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B multilayers quantum dot stacks
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Journal of Crystal Growth 284 (2005) 47–56 www.elsevier.com/locate/jcrysgro
Microsize defects in InGaAs/GaAs ðN11ÞA/B multilayers quantum dot stacks P.M. Lytvyna, I.V. Prokopenkoa, V.V. Strelchuka, Yu.I. Mazurb,, Zh.M. Wangb, G.J. Salamob a
Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, Prospect Nauky 45, 03028 Kyiv, Ukraine b Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA Received 2 February 2005; received in revised form 4 July 2005; accepted 7 July 2005 Available online 15 August 2005 Communicated by R.M. Biefeld
Abstract Surface morphology of microsize defects on the surface of various high-index GaAs substrates was investigated using an atomic force microscope (AFM). The surfaces investigated were the top layer of 1- and 17-period In0:45 GaAs0:55 =GaAs structures with quantum dots or buffer layer. These structures were characterized by the formation of oval defects on (1 0 0) surfaces, and microsize defects possessing the shape of multifaceted pits and hillocks on ðN 1 1ÞA=B ðN ¼ 7; 5; 4; 3Þ surfaces. The microsize defects were found to chaotically distribute on the surface and, as a rule, gathering in groups with some number of defects. Their density did not depend on the substrate orientation while the shape and orientation of the microsize defects were found to depend on the crystallographic orientation of the substrate. This dependence was determined to be the result of anisotropy of surface diffusion and surface elastic properties. The anisotropy of elastic properties of high-index surfaces was found to be the dominating factor in determining the microsize defect shape. We also report direct evidence of the fact that the effect of quantum dot lateral ordering observed on high-index ðN 1 1ÞB surfaces is determined by the anisotropy of surface elastic properties as well as elastic interaction between adjacent quantum dots. r 2005 Elsevier B.V. All rights reserved. PACS: 07.79.Lh; 68.35.Dv; 68.55.Jk; 68.65.+g; 81.05.Ea Keywords: A1. Atomic force microscopy; A1. Nanostructures; A1. Oval defects; A3. Molecular beam epitaxy; B2. Semiconducting III–V materials
1. Introduction Corresponding author. Tel.: +1 479 575 7476;
fax: +1 479 575 4580. E-mail address: [email protected] (Yu.I. Mazur).
Molecular beam epitaxy (MBE) offers the interesting possibility to produce semiconductor
0022-0248/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2005.07.005
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nanostructures with control at the atomic level [1]. As an example, (In,Ga)As quantum dots (QDs) obtained using the MBE [2] can play an important role in the optoelectronic industry because of the need for small, homogeneous and ordered nanostructures suitable for fabrication of highly efficient high-frequency and optical devices. In this pursuit, high-index GaAs surfaces have recently attracted significant attention based on the added control they can provide for the growth of GaAs-based nanostructures [3]. High-index surfaces can provide some control of self-assembled shape, size, and uniformity and provide unique templates for nanostructure growth [4,5]. As a result, efforts to improve the understanding of these faceted surfaces and their role in the growth of nanostructures are needed. In this paper, we have used oval defects (ODs) as a possible tool to probe the influence of anisotropic surface strain on the shape of these microsize defects and on the ability of high-index surfaces to provide unique templates for nanostructure growth. ODs are the main type of morphological defects found on GaAs films grown using the MBE method on GaAs substrates with (1 0 0) orientation. There are two types of ODs, namely: adefects and b-defects, without and with a core, respectively. When using a substrate with (1 0 0) orientation, the long axis of the OD lies along the direction h0 1 1i [6]. Typical dimensions of these defects are of the order of several micrometers depending on the epitaxial layer thickness. Also known is that an increase in the growth rate, decrease in the substrate temperature [7] or increase in the layer thickness [8] results in an increase in the OD density ranging from 102 up to 106 cm2 . A change in As/Ga flux ratio is also known to affect the defect density [9]. Although not well understood, the potential reasons for ODs to appear are: (1) gallium spitting onto gallium crucible walls [10], (2) the formation of gallium oxides on the surface [11], (3) uncontrolled impurities in the arsenic source [12], (4) substrate contamination [13,14], and (5) presence of stacking faults [15]. With these potential causes in mind, special care with arsenic and gallium molecular beams and the transport of substrates has made it
possible to reduce the OD density down to 102 cm2 [16]. The impact of the lower OD density, however, is somewhat ambiguous. It was shown, for instance, that the optical and electrical behavior of GaAs [17] and InGaAs [18] epitaxial layers considerably degrade near ODs. On the other hand, micro-Raman spectroscopy indicates that the quality of GaAs epitaxial layers near ODs is comparable to that in defect free regions [19]. While much is known about ODs, the origin and mechanism of defect formation is at best controversial. For high-index surfaces, even less can be concluded. In fact, we are unaware of any studies aimed at a systematic investigation of microsize defects in GaAs-based nanostructures grown on high-index GaAs substrates. In this work, we have investigated microsize defects on GaAs ðN 1 1ÞA/B surfaces. Most of the ODs have lateral dimensions of about 2 mm, a depth of approximately 0:1 mm, and a density that can reach 104 cm2 . On ðN 1 1ÞA/B surfaces, microsize defects form as dimples having a multifaceted shape, and in all cases, possess a (1 0 0) facet. ðN 1 1ÞA surfaces differ from ðN 1 1ÞB surfaces having hillocks of an irregular shape at the defect core. When we vary the substrate from (3 1 1)A to (7 1 1)A, the height of these hillocks is systematically reduced. The hillocks are of irregular shape, a fact that can be associated with their polycrystalline nature. For the high-index surfaces studied, the microsize defects aggregate chaotically as groups on the surface, so that their density is not a clear function of substrate orientation. (Possibly caused by a chaotically distribution of substrate surface contaminations as a result of preliminary chemical treating the surface and/or spitting Ga and/or Ga (GaO, Ga2 O, Ga2 O3 ) oxides in the course of growing the structure.) However, the shape and orientation of the microsize defects were found to depend on the substrate crystallographic orientation. We have found that this dependence is caused by anisotropic surface diffusion and anisotropic surface elastic properties inherent to high-index surfaces. Moreover, these effects were also found to influence the lateral ordering of QDs observed on high-index ðN 1 1Þ surfaces.
