Control of strain-mediated growth kinetics of self-assembled semiconductor quantum dots

Meixner, M.; Kunert, R.; Schöll, Eckehard

doi:10.1103/physrevb.67.195301

Cited by 70 publications

(48 citation statements)

References 44 publications

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“…This presents an especially acute challenge for most theoretical methods because of the relaxation of misfit strain, which introduces long-range elastic interactions and pre-empts purely local estimates of kinetic barriers. Nevertheless, KMC simulations that incorporate elastic effects to various levels of sophistication [104][105][106] suggest that including a contribution from the local elastic energy to the kinetic barriers for detachment and migration provides a useful starting point for understanding strain-induced morphologies.…”

Section: Discussionmentioning

confidence: 99%

Renormalization of stochastic lattice models: Epitaxial surfaces

Haselwandter

Vvedensky

2008

Phys. Rev. E

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We present the application of a method [Phys. Rev. E 76, 041115 (2007)] for deriving stochastic partial differential equations from atomistic processes to the morphological evolution of epitaxial surfaces driven by the deposition of new material. Although formally identical to the one-dimensional (1D) systems considered previously, our methodology presents substantial new technical issues when applied to two-dimensional (2D) surfaces. Once these are addressed, subsequent coarse-graining is accomplished as before by calculating renormalization-group (RG) trajectories from initial conditions determined by the regularized atomistic models. Our applications are to the EdwardsWilkinson (EW) model [Proc. Roy. Soc. London Ser. A 381, 17 (1982)], the Wolf-Villain (WV) model [Europhys. Lett. 13, 389 (1990)], and a model with concurrent random deposition and surface diffusion. With our rules for the EW model no appreciable crossover is obtained for either 1D or 2D substrates. For the 1D WV model, discussed previously, our analysis reproduces the crossover sequence known from kinetic Monte Carlo (KMC) simulations, but for the 2D WV model, we find a transition from smooth to unstable growth under repeated coarse-graining. Concurrent surface diffusion does not change this behavior, but can lead to extended transient regimes with kinetic roughening. This provides an explanation of recent experiments on Ge(001) with the intriguing conclusion that the same relaxation mechanism responsible for ordered structures during the early stages of growth also produces an instability at longer times that leads to epitaxial breakdown. The RG trajectories calculated for concurrent random deposition and surface diffusion reproduce the crossover sequences observed with KMC simulations for all values of the model parameters, and asymptotically always approach the fixed point corresponding to the equation proposed by Villain [J. Phys. I 1, 19 (1991)] and by Lai and Das Sarma [Phys. Rev. Lett. 66, 2899 (1991)]. We conclude with a discussion of the application of our methodology to other growth settings.

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Section: Discussionmentioning

confidence: 99%

Renormalization of stochastic lattice models: Epitaxial surfaces

Haselwandter

Vvedensky

2008

Phys. Rev. E

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“…Furthermore, the identification of a set of optimal growth parameters would be most useful to experimentalists. The kinetic Monte Carlo ͑KMC͒ has been proposed recently to study QD island self-organization by many researchers [19][20][21][22][23][24] where the growth parameters are directly involved in the simulation. 25 It has been shown that the main growth parameters affecting QD island distribution patterns are the temperature T, flux rate F to the surface during deposition, surface coverage c, and growth interruption time t i .…”

Section: Introductionmentioning

confidence: 99%

On the correlation between the self-organized island pattern and substrate elastic anisotropy

Pan

Chung

2006

Journal of Applied Physics

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, ARL-RP-168 SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTESA reprint from the Journal of Applied Physics, vol. 100, pp. 013527-1-013527-6, 2006. * Department of Civil Engineering, University of Akron, Akron, OH 44325 ABSTRACTSelf-organized quantum dots pattern depends strongly on the elastic strain energy of the substrate. It is well-known experimentally that for the elastic substrate with a high degree of anisotropy, the epitaxially grown island patterns are different for different growth orientations. In this report, by incorporating the anisotropic strain energy field into a kinetic Monte Carlo algorithm for adatom diffusion, we show that the self-organized island pattern on the surface of an anisotropic substrate is closely correlated to the elastic energy distribution on the surface. The anisotropic substrates studied are GaAs with different growth orientations (001), (111), and (113). An isotropic substrate Iso (001), reduced from GaAs, is also investigated for the purpose of comparison. The island patterns on these substrates with and without elastic strain energy are presented. Besides the effect of substrate anisotropy, different growth parameters, including temperature, coverage, and interruption time, are further investigated to identify the optimal growth values. It is observed that the strain energy field in the substrate is the key factor that controls the island pattern, and that the latter is closely correlated to the substrate orientation (anisotropy). Our simulated patterns are also in qualitative agreement with recent experimental growth results. Self-organized quantum dots pattern depends strongly on the elastic strain energy of the substrate. It is well-known experimentally that for the elastic substrate with a high degree of anisotropy, the epitaxially grown island patterns are different for different growth orientations. In this paper, by incorporating the anisotropic strain energy field into a kinetic Monte Carlo algorithm for adatom diffusion, we show that the self-organized island pattern on the surface of an anisotropic substrate is closely correlated to the elastic energy distribution on the surface. The anisotropic substrates studied are GaAs with different growth orientations ͑001͒, ͑111͒, and ͑113͒. An isotropic substrate Iso ͑001͒, reduced from GaAs, is also investigated for the purpose of comparison. The island patterns on these substrates with and without elastic strain energy...

