Self‐Consistent Tight‐Binding Method for Total Energy Calculations of Tetrahedral Semiconductors Including Surfaces and Defects

Abstract

Abstract The total energy of macroscopic electron‐ion systems as a function of ion positions is an important quantity for studies of atomic and electronic properties of ideal crystals, surfaces, and defects. For the first time a total energy calculation is presented which relies on tight binding theory and takes the electron‐electron interaction fully into account. The advantage of the method as compared to the more accurate pseudopotential‐density functional approach is its greater simplicity at still existing accuracy. The calculation relates directly to covalently bonded tetrahedrally coordinated semiconductors, but it can also be applied to ionic tetrahedral materials. The intraatomic part of the electron‐electron interaction enters the total energy through the characteristic U‐parameters whereas the long‐range interatomic contribution is approximated by a Madelung‐like Coulomb repulsion. Correlation makes that all one‐electron energy levels depend on their populations which in turn are determined by the one‐electron energies. Hence the total energy has to be calculated self‐consistently. Bonding parameters, atomic orbital energies, and parameters of electronelectron interaction are adjusted in such a way that ionization potentials of free atoms and ground‐state properties of ideal crystals as cohesive energy and bulk modulus are corectly reflected. The inclusion of the full electron‐electron interaction guarantees also the true magnitude of the total energy. The simplicity and accuracy of the presented method makes it suitable for studies of atomic rearrangements near surfaces and defects. This is demonstrated explicitly in the case of relaxed (111) 1 × 1 surfaces of covalent semiconductors.