Solid-on-Solid Monte Carlo Investigation of Islanding Kinetics During Heteroepitaxy
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on two dimensional sub-monolayer deposits. We demonstrate that our results can be interpreted in the context of a simple model which proposes the existence of a 'probabilistic nucleation barrier'. SIMULATION TECHNIQUE Our simulation employs a modified solid-on-solid Monte Carlo algorithm which is similar to that used in other studies of the early stages of epitaxy [2]. Our simulation is strictly twodimensional, only the first layer above the surface may be occupied by deposited or diffusing adatoms. A square grid of discrete lattice points represents the surface of a bulk-terminated < 100> face of a simple cubic crystal. In order to avoid boundary effects, periodic boundary conditions are employed so that an adatom leaving one side of the simulation reappears on the opposite side. This also allows clusters to extend across the boundary of the simulation. Several values representing both material properties and experimentally accessible parameters are required at runtime. These are the surface diffusion activation energy, Ed, the additional surface diffusion activation energy for an adatom which has formed n nearest neighbor bonds, nEb, the thermal energy of the system, kT and the deposition rate, d. The first two are discussed below. The depostion rate is the frequency at which new atoms are added to the system and is given by an integer which corresponds to the number of program cycles executed before another atom is deposited. A depostion rate of 1k means that the simulation will attempt to jump all of the present particles 1000 times before it deposits a new atom. New atoms are added to random unoccupied sites chosen by succesive calls to the random number generator, the first call chooses the row and the second call choses the column for depsition. All simulations reported here employ a 1282 grid. 53 Mat. Res. Soc. Symp. Proc. Vol. 399 1996 Materials Research Society
The diffusion activation energies, Ed and Eb are material specific parameters and their ratios to the thermal energy determine the probabilities that a given adatom will jump during any time step through the usual Arrhenius expression. For convenience, we consider only the probability that an adatom may jump during any time step P
-(E d + nEb )I/kT
) p x(dflb/T= P(P 1 )nl
(1)
Where Po is the probability that a lone adatom jumps during any time step. PI is a factor representing the change in an atom's jump probability as it forms nearest neighbor bonds. Nearest neighbors are atoms adjacent to the atom being tested in the up, down or either of the sideways directions (i.e. along type directions). Atoms occupying sites adjacent to the atom being tested along type directions are not counted as nearest neighbors. Whether an atom jumps is determined by comparison to a random number chosen on the interval [0,1], if this random number is less than the jump probability for that atom, the atom jumps. The direction of the jump
is chosen by a further call to the random number generator. Jumps on the square grid are only to unoccupied nearest neighbor si
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