IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 16, NO. 4, NOVEMBER 2003 621 Adaptive Control Approach of Rapid Thermal Processing Jin Young Choi, Member, IEEE, Hyun Min Do, Student Member, IEEE, and Hong Seok Choi Abstract—This paper presents an adaptive control approach for achieving the control of the wafer temperature in a rapid thermal processing system (RTP). Numerous studies have addressed the temperature control problem in RTP and most researches on this problem require exact knowledge of the systems dynamics. However, it is difficult to acquire this exact knowledge. Thus, various approaches cannot guarantee the desired performance in practical application when there exist some modeling errors be- tween the model and the actual system. In this paper, an adaptive control scheme is applied to RTP without exact information on the dynamics. The system dynamics are assumed to be an affine nonlinear form, and the unknown portion of the dynamics are estimated by a neural network referred to a piecewise linear ap- proximation network (PLAN). The controller architecture is based on an adaptive feedback linearization scheme and augmented by sliding mode control. The performance of the proposed method is demonstrated by experimental results on an RTP system of Kornic Systems Corporation, Korea. Index Terms—Adaptive feedback linearization, PLAN, RTP, sliding mode control. I. INTRODUCTION R APID thermal processing system (RTP) is a state-of- the-art technique for performing the necessary wafer fab- rication processes such as annealing, oxidation, chemical vapor deposition, etc. It has several advantages over conventional furnaces. However, some problems have prevented RTP from being applied in production environments. The main problem is temperature control. The purpose of temperature control in RTP is to provide accurate tracking to a given reference profile and to maintain a uniform temperature across the wafer [1]–[5]. Numerous studies have recently addressed this problem and most researches on this problem require exact knowledge of the systems dynamics. In the early days, most approaches to temperature control in RTP were based on the classical pro- portional-integral-derivative (PID) control method with a single lamp group and a single sensor. Norman [1] showed how an RTP system with multiple independently controllable lamps could be used to control the wafer temperature. By using linear pro- gramming techniques, he formulated and solved the problem of minimizing the worst error in the wafer temperature profile at steady-state and transient state. Since this method is based on an Manuscript received July 30, 2002; revised July 12, 2003. This work was supported by the Brain Research Program and by Kornic Systems Corporation. J. Y. Choi and H. M. Do are with the School of Electrical Engineering and Computer Science, ASRI, Seoul National University, Kwanak-gu, Seoul 151-742, Korea (e-mail: jychoi@ee.snu.ac.kr; hmdo@iccl.snu.ac.kr). H. S. Choi is with Nexreal Inc., ASRI, Seoul National University, Kwanak-Ku, Seoul 151-742, Korea (e-mail: hschoi@neuro.snu.ac.kr). Digital Object Identifier 10.1109/TSM.2003.818961 exact mathematical model, the performance may not be satisfac- tory in a real system in the presence of modeling errors between the actual RTP system and the mathematical thermal model. Schaper et al. [6] suggested a controller that combined feed- back, feedforward, and gain-scheduling mechanisms. In par- ticular, the feedback mechanism was used to compensate for modeling errors and disturbances. The feedback controller can significantly reduce the tracking error arising from the modeling errors when the controller parameters are well tuned. However, when the characteristics of RTP dynamics change in on-line en- vironments, it is not easy to tune automatically the controller parameters. The authors have proposed an iterative learning ap- proach to handle such modeling errors [7]. However, in the itera- tive learning approach, the initial conditions should be the same at every iteration, which is difficult to do in real situations and the performance might not be satisfactory for the time-varying systems. In this paper, we propose an adaptive control scheme to achieve a stable output tracking even in the time-varying systems. The overall control system is composed of a nonlinear dynamics estimator which estimates an unknown portion of the system dynamics on-line using PLAN, a controller which calculates a proper control input using a feedback linearization method and sliding mode control, and a parameter adaptation part which tunes parameters according to the adaptive laws. We also show that all variables in the proposed control system are bounded and the output tracking error converges to zero asymptotically. This paper is organized as follows. In Section II, the RTP structure and mathematical thermal model are introduced. Section III describes the controller structure and adaptation laws. Section IV presents experimental results for temperature control of the RTP system developed at Kornic Systems Corpo- ration in Korea, and finally, conclusions are drawn in Section V. II. RTP STRUCTURE AND MODELING The RTP system considered in this paper, which was devel- oped at Stanford University [1], has a three-ringed circular sym- metric lamp configuration with independent control of power to each ring. Temperature is measured at three points across the wafer, i.e., at the center, the middle, and the outer position. The overall system is, thus, a three-input, three-output system. A schematic of the system is shown in Fig. 1 [8]. The dynamics of this system are suggested by [1], [9]. It is an approximation to the heat equation in cylindrical coordinates. The wafer is partitioned into concentric elements, one cylin- drical, and the others annular. The temperature of all the wafer 0894-6507/03$17.00 © 2003 IEEE