Self-Assembled Growth of Ga Droplets on GaAs(001) - American

Article pubs.acs.org/crystal

Self-Assembled Growth of Ga Droplets on GaAs(001): Role of Surface Reconstructions Akihiro Ohtake,*,† Takaaki Mano,† Atsushi Hagiwara,‡ and Jun Nakamura‡ †

National Institute for Materials Science (NIMS), Tsukuba 305-0044, Japan Department of Engineering Science, The University of Electro-Communications (UEC-Tokyo), Chofu, Tokyo 182-8585, Japan

‡

ABSTRACT: Formation processes of Ga droplets on GaAs(001) have been systematically studied. We present the evidence that the surface atomic structures of the GaAs substrate dominate the surface diffusion of Ga atoms, which plays a key role in determining the size and density of Ga droplets. The Ga droplets are formed on the As-rich (2 × 4) and c(4 × 4)β surface after the modification of the initial surface reconstructions, while droplets are directly formed on the Ga-rich (4 × 6) surface. The density of Ga droplets on the (4 × 6) surface exceeds 1012 cm−2, which is significantly higher than that on the As-rich c(4 × 4)β surfaces.

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INTRODUCTION Self-assembled growth of semiconductor quantum dots (QDs) has been extensively studied because of their applications for optoelectronic devices. Strain-induced growth techniques, based on the Stranski−Krastanov mechanism, are commonly used to fabricate self-assembled QDs. Despite the extensive use of this technique, the mechanism requires a lattice mismatch between the substrate and the dot material, which considerably limits the range of materials for the formation of QDs. An alternative approach, which was first reported in the 1990s, is the so-called droplet epitaxy technique.1 The QDs grown by this method are free from strain accumulation, which allows for a wide range of materials combination to be used. This method has been successfully applied to the fabrication of several types of nanostructures, such as strain-free QDs,1−6 quantum rings,7 and nanowires.8 The droplet-epitaxy method consists of two basic steps: first, for III−V compound semiconductors, molecular beams of group-III atoms are initially supplied, which leads to the selfassembled formation of liquid nanoparticles (droplets). Subsequent supply of group-V atoms crystallizes the droplets into nanocrystals. Since the size and density of QDs are essentially governed by those of droplets, it is necessary to understand the initial formation processes of Ga droplets. Numerous studies have shown that the density and size of QDs fabricated by droplet epitaxy critically depend on the growth conditions, such as crystal orientation of substrates,2,3 temperature,2,4−6 and the deposition rate of Ga.5 In this paper, we focus on the effects of initial surface reconstructions on the formation of Ga droplets on GaAs(001). It is widely accepted that the GaAs(001) surface shows a variety of reconstructions ranging from the most As-rich c(4 × 4)β, through (2 × 4), (6 × 6), and c(8 × 2), and to Ga-rich (4 × 6) phases.9,10 Although the surface reconstructions affect the microscopic growth processes such as adsorption, surface diffusion, and nucleation,11 the specific role of the surface © 2014 American Chemical Society

atomic structures is far from being completely understood. Here, we present the first experimental evidence that the careful control of the initial surface reconstructions and the residual As pressures allows for the formation of Ga droplets with highly controllable size and density. The density of Ga droplets exceeding 1012 cm−2 was achieved on the Ga-rich (4 × 6) surface under conditions with low As pressure.

