Growth and characterization of site-selective quantum dots

Authors

  • Mathieu Helfrich,

    1. DFG-Center for Functional Nanostructures, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1a, 76131 Karlsruhe, Germany
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  • Philipp Schroth,

    1. Institute for Synchrotron Radiation/ANKA, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
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  • Daniil Grigoriev,

    1. Laboratory for Applications of Synchrotron Radiation, Karlsruhe Institute of Technology (KIT), Engesserstraße 15, 76131 Karlsruhe, Germany
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  • Sergey Lazarev,

    1. Institute for Synchrotron Radiation/ANKA, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
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  • Roberto Felici,

    1. ESRF, 6 rue Jules Horowitz, BP 220, 38043 Grenoble Cedex, France
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  • Taras Slobodskyy,

    1. Institute for Applied Physics, University Hamburg, Jungiusstraße 11, 20355 Hamburg, Germany
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  • Tilo Baumbach,

    1. Institute for Synchrotron Radiation/ANKA, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
    2. Laboratory for Applications of Synchrotron Radiation, Karlsruhe Institute of Technology (KIT), Engesserstraße 15, 76131 Karlsruhe, Germany
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  • Daniel M. Schaadt

    Corresponding author
    1. DFG-Center for Functional Nanostructures, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1a, 76131 Karlsruhe, Germany
    2. Institute for Energy Research and Physical Technologies, Technical University Clausthal, Am Stollen 19B, 38640 Goslar, Germany
    • Phone: +49 5323 72 2322, Fax: +49 5323 72 2175
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Abstract

A review on the growth and characterization of site-selective quantum dots (QDs) is presented. First, a theoretical model is used to describe the mechanism leading to the formation of QDs at pre-defined locations. The structural properties of site-selective QDs was revealed and their optical quality was tested. Various parameters, such as hole size, hole depth, or InAs amount, influencing the QD occupation and the QD size are discussed and possible ways to control these are presented.

original image

Ordered QD array with multiple dot nucleation (left) and single QD in dry etched hole (right).

1 Introduction

In semiconductor quantum dots (QDs), electrons and holes are three-dimensionally confined into nanometer-scale semiconductor crystals. Hence, they are referred to as zero-dimensional objects 1. As a result, the electronic density of states becomes delta-function-like, which means that QDs exhibit discrete energy levels like atoms. Semiconductor QDs can be fabricated by epitaxial techniques such as molecular beam epitaxy (MBE) by embedding nanometer sized islands of a low bandgap semiconductor material in a host matrix of a higher bandgap semiconductor material. Epitaxial QDs have several advantages compared to atoms. Unlike in atoms, the emission properties of QDs can be adjusted by changing their structure 2. Since the position of the QDs is fixed in the host matrix, the matrix including the QD can be further processed and functionalized. This has allowed to turn QDs into functional units in devices like light emitting diodes 3, 4 or lasers 3, 5. Further QD properties have been investigated in the last decade with respect to device applications with novel functionalities. QDs can, for example, confine electrons and holes for some time which makes them promising candidates for storage devices 6. The QD's ability to emit single photons makes it a non-classical light source 7. Single photon emission from a QD can be triggered optically and electrically 8. QDs were also shown to generate entangled photon pairs which might be of interest for secure quantum communication 9. The possibility to fabricate resonator systems such as micropillar cavities 10 or photonic crystal cavities 11 around the QDs allowed for the study of cavity quantum electrodynamical effects. The weak and strong coupling of optical resonator modes to excitonic states have been demonstrated 11–15. The weak coupling might be used to increase the rate of single photon emission while the strong coupling allows for a coherent manipulation of excitonic states 2. Thus, the broad potential of QDs for quantum information applications is well described.

A fundamental problem with respect to functionalization of QDs for applications is related to their fabrication. The formation of epitaxial QDs in MBE is based on the finite lattice mismatch between the QD material and the host material. Islands will form on the host substrate when the amount of the deposited QD material exceeds a critical thickness. Covering these islands with the host material finally completes the QD structure. This self-assembly process is random in nature so that the position of individual QDs cannot be controlled. But then, a key requirement for device integration is a deterministic positioning of QDs. This problem has been addressed during the last decade and different techniques have been employed to guide the nucleation of epitaxial QDs.

Self-alignment mechanisms such as growth on vicinal surfaces have been used to create ordered QD structures 16. However, ordering mainly occurs on a short range and control of absolute QD position is thus limited. As a consequence, methods to align QDs through external forces have been developed. The most versatile and therefore most advanced approach uses lithographically defined holes to guide the nucleation of QDs. Electron beam lithography (EBL) is routinely used to fabricate nanometer sized holes on the substrate surface 17, 18. The holes alter the surface chemical potential and lead to a locally increased growth rate which then allows for selective QD nucleation 19. Size, depth, and shape of the holes can be varied over a wide range, thus offering the possibility to control some of the QD properties as well as their distribution. For instance the number of QDs per hole increases with the size of the hole 20.

In general, obtaining the right conditions for a particular set of QDs is a rather tedious work. The influence of different growth parameters and geometrical features of the holes and the pattern on the QD formation process were not completely revealed. Furthermore, the possibility to control and adjust QD properties such as size, shape, or site occupation on a given pattern after growth was not emphasized. It is known that at lower temperatures QDs tend to ripen whereas they dissolve at higher temperatures 21, 22. In situ annealing experiments with self-assembled QDs have confirmed the power of this technique to alter properties such as QD size, shape, and ordering 23–25. The fact that QDs undergo morphological changes during annealing remained, however, unattended with respect to positioned QDs.

2 Mechanism of site-selective quantum dot formation

In the Stranski–Krastanov growth mode InAs QDs randomly form on the GaAs surface once a critical amount of about 1.7 ML of InAs is deposited. The reason is found in the finite lattice mismatch of f = 7% between InAs and GaAs. The deposition of InAs on GaAs leads to accumulation of strain energy in the InAs film. At the critical thickness, the energy for island formation becomes comparable to the elastic energy stored in the InAs film, so that coherent islands will form in which the strain is relaxed.

Although the nucleation of InAs islands on GaAs being random, there must be a factor that causes the island formation at a specific location. The substrate surface is never 100% flat since at least atomic steps are present and the atomic surface condition cannot be known to absolute precision. The local environment must play a role in the nucleation of islands which is influenced by the nature of the surface. The mechanisms that have been developed to guide the nucleation of QDs try to exploit this fact. The idea is to manipulate and control the surface in such a way that sites are created where islands will predominantly nucleate. The most common approach to direct and control the self-assembly of QDs makes use of intentional deformation of the substrate surface by creating small holes. The holes can be fabricated by various means and act as preferential sites for QD formation. In this case, the deformation of the surface is the driving force for localized island nucleation.

