Electron Beam Dose Correction for Proximity Effect in Lithography
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Solution Overview
Problem
The proximity effect of electron beams in micro-nano processing leads to non-uniform energy distribution and pattern distortion in lithography due to forward and backward scattering, causing energy to flow out of designed patterns.
Innovation Solution
A method and apparatus that calibrate the incident dose of electron beams through iterative calculations using a point spread function and grid-based pattern matrix, optimizing the dose to ensure uniform energy deposition across the pattern.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If conventional electron beam lithography is used with uniform dose, then the process is simple, but energy distribution becomes non-uniform due to proximity effect causing pattern distortion
Solution Approach 1:
The patent segments the exposure area into a grid of squares and divides the dose calculation into two independent parts: central exposure energy (from the square itself) and proximity effect energy (from surrounding squares). This segmentation allows each component to be calculated separately using simplified formulas, avoiding the need for complex full-pattern simulations while achieving accurate dose distribution.
Solution Approach 2:
The patent pre-calculates the point spread function (PSF) that characterizes electron scattering behavior in the photoresist and substrate. This pre-computed PSF is then reused in the iterative dose optimization process, eliminating the need to perform complex scattering simulations during each iteration and significantly reducing computational complexity.
2Manufacturing precision
If iterative dose optimization is performed to achieve uniform energy distribution, then pattern distortion is corrected, but calculation time increases
Solution Approach 1:
By segmenting the dose into central and proximity components, the patent enables efficient iterative optimization. Each iteration only requires simple convolution operations with the pre-computed PSF rather than full electromagnetic simulations, allowing rapid convergence to the optimal dose distribution that ensures uniform energy deposition.
Solution Approach 2:
The patent transforms the complex physical problem of electron scattering into a manageable computational problem by parameterizing the scattering behavior through the point spread function. This parameterization allows the use of efficient numerical methods and iterative optimization algorithms that converge quickly, reducing calculation time while achieving precise energy uniformity.
3Manufacturing precision
If high dose is used to compensate for energy loss, then exposure adequacy is ensured, but overexposure and distortion occur in dense pattern regions
Solution Approach 1:
The patent applies local quality by calculating customized dose values for each square based on its specific position and surrounding pattern density. Squares in dense regions receive lower doses to compensate for proximity effect energy accumulation, while squares in sparse regions receive higher doses to compensate for energy loss. This location-specific dose adjustment eliminates both overexposure and underexposure, achieving uniform energy distribution across the entire pattern.
Solution Approach 2:
The patent implements a feedback mechanism through iterative optimization where the calculated dose distribution is evaluated for energy uniformity, and adjustments are made in subsequent iterations. The process continuously refines the dose values based on the actual energy deposition pattern, ensuring that the final dose distribution compensates exactly for proximity effects and achieves the target uniform energy distribution.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Achieves uniform energy distribution and accurate pattern transfer without distortion by directly calculating the optimized electron beam dose for each exposed square, simplifying computations and achieving precision within few iterations.
Implementation Method 1
incident electrons subject to forward scattering due to atoms in a photoresist
Implementation Method 2
scatter backward due to atoms in a substrate
Data Source
AI summary
A method and an apparatus for correcting a proximity effect of an electron beam. An initial dose of the electron beam is preset for each exposed square, and proximity effect energy representing an influence of exposing all exposed squares other than a current exposed square on the current exposed is calculated. A corrected dose of the electron beam for the current exposed square is then calculated, and the corrected dose for each exposed square in the electron beam exposure layout matrix is successively calculated. Then, the above calculation iterates for T times to obtain a final corrected dose of the electron beam for each exposed square.