Heating and temperature-induced distortions of silicon x-ray masks

Abstract

This paper presents a detailed discussion of problems concerning mask heating, temperature distributions and resulting distortions of a boron-doped silicon mask which is exposed to intense x-ray radiation (from electron storage rings or plasma sources), having different spatial geometries and different distributions over time. For the calculations, all significant heat-loss mechanisms, e.g., radiation, thermal conduction in the mask, and heat transfer through an ambient gas, have been taken into consideration. The line-shaped synchrotron beam has a vertical Gaussian intensity distribution, with nearly time-constant radiation power. The influences of different scan modes on the temperature rise are taken into account. In the case where helium is used as the coolant gas, the temperature rise remains within acceptable limits, even at the highest possible radiation power. The plasma source emits extremely short, high power x-ray pulses having a homogeneous spatial distribution. The short pulse duration leads to a considerable temperature rise in the mask, which would introduce appreciable distortions. However, the homogeneity of the exposure combined with the stress in the mask membrane can suppress this effect.