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Si(0 0 1) quantum dots
Applied Surface Science 212–213 (2003) 296–304
Superlattices of self-assembled Ge/Si(0 0 1) quantum dots Vinh Le Thanh*, V. Yam Institut d’E´lectronique Fondamentale, UMR-CNRS 8622 Baˆt. 220, Universite´ Paris-Sud, 91405 Orsay Cedex, France
Abstract The effect of vertical ordering in superlattices of self-assembled Ge/Si(0 0 1) quantum dots was investigated by a combination of structural and optical characterizations via in situ reflection high-energy electron diffraction (RHEED), transmission electron microscopy (TEM), atomic force microscopy (AFM) and photoluminescence (PL) spectroscopy. We show that the vertical ordering observed in quantum-dot superlattices is characterized not only by the alignment of islands along the growth direction but also by a reduction of the critical thickness. The better the vertical ordering is, the more pronounced the reduction of the critical thickness will be. Such an evolution of the critical thickness could be explained by elastic strain fields induced by buried islands and propagate through the spacer layers. An important result issued from this work is the realization of superlattices in which dots can have equal size in all layers. On the other hand, experiments performed on the transformation of the island shape versus the spacer layer thickness suggest that preferential nucleation induced by surface roughness may be the main mechanism responsible for the vertical ordering observed in quantum-dot superlattices. # 2003 Elsevier Science B.V. All rights reserved. PACS: 68.65.-k; 85.35.Be; 05.65.þb; 78.66.-w Keywords: Quantum dots; Self-assembly; Vertical ordering; Superlattices; Germanium; Silicon
1. Introduction Since the first observation of the formation of defect-free three-dimensional (3D) islands in the early stage of germanium deposition on silicon, the growth of Ge/Si self-assembled quantum dots has attracted a considerable interest [1]. The formation of such coherent islands is a spontaneous process that occurs when the deposited film thickness exceeds a critical value. The driving force of this spontaneous formation of islands is the relief of the built-in elastic strain accumulated in the grown film due to the lattice-mismatch * Corresponding author. Present address: Centre de Recherche sur les Me´canismes de la Croissance Cristalline (CRMC2-CNRS), Campus de Luminy, Case 913, 13288 Marseille Cedex 9, France. E-mail address: [email protected] (V. Le Thanh).
between film and substrate (the so-called Stranski– Krastanow growth) [2]. The defect-free three-dimensional nanocrystals offer new opportunities for the development of optoelectronic devices integrated on silicon. The carrier localization, the three-dimensional confinement, the high germanium content achieved with the heterostructures represent specific advantages for a new generation of devices [3]. However, one of the major limitations of the self-assembled quantum dots is that they exhibit broad distributions both in size and position. Recently, it has been shown that starting from a single layer with inhomogeneous islands one can greatly improve the island size uniformity by growing multilayer structures [4]. Another feature of particular interest observed in such structures is that under appropriate spacer thickness the dots in the upper
0169-4332/03/$ – see front matter # 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0169-4332(03)00078-3
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layers tend to grow on the top of the buried ones, giving rise to the vertical alignment of islands along the growth direction [5]. Compared to self-assembled dots formed in a single layer where no interaction between dots could be possible due to a too large interdot distance (of about 150–200 nm in the Ge/Si system [6], for example), the feature of vertical ordering in superlattices may open new areas of applications such as electronically coupled quantum dots [7] and vertical transport. The mechanisms leading to such a vertical ordering have been then the subject of numerous investigations [8–20]. It is now generally accepted that the driving force which leads to the vertical island alignment in QD superlattices is the elastic strain fields created by buried islands and mediated by spacer layers. However, the detailed mechanisms or the manner through which such strain fields manifest or affect the nucleation process of islands at the surface of the spacer layer are still not fully understood. In this work, we investigate the effect of vertical ordering in a Ge/Si(0 0 1) multilayer structure. The purpose of our work is two-fold: the first is to understand the mechanisms leading to the increase of the island dimension observed in superlattices of different materials. The second is to study the degree of the vertical correlation of islands with the aim to extract the essential physical parameters, which may govern the phenomenon of vertical ordering. We have, for this purpose, combined structural and optical characterizations, via in situ reflection highenergy electron diffraction (RHEED), atomic force microscopy (AFM), transmission electron microscopy (TEM) and photoluminescence (PL) spectroscopy, with a special attention being paid to the control of the island formation process. The article is organized into two sections: the first section is devoted to the evolution of the island dimension with increasing the number of deposited layers while the spacer thickness is kept constant. In the second section, we deal with the influence of the spacer thickness on the vertical alignment of the islands in a bilayer structure.
2. Experimental Experiments were carried out in an ultrahigh vacuum chemical-vapor deposition (UHV-CVD) system.
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Pure SiH4 and hydrogen-diluted (10%) GeH4 were used as gas sources. The system base pressure was better than 1 1010 Torr while the hydride partial pressures during growth were about 5 104 and 2 104 Torr for GeH4 (H2) and SiH4, respectively. One of the advantages of our work is the use of in situ RHEED to precisely monitor, in real-time, the two dimensional (2D)–3D growth mode transition and the capping process in a CVD system working at high hydride pressures. Indeed, our RHEED gun is equipped with a differentially-pumped system, allowing us to probe the growing surface even at hydride partial pressures up to 101 Torr. During growth, RHEED patterns were recorded using a camera-based video recording system. More details of the experimental setup and growth conditions can be found elsewhere [21]. After growth, photoluminescence measurements were performed at low temperatures, using an Arþ laser (power density of 400 mW/cm2). The PL signal was detected with a liquid nitrogencooled Ge photodetector using a standard lock-in technique. Atomic force microscopy images were recorded with a Park Scientific Instruments AFM setup operating in contact mode. Cross-sectional TEM micrographs were obtained from a JEM 4000EX high-resolution electron microscope operated at 400 keV. The Ge deposition was carried out at temperatures of 550 and 600 8C. The choice of such temperatures was guided by the fact that in this temperature range the islands in a single layer exhibit a dome shape, a point which is crucial for the study of the island shape transformation and will be discussed below. The Ge growth rate is about 1.5 monolayers (ML)/min. The Si deposition was carried out at 600 8C with a growth rate of about 2.5 nm/min. The substrates were flat, p-type Si(0 0 1) wafers. Cleaning of the substrate surface followed the newly developed procedure utilizing the hydrogenterminated Si(0 0 1) surface [22]. It consists of two steps: the first is a wet chemical treatment in NH4F solution to prepare an ideally dihydrideterminated Si(0 0 1) surface. The second step is heating in ultrahigh vacuum to desorb the passivating hydrogen layer at a temperature of about 450–500 8C. Prior to Ge deposition, a 100 nm thick Si buffer layer was grown at 700 8C to ensure a good starting surface.
