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On the location of InAs quantum dots on GaAs(0 0 1)
Surface Science 589 (2005) 91–97 www.elsevier.com/locate/susc
On the location of InAs quantum dots on GaAs(0 0 1) M.C. Xu, Y. Temko, T. Suzuki, K. Jacobi
*
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany Received 13 April 2005; accepted for publication 25 May 2005 Available online 23 June 2005
Abstract Thin layers of InAs were deposited onto GaAs(0 0 1) substrates using molecular-beam epitaxy. The transition from the two-dimensional wetting layer to three-dimensional quantum dots (QDs) of strained InAs was studied by in situ scanning tunneling microscopy with atomic resolution. Closely before the transition, the wetting layer exhibits a flat morphology with mostly straight and parallel steps. The transition occurs during a coverage increase by less than 0.2 ML only. After the transition the wetting layer shows step meandering and holes. Besides the continuously deposited InAs material from the molecular beams, mass transport from the wetting layer and even out of the substrate is concluded to contribute to QD formation. The location of the QDs with respect to the step edges is discussed within a model. 2005 Elsevier B.V. All rights reserved. Keywords: InAs; Molecular-beam epitaxy; GaAs
1. Introduction Self-assembled semiconductor quantum dots (QDs) have been extensively studied in recent years because of their potential in technological applications [1–3]. QDs are generally assumed to form under the Stranski–Krastanov growth mode [4] which often applies for heteroepitaxy in systems with lattice mismatch P2% such as Ge/Si (4.2%) *
Corresponding author. Tel.: +49 30 8413 5201; fax: +49 30 8413 5106. E-mail address: [email protected] (K. Jacobi).
or InAs/GaAs (7.2%): The deposited material with larger lattice constant first grows in the layer-bylayer mode, and then—after a critical thickness is reached—three-dimensional (3D) islands or QDs develop on the remaining wetting layer. It is believed that the relief of strain, induced by the lattice mismatch, accounts for the ‘‘2D-to-3D’’ transition, i.e., for the formation of self-assembled QDs on a wetting layer. InAs/GaAs(0 0 1) is one of the most studied QD system. Optoelectronic devices based on InAs QDs, such as QD laser, have been brought into operation already [1–3]. InAs QDs are found to
0039-6028/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2005.05.052
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form when the deposited InAs exceeds a critical thickness of 1.4–1.8 monolayer (ML) [5–10]. If one continues to condense InAs, the QDs undergo a complicated shape transition [11–13]. With respect to the shape of the QDs, most studies lack atomic resolution which makes some conclusions doubtful. In spite of the numerous studies—only some of them is given reference to—many fundamental aspects of the QD formation, especially the wetting layer evolution, the 2D-to-3D transition, the alloying with substrate material, or the localization of QDs, e.g., with respect to steps, remain poorly understood, although these processes control the electronic and optical properties of devices based on self-assembled QDs. Although the understanding of many details is still lacking, great progress has been made recently in understanding important details of the wetting layer formation from density functional theory (DFT) calculations [14] and DFT based kinetic Monte Carlo simulations [15,16]. Most interestingly, the In diffusivity shows remarkable strain dependence. The latter may even lead to self-limiting growth of strained islands [14]. It has been found that under given conditions alloying of the wetting layer occurs by intermixing of In and Ga [10,17,18]. This makes it even more difficult to study the wetting layer evolution in detail. In this respect, it was very important to show that on In0.67Ga0.33As(0 0 1) films, which are typical for the wetting layer, the In diffusion is again anisotropic and substantially enlarged compared to the conventional GaAs(0 0 1)-c(4 · 4) substrate [16]. Despite this progress in theory, one has to keep in mind that an InAs or InGaAs QD contains some 104 atoms. For such a large number, an up to date modeling—kinetic Monte Carlo simulations with the implementation of energy barriers and binding energies derived by ab initio DFT based calculations—is not feasible with the nowadays computer capacities. The aim of our work is therefore to collect information which may help in setting up future theoretical simulations. Recently, we have studied how the structure of the wetting layer and the 2D-to-3D transition depends on growth temperature [19]. At a low
growth temperature (400 C), the substrate exhibits a well-defined GaAs(0 0 1)-c(4 · 4) structure. For a disorientation of 0.7 the deposited InAs mainly forms a non-alloyed wetting layer along steps of the substrate (step-flow growth mode). Smaller 2D InAs islands are also formed on the terraces. The wetting layer displays some local c(4 · 6) reconstruction. At the low growth temperature 1.20 ML InAs already induce the 2D-to-3D transition. At a higher temperature (460 C), the critical thickness of the wetting layer for the 2Dto-3D transition is about 1.50 ML. This was explained by alloying of Ga into the InAs layer thus reducing the strain in the wetting layer. In this contribution, we report on experimental observations of the location of InAs QDs on GaAs(0 0 1) and of how the 2D-to-3D transition of InAs/GaAs(0 0 1) depends on some morphological aspects of the wetting layer. For this purpose we use in-situ, atomically-resolved scanning tunneling microscopy (STM). We confirm that the 2D-to-3D transition occurs within a small coverage interval, and give evidence that mass transport from the wetting layer as well as from the GaAs substrate takes place during the transition. The first small islands are oblate shaped with a long axis along the [1 1 0] direction. In a later growth stage the QDs are terminated by {1 3 7} facets as reported recently [8]. We propose a model for the 2D-to-3D transition which accounts for the location of the QDs relative to the step edges on the wetting layer.
