Kinetic Monte Carlo simulation of semiconductor quantum dot growth

Transcription

1 Solid State Phenomena Online: ISSN: , Vols , pp doi: / Trans Tech Publications, Switzerland Kinetic Monte Carlo simulation of semiconductor quantum dot growth C. Zhao 1, a, Y. H. Chen 1,b, J. Sun 1, W. Lei 1, C. X. Cui 1, L. K. Yu 1, K. Li 1, and Z. G. Wang 1,c 1 Key Laboratory of Semiconductor Materials Science, Institute of Semiconductors, Chinese Academy of Sciences, Beijing , China a czhao@red.semi.ac.cn, b yhchen@red.semi.ac.cn, c zgwang@red.semi.ac.cn Keywords: Monte Carlo simulation; Molecular beam epitaxy; Kinetic effect; Quantum dot Abstract Performing an event-based continuous kinetic Monte Carlo (KMC) simulation, We investigate the growth conditions which are important to form semiconductor quantum dot (QD) in molecular beam epitaxy (MBE) system. The simulation results provide a detailed characterization of the atomic kinetic effects. The KMC simulation is also used to explore the effects of periodic strain to the epitaxy growth of QD. The simulation results are in well qualitative agreement with experiments. Introduction Self-assemlbed QDs in semi-conductor heterostructures are of great intetrest because of their discrete atom-like energy levels, good optical properties, and promising device applications such as QD lasers and photodetectors[1-3]. A number of experiments have been performed in order to achieve the QDs of high optical quality and size-ordering, and these studies show that the growth mode is very complex and sensitive to the growth conditions [4-7]. Excited by experimental interest, some theoretical approaches have been developed to address the mechanisms determining the size and distribution of the QDs. Computer simulation is one of the theoretical methods, which can give some detailed information about the growth of QDs. An event-based KMC simulation has been successful in reproducing growth process in MBE syetem[8-10]. Such a simulation study is useful not only for investigating the kinetic of MBE growth but also for analyzing the growth mode and surface morphology during the growth. In this paper we develop such a Monte Carlo simulation for strained semiconductor systems. First we simulate the flux and temperature dependence of the InAs QD grown by MBE machine on GaAs(100) substrate. Some aspects of atomic kinetic during MBE growth are discussed. Then the KMC simulation is used to explore the effects of periodic strain on the substrate to the epitaxy growth of InAs QD. In contrast to earlier phenomenological work[11,12], we calculate the strain field associated with the lattice mismatch between InAs and substrate material. The simulation results are in excellent qualitative agreement with prevenient and our experiments. Kinetic Monte Carlo simulations It is known that deposition, diffusion, desorption, nucleation will all take place during the growth of semiconductor material in MBE system. In order to inhibit the atom desorption, some factors such as low temperature and high pressure of As are adopted in experiment. So in our simulation deposition, diffusion and nucleation are considered as the main relevant processes. After the atoms nucleation, they are still capable to diffuse unless its eight neighboring positions are all occupied by other atoms. In this simulation we only focus on a submonolayer heteroepitaxy growth. It is sufficient because we assume that the two-dimension inlands can be the nucleation sites and during the 2D/3D transition, the QDs formed on these 2D inlands. Moreover, a complete wetting layer which is not simulated is assumed to exist below the first simulated island layer. In simulation after all the atoms have been deposited on the substrate the system is allowed to equilibrate by a growth interruption. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-06/03/16,06:33:39)

