We review the dynamics of a high symmetry cristalline surface which grows epitaxially via atomic or molecular beams. We show the difficulties to give a rigorous continuum description of the growth dynamics in two dimensions; in one dimension the physics of microscopic processes is better understood and several models have been studied, analytically and numerically.

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Elastic effect on the adsorbate morphology is studied using a deformable lattice model in two dimensions. Surface defects such as adatoms or steps deform the substrate and induce long-range repulsive interaction inversely proportional to the square of their separations. For a heteroepitaxial overlayer the strain induces the shape transition from a monolayer to a multilayer island for a given island slze.

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We have used electron microscopy to study the drift velocity of micrometer-size monolayer-thick silicon islands on Si (001) and Si (111) under near equilibrium conditions and direct current (DC) heating. At temperatures between 1000℃ and 1100℃, the island on Si (001) perform a gliding motion at constant velocity (at a given T) in or against the current direction depending on the island reconstruction. The Stoyanov' model can explain very well this island motion. Concerning the Si (111), our results obtained at around 1200℃ show that the islands move in the opposite direction of DC , this is a qualitative prove of the existence of an Ehrlich-Schoebel effect on Si(111). The model of O. Pierre-Louis and T.L. Einstein can be used to explain this mobility.

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We begin by reviewing theoretical machinery for deducing the strength of repulsions between steps from spatial correlations. There are some noteworthy advantages to studying step-step correlation functions rather than just the terrace width distribution function (i,e, correlations between adjacent steps) . Highlights of this work are summarized. These ideas and traditional analyses of spatial and temporal correlations are applied to REM data for vicinal Si(111) above the sublimation temperature, but with a compensating flux, and find striking behavior for the apparent step repulsion strength. To distinguish the atornicscale mechanisms of evaporation-condensation and diffusion step-to-step, correlations of symmetric combinations of step displacements can be used. This idea is being applied to a chemically heterogeneous Si surface as well as the Si data. Using a Schrodinger equation approach, one can not only present a justification for the generalized continuum Wigner surmise but also contend with complicated step interactions more complicated than inverse square, as might occur due to step interactions mediated by surface states or for small step separations where contributions beyond the leading asymptotic term become important.

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By carrying out Monte Calro simulation, we study step bunching induced by drift of adatoms with anisotropic surface diffusion. In our model, like a Si(001) vicinal face, two types of terraces appear alternately. One is the terrace with fast diffusion parallel to the step and the other is the terrace with fast diffusion perpendicular to the step. When the drift is perpendicular to the steps, the step pairing occurs irrespective of the drift direction. And large bunches appear in a late stage, which qualitatively agrees with the experiments. However, bunching features in the steady stage vary with the drift direction.

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Following some previous work [O. Pierre-Louis: Phys. Rev. Lett. 87 106104 (2001)], a modifed expression of the step free energy is presented, that accounts for the existence of an intermediate adsorption state at the step.A step model is derived from this free energy. It is shown to exhibit a low temperature regime qualitatively different from the traditional approach. The macroscopic transparency kinetic coeffcient is explicitely related to the kink density. We also include the possibility of direct attachment to the kinks.

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Structural transitions on silicon surfaces during growth and oxygen exposure were investigated by in situ ultra-high vacuum reflection electron microscopy and atomic force microscopy. Consequent stages of gold three dimensional island ordering on silicon (111) surfaces were visualized over a wide temperature range of the substrate. Initial stages of surface oxidation and thermal etching were analysed in details.

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The step structure transition between a regular step and a bunched step on vicinal Si (111) surfaces induced by DC is studied by the kinetic Monte Carlo simulation in a terrace-adatom-step-kink (TASK) model of a vicinal surface. In the TASK model, effective force due to DC is taken into account explicitly on both diffusion process of Si adatoms and capture/emission process at a step edge. In the capture-limited regime, step bunching is induced by stepdown force and a regular step is formed by step-up force, corresponding to the experimental temperature range I. In the diffusion-limited regime, step bunching is induced by step-up force and in-phase wandering is induced on a regular step by step-down force, corresponding to the experimental temperature range II. The relation of the two regimes with "non-transparent" and "transparent" conditions at step edges is discussed.

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We have made a statistical mechanical study of vicinal surface with adsorption with coverage Q being less than 1. In the case of Langmuir adsorption, where the lateral interactions among the adsorbates are absent, the system shows the universal behavior of vicinal surface, Gruber-Mullins-Pokrovsky-Talapov (GMPT) behavior The step tension, the step stiffness and the roughening transition temperature are modified by adsorbates. In general cases where the lateral interactions among adsorbates are present, there occur non-GMPT phenomena such as the first-order transition in equilibrium crystal shape and the thermal step bunching.

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A newly developed ab initio-based approach was applied for understanding adsorption-desorption behavior during molecular beam epitaxial growth of GaAs. The ab initiobased approach incorporates free energy of vapor phase; therefore we can calculate how adsorption and desorption depend on growth temperature and beam equivalent pressure (BEP). Versatility of the theoretical approach was confirmed by the calculation of Ga adsorption-desorption transition temperatures and transition BEPs on Ga-rich GaAs (001)-(4×2)β2 surface. Furthermore, in order to check the feasibility of the theoretical approach for prediction of adsorption-desorption behavior of As_2 molecules, the conditions where GaAs(001)-c (4×4) reconstructed structure is stable were investigated by the calculations of stability of As-dimers on the top surface under the various temperatures and BEPs. We also applied the theoretical approach to Ga diffusion length while staying on the GaAs (001)- (2×4)β2 and - (2×4)β1 surfaces and As pressure dependence of GaAs growth rate.

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The morphologies of the terraces of a GaAs(001)-β2 (2×4) surface vicinal to (111) B in the homoepitaxial growth condition are studied by the kinetic Monte Carlo simulations. The growth simulations revealed that the morphologies of these terraces depend on the relative phase of the β2 (2×4) reconstruction between an upper terrace and a lower one. In addition, this effect leads to the growth asymmetry of a two-dimensional island. These results are in agreement with the scanning tunneling microscopy images reported in the literature.

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We have successfully performed a non-equilibrium molecular dynamics simulation of the crystal-melt interface of Lennard-Jones system. The heat balance equation, k_sG_s -k_LG_L = LρV, has been confirmed, where k_s and k_L are the thermal conductivities of the crystal and the melt, G_s and G_L are the temperature gradients in the crystal and the melt, respectively, and L, ρ, and V are the latent heat of fusion, the density, and the pulling velocity, respectively. There seem to be a tendency that V increases as G_s/G_L increases. Measurement problems similar to those in experiments are pointed out.

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A three-dimensional finite element computer code was developed to deal with the thermal stress analysis of tetragonal single crystals. They have crystal anisotropy in the elastic constants and thermal expansion coefficients, so three-dimensional analysis is required for the exact calculation of the thermal stress. A tensor transformation technique was used to obtain the components of the elastic constant matrix and the thermal strain or thermal expansion coefficient vector corresponding to an arbitrary growth direction. Using this computer program, we performed the thermal stress analysis of a PMO (PbMoO_4) bulk single crystal for various growth directions. The relationship between the thermal stress and the crystal quality was discussed.

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