A continuum model for liquid phase electroepitaxy

Abstract

This paper presents a macroscopic continuum model for liquid phase electroepitaxial growth of single crystal semiconductors. The governing equations and associated boundary and interface conditions of the model are obtained from the fundamental principles of electrodynamics and thermomechanics of continua. The constitutive equations of the substrate/source and the liquid phase are derived from an irreversible rational thermodynamic theory. By means of systematic simplifications, special forms of the governing equations and associated interface conditions are presented in order to obtain tractable equations and gain physical insight for various thermoelectric effects involved in the process. The formulation presented here is valid for general LPEE growth processes with any configuration, and takes into account electromigration and the well-known thermoelectric effects such as Joule, Peltier, Thomson, Dufour, and Sorel. The fundamental equations derived here can also be used to model the growth process of ternary compound semiconductors, either directly or with modifications depending on the type of compositions considered.