Numerical and experimental thermal analysis of polyimide-based x-ray masks at the Canadian Light Source

Abstract

In deep x-ray lithography (DXRL), synchrotron radiation is applied to transfer absorber patterns on an x-ray mask into thick photoresist to generate high quality microstructures. Fabrication of the required x-ray masks is a demanding process sequence and constitutes a bottleneck in DXRL technology. Polymer-based mask membranes offer many benefits during mask fabrication and operation, but usually suffer from large thermal distortions during x-ray exposure. These are due to the low thermal conductivity of most polymers (approximately 0.2 W/m K), which results in inefficient heat transfer to the cooled areas around mask and substrate. The power tuning capabilities at the Synchrotron Laboratory for Micro and Nano Devices beamline, Canadian Light Source, however, allow the beam power to be adjusted and consequently limit thermal distortions. In this study, x-ray masks based on 30 μm thick polyimide membranes are studied. Numerical simulations of the thermal and thermoelastic behavior were performed using the software package ansys r14.5. The beam power input parameters were calculated with the software lex-d. For experimental verification, a process to fabricate simple test masks was developed. The polymer membranes were processed on stainless steel sacrificial wafers and were patterned with 80 μm thick nickel absorbers in two macroscopic layouts. Five chromel/alumel (K-type) thermocouples where then bonded to the absorbers to measure the heat distribution. The measurements generally validated the numerical results. The simulated thermal distributions consistently overestimate the experimental values by approximately 4–6 K, which is mainly attributed to uncertainties in the experimental proximity gap settings. The thermal simulation results indicate that the dominant heating mechanism of the resist is conduction: Energy absorbed in the mask absorbers is conducted through the helium gas in the proximity gap to the nonexposed poly(methyl methacrylate) (PMMA) areas and the substrate (cooled to 18 °C). For 500 μm thick PMMA resist, exposed with a synchrotron beam power of 19.6 W, maximum temperatures in the mask are 31.0 and 25.8 °C in the resist below. Maximum single-axis resist deformations in the mask plane amount to 4.12 μm. At 250 μm resist thickness, the observed temperatures are only 25.4 °C in the mask and 22.3 °C in the resist, with maximum mask plane deformations of about 2.3 μm. Integrated over the entire absorber size of 60 mm, these deformations roughly double. Local structure accuracy results were obtained by measuring distortions in a micropatterned polyimide mask. Deformations verify simulation results, vary with the position on the layout, and scale with the incident beam power. At 3.3 W incident beam power, typical deformations around 1–1.5 μm and maximum deformations of 2.3 μm were measured in 100 μm thick resist.