Towards a standardized setup for surface energy calculations

High-throughput design of new materials with desired electronic properties, based on screening of large collections of crystal structures organized in the from of libraries or databases require fast, widely applicable, consistent and unsupervised methods to calculate the property of interest. In this work we present an approach for the calculation of surface energies of two-dimensional periodic crystal lattices which meets all these requirements. For materials slabs which are terminated with two identical surfaces, the task of calculating the surface energy is trivial. More problematic are the cases where both terminating surfaces are different, as there is no single established method allowing for equal treatment of a wide range of surface morphologies and orientations. Our proposed approach addresses this problem. It relies on appropriately chosen capping atoms, whose bonding energy contributions are used to approximate the total energy of the surface. The choice of the capping atoms is governed by a set of simple guidelines that are applicable for surfaces with different terminations. We present the results for different semiconductor materials and show that our approach leads to surface energies with errors that are below 10%, and that are as low as 2% in many cases. We show that hydrogen is not always the best choice for a capping atom if accurate surface energies are the target of the calculations.