Optimization of transient temperature uniformity in RTP systems

Abstract

Independent, dynamic control of multiple lamps in a rapid thermal processing (RTP) system is a potential solution to the problem of transient wafer temperature nonuniformity. This brief presents a technique based on linear programming for minimization of worst-case error during temperature trajectory following, given a model of an axisymmetric, multi-lamp RTP system.

Optimization of rapid thermal processing for uniform temperature distribution on wafer surface

“…But the optimal location of heating lamps can be determined by steady optimization. If the locations of lamps are determined, the unsteady lamp power profile can be optimized by multivariable control [5]. So the scope of this study is confined to steady state.…”

“…They concluded that the radiative heat transfer by reflection had an insignificant effect on the heat transfer result of RTP and heat loss and that convective heat transfer must be considered to obtain uniform temperature distributions on the wafer surface. Norman [5,6] conducted studies for wafer uniformity in steady state and transient state by multivariable control of heating lamps. There are few studies on finding the optimum positions and temperatures of heating lamps for uniform temperature distribution on the wafer surface.…”

Optimal control of a CVD reactor for prescribed temperature behavior

“…Before concluding this section, let us mention a different optimization formulation for the CVD furnace problem proposed by Norman [9] [lo]. He did not try to solve the full optimal control problem as we are.…”

Convex optimization of wafer temperature trajectories for rapid thermal processing

“…In [6], Norman formulates the RTP feedforward trajectory generation problem as a convex optimization problem wit.h various linear constraints and a quadratic objective function. In this section, we first elaborate those linear constraints and define a suitable quadratic objective function.…”