A method of cooling a wafer support at a uniform temperature in a plasma reactor

A plasma reactor having a reactor chamber and an electrostatic chuck having a surface for holding a workpiece inside the chamber includes inner and outer zone backside gas pressure sources coupled to the electrostatic chuck for applying a thermally conductive gas under respective pressures to respective inner and outer zones of a workpiece-surface interface formed whenever a workpiece is held on the surface, and inner and outer evaporators inside respective inner and outer zones of the electrostatic chuck and a refrigeration loop having respective inner and cuter expansion valves for controlling flow of coolant through the inner and outer evaporators respectively. The reactor further includes inner and outer zone temperature sensors in inner and outer zones of the electrostatic chuck and a thermal model capable of simulating heat transfer through the inner and outer zones, respectively, between the evaporator and the surface based upon measurements from the inner and outer temperature sensors, respectively. Inner and outer zone agile control processors coupled to the thermal model govern the inner and outer zone backside gas pressure sources, respectively, in response to predictions from the model of changes in the respective pressures that would bring the temperatures measured by the inner and outer zone sensors, respectively, closer to a desired temperature.