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On a Sampling Decision System usingVirtual Metrology
D. Kurz
O. Univ.-Prof. Dr. J. PilzAAU Klagenfurt, Department of Statistics
Dr. C. De LucaInfineon Technologies Austria AG
4 December 2013
D. Kurz On a Sampling Decision System usingVirtual Metrology
Innovation
Semiconductor process control: the current state-of-the-art
Based on physical measurements
Only certain number of wafers measured
Statical measurement rules
Semiconductor process control with a sampling decisionsystem
Based on virtual measurements
Virtual measurements for every wafer
Dynamical measurement rules
1 2 3
4 5 6
7 8 9
LCL
Target
UCL
a a a a a a a a
D. Kurz On a Sampling Decision System usingVirtual Metrology
Applied statistical methods
Sampling decision evaluation
Decision-theoretical modeling of virtualmeasurements
Expected utility of measurement information
Lindley information and wafer quality risk values
Monitoring reliability of virtual measurements
Quantification of performance of virtualmeasurements
Detection of unreliable virtual measurements
Update of precision of virtual measurements
PIT
Den
sity
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
VM: N(0,10²)VM: N(0,15²)
µVMk
AAA
yk����
aa
D. Kurz On a Sampling Decision System usingVirtual Metrology
Results
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0 10 20 30 40 50
−15
0−
5050
150
wafer no.
mea
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real metrologyvirtual metrology
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0 10 20 30 40 50
0.00
0.10
0.20
0.30
wafer no.
EV
ofM
I
49
50
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0 10 20 30 40 50
0.0
0.2
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wafer no.
exp.
loss
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prior riskpreposterior risk
D. Kurz On a Sampling Decision System usingVirtual Metrology
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