the intra-QD scattering process, where the broadening depends on the carrier population in the QD [54, 55]. The correlation between the additional broadening and the carrier population in the excited states of the QD, as shown in Fig. 10.24, indicates that the intra-QD process is a dominant mechanism for the broadening. From the experimental results, we conclude that an Auger scattering process with the following scenario is most probable. First, there is a relaxation of the hole into the QD from the WL and the excitation of an electron into a higher level via Coulomb interaction. As a next step, the electron relaxes to the lowest level and the hole is emitted into the WL. Theoritically, the additional broadening of several meV is possible if the capture and emission processes are efficient. Further theoretical studies that take the realistic electronic structure into consideration will be needed for the quantitative explanation of the experimental results.

Real-Space Mapping of Exciton Wave Function Confined in a QD

As described in the previous section, the near-field optical characterization of semiconductor quantum structures, with a resolution of approximately 0. 2 μm, reveals sharp PL spectra from individual quantum constituents and provides a significant contribution to the investigation of their intrinsic electronic structure and dynamics. Beyond such single-constituent spectroscopy, the next challenge of near-field optical measurement is to illustrate directly the internal features of quantum-confined systems [56]. If the spatial resolution of NSOM reaches the length scale of the quantum structure, theoretical studies predict that the NSOM will allow mapping of the real-space distribution of eigenstates (wave functions) within quantum-confined systems [57]. Moreover, in combination with ultrafast pulsed excitation, the local access to single QD systems enables control of individual eigenstates in a coherent manner, which provides a fundamental technique in quantum-information technology.

In this section, the near-field optical mapping of exciton and biexciton center-of-mass wave functions confined in 100-nm GaAs interface QDs is demonstrated. The QDs investigated in this study are much smaller than those investigated in a previous report [56]. The successful imaging of such a small quantum electronic structure is attributed to improvement in the design and fabrication of the near-field fiber probe.

The sample investigated in this study was a 5-nm (18–19 ML) GaAs QW sandwiched between layers of AlAs and Al_{0. 3}Ga_{0. 7}As grown by molecular beam epitaxy. Growth interruptions for 2 min at both interfaces led to the formation of naturally occurring QDs, as shown in Fig. 10.25. The GaAs QW was capped with a 15-nm Al_{0. 3}Ga_{0. 7}As layer and a 5-nm GaAs layer. As we see in the above section, a spatial resolution as high as 30 nm can be achieved even when QDs are covered with 20-nm cap layers. As depicted in Fig. 10.25, the sample was non-resonantly excited with He–Ne laser light (λ = 633 nm) through the aperture, and the resultant PL signal was collected via the same aperture to prevent a reduction of the spatial resolution due to carrier diffusion. The near-field PL spectra were measured at every 10-nm step in a 210-nm × 210-nm area, and the near-field images were constructed from a series of PL spectra.

Fig. 10.25

Schematic of the sample structure and the configuration of the near-field optical measurement

Figure 10.26a shows near-field PL spectra of a single QD at 9 K at excitation densities ranging from 0. 17 to 3. 8 W/cm². A single sharp emission line (denoted by X) at 1. 6088 eV is observed below 0. 4 W/cm². With an increase in excitation power density, another emission lines appear at 1. 6057 eV (denoted by XX). In order to clarify the origin of these emissions, we show the excitation power dependence of PL intensities in Fig. 10.26b. Based on the linear increase of the intensity of the X emission line and the saturation behavior, the X line is identified as an emission from a single-exciton state. The quadratic dependence of the XX emission with excitation power density indicates that XX is attributed to an emission from a biexciton state [47, 58]. The identification of the XX line is also supported by the correlation energy of 3. 1 meV (the energy difference between the XX line and the X line), which agrees well with the value reported previously [47, 58].

