Kinetic Roughening in Surfaces of Crystals Growing on Disordered   Substrates
  Substrate disorder effects on the scaling properties of growing crystalline surfaces in solidification or epitaxial deposition processes are investigated. Within the harmonic approach there is a phase transition into a low-temperature (low-noise) superrough phase with a continuously varying dynamic exponent z>2 and a non-linear response. In the presence of the KPZ nonlinearity the disorder causes the lattice efects to decay on large scales with an intermediate crossover behavior. The mobility of the rough surface hes a complex dependence on the temperature and the other physical parameters. 
Yan-Chr Tsai and Yonathan Shapir