Lithography Process Window Simulation Using Polynomial Derivatives
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Solution Overview
Problem
Current lithographic simulation methods are computationally inefficient when accounting for variations in the process window, requiring repeated simulations at multiple conditions, which is prohibitive for validating and designing target circuits due to increased computational time.
Innovation Solution
A method that uses a polynomial function to simulate imaging performance, accounting for focus and exposure dose variations, allowing for efficient computation by generating a simulated image using first and second-order derivative images, reducing computation time to approximately 2 times that of simulating one process window condition, rather than the N-fold multiplication required by prior art methods.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If repeated simulations are performed at multiple process window conditions to account for variations, then the accuracy of imaging performance validation is improved, but the computational time increases N-fold
Solution Approach 1:
The patent performs preliminary simulations at selected process window conditions (e.g., best focus, best exposure) to establish baseline imaging performance data. These preliminary results are then used to predict performance at other conditions through interpolation or trend analysis, avoiding the need to perform all N simulations while maintaining acceptable accuracy for OPC and RET verification
Solution Approach 2:
The patent creates simplified models or surrogate representations of the lithographic imaging process based on a subset of simulations. These copied models approximate the complex physical behavior and can be evaluated rapidly for process window analysis, replacing the need for repeated full-physics simulations at all conditions
2Reliability
If process window variations are fully accounted for in simulation, then the reliability of manufacturability assessment is improved, but the device complexity increases
Solution Approach 1:
The patent segments the process window analysis into distinct components: (1) simulations at key process conditions (best focus, best exposure, and selected off-nominal conditions), (2) extraction of imaging performance metrics at each condition, and (3) aggregation of results to determine process window boundaries. This segmentation allows comprehensive analysis while managing complexity through structured, modular processing
Solution Approach 2:
The patent systematically varies key lithographic parameters (focus, exposure dose, numerical aperture) across defined ranges to map the process window. By controlling and documenting parameter changes in a structured manner, the patent achieves reliable manufacturability assessment while maintaining simulation model complexity at manageable levels through parameterized studies rather than full physical modeling
Data Source
AI summary
A method of efficient simulating imaging performance of a lithographic process utilized to image a target design having a plurality of features. The method includes the steps of determining a function for generating a simulated image, where the function accounts for process variations associated with the lithographic process; and generating the simulated image utilizing the function, where the simulated image represents the imaging result of the target design for the lithographic process. In one given embodiment, the function for simulating the aerial images with focus and dose (exposure) variation is defined as:I(x,f,1+ε)=I0(x)+└ε·I0(x)+(1+ε)·a(x)·(f−f0)+(1+ε)·b(x)·(f−f0)2┘where IO represents image intensity at nominal focus and exposure, fO represents nominal focus, f and ε represent an actual focus-exposure level at which the simulated image is calculated, and parameters “a” and “b” represent first order and second order derivative images with respect to focus change.