Vectorial mask optimization methods for robust optical lithography

Xu Ma; Yanqiu Li; Xuejia Guo; Lisong Dong

doi:10.1117/1.JMM.11.4.043008

15 November 2012 Vectorial mask optimization methods for robust optical lithography

Xu Ma, Yanqiu Li, Xuejia Guo, Lisong Dong

Journal of Micro/Nanolithography, MEMS, and MOEMS, Vol. 11, Issue 4, 043008 (November 2012). https://doi.org/10.1117/1.JMM.11.4.043008

Abstract

Continuous shrinkage of critical dimension in an integrated circuit impels the development of resolution enhancement techniques for low k₁ lithography. Recently, several pixelated optical proximity correction (OPC) and phase-shifting mask (PSM) approaches were developed under scalar imaging models to account for the process variations. However, the lithography systems with larger-NA (NA > 0.6) are predominant for current technology nodes, rendering the scalar models inadequate to describe the vector nature of the electromagnetic field that propagates through the optical lithography system. In addition, OPC and PSM algorithms based on scalar models can compensate for wavefront aberrations, but are incapable of mitigating polarization aberrations in practical lithography systems, which can only be dealt with under the vector model. To this end, we focus on developing robust pixelated gradient-based OPC and PSM optimization algorithms aimed at canceling defocus, dose variation, wavefront and polarization aberrations under a vector model. First, an integrative and analytic vector imaging model is applied to formulate the optimization problem, where the effects of process variations are explicitly incorporated in the optimization framework. A steepest descent algorithm is then used to iteratively optimize the mask patterns. Simulations show that the proposed algorithms can effectively improve the process windows of the optical lithography systems.

Citation Download Citation

Xu Ma, Yanqiu Li, Xuejia Guo, and Lisong Dong "Vectorial mask optimization methods for robust optical lithography," Journal of Micro/Nanolithography, MEMS, and MOEMS 11(4), 043008 (15 November 2012). https://doi.org/10.1117/1.JMM.11.4.043008

Published: 15 November 2012

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