2. Experimental The experiments were carried out in a multichamber ultrahigh vacuum system consisting of a surface-analysis-, a molecular-beam epitaxy (MBE)-, and an STM-chamber (Park Scientific Instruments, VP2) [20]. The samples, with 5 · 10 mm2 size, were cut from a GaAs(0 0 1) wafer (wafer technology, Si-doped, n = (1.1 4.8) · 1018 cm 3). After cleaning by several ion-bombardment- and annealing-cycles, about 30 nm thick GaAs buffer layers were grown by MBE at a sample temperature of 570 C. Then the samples were annealed for about 5 min at the same temperature,
M.C. Xu et al. / Surface Science 589 (2005) 91–97
cooled down to about 460 C, and InAs was deposited at a growth rate of 0.012 nm/s with an As2:In beam equivalent pressure of 70. By stabilization of the different Knudsen cells and controlling the so-called beam-equivalent pressure by a separate ionization gauge brought into the As2, Ga, and In beams, the flux was controlled and turned out to be stable within about 10%. The 2D-to-3D transition was monitored by reflection high-energy electron diffraction (RHEED) when the pattern turns from streaky to spotty. The grown samples were transferred within 1 min to the analysis chamber to be cooled down to room temperature before STM measurements were performed for the filled states in constant current mode.
3. Results and discussion Before we present some typical results, it seems worth emphasizing that the latter were reproduced at many locations all over the sample surface and for different samples. Fig. 1 shows an overview
Fig. 1. Overview STM image of InAs wetting layer grown on GaAs(0 0 1) at 460 C. The image size is 200 · 200 nm2. The inset shows an enlarged, atomically-resolved STM image.
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STM image of 1.40 ML InAs deposited onto GaAs(0 0 1). Besides the mostly straight and parallel steps, flat terraces are observed without any 3D islands and with only few defects, indicating that the deposited InAs grows layer by layer. This is understandable as the surface energy of InAs is smaller than that of GaAs so that the decreasing surface energy can compensate the growing strain energy. An enlarged image with atomic resolution is presented in the inset. Obviously, there is no long-range order on the atomically flat terraces with the smallest resolved entities being assigned to As2 dimers. Some local ordering, however, exists such as (2 · 1), c(2 · 1), etc., i.e., along [1 1 0] the basic periodicity is 2·, while along [1 1 0], it is 1·, 2·, 3·, etc. This finding is consistent with earlier results [18,19]. The disordered terraces keep atomically flat and no surface roughening is found, which was observed otherwise for Ge/Si(0 0 1) [21,22]. The image in Fig. 1 is for a wetting layer at a thickness of 1.40 ML, i.e., just below the 2D-to3D transition. In a second experiment, we deposited 1.60 ML InAs, i.e., a thickness expected to be somewhat above the transition. An overview STM image is presented in Fig. 2(a). Although the deposited amount of InAs is larger by only 0.20 ML, 3D islands can clearly be recognized. The bigger islands are rather round, and the smaller ones oblate-shaped and elongated along [1 1 0]. The steps on the wetting layer are no longer straight, instead exhibit some meandering; also 2D islands, peninsulas, and holes of different size and deepness are observed. To further characterize the QD ensemble of Fig. 2(a), the diameter distributions along the two main symmetry directions are shown in Fig. 2(d) and (e). The diameter is taken along the base of the QD. The size distributions are quite sharp as characteristic for coherent QDs, i.e., for strained QDs epitaxially grown without introduction of any dislocation at the interface. The small size of the QDs is typical for the early growth stage just after the 2D-to-3D transition. More than half of the QDs in Fig. 2 are found on the lower terraces, at locations distributed along but well separated from the steps. Some smaller islands, however, are located on the upper terrace next to the steps as shown in Fig. 2(b) and (c).