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2. Experimental procedure
3. Results and discussion
The investigated structures were grown using the MBE method on GaAs(1 0 0) and GaAsðN 1 1ÞA=B substrates (where N ¼ 7; 5; 4; 3). The degree of misorientation from GaAs(1 0 0) towards (1 1 1) is 11:4 for GaAs(7 1 1), and 15:8 for GaAs(5 1 1), and 19:5 for GaAs(4 1 1), and 25:2 for GaAs(3 1 1). All of the investigated samples were held side by side with indium on a molybdenum holder. After loading into the MBE growth chamber, the surface oxide was thermally desorbed at 600 C while exposing the surface to a 106 Torr As4 beam equivalent pressure (BEP) from a solid source valved controlled cell. This As4 BEP was kept constant for all growths. First, a 0:5 mm-thick GaAs buffer layer was grown at 580 C, and then the substrate temperature was reduced down to 540 C for the growth of (In,Ga)As multiple layers. The layers consisted of 1- and 17-periods of 6 ML In0:45 Ga0:55 As QDs and 65 ML GaAs spacers. Using the method of in situ reflection high-energy electron diffraction (RHEED), the growth rates of In0:45 Ga0:55 As and GaAs were kept to be 0.78 and 0.43 ML/s, respectively. We studied three sets of samples, namely: (1) samples containing only the GaAs buffer layer, (2) heterostructures with a single In0:45 Ga0:55 As QD layer, and (3) multilayer 17-period In0:45 Ga0:55 As=GaAs structures with QDs. The top layer of QDs was left exposed for topographic atomic force microscopy (AFM) imaging under ambient condition. Morphological investigations of the studied structure surfaces were performed using a scanning AFM NanoScope IIIa in the tapping mode. We used silicon probes with the mechanical resonance frequency equal approximately to 150 kHz and the tip radius close to 5 nm. Before and after measurements, tips were tested using the special test gratings made by NT-MDT (Molecular Devices and Tools for NanoTechnology) company [20]. The crystallographic orientations of the samples were determined using standard X-ray diffraction procedure. Homogeneity of the studied surfaces over a large area was checked up using optical microscopy with the Nu-2E (Carl Zeiss) microscope equipped with a digital processing system.
The objective of this research was to investigate the possibility of using microsize defects to study the influence of anisotropic surface elastic strain on the process of lateral ordering and on improving the homogeneity of (In,Ga)As QDs using highindex GaAs substrates. It is well known that the driving force for self-organized (In,Ga)As QD creation on a GaAs is elastic strain relaxation. In the case of Inx Ga1x As=GaAs lattice mismatched heterostructures, a 2D–3D morphological transition is realized only after the Inx Ga1x As thickness exceeds the critical thickness. However, one can assume that the In concentration could considerably exceeds the nominal value for a given critical thickness at some local places on the grown layer. Therefore, the process of strain relaxation at these high In concentration locations can be a specific source for microsize defect creation, as has been noted [21] when studying microsize defects in (In,Ga)As QDs on a GaAs(3 1 1)B surface. Therefore, our first effort in this work was to investigate the surface morphology of ODs on a GaAs buffer layer deposited onto GaAsðN 1 1ÞA/B substrates and compare with that found on GaAs(1 0 0) substrates. Fig. 1 shows the optical micrographs of a GaAs buffer layer on GaAs (1 0 0) (Fig. 1a) and GaAs(3 1 1)B (Fig. 1b) substrates. It can be seen that large areas of the sample surface are free of microsize defects. The defect density inherent to all the studied samples was practically the same and did not exceed 104 cm2 , which is in a good agreement with the results of several previous works [7–9]. The samples were grown simultaneously on the same molybdenum block so that their growth conditions are identical. For our growths we observed that the defects were likely to gather in aggregates of 3–5 defects located within small distances of each other. As seen from the insert (Fig. 1), the shape and orientation of the microsize defects differ on (1 0 0) and (3 1 1)B surfaces. For the (1 0 0) surface (Fig.1a), we deal with typical ODs oriented along ¯ direction and possessing a clear core at the [0 1 1] the defect center (b-defect) (see a classification of defects in [15]). For the (3 1 1)B surface (Fig. 1b),
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In general, the mean density and size of the ODs were comparable on both the (1 0 0) and (3 1 1)B surfaces. The observed differences in orientations and shape of the defects are caused by differences in the anisotropy of the physical properties inherent to these surfaces (values of adatom surface diffusion and elastic properties of the surface). This conclusion is supported by recent work [22] that showed that the orientation of ODs ¯ direction can be explained by the along the [0 1 1] anisotropy of Ga adatom migration. Shown in Fig. 2 are detailed AFM images of typical microsize defects present on the GaAs buffer layer surface deposited onto a substrate with (3 1 1)B orientation. The defects marked as 1 and 2 possess a comparable depth but differ in shape. Meanwhile, the shape of the defects 2 and 3 is practically the same, but the depth at the core region differs by almost an order of magnitude. Although we have no direct evidence to exclude the possibility of creating some quantity of defects directly in the process of growing the GaAs layer, the correlation between size and depth of the
Fig. 1. Optical micrograph of GaAs buffer layer grown on GaAs(1 0 0) (a) and GaAs(3 1 1)B (b) substrates. Microsize defects are marked with arrows. The inserts show 3D AFM images of corresponding defects.
the defects are multifaceted V-shaped concaves oriented along the crystallographic direction ¯ The defect core is located at its top, and [2 3¯ 3]. its depth is reduced as one moves along the direction [2¯ 3 3], giving the impression of a tail. In addition, our AFM investigations revealed that, when depositing GaAs buffer layer onto substrates with (1 0 0) orientation, in addition to b-defects one can also observe ODs with smaller sizes without any pronounced central core (adefects). Sometimes, we can observe coupled ODs as well as asymmetric a- and b-defects. Typical OD sizes varied from 1 to 12 mm. Thus, in the case of (1 0 0) surface one can see the typical and rather well studied ODs that mainly appear at the interface of the substrate and GaAs buffer layer.
Fig. 2. (dz=dx) derivative of AFM image of microsize defects typical for the surface of the GaAs buffer layer grown on GaAs(3 1 1)B substrate. The inserts show the height map for the surface with indication of cross-section lines and respective defect sections. The scale of the height axis at the defect sections is 100-fold magnified relatively to their length.
