Modeling of Mask Thermal Distortion and Its Dependency on Pattern Density

摘要

Mask distortion due to thermal loading during exposure contributes significantly to the overlay error budget and poses significant challenges for extending optical lithography to the sub-100nm regime. In this paper, we model the thermal mask distortion during the scanning exposure in 193nm lithography, and investigate its dependency on the distribution of the local pattern density on the mask. Several numerical simulation methods are investigated for accurately predicting the transient and steady-state thermal and distortion response of the mask during exposure. In particular, we find that simulating an "effective" continuous illumination power has the same thermal and distortion impact as the actual pulsed laser power delivery to the mask during IC production. This approach dramatically reduces computational cost. Our parametric analysis demonstrates that the magnitude of the thermal and distortion responses are closely related to the global pattern density and exposure dose. Furthermore, thermal mask distortion is found to be significantly dependent on the distribution of the local pattern density on the mask. Given that often the mask pattern layout can be manipulated at some level of abstraction, we conducted Monte Carlo simulation which verifies the existence of optimal pattern density distributions minimizing the mask thermal distortion, and highlights the opportunity to optimize mask pattern layout with respect to mask thermal distortion.