Oxidation of silicon-germanium alloys. II. A mathematical model

A mathematical model of oxidation of SixGe1-x alloys is presented. The growth of SiO2 is simulated in conjunction with the determination of silicon distribution in SixGe1-x using numerical methods. The main feature of the model is the assumption of simultaneous oxidation of germanium and silicon when exposing the SixGe1-x to an oxidizing atmosphere. In accordance with thermodynamics, the GeO2 formed is subsequently reduced by the (free) silicon available at the interface between the growing SiO2 and the remaining SixGe1-x through a reduction reaction. Thus, the enhanced oxidation of silicon in the presence of germanium is modeled as a result of the rapid oxidation of germanium followed by the quick reduction of GeO2 by silicon. The growth of a mixed oxide in the form of either (Si,Ge)O2 or SiO2-GeO2 only occurs when the supply of silicon to the SiO2/SixGe1-x interface is insufficient. A comparison is made between simulation and experiment for wet oxidation (in pyrogenic steam) of polycrystalline SixGe1-x films. It is found that the model gives a good account of the oxidation process. Kinetic parameters, i.e., interfacial reaction rate constant for oxidation of germanium and diffusion coefficient of silicon (germanium) in SixGe1-x, are extracted by fitting the simulation to the experiment. © 1997 American Institute of Physics.