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Fig. 2. (a) Overview STM image of InAs islands grown on GaAs(0 0 1) at 460 C. The image size is 400 · 400 nm2; (b) and (c) Enlarged STM images of InAs islands on GaAs(0 0 1). The image sizes are indicated; (d) and (e) Distributions of diameter size measured at the bottom along the indicated directions.
The phenomenon that QDs are located along steps has been observed already by others [5,7,23,24].
Interestingly, a very small island is observed in the upper right-hand side of Fig. 2(c), which occurs adjacent to a small hole. This indicates that the site adjacent to a hole is also favorable to initiate nucleation as well as the site adjacent to a step [22,25]. In fact, Patella et al. [10] have also observed that, what they call a ‘‘quasi-3D island’’, nucleates preferentially at the upper step edge. Fig. 2(b) and (c) show some holes in the wetting layer in detail; some holes are even 3 ML deep. The holes are observed only after the 2D-to-3D transition and there is no change in the MBE chamber made between different runs of the experiment. Therefore, pinning during growth due to small amounts of residual dirt can definitely be excluded as an explanation of the formation of holes. The holes in the wetting layer must have been formed during the 2D-to-3D transition, since there are only defects but not holes in the wetting layer before the transition. The formation of holes and their deepness directly reveal mass transport from the wetting layer to the QDs. This mass transport and the erosion of the wetting layer have been discussed also by others [26]. The observation of three-ML-deep holes gives evidence for mass transport also from the substrate itself which leads to alloying of Ga into the InAs QD. The alloying of QDs has been inferred also from other experiments [26] and has been attributed to the mass transport from the alloyed wetting layer due to the mixture of In and Ga during the wetting layer formation. In our experiment both processes of alloying may exist. According to a rough estimate, about 0.4 ML of InAs is contained in the QDs shown in Fig. 2. Since the evolution of QDs occurs within less than 0.20 ML, one has to conclude that—besides the incoming particles from molecular beams out of the effusion cells—mass transport from the wetting layer to the QDs largely contributes to the QD formation. A first pathway is just out of the wetting layer terrace, obviously proved by the observation of holes in the terrace as shown in Fig. 2. A second pathway seems to be detachment from steps—in a kind of reverse step flow—as indicated by the changed step edges in Fig. 2. In the following, a growth model is proposed which takes the above observations into account.
M.C. Xu et al. / Surface Science 589 (2005) 91–97
Fig. 3. Schematic model for the QD evolution at a step. The circles at the right-hand side of the QD give a growing hole in the wetting layer.
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The growth model sketched in Fig. 3 relies on the following explanation of the 2D-to-3D transition: During growth of the wetting layer the strain increases and—at a critical thickness—3D islands form. There are two limiting cases conceivable: (a) the terrace width of the wetting layer is larger than the In diffusion length, so that most 3D islands will form on the terrace and only some nucleation occurs at the steps due to kinetic limitations and (b) in the opposite case, realized in our experiment, the terrace width is smaller than the In diffusion length and the nucleation starts mainly at the steps. We think that on the strained wetting layer, the sites on the upper terraces next to steps become most favorable for nucleation since the strain can be relieved there more effectively than at other parts of the surface. So, the 3D islands nucleate on these sites first. For case (b) the evolution of a QD is schematically sketched in Fig. 3 whereby the incoming particles from the effusion cells are not indicated separately. The nucleation starts at the upper terrace at a step. During growth, the 3D island position is presumably fixed at the nucleation site, while the wetting-layer steps are moving away from the island due to the detachment of InAs in supporting the mass transfer to the 3D islands. So, the islands are gradually separated from an upper terrace. This answers the question of why in Fig. 2 many islands are located on the lower terrace, along but separated from the steps. Since the steps are no longer straight, the detachment from the steps seems to be more efficient around the
Fig. 4. Atomically-resolved STM images of small (a) and big (b) QDs. The image sizes are indicated.
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3D island. This may be explained as follows. We assume that there is detachment as well as attachment to the steps. The latter is likely to be largely suppressed when a QD near to a step collects the flow, which would have contributed to the attachment. Finally we note that case (a) is also modeled by the scheme in Fig. 3(c). Because the QD develops out of a small island, the number of small islands decreases, whereas the number of QDs increases. This explanation is consistent with the STM observation of Patella et al. [10], but in contrast to the claim [6,10] that there is no connection between the small islands and the big QDs. Of course, we do not rule out ripening including the dissolution of small islands because the small islands are certainly less stable than the big ones. With respect to the QD shape we present atomically resolved 3D STM images for small and big islands in Fig. 4(a) and (b), respectively. Their shapes have already been determined in an earlier contribution [8]. The small islands in Fig. 4(a) are terminated to the main part by four {1 3 7}A facets and to the smaller part by two non-facetted, round regions, displaying a somewhat oblate-shaped base. In the mean time we have figured out that the round region develops into {1 3 5}B and {1 1 2}B facets for the bigger islands (Fig. 4(b)) [13].
