Algebraic modeling of dose to size stochastic defects

Missing contact hole stochastic defects are modeled as the absence of a development path through layers of solubility units in a resist film. Voxels are solubility units and the probability of each voxel changing solubility is calculated as a function of the aerial image, the depth in the resist and resist parameters such as the absorbance of EUV light and the acid blur. Dose to size is modeled as the dose at which the dissolution probability of a voxel at the edge of the feature is 50%. This model can match the dependence of dose to size of experimental resists using reasonable parameters for acid blur and voxel size. The blockage probability is exponentially dependent on the dose. The overall probability of a blocked via becomes higher as the aerial image becomes worse. The top and bottom layers of the resist film show a much higher probability of blockage than the neighboring layers. This is because there are fewer neighboring voxels to the voxels in the top and bottom layers than in the middle layers, so there are fewer sources of acid to deprotect that voxel. This suggests that resists with a high R_min will show fewer missing vias than resists with no appreciable R_min.