Gaussian Random Field EUV stochastic models, their generalizations and lithographically meaningful stochastic metrics

Photon absorption statistics combined with a simple model of resist chemistry triggered by each absorbed photon leads to a family of stochastic models with a Gaussian random field (GRF) deprotection. In this paper, we discuss two important aspects of GRF models. First, we present the generalizations to stochastic reaction-diffusion models, accounting for the effects of depletion, and to models accounting for both exposure-resist stochastic and other process parameter variations. Second, we describe several options for the stochastic metrics of EUVL processes, both meaningful and useful for lithographers and fast enough to be applicable to the full-chip OPC and verification. We also present some details of their implementations for the full-chip OPC verification and the results of tests. Finally, we explain the relation of one of the introduced stochastic metrics to the stochastic-caused variability of the electrical conductance of vertical interconnects (vias).

Citation:

Azat Latypov, Gurdaman Khaira, Germain Fenger, Shuling Wang, Marko Chew, Shumay Shang, "Gaussian random field EUV stochastic models, their generalizations and lithographically meaningful stochastic metrics," Proc. SPIE 11609, Extreme Ultraviolet (EUV) Lithography XII, 1160917 (22 February 2021); https://doi.org/10.1117/12.2583792

What you’ll learn:

• What generalized Gaussian Random Field (GRF) models are and how they account for depletion effects and process parameter variations in stochastic lithography processes.
• What new stochastic metrics, Average Printed Area (APA) and Standard Deviation of Printed Area (stdPA), are and how they can be used to assess SRAF sidelobe printability and stochastic variability of critical features like vias.
• How the stdPA metric relates to the stochastic-caused variability in the electrical conductance of vertical interconnects (vias).
• How the stochastic metrics are implemented in Calibre nmModelflow and Calibre OPCverify for efficient full-chip OPC verification, including comparisons to Monte Carlo simulations.

Who should read this:

• Lithography engineers and researchers working on advanced semiconductor manufacturing processes, especially focused on EUV lithography.
• Developers of lithography simulation and verification tools, who need to incorporate stochastic modeling capabilities into their software.
• Process integration and device engineers who need to understand the impact of stochastic effects on critical features like vias and their electrical performance.