Analysis of mask distortion induced by heating during e-beam writing

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Abstract
The 3D heat diffusion equation was numerically solved to determine the e-beam writing induced local and global heating and the corresponding distortion for optical and x-ray masks. The beam was 50 kV with maximum current I equals 4 (mu) A for optical masks, and I equals 0.3 (mu) A for x-ray masks. Calculations indicate that the distortion due to the localized temperature rise is negligible for both types of masks. The global distortion for optical masks is on the order of 0.04 micrometers (for I equals 4 (mu) A), and on the order of 0.007 micrometers for x-ray masks (for I equals 0.3 (mu) A) for a dose of 10 (mu) C/cm2 under dense-pattern mask writing conditions.

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