Prediction of clamping pressure in a Johnsen-Rahbek-type electrostatic chuck based on circuit simulation

Abstract

We propose nonlinear resistance models for bulk resistance of a dielectric layer and contact resistance between a wafer and the dielectric layer used in an equivalent circuit model to predict the clamping or residual clamping pressure in Johnsen-Rahbek-type [A. Johnsen and K. Rahbek, J. Inst. Electr. Eng. 61, 713 (1923)] electrostatic chucks. It is found that the bulk resistance is presumed by a model on the basis of the space-charge-limited current model in insulator. It is also found that the contact resistance is expressed by a superposition of Ohmic resistance in the low-field strength region and a resistance on the basis of field emissions in the high-field strength region. In addition, the gap capacitance is determined based on the probability function of asperity height obtained from a surface roughness profile. The clamping pressure is simulated by calculating a charge stored in the gap, combined with the probability function with circuit simulation. Consequently, the calculation agrees with the measurement within 31% difference. It is also found that the calculation can reproduce the dependency of bulk resistance on the clamping pressure and the time response in residual clamping pressure.