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EXPERIMENTAL PROCEDURES

The experiments were performed in a system of interconnecting ultrahigh vacuum chambers for molecular-beam epitaxy (MBE) growth and for online surface characterization by means of scanning tunneling microscopy (STM) and X-ray photoelectron spectroscopy.10 The MBE chamber is equipped with reflection high-energy electron diffraction (RHEED) and reflectance difference spectroscopy (RDS) apparatuses. RDS is a surface-sensitive optical probe, which measures the difference between the normal-incidence reflectances of light polarized along two orthogonal axes.12 While the structure information available from RHEED is associated with long-range orderings, RDS provides complementary information about local electronic structures. Nondoped and nominally on-axis GaAs(001) substrates were used for the RHEED and RDS measurements, while the Si-doped (N ≈ 1−4 × 1018 cm−3) substrates were employed for the STM experiments. Cleaned GaAs(001)-(2 × 4) surfaces were first obtained by growing an undoped homoepitaxial layer (∼0.5 μm) on a thermally cleaned GaAs(001) substrate. The most As-rich c(4 × 4)β and Ga-rich (4 × 6) surfaces were prepared using procedures given in refs 13 and 14, respectively. Ga was deposited at a rate of 0.025 ML/s at a substrate temperature of 200 °C. Here, 1 ML is defined as 6.26 × 1014 atoms/ cm2, which is the site-number density of the unreconstructed GaAs(001) surface. During the Ga deposition, residual As pressure, measured at the sample position, was kept below 5 × 10−11 Torr. The RD spectra were obtained using a modified Jobin Yvon RD spectrometer. The RDS results are commonly displayed in terms of Δr̃/r̃ = (r̃11̅0 − r̃110)/r̃, where r̃11̅0 and r̃110 are the near-normalReceived: March 13, 2014 Revised: March 31, 2014 Published: May 7, 2014 3110

dx.doi.org/10.1021/cg500355f | Cryst. Growth Des. 2014, 14, 3110−3115

Crystal Growth & Design

Article

Figure 1. Typical filled-state STM images of the Ga-rich (4 × 6) (a), As-rich (2 × 4) (b), and As-rich c(4 × 4)β (c) surfaces after the deposition of Ga atoms. The image dimension is 200 nm × 200 nm. The insets show magnified images (40 nm × 40 nm) of images (A). (d−g) Structure models of the initial surface. We note that the c(8 × 2) unit cell is built from the (4 × 2) subunits shown in (g). The As coverage of the (4 × 6), (2 × 4), c(4 × 4)β, and c(8 × 2) models are 1/12, 0.75, 1.75, and 0.25 ML, respectively. incidence complex reflectances for light linearly polarized along [11̅0] and [110], respectively. We present only the data in the form Δr/r = Re(Δr̃/r̃). All the STM images were acquired at room temperature using electrochemically etched tungsten tips.

the corresponding values of critical thickness of Ga for the droplet formation. Thus, the present STM observations can be explained on the assumption that the Ga atoms initially arrived on the As-rich surfaces are bound with excess As atoms in the As-rich surface reconstructions to form a two-dimensional GaAs layer, as suggested in earlier papers.5,16 The critical Ga thickness for the droplet formation was also confirmed by RDS measurements. Figure 2 shows evolution of

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RESULTS AND DISCUSSION Figure 1a−c shows STM images of the Ga-rich (4 × 6), As-rich (2 × 4), and As-rich c(4 × 4)β surfaces, respectively, after the deposition of Ga atoms. The amount of Ga atoms required for the formation of droplets strongly depends on the initial surface reconstruction. On the Ga-rich (4 × 6) surface, the Ga atoms form droplets at the very initial stage of the growth [Figure 1aA]. On the other hand, the initial Ga depositon results in the formation of two-dimensional islands on the As-rich c(4 × 4)β surface. The initial c(4 × 4) reconstruction was almost fully covered by the two-dimensional islands at 1.5 ML [Figure 1cA], and Ga droplets are formed above 1.8 ML, as shown in Figure 1c-B. On the (2 × 4) reconstruction, droplets were hardly observed below 0.5 ML [Figure 1b-A], beyond which the formation of Ga droplets was confirmed, as shown in Figure 1b-B. We note that preferential nucleation of droplets at step edges were not observed. The surface As coverages of (4 × 6) [Figure 1d], (2 × 4) [Figure 1e], and c(4 × 4)β [Figure 1(f)] reconstructions are 1/ 12, 0.75, and 1.75 ML, respectively.15 These values are close to