Fig. 10.26

(a) Near-field PL spectra of a single QD at 9 K under various excitation power densities. (b) Excitation power dependence of PL intensities of the X and the XX emission line

High-resolution PL images in Fig. 10.27a, b were obtained by mapping the PL intensity with respect to the X and the XX lines under the excitation density of 1. 3 W/cm². In this excitation regime, both the emissions from single-exciton (X) and biexciton (XX) states appear in a PL spectrum. The two images were obtained by selecting the detection peak in a series of PL spectra. The exciton PL image in Fig. 10.27a manifests an elongation along the [ − 110] crystal axis. The image sizes along the [110] and [ − 110] axes are 80 nm and 130 nm, respectively, which are larger than the PL collection spot diameter, that is, the spatial resolution of the NSOM. The size and the elongation along the [ − 110] axis are consistent with a previous observation made with a scanning tunneling microscope [5]. These findings lead to a conclusion that the local optical probing of the NSOM directly maps out the center-of-mass wave function of an exciton confined in a monolayer–high island elongated along the [110] crystal axis.

Fig. 10.27

High-resolution PL mapping for the emissions from (a) the exciton state (X) and (b) the biexciton state (XX). The excitation power density and scanning area are 1. 3 W/cm² and 210 nm × 210 nm, respectively

We also obtained the elongated biexciton PL image along the [ − 110] crystal axis and found a clear difference in the spatial distribution between the exciton and the biexciton emissions. This tendency was reproduced for other QDs in using the same measurement. The different properties between exciton and biexciton wave functions may explain this. Since the relative-motion wave function of the biexciton state extends more widely than does that of the exciton state, the center-of-mass motion of the biexciton is more strongly confined in the monolayer–high island.

Carrier Localization in Cluster States in GaNAs

In contrast to the well-defined quantum-confined systems such as QDs grown in a self-assembled mode, the more common disordered systems with local potential fluctuations leave unanswered questions. For example, a large reduction of the fundamental band gap in GaAs with small amounts of nitrogen is relevant to the clustering behavior of nitrogen atoms and resultant potential fluctuations. NSOM characterization with high spatial resolution can give us a lot of important information that is useful in our quest to fully understand such complicated systems, such as details about the localization and delocalization of carriers, which determine the optical properties in the vicinity of the band gap.

The GaNAs and GaInNAs semiconductor alloy system has attracted a great deal of attention due to its interesting physical properties, such as its extremely large band-gap bowing [59], and its wide range of potential applications in solar cells and optoelectronic devices. In particular, for long-wavelength semiconductor laser application, high-temperature stability of the threshold current is realized in the GaInNAs/GaAs quantum well as compared to the conventional InGaAsP/InP quantum well due to strong electron confinement [60]. However, GaNAs and GaInNAs with a high nitrogen concentration of more than 1 % have been successfully grown only under nonequilibrium conditions by molecular beam epitaxy [61, 62] and metal-organic vapor phase epitaxy [63].

The incorporation of nitrogen generally induces degradation of optical properties [64–69]. To date, several groups of researchers have reported characteristic PL properties of GaNAs and GaInNAs, for example, the broad asymmetric PL spectra [64, 67, 69] and the anomalous temperature dependence of the PL peak energy [65, 68]. With respect to this characteristic PL behavior, it has been pointed out in the realm of macroscopic optical characterization that carrier localization plays an important role. By contrast, microscopic optical characterization techniques with high spatial resolution can give us a lot of important information that allows us to understand the optical properties, especially the localization or delocalization of carriers.

In this section, we show the results of spatially resolved PL spectroscopy at both 7. 5 and 300 K obtained using NSOM with a high spatial resolution of 150 nm. At low temperature, we observed sharp-structured PL spectra and the spatial distribution of the PL intensity of the GaNAs alloy. This spatial inhomogeneity is direct evidence of carrier localization in the potential minimum case caused by the compositional fluctuation [70].