After depositing In atoms on the GaAs surface, the adatoms are not built into the crystal lattice of the underlying film right away because they are subject to diffusion and so they migrate to preferential nucleation sites 26. The process of adatom migration on the GaAs surface is governed by the chemical potential of the surface. Altering the surface leads to a change in the chemical potential and therefore allows to influence the adatom migration and eventually the island nucleation.

Modeling the growth of strained films on a curved surface is very complex which is why only one-dimensional models are employed to describe the fundamental effects of surface curvature on subsequent growth. According to Wang et al., who analyzed the stability of strained thin films on wavy substrates based on a model of Srolovitz 27, 28, the surface chemical potential µ can be described as

equation image((1))

where µ0 denotes the surface chemical potential of the flat film, γ is the surface free energy per unit area, Ω is the atomic volume, κ(x) is the surface curvature, and Es is the local strain-relaxation energy relative to a flat film. The topographical evolution of the film during growth is controlled by the chemical potential. Adatoms will diffuse from regions of high chemical potential to regions of lower chemical potential. The second term in the equation contains the curvature contribution to this process. Thus, considering the first two terms, on a curved surface adatoms will diffuse from convex regions (positive curvature, i.e., higher chemical potential) to concave regions (negative curvature, i.e., lower chemical potential). This surface energy consideration alone suggests that QDs should only nucleate in dimples/holes and not on mounds. Since QD nucleation on mounds was experimentally observed, the third term is added to the chemical potential to account for the strain contributions. Convex regions are prone to strain relaxation which makes them attractive for island nucleation. Hence, the second and third term of Eq. (1) oppose each other and the concrete shape of the surface will determine favorable QD nucleation sites. The mismatched thin film is treated as a bent film in order to derive the strain on the surface which is equation image, where κ is the curvature, zs is the position of the top surface, and z0 is the position of the neutral plane of the bent film 29. The strain relaxation energy is then given by

equation image((2))

where C is an elastic constant and f is the misfit strain. Since the shape of the chemical potential is of interest here and not the absolute value, inserting Eq. (2) in (1) and rearranging the chemical potential yields

equation image((3))

In order to isolate the dependence of the surface chemical potential on the curvature, terms without curvature are replaced by the parameter b, so that a simplified representation of the surface chemical potential can be obtained:

equation image((4))

The attractive force of a chemical potential minimum on adatoms is illustrated by considering the direction of adatom diffusion, which is described by the velocity along the surface as

equation image((5))

This formulation is based on the Nernst–Einstein relation, with Ds being the surface diffusivity, kBT is the thermal energy and the derivative of the simplified chemical potential µ′ with respect to x is taken along the surface 27. The temporal change in surface profile, that is, height h, is then given by

equation image((6))

where δ denotes the number of atoms per unit area 27. Figure 1a depicts the chemical potential derived for a given hole profile (dotted black line). The hole profile was obtained from atomic force microscopy (AFM) measurements and fitted with cubic B-splines in order to calculate µ′. The chemical potential essentially follows the profile of the hole and exhibits a strong minimum at the hole center. The velocity v of adatoms related to the surface curvature was derived and is shown in Fig. 1b. Adatoms will diffuse from both sides to the bottom of the hole. Finally, the resulting change in surface profile equation image is given in Fig. 1c. Note that the prefactors in the respective equations were neglected in the calculations for simplicity. The parameter b was set to 1000 which corresponds to equation image. The net flux of adatoms toward the chemical potential minimum leads to a local increase in growth rate at this location. Due to this increased growth rate the critical thickness for island formation is reached earlier inside the hole than on the flat surface. Therefore, QDs will nucleate at locations defined by the holes. By properly designing the holes and choosing the right growth conditions, it should hence be possible to obtain well positioned QDs while avoiding random QD nucleation.

Figure 1.

(online color at: www.pss-a.com) Calculation of the chemical potential µ′ (a), the adatom diffusion velocity v (b), and the local change in surface profile equation image (c), for b = 1000 (solid blue). The hole profile is shown as reference (dotted black). A local growth rate enhancement is observed at the bottom of the hole so that QDs will nucleate at this position earlier than on the flat surface.

3 Sample fabrication

The holes used for site-selective growth were fabricated by electron beam lithography. This technique guarantees a high degree of freedom with regard to the design of hole arrangements and hole sizes. First, a 300 nm GaAs epitaxial layer is grown on an undoped epi-ready (0 0 1) GaAs wafer to obtain a perfectly flat surface. The samples were then coated with a 80 nm thick polymer resist (polymethyl methacrylate) and exposed by the electron beam. In this way, 100 µm large square arrays of circular holes were defined in the resist. Several arrays with different hole spacings and size were created. The exposed structures were then developed in a solution of methyl isobutyl ketone and isopropyl alcohol for 60 s. The structures in the resist were transferred into the GaAs substrate by etching. Different etching techniques can be employed.

Wet chemical etching (WCE) and dry etching (DE) have both their advantages and disadvantages. WCE is usually favored as it can produce smooth surfaces and does not introduce any electronic defects. This fact is reflected by the superior optical properties of QDs site-selectively grown on wet chemically etched holes compared to similar QDs grown on hole fabricated by DE 30. Nevertheless, DE might be of interest as it allows for better control of hole size and profile. The differences are illustrated in Fig. 2. The scanning electron microscopy image in (Fig. 2a) shows the profile of several holes after WCE. A solution of 1:8:800 H2SO4/H2O2/H2O yielding a low etch rate of about 1 nm/s produces crystallographic profiles as it preferentially etches {1 1 1} facets of the GaAs crystal. The measured average sidewall angle of 53.9 ± 2° compares very well with the calculated value for the angle between the (1 0 0) and the (1 1 1) planes which is 54.7°. However, the etch rates in orthogonal crystal directions are not equal. Ga rich faces, that is (1 1 1) A type facets, usually etch two to five times slower than As rich faces, that is (1 1 1) B type facets 31. This leads to an elongation of the holes in the equation image direction, as observed in the top view SEM image of a single hole (inset). A further limitation of WCE is the fact that the originally circular holes in the resist transform into rectangular ones in the GaAs substrate. This is because of the preferential etching of the {1 1 1} facets. Increased control of the hole profile can be achieved by DE, as demonstrated in (Fig. 2b). Almost vertical sidewalls were obtained after performing a reactive ion etching with inductively coupled plasma (ICP-RIE). The recipe uses a gas mixture of SiCl4/Ar with little flux. The plasma generating power (ICP power) was low in order to reduce the chemical component during etching so that the hole elongation could be minimized. Low acceleration voltages (DC bias) are required to produce flat surfaces. The ICP power was 150 W and the gas ions were accelerated by a DC bias of 60 V which results in a low etch rate.

Figure 2.