Figure 2. Evolution of RD spectra of GaAs(001)-(4 × 6) (a), (2 × 4) (b), and c(4 × 4)β (c) surfaces with the Ga thickness. 3111



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and decreases with increasing initial As coverage. Previous studies17,18 have shown that the droplet density on the (001) surface is typically limited to less than ∼2 × 1010 cm−2, which is significantly lower than that on (111)A (∼1 × 1011 cm−2) and (311)A (>1 × 1011 cm−2). However, the present results show that high densities of Ga droplets could be formed using Garich (4 × 6) surface (2.0 × 1011 cm−2). Furthermore, we confirmed that the density of droplets on the (4 × 6) surface is 3.5 × 1012 cm−2 at a lower temperature of 100 °C, as shown in Figure 4a. On the other hand, the density on the c(4 × 4)β

RD spectra of GaAs(001) surface with the Ga thickness. The shape of the RD spectra from the (4 × 6) surface [Figure 2a] stays essentially the same in the whole range of the Ga thickness (0−1.4 ML). This indicates that the deposited Ga atoms directly form the droplets on the (4 × 6) surface, leaving the initial (4 × 6) surface unchanged. Indeed, characteristic features of the (4 × 6) reconstructions are clearly visible between the droplets in the STM image [Figure 1a-C], and weak (4 × 6) RHEED patterns are observed after the 1 ML deposition. On the other hand, as shown in Figure 2b [Figure 2c], the Ga deposition on the (2 × 4) [c(4 × 4)β] surface causes a significant change in the shape of the RD spectra up to 0.7 ML (1.8 ML), which is accompanied by the disappearance of the fractional-order reflections in RHEED patterns. The spectrum shapes remain almost unchanged upon further deposition. These experimental results clearly show that ∼0.7 ML and ∼1.8 ML of Ga atoms react with the initial (2 × 4) and c(4 × 4)β reconstructions, respectively, to change their surface structures, before the formation of droplets. Figure 3a shows

Figure 4. Typical STM (a) and AFM (b) images of Ga droplets formed on the (4 × 6) (100 °C) and c(4 × 4)β (300 °C) surfaces, respectively. The image dimensions are 200 nm × 200 nm (a) and 1 μm × 1 μm (b). (c) The density of Ga droplets on the (4 × 6), (2 × 4), and c(4 × 4)β surfaces plotted as a function of the substrate temperature. The lines in (c) are calculated on the basis of the model proposed in ref 5. Figure 3. Critical thickness (a) and the base size (diameter) and density (b) of Ga droplets plotted as a function of the As coverage of the initial surface reconstructions.

surface is lower than 1 × 109 cm−2 at a higher temperature of 300 °C [Figure 4b]. Thus, as shown in Figure 4c, the changes in the initial surface reconstructions and substrate temperature make it possible to control the density of droplets by more than 3 orders of magnitude. Solid curves in Figure 4c are calculated densities on the basis of the extended scaling law described in ref 5. Using the parameters reported in ref 5, except for that related to the Ostwald ripening, Er (1.67 eV), the measured densities are well described. The energy barriers for the adatom diffusion were estimated to be 0.81, 0.61, and 0.49 eV for (4 × 6), (2 × 4), and c(4 × 4)β, respectively. Thus, it is most likely that the diffusion of Ga adatom is rather suppressed on the (4 × 6) surface, which leads to the increase in the droplet density. An important implication of the present results is that the existence of excess As atoms on the surface enhances the surface diffusion of Ga atoms, because a longer diffusion length

the integrated volume of Ga droplets plotted as a function of the Ga thickness. The critical thicknesses for the formation of Ga droplets on (2 × 4) and c(4 × 4)β are estimated to be 0.6 and 1.75 ML, respectively, being consistent with the RDS measurements, and are roughly proportional to the initial As coverage. Above the critical thickness, the volume of droplets increases in linear proportion to the deposited Ga atoms. Figure 3b compares the base size (diameter) and density of droplet formed on the various reconstructed surfaces. The amounts of deposited Ga atoms on (4 × 6), (2 × 4), and c(4 × 4)β are 1, 1.75, and 2.75 ML, respectively, so that the total amounts of Ga atoms forming the droplets on the three types of surfaces are nearly identical to 1 ML, as shown in Figure 3a. It is clearly seen that the size and density of droplets increases 3112



