Molecular Dynamics Simulation of GaAs Molecular Beam Epitaxy D. A. Murdick,1 X. W. Zhou,1 H. N. G. Wadley,1 R. Drautz,2 and D. G. Pettifor2

1Department of Materials Science and Engineering, University of Virginia, Charlottesville, Virginia 22904, USA 2Department of Materials, University of Oxford, Oxford OX1 3PH, UK

ABSTRACT

The vapor deposition of epitaxial GaAs and (Ga,Mn)As thin films during far-from-equilibrium growth is studied using classical molecular dynamics (MD) simulations. Both a Tersoff potential and a preliminary version of a bond order potential (BOP) are utilized for the simulations. The film morphology is studied at various substrate temperatures and As:Ga flux ratios. We also explore the low-temperature growth of Ga0.94Mn0.06As and the Mn clustering trends in as-grown films.

INTRODUCTION

GaAs is widely used in photonic and microelectronic applications and, more recently, is being investigated for a number of spintronic devices [1-3]. GaAs has attracted interest as a host material, which, when doped with magnetic transition metals such as Mn, creates a ferromagnetic semiconductor for spin injection applications [3]. The temperature at which the doped GaAs is ferromagnetic (Curie temperature) is believed to be maximized if Mn ions substitute Ga at Ga lattice sites and Mn clusters do not form [4]. Currently a variety of processing techniques, including low-temperature molecular beam epitaxy (MBE) [5], digital alloy deposition with annealing [6], and ion implantation in conjunction with pulsed-laser melting [7], are being explored to maximize the Curie temperature of Mn-doped GaAs systems. It has become apparent that improved techniques for the growth of GaAs thin films are needed that better control the atomic-scale mechanisms of assembly, including those responsible for the incorporation sites of dopants [8]. To explore these atomic processes and the factors that influence them, we have utilized molecular dynamics (MD) to simulate the growth of GaAs films under various processing conditions.

GaAs thin films are usually grown on (001) substrates by MBE. In MBE, effusion cells produce As2 and Ga fluxes, which propagate ballistically to a substrate where growth occurs. The fluxes are usually adjusted to result in a film growth rate of 1-3 Å/second [9]. Typical effusion cell temperatures are 520-640 K for As and 1150-1250 K for Ga [5,10].

The homoepitaxial vapor deposition of GaAs(001) under MBE conditions can be divided into a high-temperature (HT) and a low-temperature (LT) range based on the temperature of the substrate. LT MBE is typically conducted between 520 and 575 K, while HT MBE occurs between 675 and 915 K [9-11]. HT MBE is commonly used for the epitaxial growth of high quality crystalline films. LT MBE is used to make insulating GaAs films with higher defect concentrations (shortened carrier life time) or for reducing segregation and clustering of dopants. The latter is a desired outcome during the fabrication of (Ga,Mn)As ferromagnetic semiconductors [12,13].

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The As:Ga flux ratio used in MBE growth is dependent on the temperature range of the substrate. The HT MBE growth environment produces stoichiometric growth only in the presence of excess As. The growth rate is then controlled by the Ga flux because As only binds to Ga surface atoms [10]. The flux ratio for HT MBE is generally around 8 [14], but can be much larger due to the high desorption rate of As2. During LT MBE, the As2 sticking probability is much higher and stoichiometric crystals form only when the As:Ga flux ratio approaches unity [11,15]. Under LT MBE conditions, a highly defective and strained film forms when the As:Ga flux ratio is greater than unity due to excess As incorporation [11,15].

COMPUTATIONAL METHODS

The atomic assembly of GaAs from Ga and As2 vapor fluxes can be simulated by classical MD. Within MD, energies and forces are calculated at femtosecond time steps and are used to numerically integrate Newton’s equations of motion (the Lagrangian) for an ensemble of N atoms [16,17]. Our implementation of MD allows the study of atomic assembly, surface, and interface morphology evolution as a function of temperature, elemental flux ratios, flux energy, and flux angle at constant pressure and temperature [18]. This approach enables atom dynamics to be studied over times approaching microseconds for systems of atoms that are nanometers in size.

A well-defined potential energy function (PEF) is needed that accurately predicts interaction forces between the atoms and molecules of the simulated system. For the covalently bonded GaAs system, these expressions must include both radial and angular dependent components. Detailed evaluations of a variety of published PEFs [19] indicate that those best suited for MD surface simulation are the Tersoff PEF parameterization by Albe et al. [20], the Stillinger-Weber (SW) PEF by Wang and Stroud [21], and the combined SW parameterization by Angelo and Mills [22] and Grein et al. [23]. We utilize the Tersoff parameterization by Albe et al. [20] for MD vapor deposition simulations of GaAs and a preliminary bond order potential (BOP) parameterization [24] for MBE simulations of GaAs and (Ga,Mn)As.

The version of BOP utilized in this paper models σ bonding at a similar level of approximation to the Tersoff and Brenner PEF [25], but ignores π bonding and other complexities normally present within the BOP formalism [26-29]. The BOP parameterization was motivated [30] by the SW parameterization used by Grein et al. [22,23] and thus inherits its strengths and weaknesses. For example, although GaAs zinc blende cohesive energy, atomic volume, and elastic constants are well described by the parameterization, the Ga and As elemental phases are poorly described with expanded volume and weaker cohesive energies [19].

The MD simulations of MBE growth conducted here involved thousands of atoms for times up to 70 ns [31]. The initial (001) crystals measure 32 Å × 32 Å on the surface and are four atom planes deep. The bottom two layers were fixed to avoid translation of the crystal during impact. Ga atoms and As2 molecules were deposited every 17.7 ps normal to the surface with an energy of 0.1 eV/atom, which corresponds to a source temperature of 1160 K. During deposition the substrate temperature was controlled using Andersen’s algorithm to approximate isothermal-isobaric conditions [32].

