Thermodynamic Theory of Phase Separation in Nonstoichiometric Si Oxide Films Induced by High-Temperature Anneals

Abstract

High-temperature anneals of nonstoichiometric Si oxide (SiOx, x x films is proposed. The theory is based on the thermodynamic models addressing various aspects of this process which we previously developed. A review of these models is provided, including: (i) the derivation of the expressions for the Gibbs free energy of Si oxides and Si/Si oxide systems, (ii) the identification of the phase separation driving forces and counteracting mechanisms, and (iii) the crystallization behavior of amorphous Si nanoinclusions in the Si oxide matrix. A general description of the phase separation process is presented. A number of characteristic features of the nano-Si/Si oxide composites formed by SiOx decomposition, such as the local separation of Si nanoinclusions surrounded by the Si oxide matrix; the dependence of the amount of separated Si and the equilibrium matrix composition on the initial Si oxide stoichiometry and annealing temperature; and the correlation of the presence of amorphous and crystalline Si nanoinclusions with the presence of SiOx (x 2 phase, respectively, in the Si oxide matrix, are explained.

Keywords

• thermodynamic theory
• phase separation
• nonstoichiometric Si oxide
• Gibbs free energy
• Si nanoparticles
• penalty energy