Algorithm of Calculating Absolute Semi-polar Surfaces Energies of Wurtzite Crystal: An Example of GaN

A complete knowledge of absolute surface energies with any arbitrary crystal orientation is important for the improvements of devices. It determines the crystal shapes of nanostructures. It is also crucial for thin film crystal growths and surface effect studies. However, obtaining accurate absolute energies is still a huge challenge for the semipolar surfaces of compound semiconductors, mainly resulting from the asymmetry of crystal structures, and complex reconstructions of the surfaces. Here we propose a general approach to calculate the absolute surface energies for semipolar surfaces of wurtzite materials, using first-principles calculations and taking GaN as an example. We mainly focused on two common surface families: a-family (11-2X) and m-family (10-1X). For all the surfaces calculated in this work, the estimated errors are within 1.5 meV/Ų, which justifies the applicability of our method. It is applicable and straight forward to apply this idea to other materials. Our approach provides a powerful tool to investigate high index surfaces and crystal shapes for compound semiconductors accurately.