Energy density function determination in a very-high-resolution electron-beam lithography

A proximity effect correction algorithm requires an accurate knowledge of the energy density function (EDF) deposited in the electron resist layer. In case of high-resolution electron-beam lithography (EBL), whenever the required resolution is below 0.5 ?m, forward and large-angle backward scattering contribution has to be carefully analyzed. In this paper, we compare Monte Carlo (MC) simulation data with experimental point exposure measurements over different substrates and with different beam energy (range 20-40 kV). The substrates we analyze are silicon and silicon nitride membranes (2 ?m thick), indium phosphide, and gold. A good correlation between MC data and experiments is proved. Experiments and MC data suggest that the usual double Gaussian fit applied to the distribution is not suitable for the application of high-resolution lithography or with high-Z materials, These data indicate that the recently proposed triple Gaussian fit can be considered as a particular case of a more complex multi-Gaussian function. Experimental high-resolution resist profiles are then simulated successfully using MC EDFs in a cell development model.