Jianqiao Huang

Lattice-size Dependence and Dynamics of Surface Mean Slope in a Thin Film Deposition Process

Abstract This work focuses on the study of the dynamic behavior and lattice size dependence of the surface root-mean-square slope in a porous thin film deposition process taking place on a triangular lattice. The simulation results indicate that the expected mean slope square reaches quickly a steady-state value and exhibits a very weak dependence with respect to lattice size variation. The simulation findings are corroborated by an analysis of appropriate finite-difference discretizations of surface height profiles computed by an Edwards-Wilkinson-type partial differential equation that can be used to describe the dynamics of surface height profile in the thin film deposition process under consideration.

Modeling and control of aggregate thin film surface morphology using stochastic PDEs and a patterned deposition rate profile

This work focuses on modeling and control of aggregate thin film surface morphology for improved light trapping using a patterned deposition rate profile. The dynamics of the evolution of the thin film surface height profile are modeled by an Edwards-Wilkinson-type equation (a second-order stochastic partial differential equation) in two spatial dimensions. The thin film surface morphology is characterized in terms of aggregate surface roughness and surface slope. These variables are computed with respect to appropriate visible light-relevant characteristic length scales and defined as the root-mean-squares of height deviation and slope of aggregate surface height profiles, respectively. Analytical solutions of the expected aggregate surface roughness and surface slope are obtained by solving the Edwards-Wilkinson equation and are used in the controller design. The model parameters of the Edwards-Wilkinson equation can be estimated from kinetic Monte-Carlo simulations using a novel parameter estimation procedure. This parameter dependence on the deposition rate is used in the formulation of the predictive controller to predict the influence of the control action on the surface roughness and slope at the end of the growth process. The cost function of the controller involves penalties on both aggregate surface roughness and mean slope from set-point values as well as constraints on the magnitude and rate of change of the control action. The controller is applied to the two-dimensional Edwards-Wilkinson equation. Simulation results show that the proposed controller successfully regulates aggregate surface roughness and slope to set-point values at the end of the deposition that yield desired levels of thin film reflectance and transmittance levels.

Porosity control in thin film solar cells: Two-dimensional case

This work focuses on the simulation and control of a porous silicon thin film deposition process used in the manufacture of thin film solar cell systems. Initially, the process is simulated via kinetic Monte Carlo (kMC) method on a triangular lattice. Then a closed-form differential equation model is introduced to predict the dynamics of the kMC model and closed-loop system, and the model parameters in this model are identified by fitting to open-loop kMC simulation results. Finally, a model predictive controller (MPC) is designed and results demonstrate that both film thickness and porosity can be regulated to desired values.

Predictive control of aggregate surface morphology in a two-stage thin film deposition process for improved light trapping

This work focuses on the development of a model predictive control algorithm to simultaneously regulate the aggregate surface slope and roughness of a thin film growth process to optimize thin film light reflectance and transmittance. Specifically, a two-stage thin film deposition process, which involves two microscopic processes: an adsorption process and a migration process, is modeled based on a one-dimensional solidon-solid square lattice via kinetic Monte Carlo (kMC) method. The first stage of this process utilizes a uniform deposition rate profile to control the thickness of the thin film and the second stage of the process utilizes a spatially distributed deposition profile to control the surface morphology of the thin film. An Edwards-Wilkinson (EW)-type equation with appropriately computed parameters is used to describe the dynamics of the surface height profile and predict the evolution of the aggregate root-mean-square (RMS) roughness and aggregate RMS slope. A model predictive control algorithm is then developed on the basis of the EW equation model to regulate the aggregate RMS slope and the aggregate RMS roughness at desired levels.

Dependence of film surface roughness on surface migration and lattice size in thin film deposition

This work focuses on the study of the dependence of film surface roughness on surface migration and lattice size in thin film deposition processes. Two different models of thin film deposition processes, in both one-dimension and two dimensions, are considered: random deposition with surface relaxation model and deposition/migration model. Surface roughness is defined as the root-mean-squares of the surface height profile and is found to evolve (starting from a flat initial surface zero value) to steady-state values at large times. A linear and a logarithmic dependence of surface roughness square on lattice size are observed in the one-dimensional and two-dimensional lattice models, respectively, in both 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 when the migration activation energy contribution from each neighboring particle becomes significant.