Аннотация:Dynamic in-plane thermal distortion (IPTD) in an SiN x-ray mask membrane during repetitive scanning x-ray exposure for synchrotron radiation (SR) lithography has been exactly calculated using a model which is close to realistic physical conditions. In order to decide the heating model, a flow regime in the mask-to-wafer proximity gap filled with a 760-Torr helium gas is examined by using the value of the Knudsen number. Heat generated in the mask membrane, a helium gas, and a resist coated on a wafer during x-ray exposure is taken into consideration for the thermal balance equations. The effects of the proximity gap, scanning frequency, and membrane window size on the dynamic IPTD are simulated. The dynamic IPTD indicates a constant value depending on a scanning frequency within the region of the 10–100-μm gap. According to the scanning frequency dependence, the dynamic behavior of the IPTD is divided into three regions: quasistatic, transient, and saturated regions. Using >10-Hz scanning frequencies (saturated region), the dynamic IPTD appears to converge to an equivalent value obtained by a uniform exposure. In the region of >10-mm window size, the dynamic IPTD, not proportional to the window size, seems to be saturated.
