Thermoelastic effects on x-ray lithography masks under pulsed irradiation

Abstract

The purpose of this paper is to present computer calculations of thermoelastic effects in x-ray lithography masks caused by the absorption of high intensity short x-ray pulses. Several mask structures are considered with different substrate and absorber materials. In particular, substrates materials of Si, SiC, and diamond, and absorber materials including Au, W and Ta will be considered. The powerful analytical capabilities of NASTRAN were combined with the graphic input and output capabilities of CAEDS to perform the calculations using finite element analysis. The calculations were performed for x-ray masks operating in air, and in a He atmosphere with a 40 μm gap between the mask and the wafer. Thermoelastic stress calculations were performed for 8.3 Å, and 10 Å wavelength x-ray pulses. Results indicate a maximum temperature rise on the mask of the order of 30 °C for a 2 nanosecond exposure with a 10 mJ/cm2 x-ray pulse. The maximum temperature was obtained at the end of the x-ray pulse. The temperature decayed quickly, with a time constant depending on the thermal properties of the absorber and the substrate. The initial ambient temperature was reached after about 10 milliseconds. Mechanical static analysis showed that the maximum stress in the absorber films which was due to maximum temperature differences in the mask layers, also occurred at the end of the pulse. The magnitude of the induced thermoelastic stress was found comparable to the intrinsic stress level of the mask materials. The analysis indicates that when the pulse amplitude reaches 10 mJ/cm2, 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). The results also point out directions for the selection of mask materials to minimize mask fatigue and distortion. © 1990.