Discussion of “retrograde solubility in semiconductors”

Abstract

In a recent article, McKelvey[1] addresses the origin of retrograde solubility, a phenomenon of considerable importance in semiconductor processing. After reviewing the literature, McKelvey concludes that explanations given earlier are ‘‘insufficient and are based on tautological arguments which only describe the effects of the phenomenon and never its origin.’’ The purpose of this discussion is to partly dispute this conclusion and show that the article of McKelvey does not provide any new insight. In fact, the article presents only a qualitative framework that is incorrect and misleading. Figures 1 and 2 of McKelvey’s article are basic illustrations of retrograde solubility. Figure 3 is a textbook demonstration of the origin of miscibility gap in a binary system with positive enthalpy of mixing. Figure 4, which is supposed to explain retrograde solubility, is incorrect. At the Si-rich corner, the free energy of the solid solution at T3 cannot be more negative than that at T2, since T2 . T3 and enthalpy mixing is positive for the solid solution. McKelvey considers the liquid phase to be ideal and the solid solution to be regular. In this framework, defined by Eqs. [2] through [4] in McKelvey’s article, the free energy curves for the solid solution at T2 and T3 will not intersect, as shown in Figure 4. Although this figure is only a schematic representation of free energies of different phases, the relative positions of the curves are inconsistent with thermodynamic equations.