Evaluation of Equipment Models of Clustered Photolithography Tools - PowerPoint PPT Presentation

Evaluation of Equipment Models of Clustered Photolithography Tools for Fab-level Simulation Jung Yeon Park, James R. Morrison, and Kyungsu Park Department of Industrial and Systems Engineering KAIST, South Korea Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 1

Presentation Overview • Motivation • System Description: Clustered Photolithography Tool (CPT) • Equipment Models  Linear model  Affine models  Flow line models (Improved) • Numerical Experiments  Description (Three types of simulation)  Results • Concluding Remarks Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 2

Motivation Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 3

Motivation (1) - CPT • Clustered photolithography tools (CPT) • Cost up to $120 million [1] , typically $20 – 50 million • Often the fabricator bottleneck • Key contributor to fab throughput capacity and cycle time [2] Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 4

Motivation (2) – Fab-level Simulation • High construction costs • Fabs must be well-designed and operated efficiently • Fab-level Simulation • Essential decision support technology • Examples: • Detailed AMHS models (Jimenez et al. 2008, Hsieh et al. 2012) • Studies of fab behavior in relation to changes in lot size (Schmidt et al. 2006) • Cycle time reduction (Zarifoglu et al. 2008) • Equipment models are key components of fab-level simulation Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 5

Motivation (3) – Features of Equipment Models • Tradeoff: Fidelity vs. complexity • More detailed models lead to greater fidelity, but require longer computation times • Require more modeling effort • Fab conditions can often change (different lot sizes, new toolsets, changing product mix, etc.) • Models often trained on specific set of input data, may not be robust when input conditions change • Goal: Comparison of CPT Models for use in fab-level simulation • Accurate: Predict throughput with less than 1% error • Expressive: Incorporate fundamental behaviors • Computation: Very quick to calculate results • Robust: Less dependent on input data Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 6

System Description Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 7

System Description (1) – CPT Scanner C lustered P hotolithography T ool • Multi-cluster tool, robot in each cluster, IF buffers, STK buffer • Scanner is often the CPT bottleneck • Largely deterministic process times • Process time can vary by product • Setups between lots (reticle changes, pre- scan setup, …) • Wafer handling robot decision policy Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 8

System Description (2) – Performance Metrics • Notation Lot class : 𝑙 1 ∈ 1, … , . 𝐿 a i : Arrival time of lot i to the tool Number of wafers in lot i : 𝑋 S i : Start time of lot i in the tool 𝑗 C i : Completion time of lot i from the tool • Performance measures Cycle time of lot i : 𝐷𝑈 𝑗 = 𝐷 𝑗 − 𝑏 𝑗 Computation time Lot residency time of lot i : 𝑀𝑆𝑈 𝑗 = 𝐷 𝑗 − 𝑇 𝑗 Throughput time of lot i : 𝑈𝑈 𝑗 = 𝑛𝑗𝑜(𝐷 𝑗 − 𝑇 𝑗 , 𝐷 𝑗 − 𝐷 𝑗−1 ) TT 1 TT 2 TT 3 Lot 1 Lot 2 Lot 3 Time Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 9

Equipment Models Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 10

Equipment Model (1) – Linear Model Ax Model for Lot cycle time in a one module tool Wafers Wafers enter exit m 𝐵 𝑙 1 • Referred to as the Ax equipment model or linear model • Used to study recipe dedication in CPTs in an ASIC fab model [3] Lot indices per class : 𝑀 𝑙 1 = 𝑗 𝑙 𝑗 = 𝑙 1 • Com omplete Mo Model: • 𝑙 1 is current lot class 𝐵 𝑙 1 • Time between wafer completions: 𝑇 𝑗 = max{𝑏 𝑗 , 𝐷 𝑗−1 } • 𝑇 𝑗 + 𝐵 𝑙 1 × 𝑋 𝐷 𝑗 = Parameter estimation: 𝑗 𝑗∈𝑀(𝑙1) 𝐷 𝑗 −𝑛𝑏𝑦 𝑏 𝑗 ,𝐷 𝑗−1 𝐵 𝑙 1 = 𝑗∈𝑀(𝑙1) 𝑋 𝑗 Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 11

Equipment Model (1) – Linear Model Ax Model for Lot cycle time in a one module tool Wafers Wafers enter exit m 𝐵 𝑙 1 • Pros: • Simple to understand • Fast computation • Cons: • Exactly matched to single module tool, not for CPT • New lots enter only when the tool is empty (No parallelism) Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 12

Equipment Model (2) – Affine Model Ax+B Model for Lot cycle time • Referred to as the Ax+B model 𝑗∈𝑀(𝑙 1 ) 𝐷 𝑗 − 𝑛𝑏𝑦 𝑏 𝑗 , 𝐷 𝑗−1 𝐵 𝑙 1 = • Com omplete model: Basic model provided in AutoSched AP [4] 𝑗∈𝑀(𝑙 1 ) 𝑋 𝑗 𝑀 𝑙 1 , 𝑙 2 = 𝑗 𝑙 𝑗 = 𝑙 1 , 𝑙 𝑗 − 1 = 𝑙 2 • Lot indices per pairs of classes : 1 𝑇 𝑗 = 𝑛𝑏𝑦 𝑏 𝑗 , 𝐷 𝑗−1 𝐶 𝑙 1 ,𝑙 2 = 𝐷 Ω 𝑗,1 − max 𝑏 𝑗 , 𝐷 𝑗−1 𝑀(𝑙 1 , 𝑙 2 ) 𝑙 1 is current lot class, 𝑙 2 is previous lot class 𝐷 𝑗 = 𝑇 𝑗 + 𝐵 𝑙 1 × (𝑋 • 𝑗 −1) + 𝐶 𝑙 1 ,𝑙 2 𝑗∈𝑀(𝑙 1 ,𝑙 2 ) 𝐶 𝑙 1 ,𝑙 2 • First wafer delay: B is generalized to consider setups between classes • 𝐵 𝑙 1 Time between wafer completions: Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 13

