Abstract
The paper presents an analytical model for determining the resist contrast in electron lithography with nonuniform deposited energy over the depth, which is typical for low-energy electron exposure. In the classical approach, the contrast is determined from the logarithmic dependence of the residual resist thickness on the exposure dose and assumes the homogeneity of the deposited energy over the layer depth, which leads to an overestimation of the contrast value in the presence of a gradient of the deposited energy. The proposed model takes into account the linear change in the energy profile in the resist, which is neglected in existing generally accepted model, thus allowing us to extract the "true" contrast value reflecting the resist properties under given development conditions. To validate the model, experiments were carried out with an ELP-20 resist 200 nm thick on silicon substrates at an electron beam energy of 5, 15 and 25 keV. Dose wedges were exposed for each energy, followed by development and topography analysis by atomic force microscopy. By fitting the model curves to the experimental dependence of the residual resist thickness on the exposure dose for each electron energy, the values of the contrast and the parameter characterizing the gradient of the deposited energy by depth were calculated. In this case, the contrast remains almost constant when varying the energy of incident electrons and has an average value of γ = 1.67. Thus, the increase in contrast with a decrease in the electron energy observed within the classical approach should be considered as an artifact of the model used. The proposed model is applicable for precision calibration of the processes of forming three-dimensional resist structures using the grayscale lithography.