Time-Resolving Monte Carlo Simulation for Structural Fluctuation on Low Temperature Solid Sate Surfaces

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We obtained the model potential(MP) tor the dimer system on Si(001) based on the first-principles calculations. Using MP, we performed the time-resolving dynamical Monte-Carlo simulation(DMCS) at 70 K. The results from DMCS reproduce well the experimental results the time-resolving constant-height current mode STM(TCHC STM) for Si(001) at 70K. We introduced the Hamiltonian consists of the terms of the electronic system and the elecron-vibration coupling term. The electron-vibration coupling constant is obtained by the energy of the vibrational state and MP. We obtained the effective temperature Te of the dimer vibratio, using the Hamiltonian. We showed that below 20 K, Te reaches about 250 K at 100 pA of the tunneling current. The high Te appearing below 20 K, essentially explains why the symmetric STM images are observed at low temperatures. When the substrate temperature increases around 20 K, Te starts to decrease steeply, and takes the nearly same values as the substrate temperature at 60K. These low Te explains why the asymmetric STM images recover in the temperature range higher than 50 K.The vibration of the dimer on the Ge(001) surface with a high vibrational number excited coherently by tunneling current of STM, was investigated. The transformation of the local structures reported in STM is shown to be driven by the dimer vibration excited coherently by the tunneling current the sample bias voltage dependence on the excitation rate is semiquantitatively reproduced by the quasi-dimensional character of the π^*-band. We show that the excitation rate has a term that does not decay with the distance from the STM tip for the one-dimensional band.On the basis of multifractal statistics, we have clarified the dominant coherent mode of the surface dimer system by the simulation mapped onto the 2D Ising system.