Lamp configuration design for rapid thermal processing systems

We have studied lamp configuration design for rapid thermal processing (RTP) systems. We considered a configuration consisting of four concentric circular lamp zones, three of them above the wafer and one circumventing the wafer. We propose a method to determine the geometric parameters, the width, height and radius, of the lamp zones so that the configuration designed has the capacity to achieve a uniform temperature on the wafer. The method is based on a necessary and sufficient condition for uniform temperature tracking and analytic expressions of the view factors. A design example is given in which a least square open-loop control law yields good temperature uniformity.