Electron-Beam Lithography PSF Estimation via Calibration Patterns
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Solution Overview
Problem
Electron-beam lithography faces challenges in printing fine patterns due to the proximity effect caused by scattered electrons, which requires precise modeling of the point spread function (PSF) to offset distortions, but existing methods are imprecise and require digital simulation programs.
Innovation Solution
A method that prints calibration patterns with concentric zones on a substrate, measures their dimensions, and calculates the PSF without assuming the shape of the back-scattered electrons' PSF, using analytical modeling to estimate the PSF as the sum of two portions, one for substrate and resin-scattered electrons, allowing for precise dose calculation without digital simulation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the PSF is modeled using a sum of Gaussian functions with coefficients determined by solver simulation, then the pattern printing precision can be improved, but the device complexity and processing time increase due to requiring digital simulation programs
Solution Approach 1:
The invention extracts only the essential measurement data (characteristic dimensions of calibration patterns) from the complex simulation process. By measuring actual printed pattern dimensions and using these directly to determine PSF parameters, the method removes the need for complex digital solver simulations while maintaining precision.
Solution Approach 2:
The system uses its own measurement capabilities to directly obtain PSF parameters. The electron beam printing device prints calibration patterns, measures their dimensions, and uses these measurements to characterize the PSF, making the system self-calibrating without external complex simulation tools.
2Ease of manufacture
If the PSF shape is assumed to be Gaussian for back-scattered electrons, then the calculation process is simplified, but the pattern printing precision deteriorates because the actual PSFBE distribution is not Gaussian
Solution Approach 1:
The invention changes the approach from assuming a fixed Gaussian functional form to determining PSF parameters directly from measurements. By measuring characteristic dimensions of calibration patterns and using these to calculate PSF parameters, the method adapts to the actual non-Gaussian PSFBE distribution while maintaining calculation simplicity.
3Measurement precision
If digital simulation programs are used to calculate PSF parameters from calibration patterns, then the PSF can be characterized, but the processing time increases
Solution Approach 1:
The invention replaces the mechanical/computational simulation process with a direct mathematical calculation based on measurements. Instead of using iterative solver programs to simulate electron scattering, the method directly calculates PSF parameters from measured calibration pattern dimensions using analytical relationships.
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 provides precise pattern printing with enhanced precision by directly calculating the PSF from measured dimensions, accelerating the process and eliminating the need for digital simulation programs, effectively offsetting proximity effects.
Implementation Method 1
exposure of the substrate to the electron beam generates scattered electrons, including electrons scattered in the resin
Implementation Method 2
printing by means of electron-beam lithography, in a resin arranged on a substrate, a set of calibration patterns
Implementation Method 3
electrons back-scattered by the substrate, producing the so-called 'proximity effect'
Data Source
AI summary
This method for estimating patterns (M′PF,D′PF) to be printed by means of electron-beam lithography, comprises the following steps: printing (100), in a resin, a set of calibration patterns (MCF, DCF); measuring (120) characteristic dimensions (CD) of this set; supplying an estimation (140) of the point spread function (PSF) based on the characteristic dimensions (CD) measured; estimating (160) the patterns (M′PF,D′PF) to be printed by convoluting the point spread function (PSF) supplied with an initial value of the patterns (MPF,DPF).Furthermore, each calibration pattern printed includes a central zone exposed to the electron beam and a plurality of surrounding concentric zones with rotational symmetry. The characteristic dimensions measured are characteristic dimensions (CD) of the central zones of the patterns. The estimation of the point spread function (PSF) is calculated by inverting analytical modelling of the effect, on these characteristic dimensions, of applying the first point spread function portion (PSFBE) characterising electrons back-scattered by the substrate to the set of calibration patterns (MCF, DCF).