A FEM dataset of Ge film profiles and elastic energies for machine learning approximation of strain state and morphological evolution

Machine Learning (ML) can be conveniently applied to continuum materials simulations, allowing for the investigation of larger systems and longer timescales, pushing the limits of tractable systems. Here we provide a comprehensive dataset of strained Ge films on Si and their corresponding strain states, which can be used to train a ML model capable of such acceleration. Approximately 80k 2D cases are included, reporting the profiles h(x) and the corresponding elastic energy densities and strain fields. The profiles are conveniently sampled using Perlin-noise and pure-sine waves. A 100nm-large computational domain is considered. The mechanical equilibrium problem is solved using Finite Element Method (FEM). Ge is modeled as an isotropic material and an eigenstrain of 3.99% is used, as in Ge/Si(001). The database has been exploited for training a (fully) Convolutional Neural Network (CNN) which maps the free surface profile h(x) to the corresponding energy density. If plugged into the proper time-dependent Partial Differential Equation, this term can be used to accelerate continuum simulations of the morphological evolution of strained films while retaining FEM-level accuracy. Tests of the reliability of such CNN model are also provided in the repository, together with the output of surface morphology minimization procedures and morphological evolution simulations during coarsening and growth. In the latter, evolution by surface diffusion has been considered as an important case, but applications to other mechanisms are possible. Generalization examples to larger computational cells with respect to those in the dataset are also available.