  A complete knowledge of absolute surface energies with any arbitrary crystal
orientation is important for the improvements of semiconductor devices because
it determines the equilibrium and nonequilibrium crystal shapes of thin films
and nanostructures. It is also crucial in the control of thin film crystal
growth and surface effect studies in broad research fields. However, obtaining
accurate absolute formation energies is still a huge challenge for the
semi-polar surfaces of compound semiconductors. It mainly results from the
asymmetry nature of crystal structures and the complicated step morphologies
and related reconstructions of these surface configurations. Here we propose a
general approach to calculate the absolute formation energies of wurtzite
semi-polar surfaces by first-principles calculations, taking GaN as an example.
We mainly focused on two commonly seen sets of semi-polar surfaces: a-family
(11-2X) and m-family (10-1X). For all the semi-polar surfaces that we have
calculated in this paper, the self-consistent accuracy is within 1.5
meV/{\AA}^2. Our work fills the last technical gap to fully investigate and
understand the shape and morphology of compound semiconductors.