Differences between WCE and DE. Crystallographic profiles were obtained by WCE (a). The average sidewall angle is given. The sample was etched for 60 s with a rate of 1 nm/s. Vertical sidewalls can be obtained in DE (b). The sample was etched for 10 s using an ICP-RIE process based on a SiCl4/Ar gas mixture and low ICP generating power and DC bias.

After etching, the resist was stripped with strong solvents such as n-ethyl-2-pyrrolidone and the surface was cleaned in several baths of organic solvents. Finally, the residual organic contamination was removed by a UV/ozone cleaning step or in an oxygen plasma asher. This step is very important since remaining contamination might lead to the formation of unintended holes during MBE growth, which interferes with the attempt of deterministic QD positioning 32. Right before entering the MBE chamber, the native surface oxide was removed by dipping the samples in 1:3 HCl/H2O. The samples were heated to 130 °C for 1 h in the loadlock of the MBE system to remove residual H2O.

MBE growth is preceded by removal of the native oxide in the growth chamber. For this purpose, Ga-assisted deoxidation is favored over thermal deoxidation in order to avoid additional surface pitting and to obtain an atomically flat surface 34–36. The samples were repeatedly exposed for 30 s to a low Ga-flux of 1–2 ML/min followed by a 30 s break. The desorption process was monitored by reflection high energy electron diffraction (RHEED) and calibrated on un-patterned samples. After several cycles the samples were heated up to 580 °C for a quick annealing and then cooled down to the growth temperature of 500 °C. All subsequent growth steps were performed at this temperature.

Before growing QDs, a thin GaAs buffer layer (BL) was deposited on the pre-patterned samples at about 0.3 ML/s. This is to reduce the surface roughness of the etched areas. However, the enhanced mobility of Ga adatoms in the [0 1 1] and equation image directions leads to a deformation of the holes with an elongation occurring in these directions. The reason for this enhanced mobility is related to the different faces described above. During BL growth a net migration of adatoms away from Ga-terminated facets toward As-terminated ones is observed which then leads to the elongation of the hole 37. The deposition of InAs then entails the formation of QDs localized inside the defined holes and aligned along the elongated direction, see Fig. 3. The AFM images illustrate the shift of the hole elongation after BL growth and the alignment of the QDs inside the holes. In order to investigate the possibility to manipulate the QD distribution and the QD size post growth, an in situ annealing process was applied, during which the samples were kept at growth temperature for several minutes under As overpressure before being rapidly cooled down. It is important to notice that the growth rate for the QDs was rather high with about 0.07 ML/s. This is to separate the QD growth from the processes taking place during annealing.

Figure 3.

(online color at: www.pss-a.com) Shift of hole elongation after BL overgrowth. The AFM image of a sample etched by WCE for 45 s is shown before BL growth in (a). A similar sample etched for 30 s was overgrown with a 20 nm thin GaAs BL and 1.8 ML InAs. The AFM image in (b) reveals the alignment of the site-selective QDs along the hole elongation. The initial elongation along equation image as in (a) turns into an elongation along [0 1 1] due to preferential Ga adatom migration.

4 Site-selective growth of quantum dots

Site-selectively grown QDs were analyzed with respect to their structural properties and their optical quality. A possible mechanism to control the QD size as well as their distribution is presented.

4.1 Structural properties

The lithography systems used for the hole fabrication are not optimized with regard to size homogeneity of structures on the few nanometer scale. Therefore, a fluctuation in hole size on the order of 10% could not be avoided. An ordered array of QDs was fabricated in order to determine the size of the positioned QDs in this work. 1.7 ML of InAs were grown on top of 16 nm thick GaAs BL. AFM images can be used to measure the height of the QDs whereas SEM images are more useful to determine the lateral size, since the QD diameter observed in AFM images appears large than it really is due to a convolution of the finitely sized AFM tip with the measured QD. Figure 4a shows an AFM image of the ordered QD array. The holes are completely infilled which is probably related to the holes being shallower compared to the sample in Fig. 3. The spacing between the nucleation sites is 250 nm and two or three QDs are found in most of the holes. The alignment of multiple dots in the holes along [0 1 1] is observed. Few QDs are also found between the holes, indicating that the amount of deposited material was rather high. The corresponding height distribution is depicted in (Fig. 4b) and contains only the heights of positioned QDs. The average height amounts to 9.8 ± 2.9 nm. The QD diameters were exctracted from SEM images (not shown) using the image analysis software ImageJ 33 which allows for a standardized evaluation of particle sizes. The average QD diameter is 19.8 ± 5.0 nm. The corresponding QD diameter distribution is depicted in (Fig. 4c). The large fluctuations of 30 and 25% for the QD height and diameter, respectively, is likely related to the fluctuations in hole size but they are comparable to other results in literature 18, 20. In order to further evaluate these values they can be compared to the size of randomly self-assembled QDs. A reference sample was prepared for which 1.9 ML InAs was grown on a flat GaAs surface. The higher InAs amount was necessary since 1.7 ML InAs was not enough to observe QD formation on the flat surface. Only small precursor states were found in this case. The QD height and diameter distributions were both extracted from AFM images (not shown) and the average values are 13.0 ± 1.7 nm and 38.3 ± 3.9 nm, respectively. While the height value is correct, the absolute value of the diameter has to be considered with care, as a deconvolution of the AFM images was not performed. Nevertheless, the self-assembled QDs are clearly larger which is due to the increased amount of InAs. The resulting longer growth time is also known to lead to larger QDs 38. Most important, the size fluctuations are much lower compared to that of site-selective QDs. Standard deviations of 13 and 10% were found for the average height and the average diameter, respectively.

Figure 4.

(online color at: www.pss-a.com) Size statistics of positioned QDs on a hole array with 250 nm spacing. The height of the QDs was obtained from AFM height data (a). The corresponding height histogram is shown in (b). The average QD height is 9.8 ± 2.9 nm. The QD diameters were extracted from the SEM image in (c) using the software ImageJ 33. The diameter histogram is given in (c) and the average QD diameter is 19.8 ± 5.0 nm.

Two further aspects are important with respect to controlled formation of defect free QDs at defined locations. The deformation of the holes during BL overgrowth apparently influences the ordering of the QDs, as several aligned QDs were found in each hole instead of one single QD. The nucleation of these QDs must be related to the transformed shape of the hole and the exact position of the QDs inside the holes can be investigated by TEM. High resolution TEM (HRTEM) images can also be analyzed with respect to the formation of defects. Self-assembled QDs are usually coherently strained and therefore do not contain any defects provided that they were grown on a clean surface. The growth on a patterned substrate is different since the substrate surface was etched and exposed to different substances during processing. Etched surfaces are subject to roughening which is partly compensated by the growth of the thin BL. However, the restrictions on the BL thickness emerging from the fact that the holes fill up during growth possibly lead to an influence of the regrowth interface onto the formation of QDs and their coherence. Dislocations are one prominent type of defect that can be found in QDs and which are frequently observed in very large islands 39. The occurrence of defects in the QDs likely degrades their optical properties.

