Effect of wafer bow on electrostatic chucking and back side gas cooling

Electrostatic chucks (ESCs) are used in the semiconductor industry to clamp wafers to a pedestal and combined with back side gas (BSG) cooling to control temperature during processing. The effect of wafer bow in an ESC/BSG system is studied theoretically and experimentally. An equilibrium model is developed that predicts the maximum allowed bow for initial chucking and the maximum BSG pressure once the wafer is chucked. Experimental chucking and BSG pressure data show the maximum initial bow that can be chucked agree with model predictions. Hysteresis in pressure versus flow data is also consistent with the model. The model does not predict some features of thin wafers with highly stressed films. However, deviations between the model and data in this nonlinear regime are expected. By combining the theory with the experimental data, a method to determine a safe BSG/ESC operating range is given.