Time-Fluctuation of the Dimer Structure on a Ge(001) Surface Studied by a Monte Carlo Simulation and a First-Principles Calculation

Model potential of dimer system and coherence length of electron injected by scanning tunneling microscope on Ge(001) surface

“…The term of V 42 is required to obtain adequate barrier height. We have reported that the model potentials containing the term of V 42 obtained for the Si(0 0 1) and Ge(0 0 1) surfaces well reproduce results of the time-resolved constantheight current mode STM [34,37].…”

“…The third-body and higher body terms in U are assumed to be neglected for simplicity. In the model potential reported previously [37], U one is defined by piecewise interpolation between the energies per dimer in the p(2 Â 1) structure ðE pð2Â1Þ ðhÞÞ for the buckling angle h calculated by FPC [24,25]. It is very difficult to obtain the second partial derivative from the previous model potential that includes the piecewise interpolation.…”

“…The motion of the phase boundary is represented as a function of the dimer buckling angle at the phase boundary. The total energy E P ðhÞ of the minimum supercell including the phase boundary on the Ge(0 0 1) surface has been obtained by FPC [25,37] for buckling angles h of the phase boundary.…”

“…The frequency x=ð2pÞ on the Ge(0 0 1) surface is estimated to be 3 THz using the theory of absolute reaction rates and the time-resolved dynamical Monte Carlo simulation [37]. From the frequency, hx is found to be 12 meV on the Ge(0 0 1) surface.…”

“…The coupling constant on the Si(0 0 1) surface [9,31] is obtained from the second partial derivative of the model potential [34] on the Si(0 0 1) surface. We have already obtained the model potential for buckling angles of the dimer system on the Ge(0 0 1) surface [37]. The model potential, however, is not effective for obtaining the second partial derivative, because the model potential on the Ge(0 0 1) surface has a term defined by the piecewise-polynomial approximation between the energies calculated by FPC [24,25].…”