Advanced model for resist heating effect simulation in electron beam lithography

A mathematical model of resist heating was developed based on the three-dimensional classic heat conductivity equation in a multilayer object. A tabulation of special functions used for numerical calculation allows the analytical solution to be simplified to one only integral for both variably shaped beam and Gaussian beam. As a result, a dynamic distribution of temperature field in resist can be simulated for an exposure process in terms of thickness and characteristics of resist and multilayer substrate, as well as size, placement and consequence of flashes. Results of simulation are shown for both short and long time range exposures.