In order to further characterize the site-selective QDs of the sample from Fig. 4, a thin lamella containing a row of several holes with QDs was cut out of the sample by focused ion beam and thinned with a beam of Ar+. In this way, a 50–100 nm thin lamella can be obtained which is then suitable for TEM analysis. The TEM image in Fig. 5a shows the profile of several positioned QDs. The QDs are free-standing and were only covered with Pt for the fabrication of the lamella. Three holes are observed with two or three QDs nucleating inside, as indicated by the blue arrows. The spacing between the holes is 250 nm. The interface between the patterned substrate surface and the GaAs BL is not observed as the contrast is too low. Variations in the contrast might be due to electrostatic loading of the sample during investigation or variations in the thickness of the lamella. A magnified TEM image of the middle hole containing three QDs is shown in (Fig. 5b) and reveals the QD positions inside the hole. The middle QD is found in the center of the hole and is also the largest of the three, both in diameter and height. The other two QDs are found at the sloped sidewall of the hole, possibly close to the rim. This implies that two favorite sites for QD formation inside holes can be distinguished, namely at the center of the hole and on the sidewalls. The first nucleation site is consistent with the earlier analysis. The local growth rate enhancement at the center of the hole is due to increased In adatom migration to this site, compare the diagram in Fig. 1c. In this diagram, two significantly smaller local growth rate maxima emerge at each side of the central growth rate maximum, in addition. Their positions correspond very well to the observation of QDs nucleating on the sloped sidewall. The reduced height of these QDs is an indication of a lower local growth rate compared to the center. Not all holes exhibit the same QD arrangement. Other holes contain, for example, two QDs, each nucleating at the sidewall, or one QD in the center and another QD at the sidewall. Local variations in the hole profiles, sizes, and depths, which originate from imperfections in the lithographic definition of the holes, likely influence the nucleation of the QDs in the holes and therefore account for the different QD configurations which have been observed. Nevertheless, the findings are consistent with the above model for site-selective growth.

Figure 5.

(online color at: www.pss-a.com) TEM investigation of site-selective QDs. The TEM image in (a) reveals well ordered QDs nucleated in defined holes. The QDs are marked with blue arrows. The separation between the holes is 250 nm. A magnified TEM image of the part in the white frame is depicted in (b) revealing three QDs in the hole. While one QD is found at the center of the hole, two QDs have formed on the sidewalls. A HRTEM image with atomic resolution of the QD from the center of the hole is shown in (c). Dome-like shape of the QD is revealed. The inverse Fourier transform of the (1 1 1) and equation image reflexes is shown in (d) and (e), respectively. The yellow ellipses mark irregularities in the line pattern, indicating lattice defects. A few edge dislocations are also marked.

4.2 Optical properties

After structural characterization of the site-selective QDs, their optical properties are considered next. Besides growing QDs at defined locations it is important that they are of high enough optical quality in order to be useful for applications in which they act as emitters, for example. Photoluminescence (PL) measurements can be used to investigate the optical quality of the QDs. Two samples were prepared in order to refer the measured PL to a particular configuration of site-selective QDs. The first sample contains a 16 nm GaAs BL grown on a patterned substrate followed by the deposition of 1.8 ML InAs resulting in QD formation. The second sample is similar but was additionally covered with a 90 nm thick capping layer of GaAs. Mainly double QDs nucleate in the defined holes which were 58.4 ± 6.1 nm in size (measured along equation image) after lithography. The double dots are aligned in the [0 1 1] direction due to the shape transformation of the hole during BL growth. The slightly larger amount of deposited InAs leads to larger QDs compared to the data shown in Fig. 3. The average QD height amounts to 14.2 ± 4.3 nm and the average QD diameter is 33.4 ± 6.3 nm. Despite the larger size of the QDs the size uniformity is in the same range as before with the standard deviations being 30% for the height and 19% for the diameter.

The capped sample was placed into a continuous flow liquid helium cryostat and cooled down to 10 K for the PL measurement. Since only small arrays of 100 µm in size were patterned it is essential to precisely locate these arrays once the sample is in the cryostat. A pair of x- and y-nanopositioners was available in the cryostat allowing for access of different regions on the sample surface. A helium-neon laser beam at 632.8 nm is used to excite electrons in the sample above the GaAs band gap. The excited electrons in the conduction band and the emerging holes in the valance band possibly relax to their respective band edges in the InAs QD, bound together to form an exciton and finally recombine by emitting a photon. The resulting emission of the QD is collected in reflection geometry using a 100× objective. The PL signal is dispersed with a 1.26 m grating spectrometer and detected with a silicon CCD which is cooled by liquid nitrogen. The laser beam is strongly focused onto the sample so that a spatial resolution of about 1 µm is achieved, thus allowing for µ-photoluminescence measurements.

Four spectra were taken at different locations on the patterned array. For reference, another four spectra were recorded on unpatterned regions. All these spectra are shown in Fig. 6. The integration time during data acquisition was 5 s. Single QD emission lines are observed both in the patterned region, (Fig. 6a), and in the unpatterned region (Fig. 6b). A difference between the spectra on the pattern and off the pattern is not obvious at first sight. The hole spacing in the patterned area was 250 nm. Since the spatial resolution is larger than the separation between the site-selective QDs several QDs will be excited simultaneously. Further complication arises from the fact that QDs nucleating between the holes will also contribute to the PL signal. It is thus not possible to distinguish the emission of site-selective QDs from that of self-assembled QDs. A qualitative statement on the optical quality of the site-selective QDs is however desired. The average linewidth of individual peaks is about 0.6 meV.

Figure 6.

(online color at: www.pss-a.com) Micro-PL spectra were recorded in the patterned region at four different locations (a). The hole spacing is 250 nm. Since the laser spot is focused to 1 µm, several QDs are illuminated at the same time. For reference, four spectra were recorded in the unpatterned region (b).

Combining the AFM measurements of the uncapped sample with the PL data it is possible to deal with this difficulty and to estimate the degree of photoluminescence originating from positioned QDs 40. This statistical analysis is based on a comparison of the QD density in the unpatterned region with the density of QDs in the patterned region. The latter density can be further specified by distinguishing between positioned QDs and QDs nucleating between the defined sites. Thus, three different types of QDs can be identified. The densities are then related to the integrated PL intensities. It was found that the effective quantum efficiency of QDs nucleating between the holes is practically equal to that of the QDs in the unpatterned region, which is consistent since both types of QDs are formed in the same way so that they should not exhibit any differences in their optical quality. More important, the site-selective QDs have an effective quantum efficiency of about 30% of that of QDs nucleating between holes 40. The inferior optical quality is likely related to the occurrence of defects, as described above. Nevertheless, the site-selective QDs are optically active and the statistical method presented here can be very useful in the course of optimization of sample fabrication and QD growth.

