Modeling, Identification, and Control of Rapid Thermal Processing Systems

Abstract

A wafer temperature control system is developed for rapid thermal processing (RTP) semiconductor manufacturing equipment. The control algorithm is based on a physical model describing the heat transfer effects in advanced RTP equipment. A model identification procedure is proposed to estimate the uncertain parameters of the model from a set of experiments. Through singular value analysis, the impact of equipment design on feedback controller development is studied. An internal model control (IMC) design methodology is used to develop a low-order multivariable feedback control algorithm. The feedback controller is coordinated with additional modules including feedforward control and gain scheduling to achieve improved performance and flexibility. The algorithms are applied to three different multizone RTP systems. Temperature controlled ramps are demonstrated from 20 to 900~ at 45~ with less than +_5~ during the ramp at high temperatures and less than +-I~ average nonuniformity during steady state as measured by three radially distributed temperature sensors.Rapid thermal processing (RTP) is a semiconductor manufacturing technology that performs single-wafer thermal processing operations including annealing, oxidation, and chemical vapor deposition./3 In order to achieve slip-free and uniform processing, it is necessary to maintain a uniform temperature distribution over the wafer during both steady-state and transient (fast ramping of wafer temperature) situations. Furthermore, this uniform distribution must be achieved for a range of operating conditions including different pressures, gasses, and processing temperatures. In this manner, an RTP system is available for flexible manufacturing applications that can adapt and optimize to changes in the processing specifications.Recent innovations in the design of RTP systems have provided the ability for achieving temperature uniformity over a range of processing conditions. The basic requirement of the equipment is the ability to vary the spatial energy flux distribution radiating to the wafer as the necessities for wafer temperature uniformity change as a function of operating conditions. To achieve this requirement, one approach involves the use of multiple concentric circular rings (or zones) of lamps that can be manipulated independently.In this paper, we describe the development of a multivariable automatic control system for multizone RTP systems. The controller is used to compute the set of powers to the lamp zones in response to feedback information provided by an array of sensors measuring temperature at multiple points on the wafer. The objective of the control system is to minimize temperature nonuniformity while tracking a desired temperature trajectory.The control strategy is based on a first-principles model of the energy transport mechanisms in RTP systems. The nonlinear model is developed specifically for the purpose of control design as opposed to ones developed for simulation applications ~'~ or developed from a black-box approach. 8-n The model re...

Control of semiconductor manufacturing equipment: real-time feedback control of a reactive ion etcher

“…A fairly complete survey of the various efforts along this direction may be found in [23]. Some representative works in the area of control of semiconductor manufacturing equipment are [2], [ 111, [22], [25], [26] and the references cited within. It is fair to say that at the present time, control-oriented modeling and real-time control of reactive ion etching is a open research problem.…”

Iterative learning control for spatio-temporal dynamics using Crank-Nicholson discretization

“…The heat transfer equation has been used as an example but the results are more general and can be easy extended to other PDEs with more space and time indeterminates that arise in applications, such as those detailed in Zhao (2005), Fiory (2001), Schaper et al (1994) The approach first requires discretization of the defining equations followed by the use of Lyapunov functions that satisfy sufficient but not necessary conditions for error convergence but do enable control law design to be undertaken using LMIs. This last feature offsets to some degree of the conservativeness arising from not using necessary and sufficient conditions.…”

Semi-Empirical Model-Based Multivariable Iterative Learning Control of an RTP System

“…First, according to (4), the net radiant heat input on the wafer segment is represented by (5) where denotes a wafer segment other than . From (3), the net radiant heat input can also be written as (6) Writing the above for each and collecting them into a vector form, the following is obtained:…”