Improved electron backscattering representation using a new class of distribution: application to EUV masks

Abstract

Proximity Effects in electron beam lithography impact feature dimensions, pattern fidelity and uniformity. These effects are addressed using a mathematical model representing the radial exposure intensity distribution induced by a point electron source, commonly named Point Spread Function (PSF). PSF is generally approximated as a sum of Gaussian distributions. Recent works have emphasized that the Gaussian approximation was not perfectly suited in the case of Extreme UV mask substrates. In this case, an increase of backscattered energy is observed in the mid-range due to the high Z material used as an absorber in EUV mask substrates. A novel class of functions, namely Gamma probability distribution, is introduced as a new PSF model. In this work it is shown that the proposed model fits Monte-Carlo simulation data better than the conventional Gaussian model. Moreover, the analytic expression of the cumulative distribution function makes that the new model does not lead to an increase in computation complexity. Therefore, it is well suited for electron beam lithography simulation. We also show that it can be successfully implemented in Proximity Effect Correction algorithms.g