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 nonlinear response. In the presence of the Kardar-Parisi-Zhang nonlinearity the disorder causes the lattice effects to decay on large scales with an intermediate crossover behavior. The mobility of the rough surface has a complex dependence on the temperature and the other physical parameters.