MONTE-CARLO SIMULATION OF EQUILIBRIUM THERMAL ROUGHENING OF THE GE(001)2 X-1 SURFACE

Equilibrium thermal roughening of the Ge(001)2 x 1 surface is investigated using Monte Carlo (MC) simulations. The surface model incorporates explicitly the tetrahedral crystal structure and the dimerization of surface atoms. Atom-atom interactions extending as far out as second-nearest-neighbor sites are considered. This study is the first MC simulation of the equilibrium roughening behavior of a reconstructed semiconductor surface. Simulation of the equilibrium surface structure of the Ge(001)2 x 1 surface through a temperature range permits a determination of the temperature-dependence of such quantities characterizing the surface as the rms surface roughness and calculated surface X-ray diffracted intensities of certain reflections. Recent experiments have determined the temperature-dependence of these two quantities in the real system, enabling us to compare simulation and experiment. Our simulations provide qualitative agreement with experimental data and support the postulated roughening mechanism. Discrepancies between experiment and simulation are believed to be caused mainly by system size effects. The roughening transition in this Ge(001)2 x 1 surface model appears to be different to the Kosterlitz-Thouless transition which occurs in the solid-on-solid (SOS) model. We assess the influence upon the roughening behavior of incorporated details of the surface model such as the reconstruction and the presence of second-nearest-neighbor interactions.