(140f) Multiscale Modeling and Control of a Porous Thin Film Deposition Process
Thin film deposition process plays an important role in the semiconductor industry. For example, low pressure chemical vapor deposition (LPCVD) is widely used to deposit thin films of gate dielectrics and other materials as well. Due to the increased complexity and density of devices on the wafer in recent years, there is an stringent need to improve the operation conditions and yield and meet the requirements for the thin film microstructure.
For the modeling of the deposition process, there is large disparity of time and length scales between the gas phase and the wafer surface. As a macroscopic process, the dynamics of the gas phase can be adequately described by the balance equations and the conservation law. However, for the microscopic processes on the wafer surface, the assumption of continuum is not valid due to the magnitude of scales. Two different modeling methods have been developed to describe the evolution of the microscopic processes, kinetic Monte Carlo (kMC) models and stochastic differential equation (SDE) models. Recent research efforts have focused on the modeling and control design using the kMC models and the SDE models for the regulation of the film surface roughness and porosity. However, multiscale modeling and control of the thin film deposition process by bridging the scale disparity remain a challenging problem.
Motivated by these considerations, this work focuses on multiscale modeling and control of film thickness, surface roughness and porosity in a porous thin film deposition process. The microscopic processes on the wafer surface is modeled via kinetic Monte Carlo simulation on a triangular lattice with vacancies and overhangs allowed to develop inside the film. Stochastic and deterministic differential equation models are postulated to describe the evolution of the film surface height profile and the site occupancy ratio of the thin film accounting for the effect of deposition rate. The gas phase in the LPCVD reactor is modeled as a one-dimensional stagnant flow with surface reactions on the boundary. The two domains are incorporated via boundary conditions. The developed dynamic models are then used as the basis for the design of a multiscale model predictive control algorithm that includes penalty on the deviation of film thickness, surface roughness and film porosity from their respective set-point values. The reactor inlet concentration is selected as the manipulated input, which in turn affects the deposition rate and the film growth through the boundary conditions. Simulation results are provided to demonstrate the applicability and effectiveness of the proposed multiscale modeling and control approach.