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defects are more suggestive of different nucleation sources (i.e., different size, shape and composition) that originate at the substrate/GaAs buffer layer interface. It is known that the rate of Ga adatom migration on the surface of a GaAs epitaxial layer is different when deposited onto ðN 1 1ÞA versus ðN 1 1ÞB substrates with the same index N in an As-rich atmosphere [23]. In this case Ga adatom migration is strongly influenced by differences in the surface diffusion and elastic properties of the polar A and B planes. The observed effects of this surface anisotropy on the shape of microsize defects ðN 1 1ÞA and ðN 1 1ÞB are dramatic and are shown in Fig. 3 for the (3 1 1)A and (3 1 1)B surfaces. A characteristic difference of the defects observed on the (3 1 1)A surface is the presence of a hillock at the region of the defect core (Fig. 3a). These hillocks possess a clearly pronounced multifaceted shape and differ from one another by their sizes. Sometimes, these hillocks exhibit a long tail (see the insert, Fig. 3a) oriented along the [2¯ 3 3] direction. Such hillocks were not observed in the case of multifaceted defects on the (3 1 1)B surface. In fact, the presence of hillocks on the A-surface and their full absence on the B-surface is observed for all the studied ðN 1 1Þ substrate orientations. Interestingly, the hillock sizes on the ðN 1 1ÞA surfaces decrease with increasing N. Meanwhile, the most common feature between defects observed on the (3 1 1)A and (3 1 1)B surfaces is the presence of a (1 0 0) facet forming the front wall of the defect (Fig. 3). As we change the growth surface from (3 1 1) to (7 1 1), the observed microsize defects are basically similar to those observed on the (3 1 1) surface (Fig. 4a–d). The range of defect sizes and density remains practically the same for the deposition of only one In0:45 Ga0:55 As (7 ML) epitaxial layer of QDs. As seen in Fig. 4, all the microsize defects on ðN 1 1ÞB surfaces possess the multi-faceted shape and are nucleated from a nanopore (core). However, as the growth surface is changed from (3 1 1) to (7 1 1), the tail at the defect base is reduced in size, while the angle at the apex, formed by the defect facets, is increased. Moreover, the size, shape and density of the multifaceted defects do not change in the case of the multilayer 17
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Fig. 3. 3D AFM images of typical microsize defects on the surface of GaAs buffer layer grown on substrates with (3 1 1)A/ B orientations. Shown in the insert is the multifaceted defect with the hillock smoothed due to the surface diffusion transfer of material.
(In0:45 Ga0:55 As=GaAs) structure. The fact that the character of microsize defects (i.e., their depth, shape, density) does not change in any significant way when depositing either a GaAs buffer layer, 1- and 17-period In0:45 Ga0:55 As=GaAs structure, further supports the idea that the defects nucleate mainly at the interface of the substrate and GaAs buffer layer. We made a detailed analysis of the shape and orientation inherent to defects for all studied structures. Crystallographic orientations of microsize defects were determined using X-ray diffraction in symmetric and asymmetric reflections after preliminary optical and AFM studies of OD
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Fig. 4. Surface height maps (on the left) and derivatives (dz=dx) of AFM images (on the right) of typical microsize defects on the surface of In0:45 Ga0:55 As (7 ML) layer on GaAsðN 1 1ÞB substrate. There pointed are the sections (profiles) of surfaces along the dotted lines. Empty ovals point the defect cores. Quantum dots can be seen on the surfaces and on the defects.
orientations relatively to the sample side crystallographic directions. For example, we know that f0 1 1g crystallographic planes are the most preferable and ideal to cleave the high-index substrate. In case of samples grown on the (3 1 1) surface, other possible crystallographic orientations are ¯ ½2 3¯ 3 ¯ and ½0 1¯ 1 . To find the ½2¯ 3 3 ½2¯ 3 3 , ½0 1 1 ,
crystallographic direction, we measured X-ray diffraction in asymmetric reflection from the (3 2 2) crystallographic planes. These planes show that the unique position in a crystal and the diffracted beam can be detected only with rotation of the crystal in the ½2¯ 3 3 direction from the position were the signal for the 3 1 1 symmetric reflection was measured. If the crystal is rotated in ¯ ½0 1¯ 1 or ½0 1 1 , ¯ the opposite direction, i.e., ½2 3¯ 3 , no diffracted beam is registered for the detector positioned at the angle required for 3 2 2 reflection. The analogous crystallographic planes could be selected for each of ðN 1 1Þ surfaces and using the procedure described above the crystallographic directions of the samples, and the orientation of OD relative to these directions, can be determined exactly. The data show that the clearest defect facet on the ðN 1 1ÞA/B surfaces is the (1 0 0) facet (see Fig. 3a and b). The mean values of the experimentally measured angles between the (1 0 0) facet and the ðN 1 1ÞB surface as well as the depth of the defect core are given in Table 1. We believe that the growing deviation between the observed angle and the calculated angle going from the (3 1 1) to the (7 1 1) orientations is caused by a diffusion smoothing processes. Small angles between the defect facet and the substrate encourage diffusion and lead to an enhancement of diffusion smoothing of the defect facet. In addition, for defects possessing a large depth, diffusion smoothing of the defect facet is considerably reduced since the facet edges (top to bottom) are more widely spaced. As a consequence, the best agreement can be expected for large angles and deep defect cores, as is observed. It is interesting to note that the core depth for some defects can reach magnitudes ( 180 nm) very close to the total thickness of the 17-period multilayer structure. Moreover, the obtained value of the defect core depth can be even larger as a result of the limitation of the AFM probe. The latter is indicative of the fact that some large defects cannot be covered in the process of epitaxial layer deposition. In addition to surface diffusion anisotropy, the anisotropic character of the substrate elastic properties influences the microsize defect shape.
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Table 1 The angle of the defect front facet slope and defect core depth for the structures grown on GaAs substrates with ðN 1 1ÞB orientations Substrate orientation
Calculated angle between crystallographic plane (1 0 0) and surface of substrate (degrees)
Average angle between front facet of defect and surface of substrate (degrees)
Typical depth of a defect core (nm)
311 411 511 711
25.2 19.5 15.8 11.4
25 3 15 3 10 2 6 2
60 50 60 25
Fig. 5. Schematic representation of stereographic projections with indication of the elasticity modulus value distribution along crystallographic directions (left) and microsize defect AFM images with cross-sections along dotted lines for the surface of 17-period In0:45 Ga0:55 As=GaAs ðN 1 1ÞB structure (middle) when the substrate orientation is: (a) (1 0 0), (b) (3 1 1)B and (c) (7 1 1)B. Images of an enhanced resolution which illustrate formation of QD patterns are shown (right).