4. Conclusion Our atomically-resolved STM images allow us to follow the InAs QD formation on GaAs(0 0 1) more clearly than it was possible up to now. Before the 2D-to-3D transition, the InAs wetting layer exhibits a flat morphology with mostly straight and parallel steps and atomically flat terraces which exhibit presumably As dimers distributed without long-range order. The 2D-to-3D transition occurs within a small coverage interval of less than 0.20 ML. During the transition the wetting layer changes its morphology remarkably due to mass transfer toward the QDs from the wetting layer as well as out of the substrate. The first, small islands are oblate with their long axis along the [ 1 1 0] direction. For sufficiently narrow terraces we propose the following model: First nucleation
occurs at the upper step edges. Later, during growth of a QD, in most cases mass is withdrawn from the wetting layer and the step edge is retracted from the QD leaving it back at the lower terrace well separated from the step. This explains a common observation that the location of QDs follows the step edges but is well separated from them. This results also in a step roughening of the wetting layer. The indications found for mass transport out of the substrate surface give evidence for QD alloying at the growth temperature of 460 C used in this study. Acknowledgements The authors would like to thank G. Ertl for support, P. Geng for technical assistance, and M. Richard for the final designing of the figures. References [1] D. Bimberg, M. Grundmann, N.N. Ledentsov, Quantum Dot Heterostructures, Wiley, Chichester, New York, 1999. [2] M. Grundmann, Physica E (Amsterdam) 5 (2000) 167. [3] Y. Masumoto, T. Takagahara (Eds.), Semiconductor Quantum Dots, Springer, Berlin, Heidelberg, 2002. [4] I.N. Stranski, L. Krastanow, Sitzungsber. Akad. Wiss. Wien, Math.-Naturwiss. Klasse 146 (1937) 797. [5] D. Leonard, K. Pond, P.M. Petroff, Phys. Rev. B 50 (1994) 11687. [6] R. Heitz, T.R. Ramachandran, A. Kalburge, Q. Xie, I. Mikhametzhanov, P. Chen, A. Madhukar, Phys. Rev. Lett. 78 (1997) 4071. [7] Y. Hasegawa, H. Kiyama, Q.K. Xue, T. Sakurai, Appl. Phys. Lett. 72 (1998) 2265. [8] J. Ma´rquez, L. Geelhaar, K. Jacobi, Appl. Phys. Lett. 78 (2001) 2309. [9] T.J. Krzyzewski, P.B. Joyce, G.R. Bell, T.S. Jones, Surf. Sci. 532–535 (2003) 822. [10] F. Patella, S. Nufris, F. Arciprete, M. Fanfoni, E. Placidi, A. Sgarlata, A. Balzarotti, Phys. Rev. B 67 (2003) 205308. [11] H. Saito, K. Nishi, S. Sugou, Appl. Phys. Lett. 74 (1999) 1224. [12] I. Mukhametzhanov, Z. Wei, R. Heitz, A. Madhukar, Appl. Phys. Lett. 75 (1999) 85. [13] M.C. Xu, T. Suzuki, Y. Temko, K. Jacobi, in press. [14] E. Penev, P. Kratzer, M. Scheffler, Phys. Rev. B 64 (2001) 085401. [15] P. Kratzer, E. Penev, M. Scheffler, Appl. Surf. Sci. 216 (2003) 436. [16] E. Penev, S. Stojkovic, P. Kratzer, M. Scheffler, Phys. Rev. B 69 (2004) 115335.
M.C. Xu et al. / Surface Science 589 (2005) 91–97 [17] J.G. Belk, C.F. McConville, J.L. Sudijono, T.S. Jones, B.A. Joyce, Surf. Sci. 387 (1997) 213. [18] T.J. Krzyzewski, P.B. Joyce, G.R. Bell, T.S. Jones, Surf. Sci. 517 (2002) 8. [19] M.C. Xu, Y. Temko, T. Suzuki, K. Jacobi, Surf. Sci. 580 (2005) 30. [20] P. Geng, J. Ma´rquez, L. Geelhaar, J. Platen, C. Setzer, K. Jacobi, Rev. Sci. Instr. 71 (2000) 504. [21] A. Vailionis, B. Cho, G. Glass, P. Desjardins, D.G. Cahill, J.E. Greene, Phys. Rev. Lett. 85 (2000) 3672.
