Deep learning of surface elastic chemical potential in strained films: from statics to dynamics

We develop a convolutional neural network (NN) approach able to predict the elastic contribution to chemical potential μₑ at the surface of a 2D strained film given its profile h(x). Arbitrary h(x) profiles are obtained by using a Perlin Noise generator and the corresponding μₑ profiles are calculated either by a Green's function approximation (GA) or by Finite Element Method (FEM). First, a large dataset is produced by exploiting the GA method and it is then used for the training of the NN model. The performance of the trained NN is extensively examined, demonstrating its ability to predict μₑ looking both to the training/validation set and to an additional testing set containing different profiles, including sinusoids, gaussians and sharp peaks never considered in the NN training. The NN is then applied to simulate the morphological evolution of strained Ge films, where the predicted μₑ at each integration timestep plays the role of driving force for material redistribution in competition with a surface energy term (proportional to local curvature) and eventually a wetting energy contribution. Both surface diffusion and evaporation/condensation dynamics are considered and the proposed NN approach is shown to well match the evolution expected by using GA. On this basis, a smaller dataset is built with μₑ profiles calculated by FEM and a new NN model is trained on it. Once again the trained NN-model returns reliable prediction of the FEM μₑ. The findings suggest that the proposed NN-based strategy can be used in replacement of the computationally intensive FEM calculations, enabling the simulation of larger scales and longer time scales untreatable by direct FEM calculation.