2 1074 Nanoscience and Technology Atom diffusion on crystal surface is a thermally activated process: the hopping probability of a atom hop from one site to a neighboring one by overcoming a potential barrier E is given by the Arrhenius law: P=V 0 exp(-e/k B T). (1) E=E S +E N +E AD -E STR. (2) E N =(n+βm)e n -ε(n +βm )E n. (3) where E S is the atomic binding energy to the surface and E n to a single nearest neighbor atom, and n and m are the numbers of nearest and next nearest neighbor atom. n and m have the same meaning but correspond to the site which the atom will hop to. E AD represents the energy barrier effect of anisotropy diffusion. When an atom crosses an island edge, a Schwöbel barrier=0.1 ev is also considered. Some parameters used in the simulation are typical for a variety of semiconductor materials and equal to Ref.10: Es=1.3eV, En=0.3eV, V 0 =10 13 s -1, ε=0.2, β=1/ 2, and k B is Boltzmann s constant. The next task is to define a very little time interval corresponding to one Monte Carlo step during which there is only one atom can diffuse. We compute the time interval by t=1/ p i. The very efficient search method developed to date is the binary tree process which is used in our simulation to locate a atom to diffuse in every time interval. When we simulate the InAs QD grown on GaAs (100) substrate, E AD in Eq. (2) is zero because there isn t anisotropy energy barrier on this substrate surface, and E STR =E s *c, c is 7% i.e. the mismatch between GaAs and InAs. Fig. 1 and 2 show the simulation results which indicate the temperature and flux dependence of the InAs QD on GaAs (100) substrate. Before we illustrate our simulation about the effects of periodic strain on the substrate to the epitaxy growth of InAs QD, we should first introduce our experiment simply and detail information about the experiment can be find in Ref.13. The samples were grown in Riber-32P MBE machine in two steps. First, Three kinds of In x Ga 1-x As/GaAs (x=0.05, 0.1, 0.15) SuperLattice (SL) with different In composition were grown on semi-insulating GaAs (100) substrate, which were separated by 420nm thick GaAs spacer layer. The period number of each SL period was 10. And then the In x Ga 1-x As /GaAs SL sample was cleaved along (0-11) direction and the cleaved surface was (011)-oriented. On the cleaved edge one sample was grown with growth rate f=0.06 monolayer (ML)/s and growth temperature T=723K. Fig. 3 shows the atomic force microscopy (AFM) images of this sample(x=0.1 and 0.15 sections). We can find that a distinct tendency of InAs QD chains are formed on x=0.1 and x=0.15 sections of In x Ga 1-x As/GaAs SL because of the periodic strain on these sections. In order to simulate this effect of periodic strain to the QD growth and accord with the simulation discussed above, the E STR in Eq. (2) should be modified to E STR =E S (1-x)c. When the atom across the edge between In x Ga 1-x As and GaAs, an additional potential barrier will be overcomed, that is E STR = E STRA - E STRB, E STRA is the energy barrier driven by the strain of original site, E STRB corresponds to the site the atom will hop to. So under this condition Eq. (2) should be modified to E=E S +E N +E AD -E STRA - E STR, and E AD =0.1eV in simulation. Fig. 4 shows the simulation results and the x in In x Ga 1-x As/GaAs SL is 0.15 in simulation. Result and discussion We restrict in our simulation on a 200*200 grid (in units of lattice constant). Fig. 1 (a), (b) and (c) show the temperature dependence of InAs QDs on GaAs(100) substrate in simulation, and the other parameters are the same except the temperature.

3 Solid State Phenomena Vols (a) (b) (c) Fig. 1. (a) T=673K (b) T=723K. (c) T=773K. The other parameters used in simulation are: t=3s, flux=0.06ml/s, growth interruption=20s. We can find that the higher the temperature is, the larger will be the QD. It can be understand easily that at low temperatures, diffusion processes have a low probability p (given by Eq.1) and hence adatoms have a small diffusion constant. As a result each island will on average collect adatoms from a circular area of a smaller radius of the mean free path of a single adatom. So this will result in a smaller QD. (a) (b) (c) Fig. 2. (a) t=18s, flux=0.01 ML/s (b) t=1.8s, flux=0.1 ML/s (c) t=0.18s,flux=1.0 ML/s The other parameters are: T=723K, growth interruption=20s. As for flux dependence, the smaller growth flux makes the adatom have enough time to diffuse and leads to a larger mean free path. Under this condition the QD appears the same rule as at the higher temperature and can be seen from Fig. 2. This is a purely kinetic effect. The same effects have been observed in experiments [14,15]. The accordance between our simulation and experiment imply that our KMC simulation is reasonable. And then we will use it to explore the effects of periodic strain to the QD growth. For comparing with experiment, the simulation area is divided into ten periods which are the same as experiments. x=0.1 section x=0.15 section Fig. 3. AFM image of InAs deposited on cleaved edge of In x Ga 1-x As/GaAs SL Flux=0.06ML/s,T=7 23K,3μm 3μm. Fig. 4. Gray represent the GaAs layers and white represent the In 0.15 Ga 0.85 As layers. Flux=0.06ML/s, t=3s, T=723K. In Fig. 4, We can find the QDs appear alignment apparently and mainly on the white area i.e. In 0.15 Ga 0.85 As layer. From the viewpoint of energy, all the simulation results can be explained that the E STR on the GaAs layer is greater than that on the In x Ga 1-x As layer, so the surface on the In x Ga 1-x As layer is more comfortable for the deposed atom to stay in, and the deposited atoms nucleate on this area will lead to a lower system energy. From the kinetic viewpoint, the atom on the surface of GaAs layer can diffuse easily to the In x Ga 1-x As layer and difficult inversely, so finally the QDs are mainly

