Determination of resist exposure parameters in helium ion beam lithography: Absorbed energy gradient, contrast, and critical dose

We study the relationship between the true resist contrast ${\mathrm{(\gamma }}_{\mathrm{true}})$ and the apparent contrast ${\mathrm{(\gamma }}_{\mathrm{HD}}\mathrm{),}$ as determined by the slope of the Hurter–Driffield (HD) curve, in ${\mathrm{He}}^{\mathrm{+}}$ ion beam lithography. These parameters can differ significantly because the absorbed energy density is a function of depth in the resist. We formulate an analytical model, using a linear approximation to the deposited energy distribution, that permits the extraction of the absorbed energy gradient, the true resist contrast, and the critical dose from experimental HD curves. The model accurately describes both experimental and simulation results. We show that the contrast for poly(methylmethacrylate) resist is 2.9 for various ${\mathrm{He}}^{\mathrm{+}}$ ion energies even though the apparent contrast can be as low as unity at 50 keV.