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[22] P. Sutter, I. Schick, W. Ernst, E. Sutter, Phys. Rev. Lett. 91 (2003) 176102. [23] N. Ikoma, S. Ohkouchi, Jpn. J. Appl. Phys. Part 2 34 (1995) L724. [24] S. Hasegawa, K. Arakawa, M. Tanaka, H. Nakashima, J. Cryst. Growth 227–228 (2001) 1029. [25] D.E. Jesson, M. Kastner, B. Voigtlander, Phys. Rev. Lett. 84 (1999) 330. [26] P.B. Joyce, T.J. Krzyzewski, G.R. Bell, B.A. Joyce, T.S. Jones, Phys. Rev. B 58 (1998) 15981.
On the location of InAs quantum dots on GaAs(0 0 1) M.C. Xu, Y. Temko, T. Suzuki, K. Jacobi
*
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany Received 13 April 2005; accepted for publication 25 May 2005 Available online 23 June 2005
Abstract Thin layers of InAs were deposited onto GaAs(0 0 1) substrates using molecular-beam epitaxy. The transition from the two-dimensional wetting layer to three-dimensional quantum dots (QDs) of strained InAs was studied by in situ scanning tunneling microscopy with atomic resolution. Closely before the transition, the wetting layer exhibits a flat morphology with mostly straight and parallel steps. The transition occurs during a coverage increase by less than 0.2 ML only. After the transition the wetting layer shows step meandering and holes. Besides the continuously deposited InAs material from the molecular beams, mass transport from the wetting layer and even out of the substrate is concluded to contribute to QD formation. The location of the QDs with respect to the step edges is discussed within a model. 2005 Elsevier B.V. All rights reserved. Keywords: InAs; Molecular-beam epitaxy; GaAs
1. Introduction Self-assembled semiconductor quantum dots (QDs) have been extensively studied in recent years because of their potential in technological applications [1–3]. QDs are generally assumed to form under the Stranski–Krastanov growth mode [4] which often applies for heteroepitaxy in systems with lattice mismatch P2% such as Ge/Si (4.2%) *
Corresponding author. Tel.: +49 30 8413 5201; fax: +49 30 8413 5106. E-mail address: [email protected] (K. Jacobi).
or InAs/GaAs (7.2%): The deposited material with larger lattice constant first grows in the layer-bylayer mode, and then—after a critical thickness is reached—three-dimensional (3D) islands or QDs develop on the remaining wetting layer. It is believed that the relief of strain, induced by the lattice mismatch, accounts for the ‘‘2D-to-3D’’ transition, i.e., for the formation of self-assembled QDs on a wetting layer. InAs/GaAs(0 0 1) is one of the most studied QD system. Optoelectronic devices based on InAs QDs, such as QD laser, have been brought into operation already [1–3]. InAs QDs are found to
0039-6028/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2005.05.052
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form when the deposited InAs exceeds a critical thickness of 1.4–1.8 monolayer (ML) [5–10]. If one continues to condense InAs, the QDs undergo a complicated shape transition [11–13]. With respect to the shape of the QDs, most studies lack atomic resolution which makes some conclusions doubtful. In spite of the numerous studies—only some of them is given reference to—many fundamental aspects of the QD formation, especially the wetting layer evolution, the 2D-to-3D transition, the alloying with substrate material, or the localization of QDs, e.g., with respect to steps, remain poorly understood, although these processes control the electronic and optical properties of devices based on self-assembled QDs. Although the understanding of many details is still lacking, great progress has been made recently in understanding important details of the wetting layer formation from density functional theory (DFT) calculations [14] and DFT based kinetic Monte Carlo simulations [15,16]. Most interestingly, the In diffusivity shows remarkable strain dependence. The latter may even lead to self-limiting growth of strained islands [14]. It has been found that under given conditions alloying of the wetting layer occurs by intermixing of In and Ga [10,17,18]. This makes it even more difficult to study the wetting layer evolution in detail. In this respect, it was very important to show that on In0.67Ga0.33As(0 0 1) films, which are typical for the wetting layer, the In diffusion is again anisotropic and substantially enlarged compared to the conventional GaAs(0 0 1)-c(4 · 4) substrate [16]. Despite this progress in theory, one has to keep in mind that an InAs or InGaAs QD contains some 104 atoms. For such a large number, an up to date modeling—kinetic Monte Carlo simulations with the implementation of energy barriers and binding energies derived by ab initio DFT based calculations—is not feasible with the nowadays computer capacities. The aim of our work is therefore to collect information which may help in setting up future theoretical simulations. Recently, we have studied how the structure of the wetting layer and the 2D-to-3D transition depends on growth temperature [19]. At a low
