Experimental and numerical investigations of photomask substrate heating due to electron beam patterning

This paper presents a detailed discussion of issues related to substrate bu lk heating caused by energy deposition during the Electron beam (e-beam) pa tterning of photomasks. Accurate assessments of substrate thermal responses are necessary to determine induced pattern placement errors. A series of e xperiments was conducted to determine the temperature distribution across a 6-in. SiO2 mask blank under various thermal-loading conditions. Changes of substrate temperature were monitored during short- and long-term exposures . The relationship between the substrate temperature rise and thermal-load input power was determined. The experimental results were compared with tho se predicted by a numerical finite element (FE) model. The effect of the sy stem boundary conditions on the rate of heat exchange between the mask and its surroundings was investigated, and results obtained were used to optimi ze the performance of the simulations.