It is proved that in slab simulations of uniform semiconductor surfaces the electric field in the vacuum space should vanish. In standard approach this condition was achieved by introduction of the dipole correction [J. Neugebauer and M. Scheffler, Phys. Rev. B 46, 16067 (1992)]. An effective and stable method of exact solution of Poisson equation, based on Laplace correction, which attains the zero field condition in the vacuum, is described. The dipole correction to the slab energy is removed. Additionally, a method of the control of electric field within the slab is introduced, applicable in direct simulations of Fermi level influence on the properties of semiconductor surfaces.

In this paper, we present systematic improvements to a method that allows us to determine the surface phase diagrams based on ab initio calculations and atomistic thermodynamics. In particular, we include a contribution derived from thermal vibrations of the surface, which is usually omitted in such analysis. On the basis of first-principles phonon calculations, we determine a zero-point vibrational energy and thermal dependencies of vibrational entropy and free energy for atoms and molecules adsorbed on the surface. A series of polar GaN(0001) surfaces are examined. Significant changes are observed in the surface phase diagrams compared to the diagrams obtained by standard density-functional theory calculations without phononic contributions.

Laplace correction was used for solutions of Poisson equation in density functional theory (DFT) slab simulations of GaN (0001) surface. In accordance to the scenario of Meyer and Marx [Phys. Rev. B 67, 35403 (2003)], the electric field, emerging within the slab, is determined by the condition that Fermi energy is equal to the energies of valence band maximum and conduction band minimum at both sides of the slab. In contrast to their predictions that the field is identical for different slab thicknesses, it was found from DFT calculations that the electric potential difference between two sides of the slab is kept constant. Therefore, the energy of the slab does not diverge for large slab thickness. It was also found that, in most cases, the field in the slab is determined by pinning by surface states. Thus the change in opposite side slab termination, both by different types of atoms and by their location, can be used to change electric field in the slab, creating a tool that can be used to simulate the change in surface properties due to doping of the bulk. It was shown that, depending on the electric field, the energy of surface states changes in the way different from the band states. This change could be large, comparable to the bandgap. Despite the fact that the Fermi energy can be pinned to surface states, it may change its energy with respect to valence band and conduction band as a function of the doping of bulk semiconductor. These results are in agreement with the experimental data showing variation in Fermi energy at the GaN (0001) surface in function of the doping in the bulk. It was also shown using the electron density and potential profiles that ten Ga–N atomic layers are necessary to achieve small quantum overlap of the surface states of both sides of the slab, which is required for high precision simulations of the surface.

Chemical adsorption of the species at semiconductor surfaces is analyzed showing the existence of the two contributions to adsorption energy: bond creation and charge transfer. It is shown that the energy of quantum surface states is affected by the electric field at the surface, nevertheless, the potential contribution of electron and nuclei cancels out. The charge transfer contribution is Fermi level independent for pinned surfaces. Thus for Fermi level pinned at the surface, the adsorption energy is independent on the Fermi energy, i.e., the doping in the bulk. The DFT simulations of adsorption of hydrogen at clean GaN(0001) and silicon at SiC(0001) surfaces confirmed independence of adsorption energy on the doping in the bulk. For the Fermi level nonpinned surfaces, the charge contribution depends on the position of Fermi level in the bulk. Thus adsorption energy is sensitive to change of the Fermi energy in the bulk, i.e., the doping. The DFT simulations of adsorption of atomic hydrogen at 0.75 ML hydrogen covered GaN(0001) surface confirmed that the adsorption energy may be changed by about 2 eV by the doping change from n- to p-type.

Semiconductor surfaces were divided into charge categories, i.e., surface acceptor, donor, and neutral ones that are suitable for simulations of their properties within a slab model. The potential profiles, close to the charged surface states, accounting for explicit dependence of the point defects energy, were obtained. A termination charge slab model was formulated and analyzed proving that two control parameters of slab simulations exist: the slope and curvature of electric potential profiles which can be translated into a surface and volumetric charge density. The procedures of slab model parameter control are described and presented using examples of the DFT simulations of GaN and SiC surfaces showing the potential profiles, linear or curved, depending on the band charge within the slab. It was also demonstrated that the field at the surface may affect some surface properties in a considerable degree proving that verification of this dependence is obligatory for a precise simulation of the properties of semiconductor surfaces.