4 1076 Nanoscience and Technology on the surface of In x Ga 1-x As layer. From Fig. 3 and 4 we can find that the simulation results agree with the experiment very well. Summary and conclusion In brief summary, we investigate the flux and temperature dependence of the semiconductor QD growth by a KMC simulation. Some aspects of atomic kinetic during MBE growth are discussed. And the KMC model is also used to explore the effects of periodic strain on the substrate to the epitaxy growth of semiconductor QD. The simulation results are in well qualitative agreement with experiments. So this simulation approach is useful to study the growth mode and atomic kinetic during the growth of semiconductor quantum dots. Acknowledgment The above work was supported by Special Funds for Major State Basic Research Project of China (No. G ), National Natural Science Foundation of China (No , , ), and National High Technology Research and Development Program of China (No. 2002AA311070). References [1] R. Leon, P. M. Petroff, D. Leonard, S. Fafard: Science 267 (1995), [2] F. Klopf, J. P. Reithmaier, A. Forchel: Appl. Phys. Lett 77 (2000) [3] Wang Zhanguo, Chen Yonghai, Liu Fengqi, Xu Bo: J. Cryst. Growth (2001), [4] T. V. Lippen, R. Nötzel, G. J. Hamhuis, and J. H. Wolter: Appl. Phys. Lett 85 (2004),118. [5] Jie Sun, P. Jin, Z. G. Wang, H. Z. Zhang, Z.Y. Wang, L. Z. Hu: Thin Solid Films 476 (2005) 68. [6] L. K. Yu, B. Xu, Z. G. Wang, P. Jin, C. Zhao, W. Lei, J. Sun: J. Cryst. Growth (in press) [7] Jie Sun, Peng jin and Zhan-Guo Wang: Nanotechnology 15 (2004) [8] B. G. Liu, J. Wu, E. G. Wang, and Z. Zhang: Phys. Rev. Lett 83 (1999), [9] M. Meixner and E. Schöll: Phys. Rev. B 67 (2003) [10] M. Meixner, R. Kunert, and E. Schöll: Phys. Rev. B 67 (2003) [11] C. S. Lee, B. Kahng and A. L. Barabasi: Appl. Phys. Lett 78 (2001) 984. [12] E. Schöll and S. Bose: Solid State Electron 42 (1998) [13] C. X. Cui, Y. H. Chen, C. L. Zhang, P. Jin, G. X. Shi, C. Zhao, B. Xu, Z. G. Wang: Physica E (in press). [14] D. Bimberg, M. Grundmann and N. N. Ledentsov: Quantum Dot Heterostructures (John Wiley & Sons, Chichester, 1999). [15] Hideaki Saito, Kenichi Nishi, and Shigeo Sugou: Appl. Phys. Lett 74 (1999) 1224.

5 Nanoscience and Technology / Kinetic Monte Carlo Simulation of Semiconductor Quantum Dot Growth / DOI References [7] Jie Sun, Peng jin and Zhan-Guo Wang: Nanotechnology 15 (2004) / /15/12/012