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Table 1. Density (cm−2), Base Size (nm) and Volume (ML) of Ga Droplets Formed on GaAs(001) for Different Residual As Pressures 5 × 10−11 Torr

1 × 10−8 Torr

reconstruction

density

base size

volume

density

base size

volume

(4 × 6) (2 × 4) c(4 × 4)β

2.0 × 1011 8.3 × 1010 1.6 × 1010

10.9 ± 1.5 14.3 ± 3.3 21.0 ± 3.8

1.06 ± 0.53 1.23 ± 0.40 1.17 ± 0.60

6.2 × 1010 2.2 × 1010 2.2 × 1010

13.3 ± 2.1 16.4 ± 2.8 15.4 ± 2.9

0.67 ± 0.47 0.49 ± 0.34 0.41 ± 0.21

means a lower probability for adatoms to form nuclei, yielding a lower density of droplets. Numerous studies have shown that the diffusion length of Ga on the MBE-growing GaAs(001) surface is inversely proportional to the As pressure.19,20 On the other hand, the enhanced surface diffusion of cation atoms under higher As pressures has been reported for GaAs(001)21 and InAs(001).22 To study the effects of excess As atoms on the droplet formation, we performed growth experiments with residual As molecules. When the Ga droplets are formed under the residual As pressure of ∼1 × 10−8 Torr, the density and size of droplets on the (4 × 6) and (2 × 4) surfaces decreases and increases, respectively, and the opposite trend was observed on the c(4 × 4) surface, as shown Table 1. Thus, it is likely that the effect of As pressure on the Ga diffusion critically depends on the surface reconstruction, but further studies are needed to elucidate the mechanism. Another noteworthy finding in Table 1 is that the integrated volume of Ga droplets is also influenced by the existence of residual As molecules. Under sufficiently low As pressure, the integrated volume nearly equals 1 ML, while the volume of droplets formed with residual As molecules is significantly decreased. It is plausible that the deposited Ga atoms partially react with the residual As molecules, resulting in the formation of two-dimensional GaAs layers. Figure 5 shows the STM image from the (2 × 4) surface just before the droplet formation. The positions of bright spots

denoted by open squares, surface atoms at 4-fold hollow sites are clearly visible in Figure 5: the adsorption of Ga atom at the hollow site of the Ga-rich c(8 × 2) surface has been suggested by Kumpf et al.26,27 While the c(4 × 4)β surface becomes disordered after the Ga deposition, which makes it difficult to obtain information about detailed atomic structures, interesting evidence was obtained from RDS measurements. As can be seen in Figure 2, the shapes of the spectra for the three reconstructions measured just before the droplet formation are quite similar: negative peaks at ∼2.0 eV (A) and 3.0 eV (C) and positive peaks at 2.6 eV (B) and 4.3 eV (D) are commonly observed. However, observing carefully the position of the negative peak at ∼2.0 eV (A), we found that the negative peak for (2 × 4) and c(4 × 4) is shifted by ∼0.3 eV to lower energy than that for (4 × 6). Pristovsek et al. have shown that the RD spectrum of c(8 × 2) shows a negative features at the position lower by ∼0.3 eV than those of (4 × 6).28 Thus, it is plausible to consider that the Ga deposition on the As-rich (2 × 4) and c(4 × 4)β forms local atomic structures similar to that of the c(8 × 2) surface. If the formation of c(8 × 2)-like structures on the As-rich surfaces indeed enhances the surface diffusion of Ga atoms, it could be confirmed by the growth experiments on the c(8 × 2) surface. It is widely accepted that the Ga-rich c(8 × 2) is stable only at temperatures higher than 600 °C and is rearranged to (6 × 6) as the temperature is decreased.10 Thus, to prepare the c(8 × 2) reconstruction, the c(8 × 2) sample was rapidly cooled from 620 °C to below 400 °C, so that the c(8 × 2) phase was preserved on the surface with the coexisting phase of (6 × 6).10,24 Figure 6a,b shows typical STM and AFM images of the