growth temperature (400 C), the substrate exhibits a well-defined GaAs(0 0 1)-c(4 · 4) structure. For a disorientation of 0.7 the deposited InAs mainly forms a non-alloyed wetting layer along steps of the substrate (step-flow growth mode). Smaller 2D InAs islands are also formed on the terraces. The wetting layer displays some local c(4 · 6) reconstruction. At the low growth temperature 1.20 ML InAs already induce the 2D-to-3D transition. At a higher temperature (460 C), the critical thickness of the wetting layer for the 2Dto-3D transition is about 1.50 ML. This was explained by alloying of Ga into the InAs layer thus reducing the strain in the wetting layer. In this contribution, we report on experimental observations of the location of InAs QDs on GaAs(0 0 1) and of how the 2D-to-3D transition of InAs/GaAs(0 0 1) depends on some morphological aspects of the wetting layer. For this purpose we use in-situ, atomically-resolved scanning tunneling microscopy (STM). We confirm that the 2D-to-3D transition occurs within a small coverage interval, and give evidence that mass transport from the wetting layer as well as from the GaAs substrate takes place during the transition. The first small islands are oblate shaped with a long axis along the [1 1 0] direction. In a later growth stage the QDs are terminated by {1 3 7} facets as reported recently [8]. We propose a model for the 2D-to-3D transition which accounts for the location of the QDs relative to the step edges on the wetting layer.
2. Experimental The experiments were carried out in a multichamber ultrahigh vacuum system consisting of a surface-analysis-, a molecular-beam epitaxy (MBE)-, and an STM-chamber (Park Scientific Instruments, VP2) [20]. The samples, with 5 · 10 mm2 size, were cut from a GaAs(0 0 1) wafer (wafer technology, Si-doped, n = (1.1 4.8) · 1018 cm 3). After cleaning by several ion-bombardment- and annealing-cycles, about 30 nm thick GaAs buffer layers were grown by MBE at a sample temperature of 570 C. Then the samples were annealed for about 5 min at the same temperature,
M.C. Xu et al. / Surface Science 589 (2005) 91–97
cooled down to about 460 C, and InAs was deposited at a growth rate of 0.012 nm/s with an As2:In beam equivalent pressure of 70. By stabilization of the different Knudsen cells and controlling the so-called beam-equivalent pressure by a separate ionization gauge brought into the As2, Ga, and In beams, the flux was controlled and turned out to be stable within about 10%. The 2D-to-3D transition was monitored by reflection high-energy electron diffraction (RHEED) when the pattern turns from streaky to spotty. The grown samples were transferred within 1 min to the analysis chamber to be cooled down to room temperature before STM measurements were performed for the filled states in constant current mode.
3. Results and discussion Before we present some typical results, it seems worth emphasizing that the latter were reproduced at many locations all over the sample surface and for different samples. Fig. 1 shows an overview
Fig. 1. Overview STM image of InAs wetting layer grown on GaAs(0 0 1) at 460 C. The image size is 200 · 200 nm2. The inset shows an enlarged, atomically-resolved STM image.
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STM image of 1.40 ML InAs deposited onto GaAs(0 0 1). Besides the mostly straight and parallel steps, flat terraces are observed without any 3D islands and with only few defects, indicating that the deposited InAs grows layer by layer. This is understandable as the surface energy of InAs is smaller than that of GaAs so that the decreasing surface energy can compensate the growing strain energy. An enlarged image with atomic resolution is presented in the inset. Obviously, there is no long-range order on the atomically flat terraces with the smallest resolved entities being assigned to As2 dimers. Some local ordering, however, exists such as (2 · 1), c(2 · 1), etc., i.e., along [1 1 0] the basic periodicity is 2·, while along [1 1 0], it is 1·, 2·, 3·, etc. This finding is consistent with earlier results [18,19]. The disordered terraces keep atomically flat and no surface roughening is found, which was observed otherwise for Ge/Si(0 0 1) [21,22]. The image in Fig. 1 is for a wetting layer at a thickness of 1.40 ML, i.e., just below the 2D-to3D transition. In a second experiment, we deposited 1.60 ML InAs, i.e., a thickness expected to be somewhat above the transition. An overview STM image is presented in Fig. 2(a). Although the deposited amount of InAs is larger by only 0.20 ML, 3D islands can clearly be recognized. The bigger islands are rather round, and the smaller ones oblate-shaped and elongated along [1 1 0]. The steps on the wetting layer are no longer straight, instead exhibit some meandering; also 2D islands, peninsulas, and holes of different size and deepness are observed. To further characterize the QD ensemble of Fig. 2(a), the diameter distributions along the two main symmetry directions are shown in Fig. 2(d) and (e). The diameter is taken along the base of the QD. The size distributions are quite sharp as characteristic for coherent QDs, i.e., for strained QDs epitaxially grown without introduction of any dislocation at the interface. The small size of the QDs is typical for the early growth stage just after the 2D-to-3D transition. More than half of the QDs in Fig. 2 are found on the lower terraces, at locations distributed along but well separated from the steps. Some smaller islands, however, are located on the upper terrace next to the steps as shown in Fig. 2(b) and (c).
