The present understanding of semiconductor surfaces with their rich variety of
reconstructions is based on a combination of a number of experimental and
theoretical tools. A major role on the theory side plays the density functional
theory (DFT), with predicting capabilities for energetics and structure of
surfaces. System size and time scales which are relevant for semiconductor
growth are not reachable by DFT due to the numerical costs. Actual growth
simulations can be distinguished by the level of explicit details included.
There are DFT based simulations including sophisticated details as well as
simple empirical models with a small parameter sets. 

In the talk an overview will be given discussing some of the recent developments
in the field of growth simulations. The first part discusses DFT based kinetic
Monte-Carlo (KMC) simulations for III-V semiconductors with capabilities to
predict experimental results [1]. The adsorption/desorption dynamics of group
V can be mapped onto a 9 states Potts model in a special case. In the second
part some surprising results from an empirical two component KMC simulations
including nanowire [2], step bunch [3], and quantum dot formation are presented.

[1] F. Grosse etal. Phys. Rev. Lett. {\bf 89}, 116102 (2002);
    Phys. Rev. B {\bf 66}, 075320 (2002); AIP Conf. Proceedings 893
    (28th ICPS Vienna), p. 15 (2007).

[2] F. Grosse etal. Journal of Cryst. Growth {\bf 212}, 128 (2000).

[3] E.T. Croke etal. Appl. Phys. Lett. {\bf 77}, 1310 (2000).
    J. Vollmer etal. arXiv:0711.1310v1 (2007).