Thermal Re-emission Model

Starting from a continuum description, we study the non-equilibrium roughening of a thermal re-emission model for etching in one and two spatial dimensions. Using standard analytical techniques, we map our problem to a generalized version of an earlier non-local KPZ (Kardar-Parisi-Zhang) model. In 2+1 dimensions, the values of the roughness and the dynamic exponents calculated from our theory go like $ \alpha \approx z \approx 1 $ and in 1+1 dimensions, the exponents resemble the KPZ values for low vapor pressure, supporting experimental results. Interestingly, Galilean invariance is maintained althrough.