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3. Results and discussion 3.1. Evolution of island dimension in multilayer structures As we have mentioned above, a general feature observed in superlattices of different materials is that the island dimensions, both lateral size and height, have been shown to increase with increasing the number of deposited layers [4,5]. An increase, for example by a factor of about 3 has been observed in [4] after the deposition of 20 SiGe/Si periods. From the technological point of view, such an evolution of the island dimensions may be considered as one of the main drawbacks for the application of multilayer arrays. Indeed, for most QD-based applications it is desirable to have islands with sizes as small as possible to obtain an efficient quantum confinement inside the islands. In InAs/GaAs multilayers, Nakata et al. [8] have shown, from RHEED, that the InAs critical thickness in upper layers was shorter than that of the first layer. However, since the In surface segregation is known to play an important role in the InAs/GaAs growth process, it was not clear whether such a decrease of the InAs critical thickness is due to the strain induced by underlying layers or surface migration of In atoms. In Ge/Si multilayers, Schmidt et al. [10,11] have shown that the wetting-layer thickness in the upper layers was smaller than that of the first layer. However, because this result has been obtained in postgrown samples by means of TEM microanalysis, no proposal to improve the island size homogeneity has been submitted. Fig. 1(a) shows a representative [0 1 1] cross-sectional TEM image of a multilayer consisting of 10 Ge/Si periods, the thickness of the Si spacer is 22 nm. The growth temperature is 550 8C for Ge and 600 8C for Si, respectively. The Ge deposited amount in each layer was chosen to be equal to the critical thickness determined from RHEED for the first layer, which is of 4 ML. This amount was then kept constant during the deposition of all upper layers. The image clearly shows that each island in the upper layers grows on the top of the ones in the lower layers, resulting in a high vertical correlation between islands. It can be also seen from the image that the islands undergo a drastic change both in size and height from the first to
Fig. 1. (a) Typical TEM image taken along the [0 1 1] azimuth of a sample with 10 Ge/Si bilayers. The Ge deposited amount was chosen to be equal to the critical thickness of the first layer and was kept constant in all layers; (b) 11K-PL spectra of a single layer (lower curve) and of a 10-bilayer sample (upper curve).
the third layer, and they become almost stable from the fifth layer. The average island dimensions in the first layer, 100 nm in size and 7 nm in height, are respectively found to increase upto 180 and 12.3 nm in the fifth layer and then remain nearly unchanged. The PL spectrum of the corresponding sample is shown in Fig. 1(b). For comparison, we report in the lower curve the PL spectrum of a single layer. The single layer was covered with a 22 nm-thick Si cap layer, i.e. identical to the first bilayer of the multilayer sample. Apart from the narrow peak at 1098 meV which is attributed to the phonon-assisted recombination of the free-exciton in the Si substrate, the
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single-layer spectrum consists of two separate components characteristic of the Ge wetting layers (WL) and Ge islands, respectively. The WL component is characterized by two main lines located at 1024 and 967 meV, which are, respectively, due to the excitonic no-phonon (NP) and transverse–optical (TO)-phononassisted transitions of pseudomorphic Ge layers in Si [23]. The energy difference between the NP and TO lines is 57–58 meV, which corresponds to the Si–Si optical phonon energy in Si. The emission band lying at the lower energy of 768 meV can be attributed to three-dimensional Ge islands [6,23]. The multilayer spectrum also consists of two components, but, importantly, both of them now contain two separate parts. The WL component now contains four main lines, denoted to as NP1, TO1, NPn and TOn, instead of the two ones observed in the single-layer spectrum. The NP1 and TO1 lines can be attributed to arise from the first Ge wetting layer, while additional lines, NPn and TOn, can then be interpreted as arising from another Ge wetting layer, which has a thickness smaller than that of the first one. For the island-related component, isl three peaks, denoted to as ISL1, TOisl n , and NPn , can be resolved after a deconvolution by using a set of three Gaussian line-shaped peaks, which have their maxima at 768, 833 and 875 meV, respectively. The ISL1 peak stems from the islands in the first layer. The isl other two peaks, NPisl n and TOn , can be attributed to NP and TO transitions of islands from the rest of the layers. To further clarify the existence of another type of Ge WL in upper layers, we have undertaken a RHEED analysis, by measuring the Ge critical thickness in each layer. It is now well established that the 2D growth regime is associated with the observation of streaky RHEED patterns due to reflection diffraction from a smooth crystal surface, while 3D growth is characterized by spotty patterns due to transmission diffraction through 3D islands. The transition from 2D to 3D growth can be precisely determined by measuring the variation of the RHEED intensity of a bulktype diffraction spot as a function of the Ge growth time and thus Ge coverage [21]. Shown in Fig. 2(a) is the evolution of the 2D–3D transition time (left axis) and the critical thickness (right axis) versus the number of the deposited layers. The upper curve corresponds to a Si spacer thickness of 22 nm while the lower one corresponding to a
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Fig. 2. (a) Evolution of the Ge critical thickness as a function of the number of deposited layers in a multilayer consisting of 10 Ge/ Si periods for a spacer thickness of 22 and 2.5 nm. The solid lines are only guided for the eyes; (b) TEM image of a sample with 10 Ge/Si bilayers in which the Ge deposited amount was no longer kept constant but adjusted with the effective critical thickness in each layer, the spacer thickness is 22 nm. These thicknesses are of 4, 2.5, 2.25, 2.13, and 2.08 ML for the 1st, 2nd, 3rd, 4th, and the last six layers, successively.
