Off-Center Point Spread Function for Electron Beam Proximity Correction
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Solution Overview
Problem
Existing models for electron beam interaction with targets in electronic lithography and electron microscopy fail to accurately account for proximity effects, particularly at long distances, especially in extreme UV mask etching with heavy metal layers, due to their reliance on centered point spread functions that do not adequately represent backscatter phenomena.
Innovation Solution
A method using a point spread function (PSF) that includes gamma distribution functions with maximum amplitude values offset from the center of the electron beam, allowing for improved modeling of backscatter effects by positioning these maxima at the peak of electron beam diffusion, which can be combined with Gaussian functions for forward scattering.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional centered Gaussian PSF models are used, then the model simplicity is maintained, but the accuracy of backscatter effect modeling deteriorates at long distances
Solution Approach 1:
The patent applies asymmetry by using off-center Gaussian functions where the maximum amplitude is shifted from the beam center to the backscatter peak position. This asymmetric positioning allows the PSF to accurately model the physical reality of backscatter electrons that originate from deep within the target and emerge at positions displaced from the incident beam location, thereby improving modeling accuracy without excessive complexity
Solution Approach 2:
The patent changes the parameter configuration of the Gaussian PSF by introducing an offset parameter that shifts the maximum amplitude from the beam center (ξ=0) to the backscatter peak position (ξ=ξ_bs). This parameter modification transforms the traditional centered Gaussian into an off-center Gaussian that captures the essential physics of backscatter while maintaining the mathematical simplicity of the Gaussian functional form
2Reliability
If centered PSF functions are used, then the computational simplicity is maintained, but the reliability of proximity effect correction deteriorates for heavy metal layers
Solution Approach 1:
The patent implements asymmetry by positioning the Gaussian maximum at the backscatter peak location rather than at the beam center. This asymmetric placement is particularly important for heavy metal layers where backscatter is significant, as it accurately represents the physical phenomenon of electrons scattering deep within the target and emerging at displaced positions, thereby improving correction reliability
Solution Approach 2:
The patent segments the PSF into multiple Gaussian components, each centered at different positions corresponding to forward scatter and backscatter peaks. This segmentation allows independent optimization of each component's parameters (amplitude, width, position) to match the specific characteristics of different scattering processes in heavy metal targets, enhancing overall model reliability
3Measurement precision
If traditional PSF models are used, then the ease of implementation is maintained, but the accuracy of distant proximity effects deteriorates
Solution Approach 1:
The patent modifies the standard Gaussian PSF parameters by introducing an offset parameter that shifts the maximum from the beam center to the backscatter peak position. This single parameter change significantly improves distant effect accuracy while maintaining the familiar Gaussian functional form and convolution-based implementation approach, thus preserving ease of operation
Solution Approach 2:
The patent introduces dynamic positioning of the Gaussian maximum that can be adjusted based on the specific target material and beam conditions. The offset parameter can be optimized for different scenarios (heavy metal layers, acceleration voltages), allowing the model to adapt to various conditions while maintaining a simple implementation framework
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
This approach significantly reduces mean residual squared error by 49% compared to traditional centered Gaussian models and 32% compared to Kamikubo's model, providing a more accurate correction for proximity effects in electron beam interactions, especially in extreme UV mask etching.
Implementation Method 1
This interaction is notably affected by a diffusion of the electrons around the initial trajectory (effect of forward scattering or diffusion towards the front)
Implementation Method 2
as well as by a retrodiffusion (effect of back scattering or diffusion towards the back)
Data Source
Figure 1a~1b
Figure 2a~2b
Figure 2c~2d
AI summary
The method involves correcting effects of forward and backward scattering of an electronic beam (100) by calculating a point spread function i.e. linear combination of Gaussian and gamma functions, where the point spread function comprises a function i.e. gamma distribution function, whose one maximum value is not located on a center part of the electronic beam and another maximum value is located on a backward scattering peak of the electronic beam, and another function with a maximum value located on the center part of the electronic beam to model forward scattering. Independent claims are also included for the following: (1) a non-ephemeral computer-readable medium comprising a set of instructions to simulate or correct effects of forward and backward scattering of an electron beam (2) an electronic lithography system (3) a system for simulating electronic lithography (4) an electronic microscopy system.