Figure 5. Typical filled-state STM image of the (2 × 4) surface after the deposition of 0.5 ML-Ga. The image dimension is 11.3 nm × 6.8 nm. The solid lines show the (2 × 4) lattice mesh.

Figure 6. Typical STM (a) and AFM (b) images of Ga droplets on the mixture of c(8 × 2)/(6 × 6) surfaces. The image dimensions are 120 nm × 120 nm (a) and 2 μm × 2 μm (b).

sample after the deposition of 1 ML-Ga, respectively.29 While high densities of small droplets are formed in the (6 × 6) regions, the c(8 × 2) region shows a lower density of larger droplets [Figure 6b]. The density and lateral size of droplets in the (6 × 6) region are estimated to be 1.5 × 1011 cm−2 and 14 nm, respectively, which compare with the values for the (4 × 6) surface. On the other hand, the size (34 nm) and density (1.2 × 1010 cm−2) in the c(8 × 2) region are rather close to the values for the As-rich c(4 × 4) sample.

indicated by closed circles correspond to the As atoms constituting the initial β2(2 × 4) structure, and the open circles indicate the positions of surface As atoms at faulted sites relative to their bulk positions. Since the existence of As atoms at faulted sites was found only in the Ga-rich surface reconstructions of (6 × 6),23,24 c(8 × 2),25−27 and (4 × 6),12 it is most likely that the Ga deposition on the (2 × 4) surface leads to the formation of local Ga-rich region. In addition, as 3113



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for the diffusion of Ga adatoms along the [110] direction on c(8 × 2) is estimated to be 0.12 eV, which is significantly smaller than the value (0.28 eV) for (4 × 6). This is in qualitative agreement with the experiments: lower potential barrier promotes the diffusion of Ga atoms on the c(8 × 2) surface, leading to the reduced nucleation density. On the other hand, in the orthogonal direction of [11̅0], the value for (4 × 6) (0.44 eV) is much smaller than that for c(8 × 2) (0.72 eV). This means that the Ga diffusion on c(8 × 2) is highly anisotropic and that the diffusion along the [11̅0] direction is less enhanced. As shown in Figure 7c, the potential barriers of c(8 × 2) are dramatically changed when Ga atoms are adsorbed at the most stable hollow site [arrows in Figure 7b]: the barriers along the [110] and [11̅0] directions are 0.23 and 0.25 eV, respectively. The resultant c(8 × 2) structure shown in Figure 7c is essentially the same as that proposed by Kumpf et al., in which the hollow site has 19% Ga occupancy.26,27 While the structure model in Figure 7c might be a better description of the actual surface geometry, the adsorption of Ga atoms at the hollow site increases the surface energy by 0.1 eV per (1 × 1) unit cell.35 Thus, it is difficult to make a discrimination in favor of one of the models in Figure 7b,c. It is also possible that the Ga atoms partially occupy the hollow site at the very initial stage of the growth on c(8 × 2), so that the Ga diffusion is enhanced in both [110] and [11̅0] directions, giving rise to a reduced nucleation density.

