Application of cubic spline models in electron-beam lithography

Abstract

Proximity effects in electron beam lithography impact feature dimensions and uniformity. These effects are addressed using a mathematical model representing the radial exposure intensity distribution produced by a point source of electrons, commonly named point spread function (PSF). Unfortunately, the multiple Gaussian distribution approximation, the most common PSF model used till now, reaches its limits in terms of efficiency, particularly in case of high atomic number Z substrate materials. A broad family of approximating functions, known as splines, is considered here as a substitute to Gaussian. Through a simulation study using specific test structures, the authors demonstrate the high potential of cubic splines in accurately characterizing high Z substrates PSFs.