Miroslav Kotrla

Theory and simulation of crystal growth

Crystal growth phenomena are discussed with special reference to growth from vapour. The basic concepts of crystal growth are recalled, including the different growth modes, the dependence of the growth rate on disequilibrium and temperature, and the atomic processes relevant for growth. The methods used in crystal growth simulations are reviewed, with special reference to kinetic Monte Carlo methods. The roughness of growing surfaces, and the roughness properties of the discrete and continuum growth models (the latter being described via stochastic differential equations) are discussed, together with the special phenomena occurring in the vicinity of the roughening temperature. A number of simulations based on the six-vertex model and on kinetic counterparts of the BCSOS model are reviewed. Finally, the instabilities arising during growth are considered, including a discussion of phenomena such as dendritic growth and ramified cluster growth and reviewing the recent, extensive studies concerning unstable MBE growth.

Crossover effects in the Wolf-Villain model of epitaxial growth in 1+1 and 2+1 dimensions.

A simple model of epitaxial growth proposed by Wolf and Villain is investigated using extensive computer simulations. We find an unexpectedly complex crossover behavior of the original model in both 1+1 and 2+1 dimensions. A crossover from the effective growth exponent

Heterogeneous nucleation and adatom detachment at one-dimensional growth of In on Si(100)-2 X 1

\beta_{\rm eff}\!\approx\!0.37

Interplay between kinetic roughening and phase ordering

to

Competing mechanisms for step meandering in unstable growth

\beta_{\rm eff}\!\approx\!0.33

Self-organized growth of Ag islands on Si(1 1 1)-(7 × 7)-optimization of an STM experiment by means of KMC simulations

is observed in 1+1 dimensions, whereas additional crossovers, which we believe are to the scaling behavior of an Edwards--Wilkinson type, are observed in both 1+1 and 2+1 dimensions. Anomalous scaling due to power--law growth of the average step height is found in 1+1 D, and also at short time and length scales in 2+1~D. The roughness exponents

Continuous and correlated nucleation during nonstandard island growth at Ag/si(111)-7×7 heteroepitaxy

\zeta_{\rm eff}^{\rm c}

Extremal Dynamics Model on Evolving Networks

obtained from the height--height correlation functions in 1+1~D (

Effects of mobile and immobile impurities on two-dimensional nucleation

\approx\!3/4

Kinetic roughening and phase ordering in the two-component growth model

) and 2+1~D (