The Optimization of Neural Networks Model for X-ray ...

The Optimization of Neural Networks Model for X-ray ...

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

m and a wide scope of m and a wide scope of advantages for the application in se miconductor 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 m anufacturing, in the case of x-ray lit hography. Data and Existing Approach

Data source: 1327 train samples,125 test samples--Department of Electrical and C omputer 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 200,220,240,260,280,300,320,340,360,380,40011(absorber thickness) 10000,12000,14000,16000,18000,20000,22000,24000,26000,28000,30000-10(gap) -18,-14,-10,-6,-2,2,6,10,14,18,22,2612(bias) Input Range: -0.2~0.4 Train sample: 64 Test sample: 125

Approach: Radial-basis Function Parameter choosing( , ) Decrease training samples number Result: A mapping from the inputs to the outputs based on r adial-basis function is obtained by training 64 training samples and choosing the optimal parameters for ra dial-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 (Multilayer Perceptron) --A better error performance is expected to be achieved Current Result

A mapping from the inputs to the outputs based on r adial-basis function is obtained by training 64 training samples (compared with 125 training sample) and ch oosing the optimal parameters for radial-basis functio n. 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 b y increasing the number of training samples and the smallest Point to Point maximum error is 0.4%(The i deal error performance is below 0.1%).

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