Fast evaluation of Photomask Near-Fields in Sub-Wavelength 193nm Lithography

Sub-wavelength lithography places a serious limitation on the conventional ”thin mask” approximation of the field immediately behind the patterned mask. This approximation fails to account for the increasingly important topographical effects of the mask or ”thick mask” effects. This approximation of the photomask near-fields results from the direct application of Kirchhoff Boundary Conditions, which multiply the incident field by a binary transmission function of the patterned mask. Polarization dependent edge diffraction effects, as well as phase and amplitude transmission errors that arise from the vector nature of light, and the finite thickness of the substrate and chrome layers, produce significant errors in the scalar simulations of the lithographic image. Based on the comparison of aerial images at the wafer plane produced by both rigorous electromagnetic solutions of the field on the mask and their ”thin mask” counterparts, a more accurate model is proposed that consists of a fixed-width, locally-determined boundary layer of imaginary transmission coefficient added to every edge of the initial ”thin mask” approximation. The accuracy of the resultant Boundary Layer model has been exhaustively tested against rigorously simulated aerial images of isolated as well as periodic features of very different profiles and dimensions. The conclusion being that this simple approach is capable of modeling ”thick mask” effects at both 248nm and 193nm wavelength and high NA lithography. This greatly improves the accuracy of aerial image computation in photolithography simulations at a reasonable computational cost.