Impurity Content of Germanium Crystallized from the Liquid Ternary Alloy Ge-In-Sb

Abstract

The compositions of the liquid ternary alloys Ge‐In‐Sb, which coexist with either solid germanium or solid indium antimonide, are calculated with emphasis on indium‐rich alloys. Activity coefficients for the three components in the liquid ternary systems are derived by assuming that the integral molar excess free energy for the ternary system is a linear combination of those for the three binary systems, which are taken from data of Thurmond and Kowalchik for Ge‐In and Ge‐Sb and of Schottky and Bever for In‐Sb. Data of Glasow and Tschishewskaya on the solubilities of Ge in liquid are discussed. Using the activity coefficients of indium and antimony in the ternary liquid alloy in conjunction with the mass action law for the transfer of neutral impurities into the germanium, and expressing the heat energy change by the distribution coefficients of impurities in the binary alloys Ge‐In and Ge‐Sb at the melting point of the germanium, the concentrations of neutral antimony and neutral indium in the crystallized germanium are calculated. The total concentrations of antimony and indium are then obtained by taking into account the ionization equilibrium in the semiconductor. The ionization equilibrium in a semiconductor containing two kinds of impurities is discussed in the appendix from a more general viewpoint considering impurities of equal and of opposite types and degenerate and nondegenerate conditions, assuming, however, that the impurities have energy levels which coincide with the boundaries of the forbidden band. The solid solubilities of antimony and indium in germanium crystallized from a liquid ternary alloy measured recently by Zemskov et al. differ significantly from the experimental data for binary systems by Thurmond and Kowalchik and by Trumbore and from our calculated data for the ternary system.