Shown in Fig. 5, are the stereographic projections of the magnitude of the surface elasticity along various crystallographic directions corresponding to the surface orientations (1 0 0) (Fig. 5a), (3 1 1)
(Fig. 5b) and (7 1 1) (Fig. 5c) along with corresponding AFM images of areas with defects inherent to the 17-period In0:45 Ga0:55 As=GaAs structures. The values of Young’s moduli E were
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calculated according to the equation [24]: E 1 ¼ s11 ð2s11 2s12 s44 Þ ðk2 l 2 þ l 2 h2 þ h2 k2 Þ=ðh2 þ k2 þ l 2 Þ,
ð1Þ
where s11 , s12 , s44 are the elastic compliance constants given in [25,26] and h, k, l are the Miller’s indexes of crystallographic direction. Choosing different crystallographic directions hh k li within surface plane with step of about 51 we obtained a distribution picture of E value on investigated surfaces (1 0 0) and ðN 1 1Þ. The calculated values of E are in good agreement with published results [25,27]. As seen from Fig. 5, the crystallographic orientation of microsize defects coincides with the direction of the largest elastic constants. In multilayer structures grown on GaAs(1 0 0) substrates, the microsize defects are oriented in the ¯ which coincides with the direction direction [0 1 1], of the largest In/Ga adatom diffusion [28,29]. When changing the surface orientation from (1 0 0) to (7 1 1), the anisotropy of the surface elasticity modulus is considerably reduced. In our opinion, it is this effect that is responsible for the change in the microsize defect shape. That is, for the (7 1 1)B surface, the relative magnitude of the anisotropy of the elasticity modulus anisotropy is smaller than that for (1 0 0) and (3 1 1), which results in round shape defects (Fig. 5c). On the other hand, a decrease in the defect tail length with increasing N-index on GaAs ðN 1 1Þ substrates can be explained stemming from purely geometrical grounds (Fig. 6). The defect front facet coincides with the (1 0 0) crystallographic plane that has been neither smoothed nor overgrown in the course of the structure growth. It is most probable that the opposite defect facet is also limited by a crystal plane, but it is strongly subjected to diffusion smoothing and partial overgrowing. However, the angle between the front and back facets of multifaceted defects on ðN 1 1Þ surfaces remains approximately the same. As seen from Fig. 6, with increasing N-index, the defect (1 0 0) facet slope decreases relative to the ðN 1 1Þ surface. As a consequence, when the N-index reaches high values, the ðN 1 1Þ surface will cut a larger and larger part of the defect tail, and, as a result, the
Fig. 6. Changes of multifaceted defect sections with changing the orientation of the substrate surface. The scheme takes into account the angles between crystallographic planes.
defect shape will be more rounded, which is what observed experimentally. Inspite of the fact that multifaceted defects are generally not healed in any practical way, if the defect facet slope angle relative to the substrate surface is less than 7–81, then the defect facets can support QDs of sizes and densities that do not differ significantly from that observed on defectless regions (Figs. 4 and 5). However, when the defect facet slope angle is larger than 8 , QDs do not appear, except on the defect front facet (1 0 0) plane. On this facet, QDs at slope angles of 11:4 (GaAs(7 1 1)) and 25 (GaAs(3 1 1)) relative to the structure growth surface are observed. In this case, the defect facet should be considered simply as a (1 0 0) growth surface where 3D QD growth is realized via the Stranski–Krastanov mechanism. These observations were for both for a single- and multilayer In0:45 Ga0:55 As=GaAs structures. Interestingly, we observed a clear tendency in multilayer structures to form laterally ordered arrays of QDs (Fig. 5). Depending on the substrate surface orientation, one can obtain QDs ordered ¯ direction (QD chains) (Fig. 5a) along the [0 1 1] [30] or laterally ordered networks of nearly equal distant QDs [31] (Figs.5b,c) (QD chains look as aligned along the microsize defect orientation direction). Here, the defect orientation and symmetry have a one-to-one correlation with the position of QDs on the surface. The cell dimension of the QD lateral network on the less anisotropic surface (7 1 1)B is less than that on the (3 1 1)B surface, and the shape of the lateral cell is close to a rhombus shape. Lateral self-ordering of the QDs
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in multilayer structures is most probably caused by the formation of periodically changing field of elastic strains as well as an accompanying redistribution of the impurity-defect composition of the growth surface. The influence of an elastic strain far-acting field on QD lateral ordering is indirectly confirmed by Fig. 5b where the defect strain field causes fluctuations in QD lateral ordering. In the defect core region (i.e., in the ranges of the largest strain and compositional gradients), several QD rows exactly follows along the defect facet orientation directions, that is the lateral QD arrangement ‘‘feels’’ the shape of the strain field distribution around the defect.
4. Conclusions Our comparison of the obtained results for GaAs buffer layers and In0:45 Ga0:55 As=GaAs structures with QDs allows us to state that the process of residual elastic strain relaxation in a growing epitaxial layer is not the dominant cause of microsize defects, as was assumed in [21]. The shape and orientation of microsize defects are determined by the structural anisotropy observed on the GaAs(1 0 0) and GaAsðN 1 1ÞA/B substrate surfaces. The strain fields developed in the growth direction of multilayer In0:45 Ga0:55 As=GaAs structures determine the size and lateral arrangement of (In,Ga)As QDs, and their value considerably exceeds the strain fields and concentration fluctuations formed around microsize defects. The latter is developed during QD growth on the microsize defect surface and confirmed by the appearance of small fluctuations of their lateral arrangement (QD chains and networks cover defects without significant transformations). QD lateral ordering on the surface is caused by two factors: anisotropy of lateral strain fields and the effect of elastic interaction between QDs on the surface. The studied microsize defects can be used to determine surface crystallographic orientation, as indicators of anisotropy inherent to surface physical (elastic) properties. Meanwhile, sets of microsurfaces with various orientations can be used as a playing field to explore QD growth processes.
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Journal of Crystal Growth 284 (2005) 47–56 www.elsevier.com/locate/jcrysgro
Microsize defects in InGaAs/GaAs ðN11ÞA/B multilayers quantum dot stacks P.M. Lytvyna, I.V. Prokopenkoa, V.V. Strelchuka, Yu.I. Mazurb,, Zh.M. Wangb, G.J. Salamob a
Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, Prospect Nauky 45, 03028 Kyiv, Ukraine b Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA Received 2 February 2005; received in revised form 4 July 2005; accepted 7 July 2005 Available online 15 August 2005 Communicated by R.M. Biefeld
Abstract Surface morphology of microsize defects on the surface of various high-index GaAs substrates was investigated using an atomic force microscope (AFM). The surfaces investigated were the top layer of 1- and 17-period In0:45 GaAs0:55 =GaAs structures with quantum dots or buffer layer. These structures were characterized by the formation of oval defects on (1 0 0) surfaces, and microsize defects possessing the shape of multifaceted pits and hillocks on ðN 1 1ÞA=B ðN ¼ 7; 5; 4; 3Þ surfaces. The microsize defects were found to chaotically distribute on the surface and, as a rule, gathering in groups with some number of defects. Their density did not depend on the substrate orientation while the shape and orientation of the microsize defects were found to depend on the crystallographic orientation of the substrate. This dependence was determined to be the result of anisotropy of surface diffusion and surface elastic properties. The anisotropy of elastic properties of high-index surfaces was found to be the dominating factor in determining the microsize defect shape. We also report direct evidence of the fact that the effect of quantum dot lateral ordering observed on high-index ðN 1 1ÞB surfaces is determined by the anisotropy of surface elastic properties as well as elastic interaction between adjacent quantum dots. r 2005 Elsevier B.V. All rights reserved. PACS: 07.79.Lh; 68.35.Dv; 68.55.Jk; 68.65.+g; 81.05.Ea Keywords: A1. Atomic force microscopy; A1. Nanostructures; A1. Oval defects; A3. Molecular beam epitaxy; B2. Semiconducting III–V materials
1. Introduction Corresponding author. Tel.: +1 479 575 7476;
fax: +1 479 575 4580. E-mail address: [email protected] (Yu.I. Mazur).