To study the effects of atomic structure on the droplet formation, we investigated the potential-energy surface of Ga adatoms on the Ga-rich c(8 × 2) and (4 × 6) surfaces. For this purpose, first-principles calculations30,31 based on the density functional theory32 with the generalized gradient approximation33 were performed. We used the Tokyo Ab-initio Program Package (TAPP).34 A slab geometry was used for the simple calculation, which has the supercell consisting of seven atomic layers with surface dimers and of vacuum region (12 Å in thickness). The back side of the slab is terminated with fictitious H atoms which eliminate artificial dangling bonds and prevent it from coupling with the front side. The wave functions were expanded in plane waves with a kinetic energy cutoff of 16 Ry. Four k points were used for the integration in k space in the first Brillouin zones of the (4 × 6) and c(8 × 2) surfaces. The potential energy surface has been mapped on an equidistant grid with a spacing of 2 Å along the [110] and [11̅0] directions. At each position, the adatom height was fully relaxed, while the atomic positions of the substrate were fixed at those for the clean surfaces. The force on the substrate atoms after the Ga adsoprton is typically ∼1 × 10−3 [Hartree/Bohr], indicating that existence of the Ga adatoms hardly changes the atomic positions of the c(8 × 2) and (4 × 6) surfaces. We interpolated the PES from the energy values on the mesh. The calculated results are shown in Figure 7. The calculated potential barriers for the (4 × 6) surface [Figure 7a] are 0.28

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CONCLUSION We have studied the effect of the initial surface reconstructions on the formation processes of Ga droplets on GaAs(001). We found that the surface atomic structures and residual As pressures have significant effects on the diffusion of Ga atoms, which characterizes the size and density of droplets. The initial Ga deposition modifies the As-rich surface reconstructions of (2 × 4) and c(4 × 4)β before the formation of Ga droplets, while droplets are formed directly on the Ga-rich (4 × 6) surface. High-density droplets (>1012 cm−2) has been realized on the Ga-rich (4 × 6) surface under reduced residual As pressures, which exceeds the values for the (311)A and (111)A substrates.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Helpful discussions with Dr. Y. Sakuma are gratefully acknowledged. Figure 7. (a) Potential energy surface (PES) for a Ga adatom on the GaAs(001)-(4 × 6) surface. (b, c) PES of the c(8 × 2) surface with the atomic structures proposed in refs 26 and27, respectively.

REFERENCES

(1) Koguchi, N.; Takahashi, S.; Chikyow, T. J. Cryst. Growth 1991, 111, 688−692. (2) Mano, T.; Kuroda, K.; Mitsuishi, K.; Noda, T.; Sakoda, K. J. Cryst. Growth 2009, 311, 1828−1831. (3) Mano, T.; Abbarchi, M.; Kuroda, T.; McSkimming, B.; Ohtake, A.; Mitsuishi, K.; Sakoda, K. Appl. Phys. Express 2010, 3, 065203. (4) Jo, M.; Mano, T.; Sakuma, Y.; Sakoda, K. Appl. Phys. Lett. 2012, 100, 212113. (5) Heyn, Ch.; Stemmann, A.; Schramm, A.; Welsch, H.; Hansen, W.; Nemcsics, Á . Phys. Rev. B 2007, 76, 075317.

and 0.44 eV along the [110] and [11̅0] directions, respectively, and are smaller than the value (0.81 eV) estimated from the experiment [Figure 4c]. Such a disagreement was also found for Ga adatoms on the (2 × 4) surface.11 The PES of the c(8 × 2) surface [Figure 7b] is quite similar to that reported in ref 35. The energetically most stable site for the Ga adatom is the 4fold hollow site, as indicated by arrows. The potential barrier 3114



