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.

Prediction of residual clamping force for Coulomb type and Johnsen–Rahbek type of bipolar electrostatic chucks

“…After the wafer processing is finished, the voltage applied on the electrostatic chuck must be cut off immediately. As mentioned in the previous literature, 13–23 the residual clamping force resulted from the residual charges usually remains. It has become a serious issue for production efficiency and process reliability.…”

“…On the other hand, the previous works emphasized the difference between Coulomb type and J–R type, and regarded them as two quite distinct systems. 14,19–21,23 In fact, the clamping forces for all types of electrostatic chucks combine Coulomb force and J–R force to some extent, 15 and they are bound to have some characteristics in common. Therefore, it is possible and significant to seek an approach to unify the mathematical expression of the electrostatic force for both types of electrostatic chucks.…”

Modeling and control of electroadhesion force in DC voltage

“…The mechanical response is caused by elastic deformation of asperity in surface roughness [21] and macroscopic deformation of the electrodes/insulators [17]. In the previous study, the authors showed that the mechanical responses can be compensated by estimating the equivalent gap by using a built-in sensor that measures the capacitance of the paired plates [18].…”

“…This model is expressed as the equivalent circuit in Fig. 1b [19][20][21], which consists of an air-gap and conductive dielectric layers. The air gap is also assumed to have conductivity corresponding to the contact resistance.…”

“…The resulting electroadhesion force grows considerably large, much larger than typical electrostatic attraction force calculated using the text-book parallel plate model. Watanabe et al developed an electric model to describe JR effect [19], which has been extensively utilized in analyzing the conventional electrostatic chucks [20,21].…”