Equipment Model (2) – Affine Model Ax+B Model for Lot cycle time • Pros: • Simple to understand • Fast computation • Cons: • Only one module per process, so not matched to CPT • New lots enter only when the tool is empty (No parallelism) Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 14

Equipment Model (3) – Flow Line Models • Have been used for optimization and simulation modeling studies ([5] – [8]) Series of sequential processes 𝑄 1 , … , 𝑄 𝑁 • • Buffers modeled as zero process time modules • Fundamental assumption: CPT is process-bound • Modifications for CPT modeling • Consider robotic workload in process times of modules • Consider setups – reticle setup, pre-scan setup • Different number of processes for different lot classes • Two types of flow lines • Parametric flow line (PFL) : Known process times • Empirical flow line (EFL) : Unknown process times Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 15

Equipment Model (3) – Flow Line Models • Notation 𝑏 𝑥 : Arrival time of wafer w to the tool, 𝑏 𝑥 ≤ 𝑏 𝑥+1 • 𝑌 𝑥,𝑛 : Entry time of wafer w into process m of the tool • • 𝑆(𝑙, 𝑛) : number of identical servers for process m for wafer class k 𝑙 : Deterministic process time for process m for wafer class k • 𝜐 𝑛 • Modified Process Times Parametric FL Empirical FL 𝑋 𝑚 (𝑌 𝑥,𝐶+1 − 𝑌 𝑥−1,𝐶+1 ) 𝑚∈𝑀 𝑙 𝑥=2 , 𝑛 = 𝐶 𝑙 + 3𝜀 + 4𝜁, 𝜐 𝑛 𝑛 = 𝑄𝐶 𝑚∈𝑀 𝑙 𝑋 𝑚 − 1 𝑙 + 2𝜀 + 4𝜁, 𝑇 𝑙, 𝑛 = 𝜐 𝐶 𝑛 = 𝐶 𝑇 𝑙, 𝑛 = 𝑥,𝑙 𝑥 =𝑙 𝐷 𝑥 − 𝑌 𝑥,𝑛 , min 𝑛 = 𝑁 𝑙 + 𝜀 + 2𝜁, 𝜐 𝐶 𝑝𝑢ℎ𝑓𝑠𝑥𝑗𝑡𝑓 𝑥,𝑙 𝑥 =𝑙 𝑌 𝑥,𝑛+1 − 𝑌 𝑥,𝑛 , min 𝑝𝑢ℎ𝑓𝑠𝑥𝑗𝑡𝑓 • Elementary Evolution Equations 𝑌 𝑥,1 = 𝑛𝑏𝑦 𝑏 𝑥 , 𝑌 𝑥−𝑆 ′ (𝑙,1),𝑄 𝑥 +1 , 𝑌 𝑥−1,1 + 𝜐 𝑡 ′ 𝑥, 𝑛 • 𝑌 𝑥,𝑛 = 𝑛𝑏𝑦 𝑌 𝑥,𝑛−1 + 𝑇 𝑙, 𝑛 − 1 + 𝜐 𝑆 ′ 𝑥, 𝑛 , 𝑌 𝑥−𝑆′ 𝑙,𝑛 ,𝑛+1 , 𝑌 𝑥−1,𝑛 • 𝑌 𝑥,𝑁 = 𝑛𝑏𝑦 𝑌 𝑥,𝑁−1 + 𝑇 𝑙, 𝑁 − 1 , 𝑌 𝑥−𝑆′ 𝑙,𝑁 ,𝑁 + 𝑇(𝑙, 𝑁), • 𝑌 𝑥−1,𝑁 • Start and Completion Times 𝑇 𝑗 = 𝑌 𝛻(𝑗,1),𝑒(𝑙) • 𝐷 𝑗 = 𝑌 𝛻(𝑗,𝑋(𝑗)),𝑁 + 𝑇(𝑙, 𝑁) • Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 16

Numerical Experiments Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 17

Numerical Experiments (1) – Detailed Model [9] • Use CPT data from industry [9] ; create detailed CPT model using discrete event simulation • Two interface buffers (IF), one pre-scan buffer (STK) • Longest waiting pair (LWP) robot policy [10] : gives optimal steady state throughput • Robot move time : 3s, pick/place time : 1s • Deadlock avoidance rule • Reticle alignment setup (for every lot) ~Unif[240, 420] • Pre-scan track setup (for lot class change) ~ Unif[210, 260] 15,000 lots × 30 replications • • Detailed model assumed to be exact Park, Morrison, and Park – 2015 ISMI – October 17, 2015 - 18