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(6) Jo, M.; Mano, T.; Sakoda, K. Cryst. Growth Des. 2011, 11, 4647− 4651. (7) Mano, T.; Kuroda, T.; Sanguinetti, S.; Ochiai, T.; Tateno, T.; Kim, J.; Noda, T.; Kawabe, M.; Sakoda, K.; Kido, G.; Koguchi, N. Nano Lett. 2005, 5, 425−428. (8) Somaschini, C.; Bietti, S.; Trampert, A.; Jahn, U.; Hauswald, C.; Riechert, H.; Sanguinetti, S.; Geelhaar, L. Nano Lett. 2013, 13, 3607− 3613. (9) Xue, Q.-K.; Hashizume, T.; Sakurai, T. Prog. Surf. Sci. 1997, 56, 1−132. (10) Ohtake, A. Surf. Sci. Rep. 2008, 63, 295−327. (11) Kley, A.; Ruggerone, P.; Scheffler, M. Phys. Rev. Lett. 1997, 79, 5278−5281. (12) Aspnes, D. Thin Solid Films 1993, 233, 1−8. (13) Ohtake, A.; Kocán, P.; Nakamura, J.; Natori, A.; Koguchi, N. Phys. Rev. Lett. 2004, 92, 236105. (14) Ohtake, A.; Kocán, P.; Seino, K.; Schmidt, W. G.; Koguchi, N. Phys. Rev. Lett. 2004, 93, 266101. (15) The As coverages of 0 and 1 ML correspond to the ideal Gaand As-terminated (001) surfaces, respectively. (16) Koguchi, N.; Ishige, K. Jpn. J. Appl. Phys. 1993, 32, 2052−2058. (17) Watanabe, K.; Koguchi, N.; Gotoh, Y. Jpn. J. Appl. Phys. 2000, 39, L79−L81. (18) Mano, T.; Koguchi, N. J. Cryst. Growth 2005, 278, 108−112. (19) Horikoshi, Y. Semicond. Sci. Technol. 1993, 8, 1032−1051. (20) Nishinaga, T.; Shen, X. Q.; Kishimoto, D. J. Cryst. Growth 1996, 163, 60−66. (21) Yang, H.; LaBella, V. P.; Bullock, D. W.; Thibado, P. M. J. Vac. Sci. Technol. B 1999, 17, 1778−1780. (22) Grosse, F.; Barvosa-Carter, W.; Zinck, J.; Wheeler, M.; Gyure, M. F. Phys. Rev. Lett. 2002, 89, 116102. (23) Kocán, P.; Ohtake, A.; Koguchi, N. Phys. Rev. B 2004, 70, 201303(R). (24) Ohtake, A. Phys. Rev. B 2007, 75, 153302. (25) Lee, S. H.; Moritz, W.; Scheffler, M. Phys. Rev. Lett. 2000, 85, 3890−3893. (26) Kumpf, C.; Marks, L. D.; Ellis, D.; Smilgies, D.; Landemark, E.; Nielsen, M.; Feidenhans’l, R.; Zegenhagen, J.; Bunk, O.; Zeysing, J. H.; Su, Y.; Johnson, R. L. Phys. Rev. Lett. 2001, 86, 3586−3589. (27) Kumpf, C.; Smilgies, D.; Landemark, E.; Nielsen, M.; Feidenhans’l, R.; Bunk, O.; Zeysing, J. H.; Su, Y.; Johnson, R. L.; Cao, L.; Zegenhagen, J.; Fimland, B. O.; Marks, L. D.; Ellis, D. Phys. Rev. B 2001, 64, 075307. (28) Pristovsek, M.; Tsukamoto, S.; Ohtake, A.; Koguchi, N.; Orr, B. G.; Schmidt, W. G.; Bernholc, J. Phys. Status Solidi b 2003, 240, 91−98. (29) We note that small clusters (∼2 nm in diameter) observed in the c (8 × 2) regions in the STM image exist even before the Ga deposition. (30) Vanderbilt, D. Phys. Rev. B 1990, 41, 7892−7895. (31) Yamauchi, J.; Tsukada, M.; Watanabe, S.; Sugino, O. Phys. Rev. B 1996, 54, 5586−5603. (32) Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864−B871. (33) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865−3868. (34) Tsukada, M. et al. Computer Program Package TAPP; University of Tokyo: Tokyo, Japan, 1983−2014. (35) Seino, K.; Schmidt, W. G.; Bechstedt, F.; Bernholc, J. Surf. Sci. 2002, 507−510, 406−410.

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Self-Assembled Growth of Ga Droplets on GaAs(001) - American

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