| We investigated two problems related to the statistical physics of crystal surfaces using Monte Carlo simulations. First, we studied a solid-on-solid model of a layered crystal, which has five layers per repeat period in the direction normal to the surface and with only nearest-neighbor interactions, using Metropolis Monte Carlo (MC) simulation to investigate the relationship between crystal structure and the corresponding surface phases. Equilibrium properties, such as the surface specific heat, interface width, and autocorrelation times, are studied as a function of temperature and system size. Results indicate three distinct surface phases exist in this model: a low temperature flat phase, an intermediate-temperature disordered but flat phase, and a high-temperature rough phase. We suggest the possibility of introducing several intermediate phases, as well as a rough phase, in a single system by appropriate modulation of the periodicity of the crystal structure normal to the surface. At the same time, growth simulations show an interesting growth-induced smoothing in the intermediate phase where, at low supersaturations, the growing intermediate phase has a smaller interface width than it does in equilibrium.; Second, we studied surface morphology dynamics in a model of impurities interacting with a growing spiral using Kinetic Monte Carlo (KMC) method. We propose that growing spiral steps emerging from screw dislocations can interact with diffusing impurities to form spatially-ordered, self-assembled quantum dot arrays. This hypothesis is suggested by the micrometer-scale growth hillocks on natural graphite crystals. We have developed an atomistic solid-on-solid (SOS) model of a (001) surface of a simple cubic crystal and carried out Kinetic Monte Carlo simulations to investigate this hypothesis. We studied the effects of interaction energies, diffusion lengths, temperature, and chemical potential on the growth rates, step flow, kink motion and impurity diffusion and segregation. Under appropriate conditions the impurity atoms clustered together at the corners of the growth spiral. Our results suggest that a screw-dislocation-generated growth spiral may be employed as a template for controlling of the spatial organization in quantum dot self-assembly. |