Molecular beam epitaxy (MBE) offers the interesting possibility to produce semiconductor
0022-0248/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2005.07.005
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nanostructures with control at the atomic level [1]. As an example, (In,Ga)As quantum dots (QDs) obtained using the MBE [2] can play an important role in the optoelectronic industry because of the need for small, homogeneous and ordered nanostructures suitable for fabrication of highly efficient high-frequency and optical devices. In this pursuit, high-index GaAs surfaces have recently attracted significant attention based on the added control they can provide for the growth of GaAs-based nanostructures [3]. High-index surfaces can provide some control of self-assembled shape, size, and uniformity and provide unique templates for nanostructure growth [4,5]. As a result, efforts to improve the understanding of these faceted surfaces and their role in the growth of nanostructures are needed. In this paper, we have used oval defects (ODs) as a possible tool to probe the influence of anisotropic surface strain on the shape of these microsize defects and on the ability of high-index surfaces to provide unique templates for nanostructure growth. ODs are the main type of morphological defects found on GaAs films grown using the MBE method on GaAs substrates with (1 0 0) orientation. There are two types of ODs, namely: adefects and b-defects, without and with a core, respectively. When using a substrate with (1 0 0) orientation, the long axis of the OD lies along the direction h0 1 1i [6]. Typical dimensions of these defects are of the order of several micrometers depending on the epitaxial layer thickness. Also known is that an increase in the growth rate, decrease in the substrate temperature [7] or increase in the layer thickness [8] results in an increase in the OD density ranging from 102 up to 106 cm2 . A change in As/Ga flux ratio is also known to affect the defect density [9]. Although not well understood, the potential reasons for ODs to appear are: (1) gallium spitting onto gallium crucible walls [10], (2) the formation of gallium oxides on the surface [11], (3) uncontrolled impurities in the arsenic source [12], (4) substrate contamination [13,14], and (5) presence of stacking faults [15]. With these potential causes in mind, special care with arsenic and gallium molecular beams and the transport of substrates has made it
possible to reduce the OD density down to 102 cm2 [16]. The impact of the lower OD density, however, is somewhat ambiguous. It was shown, for instance, that the optical and electrical behavior of GaAs [17] and InGaAs [18] epitaxial layers considerably degrade near ODs. On the other hand, micro-Raman spectroscopy indicates that the quality of GaAs epitaxial layers near ODs is comparable to that in defect free regions [19]. While much is known about ODs, the origin and mechanism of defect formation is at best controversial. For high-index surfaces, even less can be concluded. In fact, we are unaware of any studies aimed at a systematic investigation of microsize defects in GaAs-based nanostructures grown on high-index GaAs substrates. In this work, we have investigated microsize defects on GaAs ðN 1 1ÞA/B surfaces. Most of the ODs have lateral dimensions of about 2 mm, a depth of approximately 0:1 mm, and a density that can reach 104 cm2 . On ðN 1 1ÞA/B surfaces, microsize defects form as dimples having a multifaceted shape, and in all cases, possess a (1 0 0) facet. ðN 1 1ÞA surfaces differ from ðN 1 1ÞB surfaces having hillocks of an irregular shape at the defect core. When we vary the substrate from (3 1 1)A to (7 1 1)A, the height of these hillocks is systematically reduced. The hillocks are of irregular shape, a fact that can be associated with their polycrystalline nature. For the high-index surfaces studied, the microsize defects aggregate chaotically as groups on the surface, so that their density is not a clear function of substrate orientation. (Possibly caused by a chaotically distribution of substrate surface contaminations as a result of preliminary chemical treating the surface and/or spitting Ga and/or Ga (GaO, Ga2 O, Ga2 O3 ) oxides in the course of growing the structure.) However, the shape and orientation of the microsize defects were found to depend on the substrate crystallographic orientation. We have found that this dependence is caused by anisotropic surface diffusion and anisotropic surface elastic properties inherent to high-index surfaces. Moreover, these effects were also found to influence the lateral ordering of QDs observed on high-index ðN 1 1Þ surfaces.
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2. Experimental procedure
3. Results and discussion
The investigated structures were grown using the MBE method on GaAs(1 0 0) and GaAsðN 1 1ÞA=B substrates (where N ¼ 7; 5; 4; 3). The degree of misorientation from GaAs(1 0 0) towards (1 1 1) is 11:4 for GaAs(7 1 1), and 15:8 for GaAs(5 1 1), and 19:5 for GaAs(4 1 1), and 25:2 for GaAs(3 1 1). All of the investigated samples were held side by side with indium on a molybdenum holder. After loading into the MBE growth chamber, the surface oxide was thermally desorbed at 600 C while exposing the surface to a 106 Torr As4 beam equivalent pressure (BEP) from a solid source valved controlled cell. This As4 BEP was kept constant for all growths. First, a 0:5 mm-thick GaAs buffer layer was grown at 580 C, and then the substrate temperature was reduced down to 540 C for the growth of (In,Ga)As multiple layers. The layers consisted of 1- and 17-periods of 6 ML In0:45 Ga0:55 As QDs and 65 ML GaAs spacers. Using the method of in situ reflection high-energy electron diffraction (RHEED), the growth rates of In0:45 Ga0:55 As and GaAs were kept to be 0.78 and 0.43 ML/s, respectively. We studied three sets of samples, namely: (1) samples containing only the GaAs buffer layer, (2) heterostructures with a single In0:45 Ga0:55 As QD layer, and (3) multilayer 17-period In0:45 Ga0:55 As=GaAs structures with QDs. The top layer of QDs was left exposed for topographic atomic force microscopy (AFM) imaging under ambient condition. Morphological investigations of the studied structure surfaces were performed using a scanning AFM NanoScope IIIa in the tapping mode. We used silicon probes with the mechanical resonance frequency equal approximately to 150 kHz and the tip radius close to 5 nm. Before and after measurements, tips were tested using the special test gratings made by NT-MDT (Molecular Devices and Tools for NanoTechnology) company [20]. The crystallographic orientations of the samples were determined using standard X-ray diffraction procedure. Homogeneity of the studied surfaces over a large area was checked up using optical microscopy with the Nu-2E (Carl Zeiss) microscope equipped with a digital processing system.
