Coarsening Scenarios in Unstable Crystal Growth

Crystal surfaces may undergo thermodynamical as well as kinetic, out-of-equilibrium instabilities. We consider the case of mound and pyramid formation, a common phenomenon in crystal growth and a long-standing problem in the field of pattern formation and coarsening dynamics. We are finally able to attack the problem analytically and get rigorous results. Three dynamical scenarios are possible: perpetual coarsening, interrupted coarsening, and no coarsening. In the perpetual coarsening scenario, mound size increases in time as L similar to t(n), where the coarsening exponent is n = 1/3 when faceting occurs, otherwise n = 1/4.