Lamp configuration design for rapid thermal processing systems

We study lamp configuration design for rapid thermal processing (RTP) systems, We consider a configuration consists of four concentric circular lamp zones, three of them above the wafer and one circumvallating 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 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.