Molecular simulation predictions of miscibility characteristics and critical exponents in compound semiconductors Sanjib Sikder, Punit Rathi, Jhumpa Adhikari n Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India article info Article history: Received 4 May 2010 Received in revised form 11 January 2011 Accepted 29 March 2011 Communicated by G.B. Stringfellow Available online 5 April 2011 Keywords: A1. Computer simulation A1. Phase diagrams A1. Solid solutions B2. Semiconducting III-V materials B2. Semiconducting II-VI materials B2. Semiconducting ternary compounds abstract Compound semiconductor alloys have been the focus of research as materials of construction for opto- electronic devices. The miscibility of these alloys is difficult to quantify experimentally. The literature data available, from theoretical modelling studies using the regular solution theory, shows wide variance. Hence, in this study, the molecular simulation approach is used with empirical Valence Force Field potential model to predict the miscibility diagrams, critical state properties and critical exponents for semiconductors. Simulation results indicate Al x Ga 1 x As, Al x Ga 1 x P and Al x Ga 1 x Sb alloys are completely miscible at room temperature. For the other alloys, the miscibility diagram is asymmetric and the upper critical solution temperature (UCST) increases as the lattice mismatch increases. At a temperature below UCST, wide miscibility gap exists and phase segregation occurs. The critical exponents, a C and b C , calculated are found to be in good agreement with known solution values. & 2011 Elsevier B.V. All rights reserved. 1. Introduction Compound semiconductor alloys, both III–V and II–VI, have been used or have the potential to be used in the fabrication of opto-electronic devices such as laser diodes, light emitting diodes, specialty lasers, devices used in optical data storage and fibre optics communications. Ho and Stringfellow [1] have shown that the In x Ga 1 x N alloy is thermodynamically unstable over the entire composition range relevant to the manufacture of useful photonic and electronic devices, at normal growth temperatures. An unstable alloy will undergo phase segregation and hence, affect the useful optical properties of these alloys, which are composition dependent [2]. Experimental methods and protocols for synthesizing these semiconducting alloys must work with or around the tendency to phase separate. Knowledge of the tem- perature versus composition miscibility diagram, will indicate the expected equilibrium compositions of the constituent species at a given growth temperature. This can be used as a guideline for the selection of the operating conditions for the reactors used in the growth of these alloys. Therefore, the study of the solution thermodynamics of the compound semiconductor alloys is important. The solid–solid miscibility characteristics of these semicon- ducting alloys have been studied, generally, assuming the regular solution model as the mixing model [1–11]. The interaction parameter (O) in the regular solution theory has been determined using various methods. The delta lattice parameter model devel- oped by Stringfellow [7] has been used to determine the interac- tion parameter as a function of the difference in lattice constants of the constituent compounds. Takayama et al. [2,9,10] have calculated the interaction parameter using energy minimization techniques, in conjunction with the Valence Force Field (VFF) potential. The interaction parameter is assumed to be a constant, i.e., temperature and composition independent, and is used to determine the unstable two-phase region in III–V semiconduc- tors [2]. It should be noted that the miscibility diagram predicted by Takayama et al. is symmetric. Wei et al. [8] have calculated the interaction parameter (as a function of temperature and composi- tion) from first principles methods to determine the miscibility gap and the critical state properties for III–V and II–VI semicon- ductors. Balzarotti [3] and Letardi et al. [4] have used first principles calculations and experimental results to determine the interaction parameter and hence, the miscibility character- istics, including critical properties for these semiconductors. Hassan et al. [11] have used a composition dependent interaction parameter to predict asymmetric binodal and spinodal curves for (Al,Ga)–(As,Sb) alloys. The critical state properties (T C , x C ), pre- dicted for any given ternary alloy vary widely in literature depending on the technique used to determine the interaction parameter. It is, also, difficult to quantify the solid–solid phase behaviour experimentally and consequently modelling studies using mole- cular simulation approach will help to characterize it. In this study, the molecular simulation approach has been used to predict Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jcrysgro Journal of Crystal Growth 0022-0248/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2011.03.053 n Corresponding author. E-mail address: adhikari@che.iitb.ac.in (J. Adhikari). Journal of Crystal Growth 324 (2011) 284–289