This phase-lag diffusion model extended Fick’s law by including 2 lag-times; one for the mass-flux vector and one for the density gradient. It was developed in order to predict thin film growth. Depending upon the phase lag ratio, the model characterized uniquely 4 types of reported growth kinetics. Application of the model to experimental data for Si oxidation and HgCdTe film deposition demonstrated that the model captured well the anomalous behaviour of thin film growth; from the very beginning of the process to relatively long times.

A Dual Phase-Lag Diffusion Model for Predicting Thin Film Growth J.K.Chen, J.E.Beraun, D.Y.Tzou: Semiconductor Science and Technology, 2000, 15[3], 235-41