thickness of 2.5 nm. For dSi ¼ 22 nm, the Ge critical thickness, which is of 4 ML in the first layer, is found to rapidly decrease within the three first layers and reaches a stable value of 2.08 ML after the fifth layer. As the result of RHEED analysis, the multilayer structure is found to present five critical thicknesses, which are of 4, 2.5, 2.25, 2.13, and 2.08 ML for the 1st, 2nd, 3rd, 4th, and the last six layers, successively. The finding of the decrease of the critical thickness in the upper layers of a multilayer structure has brought us to a very simple idea for the realization of a multilayer structure in which the islands may have equal size in all layers. Indeed, if one does not keep the Ge
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deposited amount constant in all layers (equal to the critical thickness of the first layer), but adjusts this amount according to the effective critical thickness in subsequent layers, this can lead to the formation of islands at the first nucleation stage in all layers. As a demonstration, a cross-sectional TEM image of a multilayer consisting of 10 Ge/Si periods produced with this approach is shown in Fig. 2(b). The Ge growth in each layer was stopped just after the appearance of 3D spots in RHEED patterns. The Si spacer-layer thickness was kept constant, being of 22 nm. As can be seen in this image, the islands still exhibit a high correlation along the growth direction. An important result is that the islands have now almost equal size and height in all layers, in contrast to the case presented in Fig. 1(b) in which the Ge amount was kept constant in all layers. What is particularly interesting is that by using this approach one can produce superlattices containing islands of uniform dimensions even when the spacer thickness is reduced down to a nanometer scale. An example for the formation of identical Ge islands for a spacer thickness reduced down to 2.5 nm is presented in Fig. 3. The variation of the corresponding critical thickness versus the number of deposited layers is reported in the lower curve of Fig. 2(a). The image clearly reveals that the Ge islands have almost equal size and height in all layers. The fact that the islands within a column can have equal size and height even in very closely spaced stacked layers offers a promising opportunity for studying the electronic coupling between islands. Indeed, only in the case of having equal size, the islands within a column can have the same energy and will provide a real effect of electronic
coupling. Work in this direction is now in progress and will be reported later. 3.2. Mechanism of vertical ordering in multilayer structures Starting with the aim to extract the main physical parameters, which may characterize the effect of vertical ordering in superlattices, we have investigated in a systematic manner the influence of the spacer thickness on the degree of the island vertical alignment. It is important to emphasize that such a study has been the subject of numerous investigations in different multilayer systems [5,9–13]. However, in these works the authors have mainly used cross-sectional TEM analysis to quantify the degree of the island position alignment. While cross-sectional TEM micrographs can give a direct view on the island alignment, the analysis, which are only based on cross-sectional TEM, reveal a very large dispersion. In Ge/Si multilayers, for example Rahmati et al. [13] reported a value of about 100 nm of the Si spacer thickness below which a perfect island correlation was observed while Kienzle et al. [9] obtained a value which is four times smaller than the above one. It is obvious that the presence of hydrogen in CVD experiments used in [13] could not explain this too large difference because at a growth temperature as high as 700 8C the growing surface is known to be free of hydrogen. Here, we have combined RHEED and TEM to study the effect of the island ordering. Motivated by our finding on the reduction of the critical thickness versus the number of deposited layers, we have
Fig. 3. TEM image of a 10-bilayer sample in which the Ge deposited amount in each layer was adjusted with the 2D–3D transition detected by RHEED. The corresponding Ge effective critical thickness in each layer is indicated in Fig. 2(a). The Si spacer layer was reduced down to 2.5 nm and was kept constant in all layers.
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Fig. 4. Variation of the Ge critical thickness in the second layer as a function of the Si spacer thickness. Note that the variation of dc2 can be divided into three distinct regions and described by straight lines with varying slopes represented by dotted lines. Shown in the inset are typical TEM images corresponding to the Si spacer thickness of 80, 90 and 160 nm.
systematically undertaken measurements of the Ge critical thickness in the second layer as a function of the thickness of the Si spacer layer. The growth temperature is 600 8C for both Ge and Si. Fig. 4 shows a typical result on the variation of the critical thickness in the second layer (dc2) versus the Si spacer thickness (dSi). dc1 is the Ge critical thickness in the first layer, which is of 4 ML. As can be seen from the figure, the variation of the Ge critical thickness in the second layer (dc2) can be divided into three distinct regions: the first region corresponds to Si spacer thicknesses above 150 nm, the second corresponds to a thickness between 150 and 85 nm and the third region corresponds to a thicknesses below 85 nm. In the first region, dc2 is equal to dc1, which clearly indicates that for spacer thicknesses larger than 150 nm, the growth of the second layer is not affected by the strain field induced by buried islands. For dSi below 150 nm, dc2 is found to decrease when decreasing the spacer thickness. It is worth noting that for very thin spacer layers, dc2 is reduced down to less than 1 monolayer of Ge. A feature of particular interest is that the reduction of the critical thickness can be described by straight
lines with varying slopes. The inflexion point of the spacer thickness corresponding to the change of the slope is at about 85 nm. This value is very close to the lateral size of the buried islands, which is of 95–100 nm. In order to see if the above behavior in the variation of the critical thickness is linked the degree of the island alignment, we have systematically undertaken TEM measurements with special attention having been paid to the spacer thicknesses at which the curve slopes change. Some representative results are shown in the inset of Fig. 4. First, it is important to emphasize that for all values of dSi going up to 85 nm, TEM measurements reveal a high vertical alignment between islands along the growth direction. An example for dSi ¼ 22 nm was already shown in Fig. 2(b), where a high correlation between islands is observed since the second Ge layer. TEM measurements of a bilayer sample with dSi ¼ 55 nm (not shown here) confirm that the islands remain highly vertically correlated. For a bilayer with dSi ¼ 80 nm, i.e. just before the change in slope of the dc2 (dSi) curve, TEM image clearly reveals that a high vertical alignment between
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islands is still preserved (Fig. 4). In the second region corresponding to dSi increasing from 85 to 150 nm, the vertical correlation was found to become progressively reduced when dSi increases. ATEM image corresponding to dSi ¼ 90 nm, i.e. just after the change in the dc2 (dSi) curve slope, is shown in Fig. 4. The islands in the second layer are now not directly formed above the buried ones but slightly laterally shifted. Finally, when dSi becomes larger than 150 nm, a value from which dc2 becomes the same as dc1, the island arrangement becomes completely random, as illustrated in the TEM image with dSi ¼ 160 nm. The above TEM and RHEED analyses provide a nice coherence between the island vertical alignment and the variation of the critical thickness in the upper layer. These results clearly indicate that the phenomenon of vertical ordering is characterized not only by the alignment in island positions but also by a reduction of the critical thickness in the upper layer. To further understand the influence of the strain fields of buried islands on the nucleation of islands in the
second layer, we performed another series of experiments with the aim to investigate the evolution of the island shape. The idea is to see how the nucleation of islands in the second layer involves when the spacer thickness passes through the three regions defined from the variation of the critical thickness. Because Ge/Si islands exhibit a large variety of surface morphology [24–26], the choice of the island morphology on the starting surface appears judicious. Indeed, depending on growth conditions, Ge/Si islands can be elongated {1 0 5} faceted hut clusters [24] or consist of both square-based pyramids and multifaceted domes [25,26]. We first investigated the island formation in a single layer as a function of the growth temperature and the GeH4 flux and we have chosen the growth parameters, so that the islands in the first layer have all a dome shape. Displayed in Fig. 5 are AFM images corresponding to three regimes of island correlation. We note that the Ge deposition in the second layer was stopped just after the appearance of 3D spots in RHEED patterns. While the starting surface only
Fig. 5. Variation of the Ge critical thickness and typical AFM images of islands in the second layer measured in three regions of island correlation: 15, 90 and 160 nm.
