Charge Self-Consistent Empirical Tight Binding Cluster Method for Semiconductor Surface Structures

A cluster method for evaluating the structure of semiconductor surfaces is formulated. The cluster includes all atoms that are expected to be displaced from their bulk positions and sufficient undisplaced neighbours to give a realistic local bonding environment for each displaced atom. The sp3 hybrid basis is used and non bonding hybrids are saturated by the inclusion of hydrogen atoms. The energy is split into two contributions as in Chadi’s prescription. The one-electron energy is calculated by diagonalising the Tight-Binding Hamiltonian, whose matrix elements are determined from the empirical values of Harrison. The difference between ion-ion and electronelectron energies is written as a sum of contributions from the bonds and evaluated for each bond by comparison with the bond energy as a function of length as determined from an accurate quantum chemistry cluster calculation. A crude form of charge self-consistency is imposed by calculating the charge on each atom and adjusting the term values on each atom to take account of the electrostatic interaction with the other atoms of the surface, and iterating to self-consistency. The displacements of the atoms are adjusted to find the minimum total energy configuration. The method is tested by calculations on GaAs(110)(l×1) giving results close to the known structure, and on Si(111)(2×1) where the surface is found not to be buckled, in agreement with the careful, self-consistent density functional calculations of Pandey and in contrast to the non self-consistent tight-binding results.