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RESULTS

Simulated GaAs thin film morphology as a function of As:Ga flux ratio and substrate temperature have been studied using both our preliminary BOP and Albe’s parameterization of Tersoff. Films grown at various As:Ga vapor flux ratios (1-15) and constant substrate temperature (900 K) are shown in Figure 1. The BOP simulations result in a crystalline film when the As and Ga fluxes are equal. Higher ratios revealed that the majority of As2 sticks to the surface, see Figure 1 (a)-(c). Flux ratios above 10 were omitted because the trend of total incorporation of As species is clearly established with the present data. The current BOP parameterization does not fully model As-As interactions and in its present form fails to predict As2 desorption under HT MBE conditions.

Simulated films using Albe’s parameterization of the Tersoff PEF show uniform crystalline GaAs deposited layers for As:Ga flux ratios of 10 or greater. An As:Ga ratio of 1 produces a disordered Ga-rich deposit, while a flux ratio of 5 produces an intermediate crystalline film with elevated Ga concentration. For ratios greater than 15, it was found that crystalline deposition would continue with only the growth rate being reduced due to the additional As desorption. The results shown in Figure 1 (d)-(g) are consistent with phenomena seen in HT MBE experiments [10].

The species incorporation rate and crystallinity of grown films are dependent on the substrate temperature for the BOP and Albe parameterizations, Figure 2. Crystalline films were grown at temperatures as low as 473 K using BOP, Figure 2 (a)-(b). From our analysis, it appears that kinetic trapping of clusters of like elements and Ga anti-site defects increase as the temperature is reduced. The top few surface layers are also much more disordered than the lower layers though they eventually transform into crystalline layers as growth proceeds or if the annealing time is extended.

As the substrate temperature is decreased (at a constant As:Ga flux ratio of 10) Albe’s Tersoff potential predicts a consistently lower concentration of As in the deposited film composition. The As:Ga ratio in the film as a function of temperature is plotted every 10 ps between 10 ns and 40 ns of the deposition run, see Figure 2 (c). The slope of the As:Ga ratio in the film versus time continuously steepens as the substrate temperature decreases from 900 K to

Figure 1. The predicted film morphology at 900 K as a function of the As:Ga ratio. Panels (a)-(c) represent results from the preliminary BOP parameterization, and panels (d)-(g) are from Albe’s Tersoff parameterization. The initial substrate at t=0 is marked with a brass-colored plate.

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500 K. At 500 K, a generally disordered deposit appears with a high concentration of Ga. However, as the temperature increases, the concentrations of Ga and As become equal and a stoichiometric crystalline films forms. This potential predicts an As2 sticking fraction that decreases with temperature, which is not consistent with experimental evidence [15].

An extended GaMnAs BOP parameterization has been used to simulate the LT MBE growth of (Ga,Mn)As, Figure 3. For the low Mn concentrations simulated, the film morphology has similar trends to the LT MBE results for GaAs, detailed above. The image in Figure 3(a) is taken as a snap shot during vapor deposition of Ga0.94Mn0.06As at 523 K with a As:Ga flux ratio of 1.14. An As dimer can be seen approaching the surface and Ga interstitials are clearly visible. Mn atoms generally substitute for Ga atoms on the lattice, but also can form interstitials. The formation of interstitial/substitutional complexes and other larger Mn clusters increases with Mn concentration, see Figure 3(b). The clustering trends shown at 550 K represent 10-20 MD simulations at each Mn concentration level [33].

CONCLUSIONS

Albe’s Tersoff [20] and our preliminary BOP [24] potentials were used to simulate vapor deposition of GaAs on the (001) surface using an MD approach. The BOP PEF predicts

Figure 2. The effect of substrate temperature on film morphology. Predicted BOP films for substrate temperatures of (a) 473 K and (b) 673 K. Albe’s Tersoff predicted (c) As:Ga ratio in the deposited film as a function of deposition time at 500 K, 700 K, and 900 K. (The As:Ga flux ratio was 1 for BOP and 10 for Tersoff.)

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Figure 3. A BOP GaAs crystal doped with Mn grown under LT MBE conditions with an As:Ga flux ratio equal to around 1: (a) Snapshot of GaAs doped with 6% Mn (T=523 K), and (b) Mn clustering trends as a function of Mn dopant concentration (T=550 K).

stoichiometric crystalline growth when the As:Ga flux ratio is near unity under all substrate temperatures studied. This parameterization of BOP seems best suited to study the LT MBE growth region where As2 desorption is not significant and stoichiometric growth occurs with an equal ratio of As and Ga fluxes. The addition of Mn into this system allows the study of Mn incorporation into LT grown crystalline films. Mn is predicted to incorporate into the GaAs lattice at substitutional Ga and interstitial sites. The Albe et al. parameterization of the Tersoff PEF predicts crystalline growth under HT MBE growth conditions over an experimentally valid range of As:Ga flux ratios. However, the As concentration in the film is incorrectly predicted to decrease as the substrate temperature is reduced. This PEF is therefore best suited for HT MBE simulations where significant As2 desorptions occur.

The Tersoff potential and simplified BOP have similar functional formats, but their respective parameterizations are suited for completely different temperature ranges. We are continuing to explore the effect of parameter sets and additional functional forms, such as π bonding in As, in the hope of developing a GaAs potential that models MBE growth under a wider range of temperatures.

ACKNOWLEDGMENTS

We gratefully acknowledge the support of DARPA/ONR under contract No. GG10551-119199, Carey Schwartz and Julie Christodoulou program managers.

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