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consist of domes, the AFM image in the highly correlated region exhibits islands, all of which have a square-based pyramidal shape. These pyramids are oriented along the [1 1 0] directions and bounded by {1 0 5} facets. This indicates that the strain field of buried islands which propagates through the Si capping layer significantly modifies the nucleation process of upper islands. Pyramids are systematically observed for Si spacer thicknesses increasing up to 85 nm, i.e. up to the change in slope of the critical thickness curve. For Si thicknesses corresponding to a reduced correlated region, i.e. for Si thickness varying from 85 to 150 nm, a bimodal dot distribution consisting of pyramids and domes is observed. An example corresponding to a Si thickness of 90 nm is shown in Fig. 5. Finally, for Si thicknesses above 150 nm, i.e. in the uncorrelated region, only dome-shaped islands are observed in the second layer (an example for a Si thickness of 160 nm is shown in the inset of Fig. 5). This situation indicates that the system has now returned to its original situation where the growth of a second layer becomes independent of the buried layers. The driving mechanisms for the island vertical correlation have been the subject of extensive studies over the past years. Because the buried islands produce a non-uniform strain field at the surface of the spacer layer, i.e. the regions above the islands are tensely strained while the regions in between islands remain compressed as in all Stranski–Krastanow systems investigated, exciting models have treated the island distribution at the spacer layer surface by considering the effect of such a strain field on surface diffusion [5] or on island nucleation [4]. Recent calculations have taken into account the effect of the elastic anisotropy of the materials [17], the surface energy [19] or the elastic interaction between the buried islands with newly deposited ones [20]. However, in all of the above models it was assumed that the surface of the spacer layer becomes perfectly flat before the deposition of a new layer. This assumption is not necessarily valid. Fig. 6 shows a zoom around a square-based pyramid of the AFM image corresponding to a Si thickness of 15 nm. A striking feature that can be seen from this image is that whereas the wetting-layer surface between islands is flat, each pyramid is found to be sitting on a square-base region, ˚. which has a roughness amplitude of about 4–5 A
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Fig. 6. A zoom around square-based pyramids of AFM image corresponding to a Si barrier thickness of 15 nm. Each pyramid is nucleated inside a square-base region, which has a roughness ˚ . These regions have a dimension of about amplitude of about 4–5 A 170 nm 170 nm and are oriented along the [1 1 0] directions.
These regions have a dimension of about 170 nm 170 nm and are oriented along the [1 1 0] directions. The dimension of this region is almost twice larger than the lateral size of the buried islands, which may give a rough estimate of the extension of the strain field of the buried islands. The pyramids have a density of the same order of magnitude as that of the first layer, confirming therefore that each pyramid grows on the top of a buried island. It should be emphasized that such roughening is not observed on single layers exhibiting square-based pyramids as well as single layers covered by dome-shaped islands. The ensemble of these results suggests that the formation of pyramidal islands in the second layer stems from preferential nucleation associated with surface roughness induced by the elastic strain fields of buried islands. In other words, preferential nucleation associated with surface roughness appears to be the dominant mechanism, leading to the vertical ordering in superlattices of self-assembled quantum dots.
4. Conclusion To summarize, we have shown that the decrease of the Ge critical thicknesses in upper layers of a multilayer is the main mechanism, which leads to the evolution of the island sizes and heights in multiplayer structures. Such a decrease of the Ge critical thickness can be explained by elastic strain fields induced by buried layers and mediated by the spacer layers.
