Photomask patterning: the influence of substrate bulk heating on placement accuracy

To create precise patterns on a photomask, it is necessary to identify every source of patterning error and strive to reduce each one. In the current work, the effects of system hardware (typical of MEBES ® systems) on the bulk heating of a SiO 2 substrate have been closely investigated using numerical finite element (FE) analysis and laboratory experiments. Direct temperature measurements of a thermally loaded substrate were performed to determine the thermal response of the photomask substrate. The current exclusive set of simulation work is distinguished from the previous set, as it includes the thermal coupling between the substrate and its surroundings to accurately determine the radiation heat transfer on the photomask, which induces distortion during patterning. Given the electron-beam parameters of 40 μC/cm 2 dose at 50 kV used in raster-beam writing, the FE simulations of a 6-inch mask predicted a maximum temperature rise of 0.913 K for 75% uniform pattern coverage. The corresponding maximum in-plane distortion and 3 σ pattern placement error were found to be 21.9 and 14.2 nm, respectively.