5 Control of quantum dot distribution and size

The general structural features of positioned QDs and their optical properties have been described. Two QD arrays have been shown which were grown under similar conditions but using different hole geometries. Double dot nucleation was found in small shallow holes whereas longer chains of four or more QDs formed inside of larger and deeper holes. Besides defining the QD position it is also important to control the QD distribution, that is, the number of QDs per hole and the overall QD density. The hole size influences the QD formation so that larger holes will accommodate more QDs. Atkinson et al. 37 investigated in detail the relationship between hole size, deposited amount of InAs and QD occupancy. They found an increase in the average number of QDs per hole for larger holes which is in agreement with the above observation. Furthermore, the QD occupancy for a given hole size depends on the deposited amount of InAs. The number of QDs per hole increases if more material is provided. The influence of several pattern and growth parameters on the QD formation is investigated in order to gain further insight into the control of QD nucleation. The lateral hole size, the BL thickness, and the amount of InAs are expected to be critical parameters in this context. In addition, the power of in situ annealing as a mechanism to control the QD distribution and size post growth is demonstrated.

5.1 Hole size

A 15 nm BL was grown on a patterned substrate followed by the deposition of 1.6 ML of InAs which is below the critical thickness of QD formation on flat GaAs layers. The holes were etched 30 nm deep into the substrate and had an average lateral size of 60 and 85 nm before overgrowth. The pattern spacing was 250 nm. AFM images containing a part of the QD arrays and representative profiles of QDs in the holes are shown in Fig. 7.

Figure 7.

(online color at: www.pss-a.com) Influence of lateral hole size on QD formation in the holes. The AFM images show parts of a QD array in which the original hole diameter before BL growth was 60 nm (a), and 85 nm (b). Representative height profiles reveal the formation of QDs inside the holes.

Although both hole types become shallower during BL overgrowth, the difference in the original hole sizes influences the growth process. The smaller holes are faster infilled during BL and QD growth so that the positioned QDs are almost at surface level. The depth of the larger holes is not as strongly decreased so that the QDs are almost completely contained inside the holes. QDs are found at the center of the hole and at the tilted sidewall, which is consistent with the earlier observation. The real height of the QDs can be deduced from the profiles and is on the order of 10 nm for both hole sizes. This is in agreement with other samples grown under similar conditions. While the QD size is rather independent of the lateral hole size, the number of QDs nucleating inside the holes is strongly affected. The average QD occupation on an array with 250 nm hole spacing (as in Fig. 7a and b) is 2.2 ± 1.8 and 3.7 ± 1.6 for the 60 and 85 nm sized holes, respectively. Larger holes can thus accommodate more QDs, which is simply related to the geometrical size of the holes. The hole spacing has a strong influence on the QD occupation in case of the larger holes (the QD occupation increases to 4.9 ± 1.4 on the 500 nm and 6.3 ± 1.3 on the 1000 nm array), but the smaller holes do not seem to be affected. This is explained by the fact that some of the small holes are close to being or have already been filled up prior to QD growth, as confirmed by the QD array shown in Fig. 7a. Hence, the hole volume is small and can only accommodate a certain amount of InAs. These holes which are not completely filled contain on average the maximum number of QDs which fit into the hole. The deposited amount of InAs is not enough to populate all holes with the maximum number of QDs on the dense array. With increasing hole separation, the individual amount of InAs increase so that more QDs can be formed. Again, the large standard deviations are likely related to non-uniformities in the original hole size.

5.2 Buffer layer thickness

Next, the BL thickness was varied. AFM images of three samples with a BL thickness of 5, 15, and 35 nm are shown in Fig. 8. The depicted holes had a lateral size of about 85 nm before growth and the separation is 500 nm. The larger holes are favored for this analysis since they are not filled up as quickly as the smaller ones during BL growth. 1.6 ML of InAs was deposited on each BL. The deposition of 5 nm GaAs does not lead to the formation of a closed BL, as seen in the AFM image. This might be related to surface undulations induced by deoxidation. Small pits are observed between the defined holes which is disadvantageous, as they lead to the nucleation of QDs beyond the defined sites. The defined holes contain only a few QDs but it is questionable whether they are coherent since the thin BL is probably not sufficient to account for the surface roughness in the hole resulting from etching. The deposition of 15 nm GaAs is enough to provide a smooth and closed BL. In general, QD nucleation is only observed in the defined holes. Several QDs are found in each hole and every hole seems to be occupied. Further increasing the BL thickness up to 35 nm slightly changes this situation because some of the originally 30 nm deep holes have been almost filled up and consequently reduce their attractive potential for site-selective QD formation. Hence, not all defined sites exhibit several QDs.

Figure 8.

(online color at: www.pss-a.com) The QD occupation is plotted with respect to the hole spacing for different BL thicknesses. The QD occupation is highest for the 15 nm BL and generally increases with larger hole spacing, once the BL forms a closed film. The lines are meant as guide to the eye.

The QD occupation was extracted from large AFM images and was related to the hole spacing (pitch) for the different BL thicknesses. The results are presented in the diagram of Fig. 6. Two different trends can be described. First, the QD occupation slightly decreases from 2.3 to 1.5 QDs/hole with increasing pitch in case of the thin BL. Second, the QD occupation increases with the pitch for the other samples. The opposed behavior is possibly explained by the formation of QDs between the holes, which is observed on the thin but not on the thicker BLs. The number of defined holes in 1 µm2 is 16, 4, and 1 for a spacing of 250, 500, and 1000 nm, respectively. An average density of 44, 57, and 75 QDs/µm2 was found between the holes for the respective spacings. The gain in random QDs per unit area with increasing spacing (13 and 17 QDs/µm2) is larger than the decrease in the hole number (12 and 3 holes/µm2). Therefore, less material possibly leading to QD formation is available for each defined hole on average. Unintentional random QDs are essentially not observed on the samples with thicker BLs. For 15 and 35 nm the average QD occupation increases with larger spacing. The reason was given above. The average QD occupation increases from 3.7 to 6.3 QDs/hole for the 15 nm BL and from 2.5 to 3.1 QDs/hole for the 35 nm BL. Despite the thick BL, all holes are still occupied which is an indication that they have not completely filled up yet. However, the QD occupation is lower on the 35 nm BL for all spacings. The reason is, that the holes become shallower with increasing BL thickness and therefore lose their attractive force for QD formation which is based on the surface curvature. The local accumulation of InAs is reduced and hence less QDs nucleate in the defined holes. The reduced potential for adatom accumulation weakens the dependence on the surrounding so that the dependence of the QD occupation on the hole spacings is reduced as well.

