Modeling, fabrication, and experimental application of clear x-ray phase masks

Phase-shifting masks are widely used in optical lithography, and the question is whether the technology can be extended to much shorter wavelengths. We have extensively modeled the use of clear phase-mask materials as absorbers for x-ray exposures. Similar to the optical domain, the imaging from x-ray phase masks is highly nonlinear, and thus can be used to produce a feature reduction of $3–5×$ compared to the mask pattern. This observation suggests that mask fabrication might be easier, but the technique is most suited for less dense pattern requirements. In this article we review some of the salient modeling, examine the requirements for effective fabrication of the masks, and provide some experimental verification of this approach to reach the sub-$50nm$ region. It is not essential to have exactly a 180° phase shift in the clear material, because mask feature reductions can be achieved with 45, 90, 180, and 270° shifts by choosing the appropriate thicknesses of the clear material. A mask with a $235nm$ feature and a 45° thickness is transformed into a $134nm$ aerial feature, but the same dose for a 180° thickness results in an $86nm$ feature. The best resolution is obtained in the so-called bright peak enhanced x-ray phase mask (BPEXPM) mode with thicknesses appropriate to 180° or greater. Previous modeling of the clear phase feature indicated a strong dependence on the wall slope, and fabrication processes are being pursued to verify the modeling and demonstrate the slope dependence on the feature profile. Silicon nitride with a phase shift of 126° is currently employed, but other materials could also be used in the mask fabrication. Experimentally, we are pursuing the feature width reduction achieved from correctly fabricated masks to produce gate width structures at the sub-$50nm$ region.