The samples investigated in this study were GaNAs epilayers grown on (001) GaAs substrates by low-pressure metal-organic vapor phase epitaxy. The details of the growth conditions are described in Ref. [71]. The GaNAs layer was sandwiched by a 100-nm thick GaAs buffer layer and a 50-nm thick GaAs cap layer. The GaNAs layer was 500 nm thick, and the N concentration was estimated to be 0. 8 % by high-resolution X-ray diffraction and secondary ion mass spectroscopy. After growth, thermal annealing was performed for 10 minutes in H₂ ambient at 700 K to improve the optical properties [71]. The macro-PL spectra were measured at both 10 and 300 K with excitation by means of a laser diode (λ = 687 nm). In the NSOM measurement, the sample was also illuminated by the laser diode through the aperture of the fiber probe, and the PL signal from the GaNAs epilayer was collected by the same aperture.

Figure 10.28a shows the excitation power dependence of the macro-PL spectrum from a GaNAs epilayer at 10 K. Broad and asymmetric PL spectra with a low-energy tail as shown in Fig. 10.28a were observed under low excitation conditions. With an increase in excitation power density, the PL intensity of the low energy-tail gradually reaches saturation, and the peak energy of the PL spectra (solid square) is shifted to the higher energy side. In the PL spectrum under the highest excitation conditions, we can see the appearance of a shoulder (open circles) corresponding to the transition energy of the band edge (1. 343 eV) determined by the photoreflectance spectrum [72]. Figure 10.28b shows the excitation power dependence of the macro-PL spectra at room temperature. In contrast to what occurs at low temperature, the peak energy indicated by the open circles and the shape of the PL spectra do not change with an increase in excitation power. Here, it should be noted that we observed no broad emission due to recombination of the carriers at a deep trap in GaAs, and the quality of this sample was high. From the PL behavior as a function of excitation power dependence, it is evident that the carrier recombination mechanism drastically changes from 10 to 300 K.

Fig. 10.28

Power dependence of the macro-photoluminescence (PL) spectra of a GaNAs epilayer at (a) 10 and (b) 300 K. The vertical axis of the PL spectrum was normalized by the maximum value of each peak

In order to investigate the spatial distribution of the optical properties, we performed spatially resolved PL spectroscopy with NSOM at room temperature. Figure 10.29a shows a typical topographic image of the sample surface. The flatness of the sample surface is within a few nanometers, which does not affect the artificial effect for near-field optical images. Figure 10.29b shows the monochromatic PL image obtained at a detection energy of 1. 268 eV with a spatial resolution of 150 nm at 300 K. Weak contrast on a large scale of a few micrometers is observed. Figure 10.29c shows the near-field and macro-PL spectra at 300 K. The near-field PL spectrum is almost the same as the macro-PL spectrum, indicating that the carriers do not localize spatially. The PL spectrum with a higher energy tail is well reproduced by the fitted curves (open circles), assuming that the carriers are found in a bulk system with Boltzmann distribution. Therefore, we can conclude that the dominant emission of the GaNAs epilayer at room temperature comes from the recombination of the delocalized carriers at the band edge.

Fig. 10.29

(a) Topographic image of the sample surface. The scanning area and power density is 4. 0 μm × 4.0 μm. (b) Monochromatic PL images obtained at a detection energy of 1. 268 eV with a spectral window of 6 meV at 300 K. (c) PL spectra obtained with the macro (dotted line) and near-field (solid line) configuration. The power density of near-field PL measurement is 200 W/cm². The open circles represent the fitted curves assuming the free-carrier recombination at the band edge

To examine the difference in the mechanism of recombination of carriers between room temperature and cryogenic temperature, we conducted a near-field PL measurement at 7. 5 K. Figure 10.30a, b show the low-temperature monochromatic PL images obtained at a detection energy of 1. 316 and 1. 328 eV, respectively. We observed high-contrast images with structures on a scale of within 1 μm, as shown in both Figs. 10.30a, b. By comparing Figs. 10.30a, b, we can see that the contrast pattern of the monochromatic image changes in accordance with the detected photon energy. These high-contrast and energy-dependent images suggest the existence of energy fluctuation on a scale of within 1 μm. Figure 10.30c shows the integrated PL intensity image obtained at a photon energy of 1. 325 eV with a spectral window of 30 meV to detect the whole PL signal at 7. 5 K. Spatial inhomogeneity of the integrated PL intensity with a scale of several hundred nanometers was observed, indicating that the density of the defect and the nonradiative recombination center are distributed spatially [73].

