Thermal and mechanical model of x-ray lithography masks under short pulse irradiation

The purpose of this paper is to present computer simulations of x-ray mask heating by fast x-ray pulses. In particular, results will be presented of temperature distributions in an x-ray mask during exposure to x-ray pulses generated by a hot plasma. Three mask structures were studied: (i) Si–Au absorber, (ii) Si–polyimide–Au absorber, and (iii) Si–W absorber. The transient thermal analysis results were obtained using finite element modelling techniques (CAEDS and NASTRAN). The x-ray exposure was assumed to have taken place in a helium atmosphere with a 40-μ gap between the mask and the wafer, which was assumed to be a heat sink at constant temperature. The temperature distributions obtained above were subsequently used as input in order to study possible mechanical deformation of the membrane. Again, finite element techniques were used and solutions were obtained by static stress methods. Results indicate a maximum temperature rise on the mask of the order of 18 °C for a 20-ns exposure by a 10 mJ/cm2 x-ray pulse. The maximum temperature was obtained at the end of the x-ray pulse. The temperature decayed quickly, reaching initial ambient temperature after about 10 ms. Mechanical analysis showed that maximum deformation, which was due to maximum temperature differences in the mask layers, also occurred at the end of the pulse. The analysis indicates that there is need for experimental study of x-ray mask distortion during exposure to short x-ray pulses (from a laser plasma or similar source) when the pulse amplitude reaches 10 mJ/cm2.