Calculation of energy deposition in thin resist films over multilayer substrates

Multilayer substrates are of great importance for direct write applications. Recently, they are getting more and more importance in mask making as well, for example in the phase shift technology. In the case of direct writing, the substrate consists of various layers of different materials while for mask fabrication, the mask plate consists of at least two different layers, e.g. Cr on glass. A new method for the calculation of energy deposition due to e-beam exposure in thin resist films over composite substrates is presented. The method is based on the solution of the Boltzmann transport equation and has proven to be very fast compared to Monte Carlo method, and its accuracy has been shown by successful comparison with experimental obtained results. The method is incorporated in a complete e-beam lithography simulator.