Appl Phys A (2008) 93: 319–333 DOI 10.1007/s00339-008-4833-3 Open-system density matrix description of an STM-driven atomic switch: H on Si(100) Karl Zenichowski · Tillmann Klamroth · Peter Saalfrank Received: 12 February 2008 / Accepted: 9 July 2008 / Published online: 15 August 2008 © Springer-Verlag 2008 Abstract Previous experiments indicate that an STM (scan- ning tunnelling microscope) can be used to switch a hydro- gen atom at a partially hydrogen-covered Si(100)-2 × 1 sur- face, 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 thresh- old” regime when the bias is large enough to directly popu- late 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 vibra- tional levels are estimated from cluster calculations, assum- ing contributions both from a dipole and a resonance scat- tering mechanism. Vibrational relaxation is also included, as well as finite temperature and field effects. The switch- ing rate in a current regime of about 1 to 10 nA scales highly non-linearly with current, and it is found to be gov- erned by vibrational “ladder climbing” and subsequent tun- nelling 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 inelas- tic scattering dominates over dipole excitation, and that the STM switch is stable also at room temperature. K. Zenichowski ( ) · T. Klamroth · P. Saalfrank Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam-Golm, Germany e-mail: zenichow@rz.uni-potsdam.de PACS 67.63.Gh · 68.43.Bc · 81.16.Ta · 82.37.Gk 1 Introduction It has been demonstrated more than 10 years ago that hy- drogen atoms can be desorbed from a hydrogen-covered Si(100)-(2 × 1):H surface by use of a STM (scanning tun- nelling microscope), operating at positive sample bias [1]. In this case electrons flow from the STM tip towards the surface, and two distinct regimes were identified, namely “above threshold” at high voltages (U> 7 V), and “be- low threshold” at lower bias voltage. Above threshold an Si–H antibonding resonance state at ≈ 7 eV can be di- rectly reached, and the desorption yield is higher than be- low threshold. Theoretical modelling [2, 3] reveals that in the above threshold regime the suddenly excited adsorbate moves along the repulsive, excited state potential away from the surface. Simultaneously, it is quenched within an excited state lifetime of τ el < 1 fs, such that desorption occurs in the ground state. Below threshold, on the other hand, a mecha- nism based on “ladder climbing” in the ground state towards the dissociation continuum is more likely. More recently, STM-induced switching of a single H atom on a half-covered (Si 2 –H) dimer from one of the two Si atoms to the other, was observed. In this case the STM operates at negative sample bias, with a maximal switch- ing rate at U =−2.7V[4, 5]. The reversible transfer of a H atom, from one well of a double-minimum potential to the other, can be considered as a simple atomic-scale “switch”. In these papers a short-lived (τ el ≈ 2 fs) hole res- onance ≈ 2.7 eV above the ground state was postulated to play a decisive role. In [6], the above threshold switching of H on a Si 2 H dimer was modelled within an open-system