A density functional view of transition state theory: Simulating the rates at which Si adatoms hop on a silicon surface

Density functional theory is used to give an operational definition for the “free energy surface” on which Si adatoms move over a (100) silicon surface. Molecular dynamics simulations using the empirical Stillinger–Weber potential are used to numerically evaluate free energy surfaces near binding sites and along the important hopping paths. Transition state theory is used to deduce hopping rates at T≈500 and 1000 K from these free energy surfaces for the basic steps responsible for “surface diffusion.” The difference in the activation free energies at these temperatures and the T=0 barrier heights is emphasized.