Modeling photoresist outgassing pressure distribution using the finite-element method

A method for modeling "vacuum"-pressure distributions is presented. The technique is based on the finite-element (FE) method. Although there are as yet no commercially available FE code having this capability, a simple transformation allows any standard code to calculate pressures in the molecular-flow regime. The transformation is based on the physical analogy between molecular flow and radiation heat transfer. The transformations are presented here. Results which were obtained using this procedure are presented for the VIISta 3000 ion implanter. The pressure distribution inside the implant chamber due to wafer outgassing is shown. Also shown are the effects of adding an aperture in the beam line and the effect of tilting the wafer. The pressure is plotted against the beamline for these cases. The gas thickness, which is the integral of pressure along the beam line, is calculated for each case. The gas thickness is an important quantity which can be used to predict relative changes in dose shift.