The objective of this research was to investigate the possibility of using microsize defects to study the influence of anisotropic surface elastic strain on the process of lateral ordering and on improving the homogeneity of (In,Ga)As QDs using highindex GaAs substrates. It is well known that the driving force for self-organized (In,Ga)As QD creation on a GaAs is elastic strain relaxation. In the case of Inx Ga1x As=GaAs lattice mismatched heterostructures, a 2D–3D morphological transition is realized only after the Inx Ga1x As thickness exceeds the critical thickness. However, one can assume that the In concentration could considerably exceeds the nominal value for a given critical thickness at some local places on the grown layer. Therefore, the process of strain relaxation at these high In concentration locations can be a specific source for microsize defect creation, as has been noted [21] when studying microsize defects in (In,Ga)As QDs on a GaAs(3 1 1)B surface. Therefore, our first effort in this work was to investigate the surface morphology of ODs on a GaAs buffer layer deposited onto GaAsðN 1 1ÞA/B substrates and compare with that found on GaAs(1 0 0) substrates. Fig. 1 shows the optical micrographs of a GaAs buffer layer on GaAs (1 0 0) (Fig. 1a) and GaAs(3 1 1)B (Fig. 1b) substrates. It can be seen that large areas of the sample surface are free of microsize defects. The defect density inherent to all the studied samples was practically the same and did not exceed 104 cm2 , which is in a good agreement with the results of several previous works [7–9]. The samples were grown simultaneously on the same molybdenum block so that their growth conditions are identical. For our growths we observed that the defects were likely to gather in aggregates of 3–5 defects located within small distances of each other. As seen from the insert (Fig. 1), the shape and orientation of the microsize defects differ on (1 0 0) and (3 1 1)B surfaces. For the (1 0 0) surface (Fig.1a), we deal with typical ODs oriented along ¯ direction and possessing a clear core at the [0 1 1] the defect center (b-defect) (see a classification of defects in [15]). For the (3 1 1)B surface (Fig. 1b),
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In general, the mean density and size of the ODs were comparable on both the (1 0 0) and (3 1 1)B surfaces. The observed differences in orientations and shape of the defects are caused by differences in the anisotropy of the physical properties inherent to these surfaces (values of adatom surface diffusion and elastic properties of the surface). This conclusion is supported by recent work [22] that showed that the orientation of ODs ¯ direction can be explained by the along the [0 1 1] anisotropy of Ga adatom migration. Shown in Fig. 2 are detailed AFM images of typical microsize defects present on the GaAs buffer layer surface deposited onto a substrate with (3 1 1)B orientation. The defects marked as 1 and 2 possess a comparable depth but differ in shape. Meanwhile, the shape of the defects 2 and 3 is practically the same, but the depth at the core region differs by almost an order of magnitude. Although we have no direct evidence to exclude the possibility of creating some quantity of defects directly in the process of growing the GaAs layer, the correlation between size and depth of the
Fig. 1. Optical micrograph of GaAs buffer layer grown on GaAs(1 0 0) (a) and GaAs(3 1 1)B (b) substrates. Microsize defects are marked with arrows. The inserts show 3D AFM images of corresponding defects.
the defects are multifaceted V-shaped concaves oriented along the crystallographic direction ¯ The defect core is located at its top, and [2 3¯ 3]. its depth is reduced as one moves along the direction [2¯ 3 3], giving the impression of a tail. In addition, our AFM investigations revealed that, when depositing GaAs buffer layer onto substrates with (1 0 0) orientation, in addition to b-defects one can also observe ODs with smaller sizes without any pronounced central core (adefects). Sometimes, we can observe coupled ODs as well as asymmetric a- and b-defects. Typical OD sizes varied from 1 to 12 mm. Thus, in the case of (1 0 0) surface one can see the typical and rather well studied ODs that mainly appear at the interface of the substrate and GaAs buffer layer.
Fig. 2. (dz=dx) derivative of AFM image of microsize defects typical for the surface of the GaAs buffer layer grown on GaAs(3 1 1)B substrate. The inserts show the height map for the surface with indication of cross-section lines and respective defect sections. The scale of the height axis at the defect sections is 100-fold magnified relatively to their length.
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defects are more suggestive of different nucleation sources (i.e., different size, shape and composition) that originate at the substrate/GaAs buffer layer interface. It is known that the rate of Ga adatom migration on the surface of a GaAs epitaxial layer is different when deposited onto ðN 1 1ÞA versus ðN 1 1ÞB substrates with the same index N in an As-rich atmosphere [23]. In this case Ga adatom migration is strongly influenced by differences in the surface diffusion and elastic properties of the polar A and B planes. The observed effects of this surface anisotropy on the shape of microsize defects ðN 1 1ÞA and ðN 1 1ÞB are dramatic and are shown in Fig. 3 for the (3 1 1)A and (3 1 1)B surfaces. A characteristic difference of the defects observed on the (3 1 1)A surface is the presence of a hillock at the region of the defect core (Fig. 3a). These hillocks possess a clearly pronounced multifaceted shape and differ from one another by their sizes. Sometimes, these hillocks exhibit a long tail (see the insert, Fig. 3a) oriented along the [2¯ 3 3] direction. Such hillocks were not observed in the case of multifaceted defects on the (3 1 1)B surface. In fact, the presence of hillocks on the A-surface and their full absence on the B-surface is observed for all the studied ðN 1 1Þ substrate orientations. Interestingly, the hillock sizes on the ðN 1 1ÞA surfaces decrease with increasing N. Meanwhile, the most common feature between defects observed on the (3 1 1)A and (3 1 1)B surfaces is the presence of a (1 0 0) facet forming the front wall of the defect (Fig. 3). As we change the growth surface from (3 1 1) to (7 1 1), the observed microsize defects are basically similar to those observed on the (3 1 1) surface (Fig. 4a–d). The range of defect sizes and density remains practically the same for the deposition of only one In0:45 Ga0:55 As (7 ML) epitaxial layer of QDs. As seen in Fig. 4, all the microsize defects on ðN 1 1ÞB surfaces possess the multi-faceted shape and are nucleated from a nanopore (core). However, as the growth surface is changed from (3 1 1) to (7 1 1), the tail at the defect base is reduced in size, while the angle at the apex, formed by the defect facets, is increased. Moreover, the size, shape and density of the multifaceted defects do not change in the case of the multilayer 17
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Fig. 3. 3D AFM images of typical microsize defects on the surface of GaAs buffer layer grown on substrates with (3 1 1)A/ B orientations. Shown in the insert is the multifaceted defect with the hillock smoothed due to the surface diffusion transfer of material.
