Ab Initio Hartree-Fock Simulation of R-Plane Sapphire

R-plane sapphire is the preferred substrate material for silicon-based radiation-hard devices and RF integrated circuits. Ab initio periodic Hartree-Fock simulations of r-plane sapphire slabs are presented with a particular focus on the surface relaxation and the surface energy. The calculations show that there is a considerable relaxation of the four outermost atomic layers of r-plane sapphire. A comparison with c-, a- and m-plane sapphire shows that the surface energy of fully relaxed r-plane sapphire is considerably larger than the surface energy of c-plane sapphire, but similar to the surface energies of a- and m-plane sapphire. The implications of these findings for chemical mechanical polishing (CMP) and electrolytic in-process dressing (ELID) grinding of sapphire are discussed briefly.