5.3 InAs amount

The increase of the number of QDs per hole with larger hole spacing was related to a larger reservoir of InAs for each individual hole on sparser arrays. Therefore, the amount of available InAs plays a role in the formation of a particular QD distribution. The amount of provided InAs was varied in order to investigate its effect on the QD occupation and size. 1.5 and 1.6 ML of InAs were deposited on a patterned substrate which was overgrown with a 35 nm GaAs BL. The QD occupation is lower on all arrays for the sample containing 1.5 ML InAs (not shown). The average QD occupation increases from 0.9 QDs/hole for the 250 nm spacing to 2.1 QDs/hole for the 1000 nm spacing. As described above, the increase of the 1.6 ML sample was from 2.5 to 3.0 QDs/hole for the respective arrays.

The QD height was analyzed with respect to the amount of InAs. A reduction in QD size is observed in the diagram of Fig. 9, where the average QD height is given with regard to the hole spacing for 1.5 and 1.6 ML of InAs. While a slight variation of the height is observed depending on the pitch, the average QD height is a factor of three lower when 1.5 ML of InAs is deposited instead of 1.6 ML. The small change in the InAs amount has a strong effect on the QD height. This has to be considered when searching for appropriate QD configurations and sizes.

Figure 9.

(online color at: www.pss-a.com) The average QD height was measured on differently spaced arrays for two amounts for InAs. While no significant dependence on the hole spacing is observed, the QD height increases with the deposited amount of InAs. The lines are meant as guide to the eye.

5.4 Hole depth

Reactive ion etching was used to partly circumvent the described limitations of WCE. EBL and RIE with an inductively coupled plasma was used to fabricate hole arrays in which the holes exhibit steep sidewalls of up to 90°. The hole shape is largely maintained and the elongation of the holes in the particular equation image direction could be reduced. A set of three samples was fabricated for which the etching time was varied in order to study the dependence of the QD occupation on the hole depth. The three samples were etched for 10, 15, and 20 s. The etch rate was about 2 nm/s but the exact depth of the holes is difficult to determine because of the steepness of the holes and therefore resulting AFM tip convolution. A 12 nm thick GaAs BL was grown on top of the patterned substrate followed by the deposition of 1.6 ML InAs. Site-selective QDs formed in the holes and essentially no random QDs nucleated on the flat surface between the holes. Two representative parts of arrays containing holes etched for 10 and 20 s are depicted in Fig. 10a and b, respectively. Representative profiles of site-selective QDs were extracted from the AFM images and reveal mainly double QDs in the shallow holes and single QDs in the deep holes. While the holes were originally of the same lateral size, a slight increase is observed with etching time. This does not interfere with the trend observed in (Fig. 10c), that the QD occupation decreases with increasing hole depth. The average QD occupation is given with respect to the etching time, thus the hole depth, for the 500 nm hole spacing. The average diameters of the analyzed holes were 101.9 ± 33.8 nm, 118.4 ± 14.0 nm, and 129.5 ± 5.5 nm for the samples etched for 10, 15, and 20 s, respectively. The average QD occupation drops from 3.0 ± 1.1 QDs/hole to 1.4 ± 0.5 QDs/hole. The tendency of higher occupation numbers for larger holes is hence replaced by the strong influence of the hole depth. In addition, the fluctuation of QD occupations has also decreased, as deduced from the lower standard deviations. Therefore, QD nucleation on the sidewalls, as found in shallow holes, is probably inhibited and QD formation is only observed at the bottom of the holes. As a consequence, site-selectivity can be improved by deeper holes. This is confirmed by the observation, that on the array with the deepest, and at the same time largest, holes (not shown) 80% of the holes are occupied with a single QD.

Figure 10.

(online color at: www.pss-a.com) AFM images of site-selective QDs formed in dry etched holes. The AFM amplitude signal is depicted for better contrast. The holes in (a) and (b) were etched for 10 and 20 s, respectively. Representative height profiles were extracted. The average QD occupation with respect to the etching time is shown in the diagram (c) for the 500 nm hole spacing, initially containing holes of equal size.

5.5 In situ annealing

Besides the investigated parameters, it is known that QD occupation and QD size are also affected by the InAs growth rate. Smaller growth rates favor the formation of larger QDs and lower QD occupations 37. However, the exact reasons for such a behavior were not emphasized so far. It is likely that the reduced growth rate gives more time to the In adatoms to rearrange on the surface during the growth process. Such a mechanism could in turn be exploited as a way to control the material distribution after growth and therefore allow for an expansion of possible QD configurations for future applications. The process of keeping a readily grown QD sample at elevated temperature without any further material deposition (besides As to stabilize the surface) is termed in situ annealing. The elevated temperature enhances the material redistribution through diffusion, desorption, and interdiffusion. The potential of this approach to control the structural properties of positioned QDs as well as the QD distribution was investigated. It was shown that double QDs merge into single dots during short annealings of 2:30 min at 500 °C 41. As a consequence, the size of the annealed QDs is larger than that of the as grown ones. This transformation can be described by a standard ripening theory according to Ostwald 42, in which large particles grow at the expense of smaller ones which slowly disappear. A similar behavior was observed for InAs QDs annealed on flat GaAs substrates under similar conditions 24. Furthermore, it was possible to get rid of unintentional QDs in between the holes, even for deposited InAs amounts as high as 2.6 ML 41. Another dominant feature of the annealing of InAs QDs at high temperature is the desorption of In atoms. The detailed study of Heyn 22 revealed that desorption of atoms from InAs QDs takes place in a layer-by-layer fashion, starting from the top of the QD.

For a quantitative analysis of the annealing effects on site-selective QDs three samples were prepared under similar conditions. First, several hole arrays with different hole sizes and spacings were fabricated on a GaAs substrate by EBL. An electron beam with a beam energy of 100 keV was used for the exposure in order to increase the hole size uniformity (<8% size fluctuation was achieved). A 20 nm GaAs BL was grown on a wet chemically etched hole pattern followed by the deposition of 1.7 ML InAs. One reference sample was immediately cooled down after QD growth while the other two where annealed for 2:30 min and 7:30 min. Figure 11 shows the average QD occupation per defined hole depending on the hole spacing (pitch) for different annealing durations. The average QD occupation for the densest array (250 nm) of the as grown sample lies below 1 QD/hole. This means that some of the holes remain unoccupied. That is due to the amount of deposited InAs which is not enough to form QDs inside each hole of the dense array. The QD occupation strongly rises with increasing pitch because of the larger available reservoir of In per hole. At a spacing of 500 nm an average of 3.0 ± 1.2 QDs is found per hole which is exceeded by 4.5 ± 1.1 QDs/hole for a pitch of 1000 nm. For larger spacings, a significant increase is not observed any more, as an average of 4.7 ± 1.4 QDs occupies each site of the 2000 nm spaced array. As described above, the size of the hole likely defines an upper bound for the number of QDs which can nucleate inside the hole.