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“…Dobbs et al theoretically estimated the variation in the QD density with increasing coverage θ using the MFREs and obtained a dog-leg curve, which was experimentally supported by experimental data on metalorganic vapor phase epitaxy growth of InP islands on the GaP-stabilized GaAs(001) substrate. 4) In addition, Meixner et al [301] simulated QD formation using the KMC simulation method and found rather good agreement between their simulation results for the island density and experimental results for both Ge/Si(001) and InAs/GaAs(001). 5) In comparison with the theoretical works of Chen and Washburn [82] and Dobbs et al [81], Wang et al [302,303], suggested an entirely different scenario.…”

Section: A Large Variety Of Experimental Data In the Literature On Thmentioning

confidence: 99%

“…6) As described in Section 3.1.2, Osipov et al [69,70] suggested a kinetic model on the basis of the CNGT for QD formation in terms of the first-order phase transformations. It is intrinsically different in nature from either the adatom aggregation model used by Chen and Washburn [82] and Meixner et al [301] and the model of Wang et al [302,303]; in the kinetic model of Osipov et al [69,70], QD nucleation occurs in a well-developed uniformly elastically strained film of thickness h trapped in a thermodynamic metastable state characterized by a "supersaturation" ζ ≡ h/h eq − 1. In this model, the QD nucleation rate, QD growth rate, and evolution of the island size distribution with increasing coverage can be calculated theoretically using the mathematical formula established for the kinetics of the first-order phase transformation.…”

Section: A Large Variety Of Experimental Data In the Literature On Thmentioning

confidence: 99%

Self-assembly of InAs quantum dots on GaAs(001) by molecular beam epitaxy

Jin

2015

Front. Phys.

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Currently, the nature of self-assembly of three-dimensional epitaxial islands or quantum dots (QDs) in a lattice-mismatched heteroepitaxial growth system, such as InAs/GaAs(001) and Ge/Si(001) as fabricated by molecular beam epitaxy (MBE), is still puzzling. The purpose of this article is to discuss how the self-assembly of InAs QDs in MBE InAs/GaAs(001) should be properly understood in atomic scale. First, the conventional kinetic theories that have traditionally been used to interpret QD self-assembly in heteroepitaxial growth with a significant lattice mismatch are reviewed briefly by examining the literature of the past two decades. Second, based on their own experimental data, the authors point out that InAs QD self-assembly can proceed in distinctly different kinetic ways depending on the growth conditions and so cannot be framed within a universal kinetic theory, and, furthermore, that the process may be transient, or the time required for a QD to grow to maturity may be significantly short, which is obviously inconsistent with conventional kinetic theories. Third, the authors point out that, in all of these conventional theories, two well-established experimental observations have been overlooked: i) A large number of “floating” indium atoms are present on the growing surface in MBE InAs/GaAs(001); ii) an elastically strained InAs film on the GaAs(001) substrate should be mechanically unstable. These two well-established experimental facts may be highly relevant and should be taken into account in interpreting InAs QD formation. Finally, the authors speculate that the formation of an InAs QD is more likely to be a collective event involving a large number of both indium and arsenic atoms simultaneously or, alternatively, a morphological/structural transformation in which a single atomic InAs sheet is transformed into a three-dimensional InAs island, accompanied by the rehybridization from the sp 2-bonded to sp 3-bonded atomic configuration of both indium and arsenic elements in the heteroepitaxial growth system.

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Control of strain-mediated growth kinetics of self-assembled semiconductor quantum dots

Cited by 70 publications

References 44 publications

Renormalization of stochastic lattice models: Epitaxial surfaces

Renormalization of stochastic lattice models: Epitaxial surfaces

On the correlation between the self-organized island pattern and substrate elastic anisotropy

Self-assembly of InAs quantum dots on GaAs(001) by molecular beam epitaxy

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