CURVE-FITTING A QUADRUPLE GAUSSIAN FUNCTION TO THE MONTE-CARLO SIMULATION RESULTS FOR PROXIMITY EFFECT CORRECTION PARAMETERS

The curve fitting of a quadruple Gaussian function to Monte Carlo simulation results of absorbed energy distributions for electron beam lithography has been investigated. Monte Carlo simulation of electron-beam exposure in a resist layer includes the effects of fast secondary electron generation and the scattering probability of a resist/substrate interface. The energy density function in an electron resist layer can be well approximated by a normalized quadruple Gaussian function in the entire electron scattering range when the ENERGY merit function is used for the Si substrate and when the LOG merit function is used for the Au substrate. The proximity correction parameters for line exposure can be mathematically obtained from the proximity correction parameters for point exposure.