Optimization of Wafer Temperature Uniformity in Rapid Thermal Processing Systems

During rapid thermal processing (RTP) of semiconductor wafers it is essential that the wafer temperature closely tracks a pre-speci ed temperature trajectory and that the temperature pro le across the wafer is nearly uniform whenever the wafer is at high temperatures. This paper considers axisymmetric RTP systems with multiple independently-controllable lamps. In such systems the relative lamp power settings can be adjusted so that the lamps provide a range of distributions of power over the wafer; this is useful because the ideal distribution of incident energy varies according to processing conditions and changes substantially during a single process cycle. In this paper numerical techniques are given for nding lamp power settings to minimize temperature error across the wafer both during steady-state hold and during transients; these numerical techniques involve the formulation of the minimumtemperature error problem as a linear programming problem. A heuristic scheme for near-optimal trajectory following is presented. Open-loop-plus-feedback control is proposed for RTP temperature control | open-loop control allows precise trajectory planning and feedback prevents drift due to disturbances and modeling errors. All of the above ideas are demonstrated in simulation on a ctional system qualitatively similar in its behavior to some real RTP systems.