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We have demonstrated that when the Ge deposited amount is no longer kept constant in all layers as frequently carried out in typical experiments but adjusted according to the effective critical thicknesses in subsequent layers, superlattices of self-assembled quantum dots in which dots have uniform dimension in all layers can be produced. Furthermore, by analyzing the transformation of the island shape versus the thickness of the spacer layer, we show that preferential nucleation induced by surface roughness may be the main mechanism responsible for the vertical ordering observed in quantum-dot superlattices. It is believed that stacked layers having identical islands represent as a promising system for studying the electronic coupling and the vertical transport between islands. References [1] D.J. Eaglesham, M. Cerullo, Phys. Rev. Lett. 64 (1990) 1943. [2] J. Tersoff, F.K. LeGoues, Phys. Rev. Lett. 72 (1994) 3570. [3] G. Abstreiter, P. Schittenhelm, C. Engel, E. Silveira, A. Zrenner, D. Meertens, W. Ja¨ ger, Semicond. Sci. Technol. 11 (1998) 1521. [4] J. Tersoff, C. Teichert, M.G. Lagally, Phys. Rev. Lett. 76 (1996) 1675; C. Teichert, M.G. Lagally, L.J. Peticolas, J.C. Bean, J. Tersoff, Phys. Rev. B53 (1996) 16334. [5] Q. Xie, A. Madhukar, P. Chen, N.P. Kobayashi, Phys. Rev. Lett. 75 (1995) 2542. [6] V. Le Thanh, P. Boucaud, D. De´ barre, Y. Zheng, D. Bouchier, J.-M. Lourtioz, Phys. Rev. B58 (1998) 13115; V. Le Thanh, P. Boucaud, Y. Zheng, A. Younsi, D. De´ barre, D. Bouchier, J.-M. Lourtioz, J. Crystal Growth 201/202 (1999) 1212. [7] G.S. Solomon, J.A. Trezza, A.F. Marshall, J.S. Harris Jr., Phys. Rev. Lett. 76 (1996) 952; M.K. Zundel, P. Specht, K. Eberl, N.Y. Jin-Philipp, F. Philipp, Appl. Phys. Lett. 71 (1997) 2972. [8] Y. Nakata, Y. Sugiyama, T. Futatsugi, N. Yokoyama, J. Crystal Growth 175/176 (1997) 713. [9] O. Kienzle, F. Ernst, M. Ru¨ hle, O.G. Schmidt, K. Eberl, Appl. Phys. Lett. 74 (1999) 269.
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Superlattices of self-assembled Ge/Si(0 0 1) quantum dots Vinh Le Thanh*, V. Yam Institut d’E´lectronique Fondamentale, UMR-CNRS 8622 Baˆt. 220, Universite´ Paris-Sud, 91405 Orsay Cedex, France
Abstract The effect of vertical ordering in superlattices of self-assembled Ge/Si(0 0 1) quantum dots was investigated by a combination of structural and optical characterizations via in situ reflection high-energy electron diffraction (RHEED), transmission electron microscopy (TEM), atomic force microscopy (AFM) and photoluminescence (PL) spectroscopy. We show that the vertical ordering observed in quantum-dot superlattices is characterized not only by the alignment of islands along the growth direction but also by a reduction of the critical thickness. The better the vertical ordering is, the more pronounced the reduction of the critical thickness will be. Such an evolution of the critical thickness could be explained by elastic strain fields induced by buried islands and propagate through the spacer layers. An important result issued from this work is the realization of superlattices in which dots can have equal size in all layers. On the other hand, experiments performed on the transformation of the island shape versus the spacer layer thickness suggest that preferential nucleation induced by surface roughness may be the main mechanism responsible for the vertical ordering observed in quantum-dot superlattices. # 2003 Elsevier Science B.V. All rights reserved. PACS: 68.65.-k; 85.35.Be; 05.65.þb; 78.66.-w Keywords: Quantum dots; Self-assembly; Vertical ordering; Superlattices; Germanium; Silicon
1. Introduction Since the first observation of the formation of defect-free three-dimensional (3D) islands in the early stage of germanium deposition on silicon, the growth of Ge/Si self-assembled quantum dots has attracted a considerable interest [1]. The formation of such coherent islands is a spontaneous process that occurs when the deposited film thickness exceeds a critical value. The driving force of this spontaneous formation of islands is the relief of the built-in elastic strain accumulated in the grown film due to the lattice-mismatch * Corresponding author. Present address: Centre de Recherche sur les Me´canismes de la Croissance Cristalline (CRMC2-CNRS), Campus de Luminy, Case 913, 13288 Marseille Cedex 9, France. E-mail address: [email protected] (V. Le Thanh).
between film and substrate (the so-called Stranski– Krastanow growth) [2]. The defect-free three-dimensional nanocrystals offer new opportunities for the development of optoelectronic devices integrated on silicon. The carrier localization, the three-dimensional confinement, the high germanium content achieved with the heterostructures represent specific advantages for a new generation of devices [3]. However, one of the major limitations of the self-assembled quantum dots is that they exhibit broad distributions both in size and position. Recently, it has been shown that starting from a single layer with inhomogeneous islands one can greatly improve the island size uniformity by growing multilayer structures [4]. Another feature of particular interest observed in such structures is that under appropriate spacer thickness the dots in the upper
0169-4332/03/$ – see front matter # 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0169-4332(03)00078-3
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layers tend to grow on the top of the buried ones, giving rise to the vertical alignment of islands along the growth direction [5]. Compared to self-assembled dots formed in a single layer where no interaction between dots could be possible due to a too large interdot distance (of about 150–200 nm in the Ge/Si system [6], for example), the feature of vertical ordering in superlattices may open new areas of applications such as electronically coupled quantum dots [7] and vertical transport. The mechanisms leading to such a vertical ordering have been then the subject of numerous investigations [8–20]. It is now generally accepted that the driving force which leads to the vertical island alignment in QD superlattices is the elastic strain fields created by buried islands and mediated by spacer layers. However, the detailed mechanisms or the manner through which such strain fields manifest or affect the nucleation process of islands at the surface of the spacer layer are still not fully understood. In this work, we investigate the effect of vertical ordering in a Ge/Si(0 0 1) multilayer structure. The purpose of our work is two-fold: the first is to understand the mechanisms leading to the increase of the island dimension observed in superlattices of different materials. The second is to study the degree of the vertical correlation of islands with the aim to extract the essential physical parameters, which may govern the phenomenon of vertical ordering. We have, for this purpose, combined structural and optical characterizations, via in situ reflection highenergy electron diffraction (RHEED), atomic force microscopy (AFM), transmission electron microscopy (TEM) and photoluminescence (PL) spectroscopy, with a special attention being paid to the control of the island formation process. The article is organized into two sections: the first section is devoted to the evolution of the island dimension with increasing the number of deposited layers while the spacer thickness is kept constant. In the second section, we deal with the influence of the spacer thickness on the vertical alignment of the islands in a bilayer structure.
