Starting from a continuum description, we study the non-equilibriumroughening of a thermal re-emission model for etching in one and two spatialdimensions. Using standard analytical techniques, we map our problem to ageneralized version of an earlier non-local KPZ (Kardar-Parisi-Zhang) model. In2+1 dimensions, the values of the roughness and the dynamic exponentscalculated from our theory go like $ \alpha \approx z \approx 1 $ and in 1+1dimensions, the exponents resemble the KPZ values for low vapor pressure,supporting experimental results. Interestingly, Galilean invariance ismaintained althrough.
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