Surface Reconstruction and Growth on InAs(001) Surfaces: From Ab Initio to Level Sets

Christian Ratsch

Department of Mathematics, UCLA,

Los Angeles, CA90095-1555

e-mail: cratsch@math.ucla.edu

In this talk, the stability of different surface reconstructions on InAs(001) and modeling of subsequent growth on such surfaces will be discussed. Density-functional theory (DFT) calculations predict four different surface reconstructions to be stable at different chemical potentials [1]. The two dominant reconstructions are the b2 (2 × 4) for high As, and the a2 (2 × 4) for low As overpressure. This trend is confirmed by scanning tunneling microscopy of carefully annealed InAs(001) surfaces. The change of this behavior upon application of external strain will be discussed.

Although DFT has been shown to accurately describe the energetics on semiconductor surfaces, it remains a very challenging task to model the kinetics on such surfaces. One question that arises in modeling epitaxial growth on III/V semiconductors is: How much detail is needed in such models ? In particular, do we need to resolve every atom on the surface, or can we accurately describe epitaxial growth with a continuum-type model with effective parameters ? In this talk, the merits and disadvantages of a very detailed kinetic Monte Carlo (KMC) method [2], and a continuum-type island dynamics model based on the level set technique [3,4] will be compared.

The high resolution KMC model is based on an energy functional that uses parameters calculated from DFT as input. By construction, it keeps track of every atom (and dimer) on the surface. It will be shown that such a model can, for example, properly reproduce the transition of growth in the a2 (2 × 4) regime to growth in the b2 (2 × 4) regime.

In contrast, adatoms are not resolved explicitly in our island
dynamics model that employs the level-set technique.
Instead, adatoms are treated by solving a mean-field diffusion equation.
Island boundaries for islands in the n*th* layer are
defined by the set of curves f= n, where f is the so-called level-set function.
The island boundaries evolve with a velocity that is
obtained from the solution of the diffusion equation.
Results for a simple cubic model in comparison to a
corresponding KMC model will be shown [5]. Finally, the possible
extension of such a model to describe growth of III-V
semiconductor systems will be discussed.

[1] C. Ratsch, W. Barvosa-Carter, F. Grosse, J.H.G. Owen, and J.J. Zinck,
Phys. Rev. B **62**, R7719 (2000).

[2] F. Grosse, W. Barvosa-Carter, and M.F. Gyure, submitted.

[3] S. Osher and J.A. Sethian, J. Comput. Phys. ** 79**, 12 (1988).

[4] S. Chen et al., J. Comput. Phys., in press.

[5] C. Ratsch, M.F. Gyure, S. Chen, M. Kang, and D.D. Vvedensky, Phys. Rev. B **61**,
R10598 (2000).