2. Experimental Experiments were carried out in an ultrahigh vacuum chemical-vapor deposition (UHV-CVD) system.
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Pure SiH4 and hydrogen-diluted (10%) GeH4 were used as gas sources. The system base pressure was better than 1 1010 Torr while the hydride partial pressures during growth were about 5 104 and 2 104 Torr for GeH4 (H2) and SiH4, respectively. One of the advantages of our work is the use of in situ RHEED to precisely monitor, in real-time, the two dimensional (2D)–3D growth mode transition and the capping process in a CVD system working at high hydride pressures. Indeed, our RHEED gun is equipped with a differentially-pumped system, allowing us to probe the growing surface even at hydride partial pressures up to 101 Torr. During growth, RHEED patterns were recorded using a camera-based video recording system. More details of the experimental setup and growth conditions can be found elsewhere [21]. After growth, photoluminescence measurements were performed at low temperatures, using an Arþ laser (power density of 400 mW/cm2). The PL signal was detected with a liquid nitrogencooled Ge photodetector using a standard lock-in technique. Atomic force microscopy images were recorded with a Park Scientific Instruments AFM setup operating in contact mode. Cross-sectional TEM micrographs were obtained from a JEM 4000EX high-resolution electron microscope operated at 400 keV. The Ge deposition was carried out at temperatures of 550 and 600 8C. The choice of such temperatures was guided by the fact that in this temperature range the islands in a single layer exhibit a dome shape, a point which is crucial for the study of the island shape transformation and will be discussed below. The Ge growth rate is about 1.5 monolayers (ML)/min. The Si deposition was carried out at 600 8C with a growth rate of about 2.5 nm/min. The substrates were flat, p-type Si(0 0 1) wafers. Cleaning of the substrate surface followed the newly developed procedure utilizing the hydrogenterminated Si(0 0 1) surface [22]. It consists of two steps: the first is a wet chemical treatment in NH4F solution to prepare an ideally dihydrideterminated Si(0 0 1) surface. The second step is heating in ultrahigh vacuum to desorb the passivating hydrogen layer at a temperature of about 450–500 8C. Prior to Ge deposition, a 100 nm thick Si buffer layer was grown at 700 8C to ensure a good starting surface.
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3. Results and discussion 3.1. Evolution of island dimension in multilayer structures As we have mentioned above, a general feature observed in superlattices of different materials is that the island dimensions, both lateral size and height, have been shown to increase with increasing the number of deposited layers [4,5]. An increase, for example by a factor of about 3 has been observed in [4] after the deposition of 20 SiGe/Si periods. From the technological point of view, such an evolution of the island dimensions may be considered as one of the main drawbacks for the application of multilayer arrays. Indeed, for most QD-based applications it is desirable to have islands with sizes as small as possible to obtain an efficient quantum confinement inside the islands. In InAs/GaAs multilayers, Nakata et al. [8] have shown, from RHEED, that the InAs critical thickness in upper layers was shorter than that of the first layer. However, since the In surface segregation is known to play an important role in the InAs/GaAs growth process, it was not clear whether such a decrease of the InAs critical thickness is due to the strain induced by underlying layers or surface migration of In atoms. In Ge/Si multilayers, Schmidt et al. [10,11] have shown that the wetting-layer thickness in the upper layers was smaller than that of the first layer. However, because this result has been obtained in postgrown samples by means of TEM microanalysis, no proposal to improve the island size homogeneity has been submitted. Fig. 1(a) shows a representative [0 1 1] cross-sectional TEM image of a multilayer consisting of 10 Ge/Si periods, the thickness of the Si spacer is 22 nm. The growth temperature is 550 8C for Ge and 600 8C for Si, respectively. The Ge deposited amount in each layer was chosen to be equal to the critical thickness determined from RHEED for the first layer, which is of 4 ML. This amount was then kept constant during the deposition of all upper layers. The image clearly shows that each island in the upper layers grows on the top of the ones in the lower layers, resulting in a high vertical correlation between islands. It can be also seen from the image that the islands undergo a drastic change both in size and height from the first to
Fig. 1. (a) Typical TEM image taken along the [0 1 1] azimuth of a sample with 10 Ge/Si bilayers. The Ge deposited amount was chosen to be equal to the critical thickness of the first layer and was kept constant in all layers; (b) 11K-PL spectra of a single layer (lower curve) and of a 10-bilayer sample (upper curve).
the third layer, and they become almost stable from the fifth layer. The average island dimensions in the first layer, 100 nm in size and 7 nm in height, are respectively found to increase upto 180 and 12.3 nm in the fifth layer and then remain nearly unchanged. The PL spectrum of the corresponding sample is shown in Fig. 1(b). For comparison, we report in the lower curve the PL spectrum of a single layer. The single layer was covered with a 22 nm-thick Si cap layer, i.e. identical to the first bilayer of the multilayer sample. Apart from the narrow peak at 1098 meV which is attributed to the phonon-assisted recombination of the free-exciton in the Si substrate, the
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single-layer spectrum consists of two separate components characteristic of the Ge wetting layers (WL) and Ge islands, respectively. The WL component is characterized by two main lines located at 1024 and 967 meV, which are, respectively, due to the excitonic no-phonon (NP) and transverse–optical (TO)-phononassisted transitions of pseudomorphic Ge layers in Si [23]. The energy difference between the NP and TO lines is 57–58 meV, which corresponds to the Si–Si optical phonon energy in Si. The emission band lying at the lower energy of 768 meV can be attributed to three-dimensional Ge islands [6,23]. The multilayer spectrum also consists of two components, but, importantly, both of them now contain two separate parts. The WL component now contains four main lines, denoted to as NP1, TO1, NPn and TOn, instead of the two ones observed in the single-layer spectrum. The NP1 and TO1 lines can be attributed to arise from the first Ge wetting layer, while additional lines, NPn and TOn, can then be interpreted as arising from another Ge wetting layer, which has a thickness smaller than that of the first one. For the island-related component, isl three peaks, denoted to as ISL1, TOisl n , and NPn , can be resolved after a deconvolution by using a set of three Gaussian line-shaped peaks, which have their maxima at 768, 833 and 875 meV, respectively. The ISL1 peak stems from the islands in the first layer. The isl other two peaks, NPisl n and TOn , can be attributed to NP and TO transitions of islands from the rest of the layers. To further clarify the existence of another type of Ge WL in upper layers, we have undertaken a RHEED analysis, by measuring the Ge critical thickness in each layer. It is now well established that the 2D growth regime is associated with the observation of streaky RHEED patterns due to reflection diffraction from a smooth crystal surface, while 3D growth is characterized by spotty patterns due to transmission diffraction through 3D islands. The transition from 2D to 3D growth can be precisely determined by measuring the variation of the RHEED intensity of a bulktype diffraction spot as a function of the Ge growth time and thus Ge coverage [21]. Shown in Fig. 2(a) is the evolution of the 2D–3D transition time (left axis) and the critical thickness (right axis) versus the number of the deposited layers. The upper curve corresponds to a Si spacer thickness of 22 nm while the lower one corresponding to a
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Fig. 2. (a) Evolution of the Ge critical thickness as a function of the number of deposited layers in a multilayer consisting of 10 Ge/ Si periods for a spacer thickness of 22 and 2.5 nm. The solid lines are only guided for the eyes; (b) TEM image of a sample with 10 Ge/Si bilayers in which the Ge deposited amount was no longer kept constant but adjusted with the effective critical thickness in each layer, the spacer thickness is 22 nm. These thicknesses are of 4, 2.5, 2.25, 2.13, and 2.08 ML for the 1st, 2nd, 3rd, 4th, and the last six layers, successively.
