Methods for controlling clamping of insulator-type substrate on electrostatic-type substrate support structure

An insulator-type substrate is positioned on a support surface of a substrate support structure in exposure to a plasma. An initial clamping voltage is applied to an electrode within the substrate support structure to rapidly accumulate electrical charge on the support surface to hold the substrate. A backside cooling gas is flowed to a region between the substrate and the support surface, and a leak rate of the backside cooling gas is monitored. A steady clamping voltage is applied to the electrode, and the steady clamping voltage is adjusted in a step-wise manner to maintain the monitored leak rate of the backside cooling gas at just less than a maximum allowable leak rate. Or, a pulsed clamping voltage is applied to the electrode, and the pulsed clamping voltage is adjusted to maintain the monitored leak rate of the backside cooling gas at just less than the maximum allowable leak rate.