The Optimization of Neural Networks Model for X-ray Lithography of Semiconductor

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1 Νοε 2013 (πριν από 4 χρόνια και 7 μέρες)

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The Optimization of Neural Networks
Model for X
-
ray Lithography of
Semiconductor

ECE 539 Project

Jialin Zhang

Introduction


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



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



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


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


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


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 (Multi
-
layer Perceptron)


--
A better error performance is expected to be achieved

Current Result


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%
)
.