Thin-film silicon solar cells are currently the most widely developed and applied thin-film solar cells. However, an improved conversion efficiency of the solar energy is desired for a wider application of thin-film silicon solar cells. In this direction, research has been conducted on the optical and electrical modeling of thin-film silicon solar cells, which indicates a direct relationship between the light scattering/trapping properties of the thin film interfaces and the conversion efficiencies of thin-film silicon solar cells . Recent studies on enhancing thin-film solar cell performance  have shown that film surface and interface morphology, characterized by root-mean-square roughness (RMS roughness, r) and root-mean-square slope (RMS slope, m), play an important role in enhancing absorption of the incident light by the semiconductor layers. Specifically, significant increase of conversion efficiency by introducing appropriately rough interfaces has been reported in several works . Therefore, it is important to tailor thin film surface morphology characteristics to desired values. In the context of modeling and control of thin film surface morphology, kinetic Monte Carlo (kMC) methods are widely used to simulate thin film microscopic processes based on the microscopic rules. However, the dynamics, scaling properties, and the influence of preferential migration on RMS slope and roughness of surface height profiles in thin film deposition processes has received no attention.
Motivated by the above considerations, this work focuses on the study of the dependence of film surface roughness and slope on the lattice size in thin film deposition processes. Two different models of deposition processes are considered: a random deposition with surface relaxation model and a process model involving deposition and surface migration. Both models are constructed on a square lattice in both one-dimension and two-dimensions using the solid-on-solid assumption. Kinetic Monte Carlo methods are used to simulate both models. In the random deposition with surface relaxation model, a just-deposited particle is allowed to instantaneously relax to a neighboring site of lower height. The deposition/migration process model involves a random particle deposition event and a surface particle migration event. The probability of migration of a surface particle depends on the substrate temperature and the number of the neighboring particles. Each neighboring particle contributes equally to the activation energy of the migrating particle. The surface roughness and surface slope are defined as the root-mean-squares of the surface height profile and of the surface slope profile, respectively. We find that both surface roughness and slope evolve to steady-state values at large times but are subject to different dynamics and scaling properties. A linear dependence and a logarithmic dependence of surface roughness square on the lattice size are observed in the one-dimensional and two-dimensional models, respectively, of the random deposition with surface relaxation model and the deposition/migration model with zero activation energy contribution from each neighboring particle. Furthermore, a stronger lattice-size dependence is found in the deposition/migration model with a significant migration activation energy contribution from each neighboring particle. This finding suggests that preferential migration (i.e., surface particles with zero or one nearest neighbors dominate the migration events) results in a stronger dependence of surface roughness on the lattice size in thin film deposition processes. Contrary, a weak lattice-size dependence is found for the surface mean slope, especially at large lattice sizes. Finally, the different dynamics of surface roughness and slope evaluated under different characteristic length scales is investigated, and the need for spatially distributed control actuation to induce desired roughness and slope levels at large characteristic length scales is demonstrated.
 J. Krc, F. Smole, and M. Topic. Analysis of light scattering in amorphous Si:H solar cells by a one-dimensional semi-coherent optical model. Progress in Photovoltaics: Research and Applications, 11:15-26, 2003.
 J. Springer and A. Poruba. Improved three-dimensional optical model for thin-film silicon solar cells. Journal of Applied Physics, 96:5329-5337,2004.
 J. Krc and M. Zeman. Experimental investigation and modelling of light scattering in a-Si:H solar cells deposited on glass/ZnO:Al substrates. Material Research Society, 715, 2002.
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