thickness of 2.5 nm. For dSi ¼ 22 nm, the Ge critical thickness, which is of 4 ML in the first layer, is found to rapidly decrease within the three first layers and reaches a stable value of 2.08 ML after the fifth layer. As the result of RHEED analysis, the multilayer structure is found to present five critical thicknesses, which are of 4, 2.5, 2.25, 2.13, and 2.08 ML for the 1st, 2nd, 3rd, 4th, and the last six layers, successively. The finding of the decrease of the critical thickness in the upper layers of a multilayer structure has brought us to a very simple idea for the realization of a multilayer structure in which the islands may have equal size in all layers. Indeed, if one does not keep the Ge
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deposited amount constant in all layers (equal to the critical thickness of the first layer), but adjusts this amount according to the effective critical thickness in subsequent layers, this can lead to the formation of islands at the first nucleation stage in all layers. As a demonstration, a cross-sectional TEM image of a multilayer consisting of 10 Ge/Si periods produced with this approach is shown in Fig. 2(b). The Ge growth in each layer was stopped just after the appearance of 3D spots in RHEED patterns. The Si spacer-layer thickness was kept constant, being of 22 nm. As can be seen in this image, the islands still exhibit a high correlation along the growth direction. An important result is that the islands have now almost equal size and height in all layers, in contrast to the case presented in Fig. 1(b) in which the Ge amount was kept constant in all layers. What is particularly interesting is that by using this approach one can produce superlattices containing islands of uniform dimensions even when the spacer thickness is reduced down to a nanometer scale. An example for the formation of identical Ge islands for a spacer thickness reduced down to 2.5 nm is presented in Fig. 3. The variation of the corresponding critical thickness versus the number of deposited layers is reported in the lower curve of Fig. 2(a). The image clearly reveals that the Ge islands have almost equal size and height in all layers. The fact that the islands within a column can have equal size and height even in very closely spaced stacked layers offers a promising opportunity for studying the electronic coupling between islands. Indeed, only in the case of having equal size, the islands within a column can have the same energy and will provide a real effect of electronic
coupling. Work in this direction is now in progress and will be reported later. 3.2. Mechanism of vertical ordering in multilayer structures Starting with the aim to extract the main physical parameters, which may characterize the effect of vertical ordering in superlattices, we have investigated in a systematic manner the influence of the spacer thickness on the degree of the island vertical alignment. It is important to emphasize that such a study has been the subject of numerous investigations in different multilayer systems [5,9–13]. However, in these works the authors have mainly used cross-sectional TEM analysis to quantify the degree of the island position alignment. While cross-sectional TEM micrographs can give a direct view on the island alignment, the analysis, which are only based on cross-sectional TEM, reveal a very large dispersion. In Ge/Si multilayers, for example Rahmati et al. [13] reported a value of about 100 nm of the Si spacer thickness below which a perfect island correlation was observed while Kienzle et al. [9] obtained a value which is four times smaller than the above one. It is obvious that the presence of hydrogen in CVD experiments used in [13] could not explain this too large difference because at a growth temperature as high as 700 8C the growing surface is known to be free of hydrogen. Here, we have combined RHEED and TEM to study the effect of the island ordering. Motivated by our finding on the reduction of the critical thickness versus the number of deposited layers, we have
Fig. 3. TEM image of a 10-bilayer sample in which the Ge deposited amount in each layer was adjusted with the 2D–3D transition detected by RHEED. The corresponding Ge effective critical thickness in each layer is indicated in Fig. 2(a). The Si spacer layer was reduced down to 2.5 nm and was kept constant in all layers.
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Fig. 4. Variation of the Ge critical thickness in the second layer as a function of the Si spacer thickness. Note that the variation of dc2 can be divided into three distinct regions and described by straight lines with varying slopes represented by dotted lines. Shown in the inset are typical TEM images corresponding to the Si spacer thickness of 80, 90 and 160 nm.
