First-principles theory of inelastic currents in a scanning tunneling microscope

A first-principles theory of inelastic tunneling between a model probe tip and an atom adsorbed on a surface is presented, extending the elastic tunneling theory of Tersoff and Hamann. The inelastic current is proportional to the change in the local density of states at the center of the tip due to the addition of the adsorbate. We use the theory to investigate the vibrational heating of an adsorbate below a scanning tunneling microscopy tip. We calculate the desorption rate of H from $\mathrm{Si}\left(100\right)-\mathrm{H}(2\mathrm{}\times 1)$ as a function of the sample bias and tunnel current, and find excellent agreement with recent experimental data.