Step-Edge Barriers on GaAs(001)
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F E=E +2E
E=E
Figure 1: One-dimensional illustration of a two-parameter simulation model (Clarke and Vveden-
sky [41). barriers to interlayer atomic transport. KINETIC MONTE CARLO MODEL Kinetic Monte Carlo (KMC) simulations of a solid-on-solid (SOS) model are at present the most versatile and powerful tool for investigating both epitaxial growth and the removal of material. The basic variant of the model we use was proposed as a direct descendant of the SOS model developed in the 1970s by Gilmer and co-workers [3] in which the crystal substrate is treated as a simple cubic lattice with neither bulk vacancies nor overhangs allowed. Clarke and Vvedensky [4] adopted a strategy very different from previous modeling work on growth of Ill-V compounds [5]. Instead of trying to replicate complicated details of GaAs(OO) surface chemistry, they developed a model for simulating growth under typical growth conditions, i.e., with sufficiently large As overpressure [1]. The model is thus based on the assumption that As incorporation kinetics are not a rate-limiting step of the growth process and need not be included explicitly in its description. The model can be thought of as focusing on the Ga incorporation while the effects of As incorporation and other fast processes, as well as specific features of the GaAs(OO I) surface such as the existence of surface reconstructions and the resulting anisotropy in surface diffusion and sticking coefficients, affect only the effective model parameters. This strategy allowed the authors of Ref. (4] to develop a model with only two free parameters while retaining the essential features of the growth kinetics. It is important to bear in mind that such a simplification restricts the applicability of the model (e.g., the effects resulting from variations of As pressure cannot be straightforwardly investigated) but this is outweighed by benefits of having only a few model parameters and higher computational efficiency. Two kinetic processes were included in the original model to describe growth (see Fig. 1): random deposition of atoms onto the substrate and migration of surface adatoms. Desorption is neglected in accordance with experimental observations [6]. Surface migration is modeled as a nearest-neighbor hopping process, with the hopping rate of the Arrhenius form, k(E, T) = ko exp(-E/kBT), where k0 is the attempt frequency (usually taken to be equal to 2kBT/h), T is the substrate temperature, kB is Boltzmann's constant, h is Planck's constant and E is the energy barrier to hopping. The barrier E depends on the adatom environment and comprises a substrate term, Es, and a contribution, EN, from each lateral nearest neighbor in the original position of the hopping atom (cf. Fig. 1). Note that the growth of GaAs was found to be best modeled using
Es >
EN.
Another important feature of the approach adopted in Ref. [4] concerns the modeling of the evolution of the RHEED specular-beam intensity during growth. While RHEED is in principle a straightforward experimental technique, its theoret
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