(In0:45 Ga0:55 As=GaAs) structure. The fact that the character of microsize defects (i.e., their depth, shape, density) does not change in any significant way when depositing either a GaAs buffer layer, 1- and 17-period In0:45 Ga0:55 As=GaAs structure, further supports the idea that the defects nucleate mainly at the interface of the substrate and GaAs buffer layer. We made a detailed analysis of the shape and orientation inherent to defects for all studied structures. Crystallographic orientations of microsize defects were determined using X-ray diffraction in symmetric and asymmetric reflections after preliminary optical and AFM studies of OD
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Fig. 4. Surface height maps (on the left) and derivatives (dz=dx) of AFM images (on the right) of typical microsize defects on the surface of In0:45 Ga0:55 As (7 ML) layer on GaAsðN 1 1ÞB substrate. There pointed are the sections (profiles) of surfaces along the dotted lines. Empty ovals point the defect cores. Quantum dots can be seen on the surfaces and on the defects.
orientations relatively to the sample side crystallographic directions. For example, we know that f0 1 1g crystallographic planes are the most preferable and ideal to cleave the high-index substrate. In case of samples grown on the (3 1 1) surface, other possible crystallographic orientations are ¯ ½2 3¯ 3 ¯ and ½0 1¯ 1 . To find the ½2¯ 3 3 ½2¯ 3 3 , ½0 1 1 ,
crystallographic direction, we measured X-ray diffraction in asymmetric reflection from the (3 2 2) crystallographic planes. These planes show that the unique position in a crystal and the diffracted beam can be detected only with rotation of the crystal in the ½2¯ 3 3 direction from the position were the signal for the 3 1 1 symmetric reflection was measured. If the crystal is rotated in ¯ ½0 1¯ 1 or ½0 1 1 , ¯ the opposite direction, i.e., ½2 3¯ 3 , no diffracted beam is registered for the detector positioned at the angle required for 3 2 2 reflection. The analogous crystallographic planes could be selected for each of ðN 1 1Þ surfaces and using the procedure described above the crystallographic directions of the samples, and the orientation of OD relative to these directions, can be determined exactly. The data show that the clearest defect facet on the ðN 1 1ÞA/B surfaces is the (1 0 0) facet (see Fig. 3a and b). The mean values of the experimentally measured angles between the (1 0 0) facet and the ðN 1 1ÞB surface as well as the depth of the defect core are given in Table 1. We believe that the growing deviation between the observed angle and the calculated angle going from the (3 1 1) to the (7 1 1) orientations is caused by a diffusion smoothing processes. Small angles between the defect facet and the substrate encourage diffusion and lead to an enhancement of diffusion smoothing of the defect facet. In addition, for defects possessing a large depth, diffusion smoothing of the defect facet is considerably reduced since the facet edges (top to bottom) are more widely spaced. As a consequence, the best agreement can be expected for large angles and deep defect cores, as is observed. It is interesting to note that the core depth for some defects can reach magnitudes ( 180 nm) very close to the total thickness of the 17-period multilayer structure. Moreover, the obtained value of the defect core depth can be even larger as a result of the limitation of the AFM probe. The latter is indicative of the fact that some large defects cannot be covered in the process of epitaxial layer deposition. In addition to surface diffusion anisotropy, the anisotropic character of the substrate elastic properties influences the microsize defect shape.
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Table 1 The angle of the defect front facet slope and defect core depth for the structures grown on GaAs substrates with ðN 1 1ÞB orientations Substrate orientation
Calculated angle between crystallographic plane (1 0 0) and surface of substrate (degrees)
Average angle between front facet of defect and surface of substrate (degrees)
Typical depth of a defect core (nm)
311 411 511 711
25.2 19.5 15.8 11.4
25 3 15 3 10 2 6 2
60 50 60 25
Fig. 5. Schematic representation of stereographic projections with indication of the elasticity modulus value distribution along crystallographic directions (left) and microsize defect AFM images with cross-sections along dotted lines for the surface of 17-period In0:45 Ga0:55 As=GaAs ðN 1 1ÞB structure (middle) when the substrate orientation is: (a) (1 0 0), (b) (3 1 1)B and (c) (7 1 1)B. Images of an enhanced resolution which illustrate formation of QD patterns are shown (right).
Shown in Fig. 5, are the stereographic projections of the magnitude of the surface elasticity along various crystallographic directions corresponding to the surface orientations (1 0 0) (Fig. 5a), (3 1 1)
(Fig. 5b) and (7 1 1) (Fig. 5c) along with corresponding AFM images of areas with defects inherent to the 17-period In0:45 Ga0:55 As=GaAs structures. The values of Young’s moduli E were
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calculated according to the equation [24]: E 1 ¼ s11 ð2s11 2s12 s44 Þ ðk2 l 2 þ l 2 h2 þ h2 k2 Þ=ðh2 þ k2 þ l 2 Þ,
ð1Þ
where s11 , s12 , s44 are the elastic compliance constants given in [25,26] and h, k, l are the Miller’s indexes of crystallographic direction. Choosing different crystallographic directions hh k li within surface plane with step of about 51 we obtained a distribution picture of E value on investigated surfaces (1 0 0) and ðN 1 1Þ. The calculated values of E are in good agreement with published results [25,27]. As seen from Fig. 5, the crystallographic orientation of microsize defects coincides with the direction of the largest elastic constants. In multilayer structures grown on GaAs(1 0 0) substrates, the microsize defects are oriented in the ¯ which coincides with the direction direction [0 1 1], of the largest In/Ga adatom diffusion [28,29]. When changing the surface orientation from (1 0 0) to (7 1 1), the anisotropy of the surface elasticity modulus is considerably reduced. In our opinion, it is this effect that is responsible for the change in the microsize defect shape. That is, for the (7 1 1)B surface, the relative magnitude of the anisotropy of the elasticity modulus anisotropy is smaller than that for (1 0 0) and (3 1 1), which results in round shape defects (Fig. 5c). On the other hand, a decrease in the defect tail length with increasing N-index on GaAs ðN 1 1Þ substrates can be explained stemming from purely geometrical grounds (Fig. 6). The defect front facet coincides with the (1 0 0) crystallographic plane that has been neither smoothed nor overgrown in the course of the structure growth. It is most probable that the opposite defect facet is also limited by a crystal plane, but it is strongly subjected to diffusion smoothing and partial overgrowing. However, the angle between the front and back facets of multifaceted defects on ðN 1 1Þ surfaces remains approximately the same. As seen from Fig. 6, with increasing N-index, the defect (1 0 0) facet slope decreases relative to the ðN 1 1Þ surface. As a consequence, when the N-index reaches high values, the ðN 1 1Þ surface will cut a larger and larger part of the defect tail, and, as a result, the
Fig. 6. Changes of multifaceted defect sections with changing the orientation of the substrate surface. The scheme takes into account the angles between crystallographic planes.
