Open-system density matrix description of an STM-driven atomic switch: H on Si(100)

Previous experiments indicate that an STM (scanning tunnelling microscope) can be used to switch a hydrogen atom at a partially hydrogen-covered Si(100)-2×1 surface, from one Si atom of a Si dimer to a neighbouring, empty Si site [U.J. Quaade et al., Surf. Sci. 415, L1037, 1998]. It has been suggested that the switching occurs via a transient positive ion resonance state. In an earlier paper, we have examined the switching process for the “above threshold” regime when the bias is large enough to directly populate the positive ion resonance. In the present paper we study the “below threshold” regime instead, where the switching is more appropriately modelled as a ladder climbing over the barrier, in the ground electronic state. For this purpose we solve the Liouville–von Neumann equation in Lindblad form, describing a switching H atom on a Si dimer. STM-induced transition rates between vibrational levels are estimated from cluster calculations, assuming contributions both from a dipole and a resonance scattering mechanism. Vibrational relaxation is also included, as well as finite temperature and field effects. The switching rate in a current regime of about 1 to 10 nA scales highly non-linearly with current, and it is found to be governed by vibrational “ladder climbing” and subsequent tunnelling through the top of the ground state barrier. Multi-phonon processes also play a role. As a result of tunnelling, pronounced isotope effects are observed when replacing H with D. It is further argued that resonance-mediated inelastic scattering dominates over dipole excitation, and that the STM switch is stable also at room temperature.