Gibbs free energy and equilibrium states in the Si/Si oxide systems

Abstract

In this paper, the equilibrium states in the Si/Si oxide systems formed as a result of the phase separation of nonstoichiometric silicon oxide films are studied. The expressions for the Gibbs free energy of Si oxide and Si/Si oxide systems are derived thermodynamically. The transformations of the Gibbs free energy in the amorphous Si/Si oxide and the crystalline Si/Si oxide systems with the change in the amount of separated silicon and the composition of the silicon oxide phase are analyzed. By minimizing the Gibbs free energy of these systems, the equilibrium stoichiometry indices of silicon oxide are calculated as functions of its initial stoichiometry and the temperature. The solubility limits of Si in SiO2 in equilibrium with amorphous and crystalline Si are determined. The obtained results form the basis for the development of a complete thermodynamic theory of phase separation in nonstoichiometric silicon oxide films with the formation of Si nanoinclusions in the silicon oxide matrix.