Transient thermal stability of the x-ray mask SiC-W under short pulse irradiation

Abstract

The transient thermal stability of x-ray mask SiC-W has been numerically studied with special reference to the effect of silicon carbide (SiC) thermal conductivity. This paper presents the transient modeling of an x-ray lithography mask undergoing short x-ray pulses (from a laser plasma or similar source). The computations based on a finite element method are performed for a SiC-W mask under a helium gas environment using powerful analytical capabilities of NISA®. Heat generated in the mask membrane, a tungsten absorber, and helium during x-ray exposure is taken into consideration for the transient thermal stability simulation. Parametric studies are performed to identify the effects of the SiC's thermal conductivity, pulse length, x-ray wavelength and pulses repetition rate. Three thermal conductivity values of SiC were studied: 0.41, 1.9 and 3.5 W/cm °C. The temperature distributions obtained were used as input in order to study the mechanical deformations of the membrane and absorber. A three-dimensional finite element models are developed to analyze the heat transfer mechanisms in the mask and mapping the mask distortions resulting from the short pulse irradiation. Results show that pattern thermal distortion can be minimized if low thermal conductivity of the deposit SiC membrane was obtained.