Improvement of Temperature Uniformity in Rapid Thermal Processing Systems Using Multivariable Control

During rapid thermal processing (RTP) of a semiconductor wafer, maintenance of nearuniform wafer temperature distribution is necessary. This paper addresses the problem of insuring temperature uniformity in a cylindrical RTP system with multiple concentric circular lamps.A numerical technique is presented for optimizing steady-state temperature distribution by independently varying the power radiated by each lamp. It is shown for a simulated system, over a wide range of temperature setpoints, that the temperature uniformity achievable with multivariable (“multiple knob”) control of lamp powers is significantly better than that achievable with scalar (“single knob”) control.The difficulties of using scalar control in RTP are more severe in the case of temperature trajectory design than in the case of steady-state temperature maintenance. For example, with scalar control the rate of temperature increase during ramping is limited because temperature nonuniformity can cause slip defects in the wafer. A numerical technique is presented for designing multivariable lamp power trajectories to obtain near-optimal temperature uniformity while wafer temperature tracks a specified ramp, resulting in slip-free ramp rates much faster than those achievable with scalar control.