مطالعه شبیه سازی مولکولی از خواص ساختاری در حالت آلیاژهای InxGa1-xAs،: مقایسه بین ظرفیت نیروی میدان و مدل بالقوه ترسافت

The thermodynamic and structural properties of compound semiconductor alloys have been generally modelled using either the Valence Force Field model or the Tersoff potential model. This work compares the properties, such as lattice constant and bond length, of the InxGa1−xAs alloy as predicted by Monte Carlo simulations in the semigrand isothermal isobaric ensemble using both the potential models, with experimental data. The lattice constants are expected to follow the Vegard’s law at any given temperature. Valence Force Field model predicts bond length data which follows the experimentally determined values at 300 K; whereas the Tersoff model forecasts that the virtual crystal approximation will be followed. The VFF model, with its experimentally determined parameters, is found to be better for modelling the alloy at room temperature. The Tersoff model, with its fitted parameters, on the other hand predicts the effect of temperature on the microscopic structure of the alloy better. The parameters of the Tersoff potential characterizing the In–Ga interactions can be further improved to predict bond lengths more accurately.

Compound semiconductor alloys are used in the fabrication of many useful optoelectronic devices [1]. The InxGa1−xAs system is studied here as a representative example of III–V compound semiconductor alloys. These alloys are of technological importance as they find extensive application in the manufacture of electronic devices. The energy band gap of the alloy ranges from 0.33 eV for InAs to 1.43 eV for GaAs [2]. By mixing the two binary compounds, the properties of the resulting ternary alloy can be tuned to intermediate values. While the energy band gap is tuned with composition, the lattice constant also changes causing a lattice mismatch with the substrate on which the alloy is grown and the quality of the crystal grown may suffer. Prediction of properties using molecular simulations will allow the selection of the substrate with matching lattice constant or one with the least mismatch reducing the need for experimentation with the material itself. Knowledge of the linear thermal expansion coefficient (αT) is important as many semiconductor devices consist of permanently joined layers of different materials. In this paper, we therefore endeavour to model the structure of this alloy using two different empirical potential models and compare the simulation results with experimental data where available. The effect of changes in composition and temperature on the microscopic structural properties is also considered. The main objective of this study is to establish the conditions where the physical properties predicted by molecular simulations in conjunction with the potential models are valid. Ho and Stringfellow [3] and [4] first used the Valence Force Field (VFF) model, also known as the Keating model [5], to study the solution thermodynamics of InGaN and other III–V alloys. Takayama et al. [6] and [7] have since refined the molecular model and have determined the miscibility characteristics and microstructure of other ternary and quaternary compound semiconductor alloys using the energy minimization approach of Ho and Stringfellow [3] and [4]. Adhikari and Kofke [8] and [9] used the molecular simulation approach to predict the miscibility diagram and local composition using the Valence Force Field (VFF) model for the InGaN, InAlN, GaAlN and InGaAlN alloys. Tersoff developed another empirical potential to model covalent systems such as silicon, germanium, SiGeC [10], [11] and [12]. The Tersoff model has a longer range than the VFF model and this range can be adjusted. Unlike the VFF model, which is limited to modelling crystals with tetrahedral structure allowing only small distortions, the Tersoff model allows for more significant deformations. The potential was found by Tersoff to predict the properties of Si with various polymorphous forms with good accuracy and was also found to have transferability. However, the potential function was found by Tersoff to be not long-ranged enough to describe Si melts successfully. This model was extended to III–V systems such as InGaAlAs by other authors by calculating the various fitting parameters. The growth of the InGaAs alloy has been studied by Ashu et al. using the molecular dynamics approach in 1995 [13] and modifications to the potential were introduced by Nakamura et al. in 2000 [14]. Nakamura et al. pointed out that the bonds in InGaAs alloy have some ionic character and introduced an additional Coulombic term. Tersoff applied his form of the potential function to SiC in the rocksalt (NaCl) structure, which has a considerable ionic character and observed the lattice constant and cohesive energy to be a reasonable approximation (slight underestimation) of the experimental data; whereas for the cubic structure, the results were in excellent agreement as compared to experimental values. The III–V alloys crystallize in the cubic zinc-blende structure and the hexagonal wurtzite structures, which have similar tetragonal nearest-neighbour arrangements. As Tersoff has noted, in the short-range of the potential, the difference in energy between the two structures is minor. Thus, for purposes of the present study, the cubic zinc-blende structure is considered and the improvement in accuracy provided by the introduction of the Coulombic term does not merit the reduction in computational speed that the additional calculations will cause. Ashu et al. utilized the potential in the form used in this study and successfully determined the critical thickness for the formation and extension of interface misfit dislocations. Molecular dynamics has also been used to predict structural and thermodynamic properties of binary alloys such as BAs [15], GaN [16] and AlN [17]. The structural and thermodynamic properties of InAs and GaAs have also been predicted successfully using Monte Carlo methods by Adhikari and Kumar [18]. This paper is organized to include in Section 2 a description of the two potential models used, viz., VFF and Tersoff potential energy functions (PEF). The details of the simulation method used are presented in Section 3. In Section 4, the simulation results and an analysis of the same has been made. The conclusions follow in the last Section 5.

At room temperature, the VFF model shows a good agreement with the lattice constant and bond length values determined experimentally. However, the effects of change in temperature on both these properties for the VFF model are not as expected to arise in nature as both structural properties show decrease in value with increase in temperature. Tersoff model, on the other hand, while showing a good agreement with experiment on the lattice constants at 300 K, predicts the bond lengths to be as given by the VCA and not as determined by experiments. Contrasting with the VFF model however, the Tersoff model predicts an increase in values of lattice constants and bond lengths with increasing temperature. The linear thermal expansion coefficient values have been determined only for the Tersoff model and reported in Table 4. At a given temperature, both the potential models predict only slight deviations from the Vegard’s law and the magnitude of this deviation is independent of temperature. The parameters, α and β, in the VFF model are not fitted parameters but are determined from experiments [7] and [24]. The parameters have been presumed to be independent of temperature, and this assumption has been found to be unacceptable while predicting structural properties using this model. Experiments will have to be conducted at each temperature condition to determine the value of the parameters at that temperature to further refine this model. The parameters in the Tersoff model, on the other hand, are best fit to a data base of properties of the alloys [13]. Previous work with the binary alloys, InAs and GaAs, [18] has shown that the parameters describing the In–In, In–As, As–As, Ga–As and Ga–Ga interactions in the corresponding binary alloys are adequate to be used with molecular simulation approach to predict the structural and thermodynamic properties of these binary alloys. An improvement in the parameterization of the In–Ga interactions to account for the fact that the bond lengths in the ternary alloy do not follow the VCA exactly (though not in the scope of this paper) will be helpful in further enhancing the usefulness of the Tersoff model. The molecular simulation approach has the advantage of not making any assumptions or approximations (such as regular solution model for mixing) other than the interatomic PEF which describes the interactions between the atoms of the constituents of any alloy. Thus, we can conclude that the VFF model can be used to predict properties at room temperature, whereas, the Tersoff model is preferred when temperature change effects need to be determined.