Wafer Fabrication Facility Based on Gaussian Process Regression - - PowerPoint PPT Presentation

Prediction Model for Long-term Performance Indicators of Semiconductor Wafer Fabrication Facility Based on Gaussian Process Regression

Zhihong Min Presenter

Zhihong Min， Li Li

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OUTLINE

I

• MOTIVATION & FORMULATION

II

• MODEL & ANALYSIS

III

• CONCLUSION & DISCUSSION

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Motivation

 Semiconductor Manufacturing

Background

Information society

Computer X-Box Pad Router Flash Disk Cell phone

Factory

Customers

Time...

Challenges and Opportunities

Motivation

Challenges

Multiple re-entrant feature Complicated working conditions Draw plan by experience

Opportunities

Big Data Prediction Method (LR) Cloud Manufacturing

Factory Customer

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KPI Prediction Platform

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Motivation

Background

 A bridge for factory and customers

Work in Process Queue Length Move ment Through put Equipm ent Utility On-time Delivery Rate Cycle Time

Short-term KPI Long-term KPIs To choose proper supplier according to the prediction results To make daily feeding plans from the perspective

• f overall optimization and satisfy customer requirements

Main concern: When does my proposed

• rder could be

delivered? Make production plan according to the current working condition and order request Build a prediction Model Real-time collected by the real fab line

Previous Work

Motivation

 Multi-linear Regression

• It is an approach for modeling the relationship between a scalar dependent

variable y and one or more explanatory variables (or independent variables) denoted X.

• Define Loss function
• To obtain the parameters which makes loss function minimum.

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OUTLINE

I

• MOTIVATION & FORMULATION

II

• MODEL & ANALYSIS

III

• CONCLUSION & DISCUSSION

Process Overview

MODEL & ANALYSIS

Data Pre-Processing

• Data cleansing
• Statistics for

KPIs (long/short) Short-term KPI Selection Process

• Pearson

correlation coefficients

• Selection Process

Prediction Method

Data Set Database Training Set

Experiment

• Gaussian Process

Regression

• Test &

Comparison of GPR & LR

• Error Analysis

GPR VS. LR Test Set

STEP 1 STEP 4 STEP 2 STEP 3

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Data Pre-processing

MODEL

 Data cleansing and filtration  Statistics for KPI（long-term & short-term)

• one-year daily production database，6 sampling times everyday
• 31 sheets everyday，covering almost all information throughout the whole fab
• Delete wrong data
• Compute long-term KPI according to the production type
• Computer short-term KPI everyday

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Short-term KPI Selection Process

Model

 Pearson correlation coefficients

To measure the correlation between KPIS.

Move An important KPI to measure the overall performance of Fab Work In Process Being fabricated or waiting for further processing in a queue

• r a buffer storage

Queue Length Number of lots queued at a particular station during a period of time Equipment Utility Rate of the operation time of some equipment during a period

• f time
• higher processing capability of semi-conductor

wafer fab

• higher utility of equipment
• more completed processing tasks.

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Short-term KPI Selection Process

Model & Analysis

 Ranking results of Pearson correlation coefficients

0.2 0.4 0.6 0.8 1 1.2 1 2 3 4 5 6 7 8 9 10 11 12

WIP-MOVE Coefficient

• 0.2

0.2 0.4 0.6 0.8 1 1.2 1 2 3 4 5 6 7 8 9 10 11 12

QL-MOVE Coefficient The impact put by a single variable on Move when WIP is higher, is not greater than when WIP is low.

• The coefficient for EQP UTI and Move is smaller than that

for WIP and Move and that for QL and Move, which clearly indicates that WIP and QL have greater impact on the key short-term performance Move.

