ECE 539 Project Jialin Zhang

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ECE 539 Project Jialin Zhang 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%).