Monte Carlo simulation of line edge profiles and linewidth control in x-ray lithography

Abstract

X-ray lithography exposures of PMMA on silicon have been simulated with a Monte–Carlo method including the energy backscattering from the substrate. The line-edge acuity of the resist image has been modeled with experimentally determined x-ray spectra of various sources (aluminum, tungsten, and palladium) and various source diameters (0.1, 1.5, and 3 mm). The intrinsic line-edge degradation due to secondary electron exposure is derived from the point source images while the finite-source effect (penumbra) is extracted from the additional degradation at finite source diameters. The penumbra effect is found to be rather small in PMMA. Depth profiles of the energy absorbed in PMMA demonstrate the significance of the energy backscattering from the substrate for energetic x rays. This effect can be significantly reduced by an organic spacer layer. The extent of the geometric projection effect has been modeled with the aluminum source. The results show that a finite angle of incidence of the x rays causes a sizable enlargement of the mask shadow due to the finite absorber thickness ultimately restricting the usable field size. The resultant linewidth variation is more pronounced for a mask with vertical profiles than for one with 20° wall angle. It can be reduced by thinning the absorber although at the expense of the mask contrast. The angle of incidence is replicated in the resist profiles causing an increasing tilt of the lines further away from the center of the wafer. This also restricts the field size but can be controlled to some extent by the thickness of the imaging resist layer.