Feedback control of surface roughness of GaAs [001] thin films using kinetic Monte-Carlo models

We follow the methodology presented in Y. Lou and P.D. Christofides (2003) to study estimation and control of surface roughness of gallium arsenide (GaAs) [001] thin films during deposition in a horizontal-flow quartz reactor using triisobutylgallium (TIBGa) and tertiarybutylarsine (TBAs) as precursors and H/sub 2/ as the carrier gas. The adsorption of TIBGa onto the surface and the migration of Ga atoms on the surface are considered as the two rate-limiting steps in the film growth and are explicitly modelled within a kinetic Monte-Carlo simulation framework. The energy barriers and the pre-exponential factor of the migration rates of Ga atoms on the surface used in the simulations are initially determined by fitting the simulation results to experimental data reported in D.C. Law, et al, (2000). Then, a roughness estimator is constructed that allows computing estimates of the surface roughness of the GaAs thin films at a time-scale comparable to the real-time evolution of the process using discrete on-line roughness measurements. The roughness estimates are fed to a proportional-integral (PI) feedback controller, which is used to control the surface roughness to a desired level by manipulating the substrate temperature. Application of the proposed estimator/controller structure to the process model based on a large-lattice kinetic Monte-Carlo simulator demonstrates successful regulation of the surface roughness to the desired level. The proposed approach is shown to be superior to PI control with direct use of the discrete roughness measurements. The reason is that the available measurement techniques do not provide measurements at a frequency that is comparable to the time-scale of evolution of the dominant film growth dynamics.