Figure 11.

(online color at: www.pss-a.com) Evolution of average QD occupation during annealing. The average number of QDs per hole with respect to the hole spacing (pitch) is plotted for different annealing times. The occupation is continuously reduced throughout the annealing process. Representative SEM images for the different annealing stages are shown 43.

After annealing for 2:30 min the QD occupation decreases for all spacings. The decrease is strongest for the 500 nm spaced array where the QD occupation drops below 1 QD/hole. Nonetheless, the dependence of the QD occupation on the array spacing remains unchanged since the decrease of the number of QDs per hole is similar for both 1000 and 2000 nm pitches. The standard deviations of the average values have become smaller which is an advantage when trying to obtain uniform positioned QD ensembles. Even longer annealing for 7:30 min leads to a further decrease of the QD occupation with the result that the arrays become sparsely filled since the average occupation drops below 1 QD/hole for all spacings. The differences in QD occupation for the various hole spacings fade, especially after longer annealing. The overall reduction in QD occupation is in agreement with the earlier observation where two QDs merged into a single one. Furthermore, a reduction of the QD occupation distribution could be observed so that more than 50% of the holes on the 1000 nm array become filled with a single QD after long annealing. In order to determine whether pure ripening takes place or if desorption is also effective the evolution of the QD size was also investigated.

The SEM images in Fig. 11 indicate an increase in QD size for short annealing and a decrease after longer annealing time. The observed increase in QD diameter is related to the described ripening process. The observed reduction of the number of QDs per hole confirms this explanation. The average QD occupation decreases by more than 40% during short annealing but the QD diameter increases by at least 15%. Together with an increase in QD height, the increase in average volume of the QDs becomes larger than the decrease in QD occupation. Hence, desorption might be present but the ripening process dominates the QD evolution for short annealings and further In is accumulated from the surrounding of the holes. After 7:30 min of annealing, a strong reduction of the QD diameter was found on all arrays with the average diameters dropping down to or even below the initial values. The average QD height showed the same evolution. It increases for short annealing times and drastically decreases after longer annealing times. The relative change of the QD height is stronger compared to the QD diameter. Especially a decrease of 40% in height compared to the original value after 7:30 min of annealing supports the assumption of strong In desorption from the top of the QDs 22.

Two annealing regimes were hence identified. The QD evolution is mainly governed by a ripening process for short annealing times while In desorption becomes dominant at longer annealing times. The analysis proves that it is possible to control the size of positioned QDs after growth by employing an adequate annealing recipe. Both increase and decrease in QD size could be achieved by adjusting the annealing time.

6 Large scale characterization of ordered nanostructures

In order to gain further insight into ordering of site-selective QDs and the effects on the distribution due to in situ annealing X-ray diffraction measurements were performed at the European Synchrotron Radiation Facility (ESRF).

In the past 20 years high resolution X-ray diffraction (HRXRD) was widely applied for the non-destructive investigation of laterally patterned nanostructures 44–48. In the symmetrical HRXRD, the vertical lattice parameter of the crystal is probed. Thus, vertical distortions of the lattice induced by strained epitaxial layers could be accessed. In order to gain information about the lateral lattice parameter as well, one usually applies the asymmetrical case of HRXRD. However, a drawback of this method is that the gained information comprises the lattice parameter in lateral and vertical direction, and the shape of the nanostructures, and its composition profile at the same time. These components have to be clearly separated for the latter interpretation.

The grazing incidence diffraction (GID) overcomes these problems, being sensitive to the lateral lattice parameter, only. In grazing incidence geometry, one makes use of the effect of total external reflection (TER), which occurs when the X-ray beam impinges on the surface of the crystal under a grazing angle. In this case only an evanescent wave penetrates into the sample. Thus the scattering volume is concentrated in a very thin surface layer making GID a perfect tool to investigate surface nanostructures.

In the past decade, various kinds of nanostructures were investigated profiting of the benefits of this non-destructive method. Depending on the focusing of the X-ray beam, the grazing incidence angle results in a rather large footprint of the incoming beam on the sample surface. Accordingly, the collected information gives an average over a large number of illuminated nanoobjects (ranging to several billions) by the incoherent summation of several coherently illuminated areas 49. Sizing down the beam to the nanometer-scale by focusing optics like Fresnel zone-plates, diffraction by single nanoobjects 50 becomes possible. Moreover, the depth sensitivity of grazing incidence methods may be tuned by altering the angle of incidence. Therefore, not only structural information of free-standing nanoobjects but also depth dependent information of buried structures could be obtained 44.

In the GID pattern, the information about strain and effective shape of the scattering volume are entangled with each other. Thus, special methods for interpretation have to be applied. One method to treat GID patterns is based on the iso-strain scattering model 51. This model considers the scattering volume to be composed of a stack of iso-strain layers with average lattice parameter. Since years this model is widely used interpreting GID data. Essential data on shape, and spatial ordering disentangled from strain induced effects could be accessed by grazing incidence small angle scattering (GISAXS). For instance, this method has proven to be sensitive to changes in morphology and ordering induced by post-growth annealing 25. Built on the same effects of TER as GID it benefits from very high intensity of the specular reflected beam. This results in short exposure times and fast scans which makes it, alike GID, to a well-suited tool for in situ studies of the surface morphology.

6.1 Sample layout

The sample layout was specifically designed to meet the needs of the HRXRD investigation. Since EBL was used to fabricate the holes, the samples consisting of a quarter of a 2″ wafer could not be completely covered with holes. Instead, a 500 µm × 500 µm large mesa was defined by EBL at the center of the sample on top of which the hole array was fabricated. The spacing between the holes is 250 nm and the pattern orientation was rotate by 45° on one sample. The parts of the sample surrounding the mesa were covered with a gold (Au) layer. As before, a 20 nm GaAs BL was grown before the deposition of about 1.7 ML of InAs. The Au cover around the mesa inhibits the formation of an epitaxial GaAs film and the subsequent formation of QDs so that only the surface of the mesa is of mono-crystalline quality. Two types of patterns were investigated (see Fig. 12).

Figure 12.

Layout of the two patterns. The pattern on the left is oriented along [1 1 1] direction and the corresponding sample will be called “P1.” The pattern on the right is oriented along [1 0 0] direction and will be called “P2.”

6.2 X-ray investigations of the patterned structure

X-ray experiments in grazing incidence conditions prove the quality of the pattern. The experiments were performed at the surface diffraction beamline ID03, ESRF. A focused X-ray beam (spot size 50 µm × 50 µm) with E = 13 keV was used at a grazing incoming angle of αi = 0.5°. A full polar GISAXS scan was achieved by rotating the sample around the surface normal for 360° (see Fig. 13). The intensity is integrated along the vertical direction and projected on the Q110, Q−110-plane.

