The Asaro-Tiller-Grinfeld instability revisited

Deposition of a thin film on a solid substrate in the presence of a misfit leads to a growth instability that favors three-dimensional (3D) morphology of the free surface. The amount of the misfit and the conditions of the fi lm deposition (molecular beam epitaxy) lead to an elastic problem, where su rface energy has the same order of magnitude as the bulk energy. The instab ility occurs at a critical thickness of the film. The value of the critical thickness is shown to be given by the competition between the bulk and sur face effects. We investigate (via a Fourier method) the Asar-Tiller-Grinfel d instability for cubic materials and in the presence of an arbitrary misfi t. We solve the problem in the general case and we specialize our results t o recover values which are in good agreement with experimental data in the case of a In1-xGaxAs alloy. We consider in a 3D framework sinusoidal pertur bations of the free boundary at arbitrary orientations with respect to crys tallographic axes. Thus, we are able to minimize the sum of the bulk and su rface energies with respect to the orientation and therefore to predict qua litative aspects of the surface morphology. (C) 2001 Elsevier Science Ltd. Ah rights reserved.