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Short-term KPI Selection Process

Model

 Selection Rule

0.1 0.2 0.3 0.4 0.5 0.6 0.7

• Too much equipment would be used in each month
• Varing considerably

18 Equipment

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Training Set

Model

CT

UTI

Lot-in-time

Move

TH

QL

ODR

QL

WIP

Lot-in-time

WIP

Move Product ② Product ① Product③

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Prediction Method

Model

 Gaussian Regression Process

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• Gaussian distribution over functions, a collection of random variables
• Function-space view:
• Every point in some input space is associated with normally distributed

random variable

• Every finite collection of those random variables has a multivariate

normal distribution

𝝂

𝚻

𝒣𝒬( 𝑛 𝑦 , 𝑙(𝑦, 𝑦′ )

Mean Function: 𝑛 𝑦 = 𝐹 𝑔 𝑦 For notational simplicity: 𝑛 𝑦 = 0 Covariance function: 𝑙 𝑦, 𝑦′ = 𝐹[(𝑔 𝑦 − 𝑛 𝑦 )(𝑔 𝑦′ − 𝑛(𝑦′ ))] Squared exponential (SE): 𝑙 𝑦, 𝑦′ = 𝐟𝐲𝐪(− 𝟐 𝟑 𝒚 − 𝑦′ )

Prediction Method

Model

 Gaussian Regression Process

* A consistency requirement: if the GP e.g. specifies (𝒛𝟐, 𝒛𝟑) ~ N ( 𝝂,𝚻 ), then it must also specify property:𝒛𝟐 ~ N ( 𝝂𝟐,𝚻𝟐𝟐) , where 𝚻𝟐𝟐 is the relevant submatrix of 𝚻 .

• In predicting problems, when given training data

we want to make predictions f* at test points X* .

• Joint distribution of f and f* ：
• Calculating f* can be simplified to calculating the posterior based on

the known observations

• Predicted value

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OUTLINE

I

• MOTIVATION & FORMULATION

II

• MODEL & ANALYSIS

III

• CONCLUSION & DISCUSSION

Error Rate Comparison

Experiment

 Data Analysis

Product GPR LR B0 9.55% 28.03% B9 10.01% 26.38% 6L1 14.04% 17.57% 6M1 14.79% 25.71% B1 9.59% 13.50% 6B1 12.33% 30.30% 6M0 12.98% 25.26% 6M9 4.73% 24.87% Product GPR LR B0 3.14% 10.96% B9 2.04% 5.01% 6L1 4.30% 20.51% 6M1 2.54% 12.96% B1 1.08% 2.79% 6B1 4.25% 24.56% 6M0 4.35% 10.69% 6M9 2.07% 7.02%

• Error Rate Comparison Form for ODR
• Error Rate Comparison Form for CT

RESULTS:

• Error rate improves for every kind of product, compared to linear regression
• Accuracy of ODR is much higher than that of CT
• Huge fluctuations of cycle time.
• Other factors not included

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Error Rate Comparison

Experiment

 Chart Analysis

0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00% B0 B9 6L1 6M1 B1 6B1 6M0 6M9 GPR LR 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% B0 B9 6L1 6M1 B1 6B1 6M0 6M9 GPR LR

CT error rate comparison histogram ODR error rate comparison histogram

RESULT

• Improvement of error rates on CT dataset are less than that on ODR dataset, compared to

multi-linear regression

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Radar comparison map

Experiment

 Cycle Time

20 40 60

CT_6B1

20 40 60 80

CT_6M1

20 40 60

CT_6M0

10 20 30

CT_6M9

2 4 6 8 10

CT_6L1

20 40 60

CT_B0

10 20 30 40

CT_B1

10 20 30 40

CT_B9

*Blue denotes predicted value. Orange denotes actual value.

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Radar comparison map

Experiment

 On-time Delivery Rate

0.2 0.4 0.6 0.8 1

ODR_6B1

0.75 0.8 0.85 0.9 0.95 1

ODR_6M0

0.5 1 1.5

ODR_6M1

0.9 0.92 0.94 0.96 0.98 1 1.02

ODR_6M9

0.2 0.4 0.6 0.8 1

ODR_6L1

0.8 0.85 0.9 0.95 1 1.05

ODR_B0

0.85 0.9 0.95 1

ODR_B1

0.96 0.97 0.98 0.99 1

ODR_B9

*Blue denotes predicted value. Orange denotes actual value.

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Conclusion

CONCLUSION & DISCUSSION

• Prediction Model for Long-term Performance

Indicators of Semiconductor Wafer Fabrication Facility

• Short-term KPI Selection Process
• Gaussian Process Regression

Discussion

• Incorporate More quantifiable factors
• working condition /equipment utility /resource allocation /staff

allocation

• Incorporate other relations between a few factors
• Little’s Law...

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Thank you for your attention!