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Fig. 2. (a) Overview STM image of InAs islands grown on GaAs(0 0 1) at 460 C. The image size is 400 · 400 nm2; (b) and (c) Enlarged STM images of InAs islands on GaAs(0 0 1). The image sizes are indicated; (d) and (e) Distributions of diameter size measured at the bottom along the indicated directions.
The phenomenon that QDs are located along steps has been observed already by others [5,7,23,24].
Interestingly, a very small island is observed in the upper right-hand side of Fig. 2(c), which occurs adjacent to a small hole. This indicates that the site adjacent to a hole is also favorable to initiate nucleation as well as the site adjacent to a step [22,25]. In fact, Patella et al. [10] have also observed that, what they call a ‘‘quasi-3D island’’, nucleates preferentially at the upper step edge. Fig. 2(b) and (c) show some holes in the wetting layer in detail; some holes are even 3 ML deep. The holes are observed only after the 2D-to-3D transition and there is no change in the MBE chamber made between different runs of the experiment. Therefore, pinning during growth due to small amounts of residual dirt can definitely be excluded as an explanation of the formation of holes. The holes in the wetting layer must have been formed during the 2D-to-3D transition, since there are only defects but not holes in the wetting layer before the transition. The formation of holes and their deepness directly reveal mass transport from the wetting layer to the QDs. This mass transport and the erosion of the wetting layer have been discussed also by others [26]. The observation of three-ML-deep holes gives evidence for mass transport also from the substrate itself which leads to alloying of Ga into the InAs QD. The alloying of QDs has been inferred also from other experiments [26] and has been attributed to the mass transport from the alloyed wetting layer due to the mixture of In and Ga during the wetting layer formation. In our experiment both processes of alloying may exist. According to a rough estimate, about 0.4 ML of InAs is contained in the QDs shown in Fig. 2. Since the evolution of QDs occurs within less than 0.20 ML, one has to conclude that—besides the incoming particles from molecular beams out of the effusion cells—mass transport from the wetting layer to the QDs largely contributes to the QD formation. A first pathway is just out of the wetting layer terrace, obviously proved by the observation of holes in the terrace as shown in Fig. 2. A second pathway seems to be detachment from steps—in a kind of reverse step flow—as indicated by the changed step edges in Fig. 2. In the following, a growth model is proposed which takes the above observations into account.
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Fig. 3. Schematic model for the QD evolution at a step. The circles at the right-hand side of the QD give a growing hole in the wetting layer.
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The growth model sketched in Fig. 3 relies on the following explanation of the 2D-to-3D transition: During growth of the wetting layer the strain increases and—at a critical thickness—3D islands form. There are two limiting cases conceivable: (a) the terrace width of the wetting layer is larger than the In diffusion length, so that most 3D islands will form on the terrace and only some nucleation occurs at the steps due to kinetic limitations and (b) in the opposite case, realized in our experiment, the terrace width is smaller than the In diffusion length and the nucleation starts mainly at the steps. We think that on the strained wetting layer, the sites on the upper terraces next to steps become most favorable for nucleation since the strain can be relieved there more effectively than at other parts of the surface. So, the 3D islands nucleate on these sites first. For case (b) the evolution of a QD is schematically sketched in Fig. 3 whereby the incoming particles from the effusion cells are not indicated separately. The nucleation starts at the upper terrace at a step. During growth, the 3D island position is presumably fixed at the nucleation site, while the wetting-layer steps are moving away from the island due to the detachment of InAs in supporting the mass transfer to the 3D islands. So, the islands are gradually separated from an upper terrace. This answers the question of why in Fig. 2 many islands are located on the lower terrace, along but separated from the steps. Since the steps are no longer straight, the detachment from the steps seems to be more efficient around the
Fig. 4. Atomically-resolved STM images of small (a) and big (b) QDs. The image sizes are indicated.
