Control of an integrated bake/chill system

Considers the heater design and temperature control of a silicon wafer in an integrated bake/chill system for a lithography process. The main problem involves baking the wafer to a pre-specified temperature and maintaining a uniform spatial distribution at this temperature on the entire wafer at steady state. Typically, in such a heat transfer problem, maintaining temperature uniformity is non-trivial because of nonuniform heat losses at the boundaries between the ambient and the wafer. As a result, nonlinear temperature gradients exist, leading to poor spatial distribution. In order to compensate for the nonlinear heat loss, many degrees of freedom have to be provided in the heating process. The degree of non-uniformity is essentially a trade-off between the complexity of the heater design versus achievable temperature distribution. In the paper, this trade-off is considered in the design of a multi-zone heater. With a proportional plus integral controller for each zone of the heater, we show, via simulations, that the temperature on the surface of a 300 mm wafer can be maintained to within less than 0.1°C using 9 zones. We assume uniform heat flux from each zone of the heater and that heat loss coefficients are linearly related to temperatures