Thermoelastic behavior of X-ray lithography masks during irradiation

This paper presents computer calculations of thermoelastic effects in X-ray lithography masks caused by the absorption of X-rays during exposure. Several mask structures are considered, with different substrate and absorber materials, using finite element analysis. Part I of the paper deals with short-pulse X-ray irradiation (e.g., from gas plasma, laser-heated plasma, or exploding wire sources), and Part II describes irradiation during exposure with a synchrotron-storage-ring X-ray source. For the short-pulse irradiation, results indicate a maximum rise in temperature on the mask of about 30°C for a 2-ns exposure with a 10-mJ/cm
²
X-ray pulse. Mechanical static analysis shows that the maximum stress in the absorber films, which is due to maximum temperature differences in the mask layers, occurs at the end of the pulse. The magnitude of the induced thermoelastic stress is found comparable to the intrinsic stress level of the mask materials (typically 2–5 × 10
⁸
dyn/cm
²
). The analysis indicates that when pulse amplitudes reach 10 mJ/cm
²
, there will be a need for experimental study of X-ray mask distortion during exposure to short X-ray pulses. A one-dimensional model is developed for the case of storage-ring irradiation. The model predicts distortions of the printed image due to a thermal wave developed on the mask by scanning on the X-ray beam. Experimental results are presented showing that the effect is negligible under normal operating conditions but may become noticeable for operation in vacuum or without proper heat sinks.