Reentrant Growth in Kinetic Thin-Film Deposition on Stepped Surfaces
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simplicity, we outline only the part relevant to the current work. In brief, we have considered three microscopic events, namely, particle impingement, evaporation and surface diffusion. The impingement is characterized by an impingement flux J, which takes the simple form J = Jeq (1+(X)
,
(1)
where Jeq is the equilibrium impingement flux, and a is a parameter that characterizes the net deposition of particles with respect to Jeq- After impinging on the surface, particles can either remain at the original site, return to the vapor (evaporate) or continue to wander to an unoccupied neighboring site (surface diffusion). The rates of both evaporation and surface diffusion are sensitive to the local configuration of the site from which an atom is to be dislodged. Following our earlier work [2,3], we cast the evaporation rate into the site dependent form (2) Ki- = v exp(-Ei/kT) , where v is a lattice vibration factor and Ei is the total interaction (evaporation) energy of the interfacial atom i with its solid neighbors. To simplify the problem, in this work we have only included particle interactions with the nearest solid neighbors characterized by a bond strength For surface diffusion, the hopping rate of an atom obeys the Arrhenius kinetic equation Ki -.j = Vs exp(-BEi/kT) ,
where v . is a surface vibration factor and 8Ei the activation energy: 8Ei = moL+ "qno// ,
(3)
(4)
with j_L being the diffusion barrier associated with the underlying substrate (in) atoms (m= 1 for a simple cubic lattice and considering the first nearest neighbor interaction only), and // the bond strength with the lateral neighboring (n) atoms, and -q(< 1) a dimensionless parameter characterizing the effective contribution to the 8Ei from the lateral bonds. This equation is based on the fact that a diffusing atom must completely break its vertical bonds with the underlying atoms but only needs to partially break its lateral bonds with the solid neighbors on the same 0//= 0 (for homoepitaxy). The vs, in layer. In our simulation, we have chosen i1= 0.5, and j_L= general, is different from the v in Eq.(2) for evaporation. However, in this simulation we have neglected the difference. The corresponding probabilities for attachment, detachment and surface diffusion can be obtained from Eqs.(l)-(3) [3]. The final input parameters in the simulation are only a and &/kT. The simulation is conducted for a simple cubic lattice in square areas of at least 60 lattice-units. To simulate a vicinal surface, a peculiar periodic boundary condition in the ydirection with vertical-shift along the z-direction is considered. That is, if an atom leaves from the lowest terrace on the far right it will return to the highest terrace on the far left at the same x value. The actual shift is determined by the tilting angle of the vicinal surface [3]. For the simulation of a screw dislocation, a slip line cut vertically from the middle of the surface is assumed [2], at the beginning of the simulation. To mimic the high vacuum condition and large mean-free path of atom
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