A Dual-Phase-Lag Diffusion Model for Predicting Thin Film Growth

A dual-phase-lag diffusion (DPLD) model, which extends Fick’s law by including two lagging times, τ_j for the mass flux vector and τ_ρ for the density gradient, is developed to predict thin film growth. Depending upon the phase lag ratio τ_ρ/τ_j, the proposed model uniquely characterizes four types of growth kinetics as reported in the literature. The model validation with the experimental data of silicon oxidation and Hg_1-xCd_xTe film deposition demonstrates that the DPLD model captures the anomalous behavior of thin film growth from the very beginning of the process to relatively long times very well.