Yiming Lou

Estimation and control of surface roughness in thin film growth using kinetic Monte-Carlo models

Abstract In this work, we present an approach to estimation and control of surface roughness in thin film growth using kinetic Monte-Carlo (MC) models. We use the process of thin film growth in a stagnation flow geometry and consider atom adsorption, desorption and surface migration as the three processes that shape film micro-structure. A multiscale model that involves coupled partial differential equations (PDEs) for the modeling of the gas phase and a kinetic MC simulator, based on a high-order lattice, for the modeling of the film micro-structure, is used to simulate the process. A roughness estimator is constructed that allows computing estimates of the surface roughness at a time-scale comparable to the real-time evolution of the process using discrete on-line roughness measurements. The estimator involves a kinetic MC simulator based on a reduced-order lattice, an adaptive filter used to reduce roughness stochastic fluctuations and an error compensator used to reduce the error between the roughness estimates and the discrete roughness measurements. The roughness estimates are fed to a proportional-integral (PI) controller. Application of the proposed estimator/controller structure to the multiscale process model demonstrates successful regulation of the surface roughness at the desired value. 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.

Robust stabilization of infinite-dimensional systems using sliding-mode output feedback control

Sliding mode based feedback control has long been recognized as a powerful, yet easy-to-implement, control method to counteract non-vanishing external disturbances and unmodelled dynamics. Recently, research attention has focused on the development of sliding mode feedback control methods for various classes of infinite-dimensional systems. However, the existing methods are based on the assumption that distributed sensing and actuation is available, which significantly restricts their applicability to distributed process control applications. In this work, a sliding mode output feedback control method is developed for a class of linear infinite-dimensional systems with finite-dimensional unstable part using finite-dimensional sensing and actuation. Modal decomposition is initially used to decompose the original infinite-dimensional system into an interconnection of a finite-dimensional (possibly unstable) system and an infinite-dimensional stable system. Then, a sliding mode-based stabilizing state feedback controller is constructed on the basis of the finite-dimensional system. Subsequently, an infinite-dimensional Luenberger state observer, which utilizes a finite number of measurements, is constructed to provide estimates of the state of the infinite-dimensional system. Finally, an output feedback controller design is completed by coupling the infinite-dimensional Luenberger state observer and the sliding mode-based state feedback controller. Implementation, performance and robustness issues of the sliding-mode output feedback controller are illustrated in a simulation study of a distributed parameter system governed by the linearization around the spatially-uniform steady-state solution of the Kuramoto–Sivashinsky partial differential equation with periodic boundary conditions.

Feedback control of surface roughness in sputtering processes using the stochastic Kuramoto-Sivashinsky equation

This work focuses on control of surface roughness in sputtering processes including two surface micro-processes, diffusion and erosion. The fluctuation of surface height of such sputtering processes can be described by the stochastic Kuramoto–Sivashinsky equation (KSE), a fourth-order stochastic partial differential equation (PDE). Specifically, we consider sputtering processes, including surface diffusion and erosion, on a one-dimensional lattice and design feedback controllers based on stochastic PDEs to regulate the surface roughness at desired levels. We initially reformulate the stochastic KSE into a system of infinite stochastic ordinary differential equations (ODEs) by using modal decomposition. A finite-dimensional approximation of the stochastic KSE is then derived that captures the dominant mode contribution to the surface roughness. A state feedback controller is designed based on the finite-dimensional approximation to control the surface roughness. Feedback control of surface roughness in three different sputtering processes with different sputtering yield functions and different ratios of erosion and diffusion rates is subsequently studied. Kinetic Monte-Carlo simulations are first performed to simulate the evolution of the surface height fluctuation in the three sputtering processes. Then, a systematic identification approach is used to identify the parameters of the stochastic KSE models describing the sputtering processes by using the data from kinetic Monte-Carlo simulations. Specifically, the evolution of state covariance of the stochastic KSE models is directly obtained from multiple kinetic MonteCarlo simulation runs. The correlations between model parameters and the state covariance of the stochastic KSE models are established and the parameters of the stochastic KSE models are subsequently computed by using least-mean-square fitting so that the evolution of the surface roughness computed from the stochastic KSE models is consistent with that computed from kinetic Monte-Carlo simulations. Feedback controllers are designed and applied to kinetic Monte-Carlo models of the sputtering processes to control the surface roughness to desired levels.

Real-time carbon content control for PECVD ZrO/sub 2/ thin-film growth

We present a methodology for real-time control of thin-film carbon content in a plasma-enhanced metal-organic chemical vapor deposition process using combination of online gas phase measurements obtained through optical emission spectroscopy and off-line (ex situ) measurements of film composition obtained via X-ray photoelectron spectroscopy (XPS). Initially, an estimation model of carbon content of ZrO/sub 2/ thin films based on real-time optical emission spectroscopy data is presented. Then, a feedback control scheme, which employs the proposed estimation model and a proportional-integral controller, is developed to achieve carbon content control. Using this approach, a real-time control system is developed and implemented on an experimental electron cyclotron resonance high-density plasma-enhanced chemical vapor deposition system to demonstrate the effectiveness of real-time feedback control of carbon content. Experimental results of depositions and XPS analysis of deposited thin films under both open-loop and closed-loop operations are shown and compared. The advantages of operating the process under real-time feedback control in terms of robust operation and lower carbon content are demonstrated.

