Transcript Presentation

The Optimization of Neural Networks
Model for X-ray Lithography of
Semiconductor
ECE 539 Project
Jialin Zhang
Introduction
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X-ray lithography with nm-level
wavelengths provides both high
structural resolution as good as 0.1
μm and a wide scope of
advantages for the application in
semiconductor production. The
parameters such as gap, bias,
absorb thickness are important to
determine the quality of the
lithography.
This project deals with optimization
of parameters for semiconductor
manufacturing, in the case of x-ray
lithography.
Data and Existing Approach
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Data source:
1327 train samples,125 test samples--Department of Electrical
and Computer Engineering and Center for X-ray Lithography
Data structure:
3 inputs--absorber thickness, gap, bias
3 outputs--linewidth, integrated modulation transfer function,
fidelity
Existing Approach: A neural network based on radial-basis
function
the multivariate function:
(linewidth, IMTF, fidelity)=F(absorber thickness, gap, bias)
125 training samples: regularly distributed in the input space
error performance: (tested on the test samples, ”Point to Point”)
mean error: 0.2% ~0.4 %
maximum error: 4%
Goal
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decrease the number of training samples
necessary to obtain a mapping from the
inputs to the outputs
improve the error performance
---the ideal maximum error is below 0.1%
Decrease training samples number
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Pre-Process the training data
Data distribution feature: (After recombining the data set )
Range of the data set of 1452 sample：
200,220,240,260,280,300,320,340,360,380,400—11(absorber thickness)
10000,12000,14000,16000,18000,20000,22000,24000,26000,28000,30000-10(gap)
-18,-14,-10,-6,-2,2,6,10,14,18,22,26—12(bias)
Input Range: -0.2~0.4
Train sample: 64 Test sample: 125
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Approach: Radial-basis Function
Parameter choosing( λ, σ)
Decrease training samples number
Result:
 A mapping from the inputs to the outputs based on
radial-basis function is obtained by training 64
training samples and choosing the optimal
parameters for radial-basis function.
 The “Point to Point” mean errors: 0.7%~0.9%
 The “Point to Point” maximum error is 5.6%
Improve the error performance
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Approach:
Increase the number of training samples
--the smallest “Point to Point” maximum error that has ever
achieved is 0.4%.
use different types of neural networks (Multilayer Perceptron)
--A better error performance is expected to be achieved
Current Result
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A mapping from the inputs to the outputs based on
radial-basis function is obtained by training 64
training samples (compared with 125 training sample)
and choosing the optimal parameters for radial-basis
function. The “Point to Point” mean errors are
0.7%~0.9% (compared with 0.2%~0.4%)and
maximum error is 5.6%(compared with 4%).
The error performance of the mapping is improved
by increasing the number of training samples and
the smallest “Point to Point” maximum error is
0.4%(The ideal error performance is below 0.1%).