Robust resolution enhancement optimization methods to process variations based on vector imaging model

Xu Ma; Yanqiu Li; Xuejia Guo; Lisong Dong

doi:10.1117/12.916147

13 March 2012 Robust resolution enhancement optimization methods to process variations based on vector imaging model

Xu Ma, Yanqiu Li, Xuejia Guo, Lisong Dong

Proceedings Volume 8326, Optical Microlithography XXV; 83262A (2012) https://doi.org/10.1117/12.916147
Event: SPIE Advanced Lithography, 2012, San Jose, California, United States

Abstract

Optical proximity correction (OPC) and phase shifting mask (PSM) are the most widely used resolution enhancement techniques (RET) in the semiconductor industry. Recently, a set of OPC and PSM optimization algorithms have been developed to solve for the inverse lithography problem, which are only designed for the nominal imaging parameters without giving sufficient attention to the process variations due to the aberrations, defocus and dose variation. However, the effects of process variations existing in the practical optical lithography systems become more pronounced as the critical dimension (CD) continuously shrinks. On the other hand, the lithography systems with larger NA (NA>0.6) are now extensively used, rendering the scalar imaging models inadequate to describe the vector nature of the electromagnetic field in the current optical lithography systems. In order to tackle the above problems, this paper focuses on developing robust gradient-based OPC and PSM optimization algorithms to the process variations under a vector imaging model. To achieve this goal, 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. The steepest descent algorithm is used to optimize the mask iteratively. In order to improve the efficiency of the proposed algorithms, a set of algorithm acceleration techniques (AAT) are exploited during the optimization procedure.

Citation Download Citation

Xu Ma, Yanqiu Li, Xuejia Guo, and Lisong Dong "Robust resolution enhancement optimization methods to process variations based on vector imaging model", Proc. SPIE 8326, Optical Microlithography XXV, 83262A (13 March 2012); https://doi.org/10.1117/12.916147

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KEYWORDS

Optical proximity correction

Photomasks

Imaging systems

Optical lithography

Optimization (mathematics)

Detection and tracking algorithms

Semiconducting wafers

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