systematically undertaken measurements of the Ge critical thickness in the second layer as a function of the thickness of the Si spacer layer. The growth temperature is 600 8C for both Ge and Si. Fig. 4 shows a typical result on the variation of the critical thickness in the second layer (dc2) versus the Si spacer thickness (dSi). dc1 is the Ge critical thickness in the first layer, which is of 4 ML. As can be seen from the figure, the variation of the Ge critical thickness in the second layer (dc2) can be divided into three distinct regions: the first region corresponds to Si spacer thicknesses above 150 nm, the second corresponds to a thickness between 150 and 85 nm and the third region corresponds to a thicknesses below 85 nm. In the first region, dc2 is equal to dc1, which clearly indicates that for spacer thicknesses larger than 150 nm, the growth of the second layer is not affected by the strain field induced by buried islands. For dSi below 150 nm, dc2 is found to decrease when decreasing the spacer thickness. It is worth noting that for very thin spacer layers, dc2 is reduced down to less than 1 monolayer of Ge. A feature of particular interest is that the reduction of the critical thickness can be described by straight
lines with varying slopes. The inflexion point of the spacer thickness corresponding to the change of the slope is at about 85 nm. This value is very close to the lateral size of the buried islands, which is of 95–100 nm. In order to see if the above behavior in the variation of the critical thickness is linked the degree of the island alignment, we have systematically undertaken TEM measurements with special attention having been paid to the spacer thicknesses at which the curve slopes change. Some representative results are shown in the inset of Fig. 4. First, it is important to emphasize that for all values of dSi going up to 85 nm, TEM measurements reveal a high vertical alignment between islands along the growth direction. An example for dSi ¼ 22 nm was already shown in Fig. 2(b), where a high correlation between islands is observed since the second Ge layer. TEM measurements of a bilayer sample with dSi ¼ 55 nm (not shown here) confirm that the islands remain highly vertically correlated. For a bilayer with dSi ¼ 80 nm, i.e. just before the change in slope of the dc2 (dSi) curve, TEM image clearly reveals that a high vertical alignment between
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islands is still preserved (Fig. 4). In the second region corresponding to dSi increasing from 85 to 150 nm, the vertical correlation was found to become progressively reduced when dSi increases. ATEM image corresponding to dSi ¼ 90 nm, i.e. just after the change in the dc2 (dSi) curve slope, is shown in Fig. 4. The islands in the second layer are now not directly formed above the buried ones but slightly laterally shifted. Finally, when dSi becomes larger than 150 nm, a value from which dc2 becomes the same as dc1, the island arrangement becomes completely random, as illustrated in the TEM image with dSi ¼ 160 nm. The above TEM and RHEED analyses provide a nice coherence between the island vertical alignment and the variation of the critical thickness in the upper layer. These results clearly indicate that the phenomenon of vertical ordering is characterized not only by the alignment in island positions but also by a reduction of the critical thickness in the upper layer. To further understand the influence of the strain fields of buried islands on the nucleation of islands in the
second layer, we performed another series of experiments with the aim to investigate the evolution of the island shape. The idea is to see how the nucleation of islands in the second layer involves when the spacer thickness passes through the three regions defined from the variation of the critical thickness. Because Ge/Si islands exhibit a large variety of surface morphology [24–26], the choice of the island morphology on the starting surface appears judicious. Indeed, depending on growth conditions, Ge/Si islands can be elongated {1 0 5} faceted hut clusters [24] or consist of both square-based pyramids and multifaceted domes [25,26]. We first investigated the island formation in a single layer as a function of the growth temperature and the GeH4 flux and we have chosen the growth parameters, so that the islands in the first layer have all a dome shape. Displayed in Fig. 5 are AFM images corresponding to three regimes of island correlation. We note that the Ge deposition in the second layer was stopped just after the appearance of 3D spots in RHEED patterns. While the starting surface only
Fig. 5. Variation of the Ge critical thickness and typical AFM images of islands in the second layer measured in three regions of island correlation: 15, 90 and 160 nm.
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consist of domes, the AFM image in the highly correlated region exhibits islands, all of which have a square-based pyramidal shape. These pyramids are oriented along the [1 1 0] directions and bounded by {1 0 5} facets. This indicates that the strain field of buried islands which propagates through the Si capping layer significantly modifies the nucleation process of upper islands. Pyramids are systematically observed for Si spacer thicknesses increasing up to 85 nm, i.e. up to the change in slope of the critical thickness curve. For Si thicknesses corresponding to a reduced correlated region, i.e. for Si thickness varying from 85 to 150 nm, a bimodal dot distribution consisting of pyramids and domes is observed. An example corresponding to a Si thickness of 90 nm is shown in Fig. 5. Finally, for Si thicknesses above 150 nm, i.e. in the uncorrelated region, only dome-shaped islands are observed in the second layer (an example for a Si thickness of 160 nm is shown in the inset of Fig. 5). This situation indicates that the system has now returned to its original situation where the growth of a second layer becomes independent of the buried layers. The driving mechanisms for the island vertical correlation have been the subject of extensive studies over the past years. Because the buried islands produce a non-uniform strain field at the surface of the spacer layer, i.e. the regions above the islands are tensely strained while the regions in between islands remain compressed as in all Stranski–Krastanow systems investigated, exciting models have treated the island distribution at the spacer layer surface by considering the effect of such a strain field on surface diffusion [5] or on island nucleation [4]. Recent calculations have taken into account the effect of the elastic anisotropy of the materials [17], the surface energy [19] or the elastic interaction between the buried islands with newly deposited ones [20]. However, in all of the above models it was assumed that the surface of the spacer layer becomes perfectly flat before the deposition of a new layer. This assumption is not necessarily valid. Fig. 6 shows a zoom around a square-based pyramid of the AFM image corresponding to a Si thickness of 15 nm. A striking feature that can be seen from this image is that whereas the wetting-layer surface between islands is flat, each pyramid is found to be sitting on a square-base region, ˚. which has a roughness amplitude of about 4–5 A
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Fig. 6. A zoom around square-based pyramids of AFM image corresponding to a Si barrier thickness of 15 nm. Each pyramid is nucleated inside a square-base region, which has a roughness ˚ . These regions have a dimension of about amplitude of about 4–5 A 170 nm 170 nm and are oriented along the [1 1 0] directions.
These regions have a dimension of about 170 nm 170 nm and are oriented along the [1 1 0] directions. The dimension of this region is almost twice larger than the lateral size of the buried islands, which may give a rough estimate of the extension of the strain field of the buried islands. The pyramids have a density of the same order of magnitude as that of the first layer, confirming therefore that each pyramid grows on the top of a buried island. It should be emphasized that such roughening is not observed on single layers exhibiting square-based pyramids as well as single layers covered by dome-shaped islands. The ensemble of these results suggests that the formation of pyramidal islands in the second layer stems from preferential nucleation associated with surface roughness induced by the elastic strain fields of buried islands. In other words, preferential nucleation associated with surface roughness appears to be the dominant mechanism, leading to the vertical ordering in superlattices of self-assembled quantum dots.
4. Conclusion To summarize, we have shown that the decrease of the Ge critical thicknesses in upper layers of a multilayer is the main mechanism, which leads to the evolution of the island sizes and heights in multiplayer structures. Such a decrease of the Ge critical thickness can be explained by elastic strain fields induced by buried layers and mediated by the spacer layers.
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