Mask Pattern Analysis Using Perturbation Look-Up Table Jacobian
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Solution Overview
Problem
Current mask synthesis and optimization techniques face challenges in efficiently analyzing complex mask patterns for integrated circuits, particularly due to the complexity of modeling mask effects and the resource-intensive nature of analytical approaches, which can lead to inaccurate results and high computational demands.
Innovation Solution
A method utilizing a perturbation look-up table and Jacobian matrix to generate a cost function gradient, allowing for a numerical analysis that approximates the analytical derivative of a cost function, thereby simplifying and optimizing mask pattern analysis by reducing the need for extensive simulations and resource usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If analytical approaches are used to model mask effects, then measurement precision is improved, but device complexity and computational resources increase
Solution Approach 1:
The patent transforms the continuous analytical derivative calculation into discrete numerical differences by parameterizing the perturbation amount and using lookup tables to store pre-computed intensity values. This discretization reduces computational complexity while maintaining sufficient accuracy for mask optimization.
Solution Approach 2:
The patent pre-computes and stores intensity values in lookup tables before the actual optimization process. By preparing these reference data structures in advance, the method avoids repeated expensive simulations during gradient computation, thereby reducing real-time computational complexity.
2Measurement precision
If analytical derivative computation is used, then measurement precision is improved, but loss of time increases
Solution Approach 1:
The patent uses finite difference approximations that copy and compare intensity values from lookup tables rather than performing full analytical derivations. This copying approach significantly reduces computational time while providing sufficiently accurate gradient estimates for optimization purposes.
Solution Approach 2:
By pre-computing intensity values and storing them in lookup tables before optimization begins, the patent eliminates the need for repeated time-consuming simulations during gradient calculation, thereby reducing overall computational time.
3Measurement precision
If extensive simulations are performed, then measurement precision is improved, but use of energy increases
Solution Approach 1:
The patent performs intensive simulation work once beforehand to populate lookup tables, then reuses these pre-computed results repeatedly during optimization. This preliminary action distributes the energy cost over time, making the actual optimization process energy-efficient.
Solution Approach 2:
Instead of re-simulating mask effects repeatedly, the patent copies intensity values from pre-computed lookup tables. This copying operation consumes minimal energy compared to full simulations, thereby reducing overall energy usage.
Data Source
AI summary
Aspects described herein relate to obtaining a mask pattern using a cost function gradient (CFG) generated from a Jacobian matrix generated from a perturbation look-up table (PLT). In an example method, a PLT is populated (108). Each table entry of the PLT is based on a respective perturbed intensity signal. The respective perturbed intensity signal is based on a simulated signal received at an image surface using a mask pattern having a perturbed element of the mask pattern. The mask pattern is for a design of an integrated circuit. A matrix is populated (110) using the PLT and a target intensity signal. The target intensity signal is based on a signal received at the image surface to form target features at the image surface. A CFG is defined (112) based on the matrix. An analysis is performed (114) on the mask pattern based on the CFG.