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3D island. This may be explained as follows. We assume that there is detachment as well as attachment to the steps. The latter is likely to be largely suppressed when a QD near to a step collects the flow, which would have contributed to the attachment. Finally we note that case (a) is also modeled by the scheme in Fig. 3(c). Because the QD develops out of a small island, the number of small islands decreases, whereas the number of QDs increases. This explanation is consistent with the STM observation of Patella et al. [10], but in contrast to the claim [6,10] that there is no connection between the small islands and the big QDs. Of course, we do not rule out ripening including the dissolution of small islands because the small islands are certainly less stable than the big ones. With respect to the QD shape we present atomically resolved 3D STM images for small and big islands in Fig. 4(a) and (b), respectively. Their shapes have already been determined in an earlier contribution [8]. The small islands in Fig. 4(a) are terminated to the main part by four {1 3 7}A facets and to the smaller part by two non-facetted, round regions, displaying a somewhat oblate-shaped base. In the mean time we have figured out that the round region develops into {1 3 5}B and {1 1 2}B facets for the bigger islands (Fig. 4(b)) [13].
4. Conclusion Our atomically-resolved STM images allow us to follow the InAs QD formation on GaAs(0 0 1) more clearly than it was possible up to now. Before the 2D-to-3D transition, the InAs wetting layer exhibits a flat morphology with mostly straight and parallel steps and atomically flat terraces which exhibit presumably As dimers distributed without long-range order. The 2D-to-3D transition occurs within a small coverage interval of less than 0.20 ML. During the transition the wetting layer changes its morphology remarkably due to mass transfer toward the QDs from the wetting layer as well as out of the substrate. The first, small islands are oblate with their long axis along the [ 1 1 0] direction. For sufficiently narrow terraces we propose the following model: First nucleation
occurs at the upper step edges. Later, during growth of a QD, in most cases mass is withdrawn from the wetting layer and the step edge is retracted from the QD leaving it back at the lower terrace well separated from the step. This explains a common observation that the location of QDs follows the step edges but is well separated from them. This results also in a step roughening of the wetting layer. The indications found for mass transport out of the substrate surface give evidence for QD alloying at the growth temperature of 460 C used in this study. Acknowledgements The authors would like to thank G. Ertl for support, P. Geng for technical assistance, and M. Richard for the final designing of the figures. References [1] D. Bimberg, M. Grundmann, N.N. Ledentsov, Quantum Dot Heterostructures, Wiley, Chichester, New York, 1999. [2] M. Grundmann, Physica E (Amsterdam) 5 (2000) 167. [3] Y. Masumoto, T. Takagahara (Eds.), Semiconductor Quantum Dots, Springer, Berlin, Heidelberg, 2002. [4] I.N. Stranski, L. Krastanow, Sitzungsber. Akad. Wiss. Wien, Math.-Naturwiss. Klasse 146 (1937) 797. [5] D. Leonard, K. Pond, P.M. Petroff, Phys. Rev. B 50 (1994) 11687. [6] R. Heitz, T.R. Ramachandran, A. Kalburge, Q. Xie, I. Mikhametzhanov, P. Chen, A. Madhukar, Phys. Rev. Lett. 78 (1997) 4071. [7] Y. Hasegawa, H. Kiyama, Q.K. Xue, T. Sakurai, Appl. Phys. Lett. 72 (1998) 2265. [8] J. Ma´rquez, L. Geelhaar, K. Jacobi, Appl. Phys. Lett. 78 (2001) 2309. [9] T.J. Krzyzewski, P.B. Joyce, G.R. Bell, T.S. Jones, Surf. Sci. 532–535 (2003) 822. [10] F. Patella, S. Nufris, F. Arciprete, M. Fanfoni, E. Placidi, A. Sgarlata, A. Balzarotti, Phys. Rev. B 67 (2003) 205308. [11] H. Saito, K. Nishi, S. Sugou, Appl. Phys. Lett. 74 (1999) 1224. [12] I. Mukhametzhanov, Z. Wei, R. Heitz, A. Madhukar, Appl. Phys. Lett. 75 (1999) 85. [13] M.C. Xu, T. Suzuki, Y. Temko, K. Jacobi, in press. [14] E. Penev, P. Kratzer, M. Scheffler, Phys. Rev. B 64 (2001) 085401. [15] P. Kratzer, E. Penev, M. Scheffler, Appl. Surf. Sci. 216 (2003) 436. [16] E. Penev, S. Stojkovic, P. Kratzer, M. Scheffler, Phys. Rev. B 69 (2004) 115335.
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