Figure 13.

(online color at: www.pss-a.com) The measured in-plane GISAXS map of P1 is shown. The intensity is integrated along Q001. The peak to peak distance in the intensity pattern in reciprocal space corresponds to the 250 nm period of the real space hole pattern. The intensity is given in logarithmic scale.

During this 360° rotation there are two positions where the incoming beam is parallel to the long sidewalls of the holes. At these very positions each sidewall gives rise to a scattering maximum or, regarding the two maxima it resembles a “chevron”. The rather diffuse signal originating from the shape of the holes is then modulated by the interference function due to the long range order of the holes which can be identified in the sharp periodic maxima along the equation image direction. Evaluating the angle of the “chevrons” with respect to the horizon in Fig. 14 a good agreement with AFM data regarding the slope of the holes' sidewalls is achieved, proving a rather homogeneous shape averaged over a large ensemble of holes.

Figure 14.

(online color at: www.pss-a.com) GISAXS signal of P1 on the detector. The sample is irradiated along the [1 1 0] direction which means parallel to the long axis of the holes. Periodicity due to the real space pattern and chevrons originating from facets of the holes are visible.

GID reciprocal space data were obtained by measuring a small region in the vicinity of the GaAs equation image Bragg peak. A reciprocal space map is shown in Fig. 15. The sample P2 which was measured by GID features a pattern which is rotated by 45° in respect to the pattern along the [1 1 0] and equation image directions. The sharp periodic maxima perfectly correspond to the reciprocal coordinates of the pattern. A diffuse cloud above and below the GaAs Bragg peak is visible. The whole GID pattern is a convolution of effects with different origin. First, the ordered, real space period of the pattern gives an interference function which results in the sharp maxima at the periodic positions. Secondly, the sidewalls of the holes provides a shape function, visible in the diffuse contributions and similar to GISAXS. In order to give a proof, it is insufficient to regard only a 2D reciprocal space map of GID, where the component in vertical scattering direction is integrated. By this integration, information about the scattering object related to the vertical scattering direction is lost. Thus, it is necessary to compare simulations to the whole 3D reciprocal space data.

Figure 15.

(online color at: www.pss-a.com) Reciprocal space map of the equation image GaAs reflection of P2 in grazing incidence geometry. The intensity is given in logarithmic scale, the integration was done along Q001.

3D GID simulations of a single unoccupied hole using first order Born approximation are compared with the experimental data in Fig. 16. For comparison of the 3D data, the depicted GaAs equation image reflection was split in the middle along the equation image direction. Due to the reflection's symmetry to this axis, it is possible to compare the left part of the reflection (experiment) which is given by the red iso-intensity surface with the right part (simulation) which is shown in the colored volume. Regarding the experiment, the intensity maxima are found at certain positions in the lateral Q110, Q1–10-plane, defined by the real-space hole pattern. Thus, the experimental GID data of the patterned structure can be identified as the regular grid of vertical rods. Moreover, the intensity maxima show a dependence on the vertical momentum transfer, Q001, comparable to GISAXS measurements (Fig. 15). Additionally, the intensity has the lateral periodicity of the substrate pattern and is furthermore modulated by the shape function of the scattering holes which causes the vertical rods to be only visible on a chevron. The crystal truncation rod can be found at the coordinates of the equation image GaAs Bragg peak extending into vertical direction at the center of the figure.

Figure 16.

(online color at: www.pss-a.com) Comparison of the 3D reciprocal space scattering volume of the equation image GaAs reflection in grazing incidence geometry (front, red iso-intensity surface) with the simulation (back, colored volume). Q001 goes along the vertical axis.

The simulation is depicted in a colormap behind the experimental data. Around the Bragg peak the major features in the simulation are, like in GISAXS, the shape-related “chevrons” and Bessel-like fringes which correspond to the Fourier transform of the lateral shape of the hole. For the simulation, AFM data was used as an input to model the shape function of the single hole by finite element method (FEM). Thus, the pattern is not part of the model and consequently not visible in the simulated intensity, which can be interpreted as an envelope for the experimental data. Considering that the scattered intensity in GID is a convolution of the scatterer's shape and the lateral distortions in the crystal lattice, and the interference function due to long-range ordering of the holes, strong signal of scattered intensity will only be found at areas, where these contributions are maximal. Comparing the full 3D reciprocal space volume (Fig. 16) we found, that only in regions, where the simulation obtains its maximal values, the scattered intensity is seen in the experiment. Thus, it can be concluded that the average shape function of the scattering hole can be precisely reconstructed by FEM modeling and GID simulations. A proper understanding of the contributions from hole shape and pattern is essential in order to further investigate the ordering of QDs nucleating inside regularly spaced holes.

7 Conclusions

A review of different aspects in site-selective growth of InAs QDs was given. A theoretical model was used to explain the influence of surface curvature on local variations in the growth rate, consequently leading to site-selective growth of QDs in nanometer sized holes on the substrate surface. The structure of site-selective QDs was discussed and high resolution transmission electron microscopy was used to investigate the preferential nucleation sites inside the defined holes as well as the internal QD structure. The site-selective QDs are coherently strained with defects possibly forming close to their surface. A statistical method can be used to identify the optical quality of the QDs by correlating photoluminescence and atomic force microscopy measurements. The effective photoluminescence of the site-selective QDs was only 30% of that from random self-assembled QDs, which was related to possible defects. The influence of different growth and pattern parameters on the QD occupation and QD size was discussed and it was shown that in situ annealing is a powerful tool to manipulate these properties post growth. QD occupations ranging from 1 QDs/hole up to 6 QDs/hole could be fabricated and QD diameter and QD height could be increased up to 30 and 70% or decreased down to 7 and 40% of the original value. Finally, the patterned structure was analyzed by HRXRD in order to pave the way for further in situ investigations on the ordering of site-selective QDs nucleating inside nanoscaled holes.

Acknowledgements

The authors acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG) and the State of Baden-Württemberg through the DFG-Center for Functional Nanostructures (CFN) within subproject A2.6. The authors thank R. Felici and T. Dufrane for preparing the experimental setup at the ESRF beamline ID03 and B. Terhalle of Paul Scherrer Institut for patterning samples by high resolution electron beam exposure. The authors further thank C. Mayer of KIT for his support with sample preparation and characterization as well as D. Litvinov and E. Müller, both of KIT, for TEM measurements and interpretation.

Biographical Information

Mathieu Helfrich obtained his diploma in physics from Karlsruhe Technical University in 2009, working on the fabrication of site-selective quantum dots in the research group of Daniel Schaadt at the DFG-Center for Functional Nanostructures. He continued his work in the same group at the Karlsruhe Institute of Technology and focused on controlling the structural properties of site-selective quantum dots. He completed his PhD in July 2012.

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