defect shape will be more rounded, which is what observed experimentally. Inspite of the fact that multifaceted defects are generally not healed in any practical way, if the defect facet slope angle relative to the substrate surface is less than 7–81, then the defect facets can support QDs of sizes and densities that do not differ significantly from that observed on defectless regions (Figs. 4 and 5). However, when the defect facet slope angle is larger than 8 , QDs do not appear, except on the defect front facet (1 0 0) plane. On this facet, QDs at slope angles of 11:4 (GaAs(7 1 1)) and 25 (GaAs(3 1 1)) relative to the structure growth surface are observed. In this case, the defect facet should be considered simply as a (1 0 0) growth surface where 3D QD growth is realized via the Stranski–Krastanov mechanism. These observations were for both for a single- and multilayer In0:45 Ga0:55 As=GaAs structures. Interestingly, we observed a clear tendency in multilayer structures to form laterally ordered arrays of QDs (Fig. 5). Depending on the substrate surface orientation, one can obtain QDs ordered ¯ direction (QD chains) (Fig. 5a) along the [0 1 1] [30] or laterally ordered networks of nearly equal distant QDs [31] (Figs.5b,c) (QD chains look as aligned along the microsize defect orientation direction). Here, the defect orientation and symmetry have a one-to-one correlation with the position of QDs on the surface. The cell dimension of the QD lateral network on the less anisotropic surface (7 1 1)B is less than that on the (3 1 1)B surface, and the shape of the lateral cell is close to a rhombus shape. Lateral self-ordering of the QDs
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in multilayer structures is most probably caused by the formation of periodically changing field of elastic strains as well as an accompanying redistribution of the impurity-defect composition of the growth surface. The influence of an elastic strain far-acting field on QD lateral ordering is indirectly confirmed by Fig. 5b where the defect strain field causes fluctuations in QD lateral ordering. In the defect core region (i.e., in the ranges of the largest strain and compositional gradients), several QD rows exactly follows along the defect facet orientation directions, that is the lateral QD arrangement ‘‘feels’’ the shape of the strain field distribution around the defect.
4. Conclusions Our comparison of the obtained results for GaAs buffer layers and In0:45 Ga0:55 As=GaAs structures with QDs allows us to state that the process of residual elastic strain relaxation in a growing epitaxial layer is not the dominant cause of microsize defects, as was assumed in [21]. The shape and orientation of microsize defects are determined by the structural anisotropy observed on the GaAs(1 0 0) and GaAsðN 1 1ÞA/B substrate surfaces. The strain fields developed in the growth direction of multilayer In0:45 Ga0:55 As=GaAs structures determine the size and lateral arrangement of (In,Ga)As QDs, and their value considerably exceeds the strain fields and concentration fluctuations formed around microsize defects. The latter is developed during QD growth on the microsize defect surface and confirmed by the appearance of small fluctuations of their lateral arrangement (QD chains and networks cover defects without significant transformations). QD lateral ordering on the surface is caused by two factors: anisotropy of lateral strain fields and the effect of elastic interaction between QDs on the surface. The studied microsize defects can be used to determine surface crystallographic orientation, as indicators of anisotropy inherent to surface physical (elastic) properties. Meanwhile, sets of microsurfaces with various orientations can be used as a playing field to explore QD growth processes.
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Acknowledgements The authors acknowledge the financial support of the National Science Foundation of US (through Grant nos. PHY-0099496 and DMR0080054) and Ukrainian State Foundation for Fundamental Researches. References [1] L.L. Chang, K.L. Ploog (Eds.), Molecular Beam Epitaxy and Heterostructures, in NATO ASI Series, Nijhoff, Dordrecht, The Netherlands, 1985, p. 584. [2] D. Bimberg, M. Grundman, N.N. Ledentsov, Quantum Dot Heterostructures, Wiley, New York, 2001, p. 328. [3] P.M. Petroff, A. Lorke, A. Imamoglu, Phys. Today 54 (2001) 46. [4] Z.M. Wang, H. Wen, Y.R. Yazdanpanah, J.L. Shultz, G.J. Salamo, Appl. Phys. Lett. 82 (2003) 1688. [5] Y. Chen, G.H. Li, Z.M. Zhu, H.X. Han, Z.P. Wang, W. Zhou, Z.G. Wang, Appl. Phys. Lett. 76 (2000) 3188. [6] K. Mehta, R. Muralidharam, G.D. Sharda, R.K. Jain, Semicond. Sci. Technol. 7 (1992) 635. [7] G.M. Metze, A.R. Calawa, J.G. Mavroids, J. Vac. Sci. Technol. B 1 (1983) 166. [8] S.L. Weng, Appl. Phys. Lett. 49 (1986) 345. [9] T. Ito, M. Shinohara, Y. Imamura, Jpn. J. Appl. Phys. 23 (1984) L524. [10] M. Shinora, T. Ito, J. Appl. Phys. 65 (1989) 4260. [11] S.L. Weng, J. Vac. Sci. Technol. B 5 (1987) 725. [12] Y. Suzuki, M. Seki, Y. Horikoshi, H. Okamoto, Jpn J. Appl. Phys. 23 (1984) 164. [13] S.L. Weng, C. Webb, Y.G. Chai, S.G. Bandy, Appl. Phys. Lett. 47 (1985) 391. [14] S. Izumi, N. Hajafuji, T. Sonoda, S. Takamiya, S. Mitsui, J. Crystal Growth 150 (1995) 7. [15] N.J. Kadhim, D. Mukherjee, J. Mater. Sci. Lett. 18 (1999) 229; L. Lazzarini, G. Salviati, S. Franchi, E. Napolitani, Mater. Sci. Eng. B 80 (2001) 120. [16] C.Y. Chang, F. Kai, GaAs High-Speed Devices: Physics, Technology, and Circuit Applications, Wiley, New York, 1994, p. 612. [17] Jun-ichi Kasai, M. Kawata, Appl. Phys. Lett. 73 (1998) 2012. [18] J.J. Russell-Harriott, J. Zou, A.R. Moon, D.J.H. Cockayne, B.F. Usher, Appl. Phys. Lett. 73 (1998) 3899. [19] P.S. Dobalyz, H.D. Bisty, S.K. Mehtax, R.K. Jain, Semicond. Sci. Technol. 11 (1996) 315. [20] V. Bykov, A. Gologanov, V. Shevyakov, Appl. Phys. A 66 (1998) 499 (Company’s internet address: www.ntmdt.ru). [21] K. Akahane, K. Okino, Y. Okada, M. Kawabe, Solid State Electron. 42 (1998) 1613. [22] M. Kaniewska, K. Klima, Mater. Sci. Eng. B91–92 (2002) 512.
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