(369q) Multivariable Control of Thermal Budget for Rapid Thermal Processing Systems
Single wafer rapid thermal processing (RTP) is widely used in the fabrication of semiconductor devices. It has become one of the key technologies due to faster wafer processing with precise control of thermal budget. The thermal budget is an important process issue contributed from the duration and maximum of temperature beyond a specific reference value. This index needs a tight process control in many processes, such as rapid thermal annealing, oxidation in semiconductor manufacturing and reflow soldering in IC packaging industry. The traditional annealing process uses a soak-shaped temperature profile. However, as dimension keeping shrinking, the demand of shallow junctions requires very tiny and precise applied thermal energy. Therefore, the spike annealing process is the way to keep scaling requirements.
The criteria of temperature trajectory for thermal budget control usually contain three indices: the duration of exceeding the reference value, the maximum temperature, and the ramp-up/down rate. As a result, a triangular-shaped set-point profile is usually applied for thermal budget control. In literature, various control methods have been proposed for RTP to follow the desired temperature trajectory. But most of them deal with the soak annealing process. However, achieving desired thermal budget by designing a tightened servo control system is difficult and complex in spike annealing process due to high set-point ramp-up/down rate. Therefore, our previous work (Lee et al., 2009) considered targeting the control performance on the indices for thermal budget, instead of set-point tracking, by designing both the set-point profile and the controller. In this way, the thermal budget can be precisely controlled and the controller (PI or PI2D) design is much simpler. However, the previous work used a simple first-order model to represent the RTP system and considered the single-input single-output (SISO) control problem only. In practice, the RTP system is a multivariable process in nature since the wafer temperatures at different positions are controlled by manipulating the power sources from several rings of tungsten-halogen lamps. Thus, the wafer temperature uniformity is also a very important specification. Moreover, the RTP system is more accurately modeled as a nonlinear model due to effects of thermal radiation. To solve theses problems, this study extends the previous work to multivariable control scheme based on nonlinear models of RTP system.
This paper proposes the use of block-oriented nonlinear models, such as Wiener model or Hammerstein-Wiener model, to represent the RTP system. In a Hammerstein-Wiener model, an input nonlinear static function, Fi, a linear dynamic subsystem, G, and an output nonlinear static function, Fo, are connected in a series. An algorithm is proposed to identify a Hammerstein-Wiener model, and then the identified model can be used to design a simple linearizing control system. The resulting control system is equivalent to a linear control system so that the earlier developed thermal budget control approach for SISO system can be directly applied to design the linear controller for the linear dynamic subsystem, G. Simulation examples will be given to demonstrate that RTP thermal budget can be precisely controlled and wafer temperature uniformity can be maintained by the proposed nonlinear multivariable control strategy.
References: Lee B. C., Su A. J. and Jeng J. C. "Thermal Budget Control for Processes with Spike-Shaped Temperature Profile: Application to Rapid Thermal Annealing," Proc. CACS International Automatic Control Conference, 2009.