Fig. 10.30

(a), (b) Monochromatic PL images obtained at a photon energy of 1. 316 and 1. 328 eV, respectively, with a spectral resolution of 4 meV, measured at 7. 5 K. (c) Integrated PL intensity image obtained at a photon energy of 1. 325 eV with a spectral window of 30 meV. The scanning area and excitation power density are 4. 0 μm × 4.0 μm and about 5 W/cm², respectively

Figure 10.31a shows the near-field PL spectrum and its power dependence as determined by fixing the fiber probe at a certain position. Under the lowest excitation conditions (the lowest spectrum in Fig. 10.31a), several sharp peaks at around 1. 32 eV, not seen in the macro-PL spectrum (dotted line), are clearly observed. With an increase in excitation density, the sharp PL peaks gradually show saturation, and the center of gravity in the PL spectrum shifts to the higher energy side. Finally, we observed structureless PL spectra similar to the macro-PL spectra. Judging from the sharp spectral features and the rapid saturation behavior, it seems that the sharp PL peaks observed under low excitation conditions come from the recombination of localized carriers (excitons).

Fig. 10.31

(a) Near-field PL spectra at various excitation power densities at 7. 5 K. The dotted line represents the macro-PL spectrum. (b) Near-field PL spectra obtained in different positions under low excitation conditions

To confirm whether these sharp PL peaks originate from the recombination of localized carriers (excitons), we measured the position dependence of the near-field PL spectra shown in Fig. 10.31b. These four PL spectra were obtained at different positions under low excitation conditions. The number of sharp peaks and these energy positions in each spectrum is drastically different from position to position. These sharp emissions occur in a small area on a scale of within 150 nm, that is, in the local potential minimum, and the scale of the local potential fluctuation is estimated to be at least within 150 nm. Therefore, we conclude that the dominant emission mechanism at low temperature is recombination of the tapped and localized carriers (excitons) due to energy fluctuation. This energy fluctuation could come from the compositional variation of nitrogen, since the spatial distribution of the optical properties strongly depends on the nitrogen concentration and the scale of the inhomogeneity decreases with an increase in nitrogen concentration.

Perspectives

The quality and reproducibility of aperture NSOM measurements have been greatly improved in the last decade by the introduction of high-definition fiber probes made by combining chemical etching with ion-beam milling or by using a simpler impact method. The flat end of the probe provides high spatial resolution determined solely by the aperture size, down to 10 nm. The probes, however, should be improved with respect to optical transmission, tip stability, and damage threshold for routine applications in material characterization, device diagnostics, and industrial testing. Micromachined, cantilever-based probes offer a promising solution to these difficulties. Recently, these kinds of high-performance probes are available as commercial products and contribute to expanding NSOM users and its application field. Nano-imaging spectroscopy of semiconductor nanostructures will continue to attract much attention by extending the operation wavelength into infrared region. At such wavelength we can determine the free-carrier density and hence the dopant concentration nondestructively. Also near-field imaging of thermal radiation will reveal the possibility of enhanced heat transfer. NSOM working in THz regime will allow spatiotemporal visualization of phonon dynamics and phase transition process. In combination with polarization control and measurement, NSOM makes it possible to generate, manipulate, and read out the electron spin state at the nanoscale. This will open new perspectives towards nano-spin photonics with semiconductor nanostructures.