Fault-tolerant control of fluid dynamic systems via coordinated feedback and switching

Abstract This work addresses the problem of designing a fault-tolerant control system for fluid dynamic systems modeled by highly-dissipative partial differential equations (PDEs) with constrained control actuators. The proposed approach is predicated upon the idea of coordinating feedback controller synthesis and switching between multiple, spatially-distributed control actuator configurations. Using appropriate finite-dimensional approximations of the PDE system, a stabilizing feedback controller is designed for a given actuator configuration, and an explicit characterization of the constrained stability region is obtained. Switching laws are then derived, on the basis of these stability regions, to orchestrate the switching between the control actuator configurations, in a way that guarantees constraint satisfaction and preserves closed-loop stability of the infinite-dimensional system in the event of actuator failures. The results are demonstrated through an application of the proposed methodology to the suppression of wave formation in falling liquid films via the stabilization of the zero solution of the one-dimensional Kuramoto–Sivashinsky equation (KSE), with periodic boundary conditions, subject to actuator constraints and failures.

Nonlinear Feedback Control of Surface Roughness Using a Stochastic PDE

In this work, we develop a method for nonlinear feedback control of the roughness of a one-dimensional surface whose evolution is described by the stochastic Kuramoto-Sivashinsky equation (KSE), a fourth-order nonlinear stochastic partial differential equation. We initially formulate the stochastic KSE into a system of infinite nonlinear stochastic ordinary differential equations by using modal decomposition. A finite-dimensional approximation of the stochastic KSE is then derived that captures the dominant mode contribution to the surface roughness. A nonlinear feedback controller is then designed based on the finite-dimensional approximation to control the surface roughness. An analysis of the closed-loop nonlinear infinite-dimensional system is performed to characterize the closed-loop performance enforced by the nonlinear feedback controller in the closed-loop infinite-dimensional system. The effectiveness of the proposed nonlinear controller and the advantages of the nonlinear controller over a linear controller resulting from the linearization of the nonlinear controller around the zero solution are demonstrated through numerical simulations.

Optimal actuator/sensor placement for nonlinear control of the Kuramoto-Sivashinsky equation

In this work, we use the methodology that was recently proposed by Antoniades et al. (2001) to compute the optimal actuator/sensor locations for the stabilization, via nonlinear static output feedback control of the zero solution of the Kuramoto-Sivashinsky equation (KSE) for values of the instability parameter for which this solution is unstable. The theoretical results are illustrated through computer simulations of the closed-loop system using a high-order discretization of the KSE.

Dynamic output feedback covariance control of linear stochastic dissipative partial differential equations

In this work, we develop a method for dynamic output feedback covariance control of the state covariance of linear dissipative stochastic partial differential equations (PDEs) using spatially distributed control actuation and sensing with noise. Such stochastic PDEs arise naturally in the modeling of surface height profile evolution in thin film growth and sputtering processes. We begin with the formulation of the stochastic PDE into a system of infinite stochastic ordinary differential equations (ODEs) by using modal decomposition. A finite-dimensional approximation is then obtained to capture the dominant mode contribution to the surface roughness profile (i.e., the covariance of the surface height profile). Subsequently, a state feedback controller and a Kalman-Bucy filter are designed on the basis of the finite-dimensional approximation. The dynamic output feedback covariance controller is subsequently obtained by combining the state feedback controller and the state estimator. The steady-state expected surface covariance under the dynamic output feedback controller is then estimated on the basis of the closed-loop finite-dimensional system. An analysis is performed to obtain a theoretical estimate of the expected surface covariance of the closed-loop infinite- dimensional system. Applications of the linear dynamic output feedback controller to the linearized stochastic Kuramoto- Sivashinsky equation are presented.

Real-Time Feedback Control of Carbon Content of Zirconium Dioxide Thin Films Using Optical Emission Spectroscopy

Abstract In this work, we present a methodology for real-time carbon content feedback control of a plasma-enhanced metal organic chemical vapor deposition process using optical emission spectroscopy. Initially, an estimation model of carbon content of ZrO2 thin films based on real-time optical emission spectroscopy data is presented. Then, a feedback control scheme, which employs the proposed estimation model and a proportional-integral controller, is developed to achieve carbon content control. Using this approach, a real-time control system is developed and implemented on an experimental electron cyclotron resonance high density plasma-enhanced chemical vapor deposition system at UCLA to demonstrate the effectiveness of real-time feedback control of carbon content. Experimental results of the deposition process under both open-loop and closed-loop operations are shown and compared. The advantages of operating the process under real-time feedback control in terms of higher productivity, reduced process variation and lower carbon content are demonstrated

Robust stabilization of infinite-dimensional systems using discontinuous output feedback control

In this work, a discontinuous output feedback control method based on sliding modes is developed for a class of linear infinite-dimensional systems with finite-dimensional unstable part using finite-dimensional sensing and actuation. The control method is applied to a distributed parameter system governed by the linearization around the spatially-uniform steady-state solution of the Kuramoto-Sivashinsky equation subject to periodic boundary conditions.