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Multiphysics Simulation of Conjugated Heat Transfer

and Electric Field on Application of Electrostatic

Chucks (ESCs) Using 3D-2D Model Coupling

Kuo-Chan Hsu1，Chih-Hung Li1，Jaw-Yen Yang1,2

Jian-Zhang Chen1，Jeng-Shian Chang1

1Institute of Applied Mechanics, National Taiwan University, Taiwan (R.O.C)2Center for Advanced Study in Theoretical Sciences, National Taiwan University, Taiwan (R.O.C)

Excerpt from the Proceedings of the 2014 COMSOL Conference in Shanghai

Outlinei. Overview of Electrostatic Chucks (ESCs)

ii. Why is Multiphysics?

iii. Boundary Conditionsa) Electric field model

b) Conjugated heat transfer model

iv. Result of Simulationa) Electric field model

b) Conjugated heat transfer model

vi. Conclusion

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Excerpt from the Proceedings of the 2014 COMSOL Conference in Shanghai

Overview

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The main thermal resistances in the heat path are the ceramic and the transition fromthe ceramic to the cooling liquid.Thermal energy is transferred to the wafer surrounding through ion bombardment,and the chuck is required to remove large amounts of heat from the wafer whilemaintaining a stable and uniform temperature.

Simulation model

Excerpt from the Proceedings of the 2014 COMSOL Conference in Shanghai

Ref:1.Four Decades of Research on Thermal Contact, Gap,and Joint Resistance in Microelectronics Yovanovich, M.M. Components and Packaging Technologies, IEEE Transactions on Volume: 28, Issue: 2 , 20052.Microscopic approach to an equation for the heat flow between wafer and E-chuck, M Klick, M Bernt - Journal of Vacuum Science & Technology B, 20063.J.YOO et al., Proceeding of International Conference on Electrical Machines and Systems (2007)

Multiphysics

Exploded drawing of the ESC

Electrode

Groove for Helium

Physics

Heat transfer

Electrostatic force

Physics

0.000 0.004 0.008 0.012 0.016 0.020 0.0240

500

1000

1500

2000

2500

3000

P2

Ele

ctr

ic p

reassu

re (

Pa)

X-axis position (m)

Bottom of wafer

Top of wafer

P1

Groove for water

Fluid dynamics

Physics TheoryNavier-Stokes Equation

Principal Dependencies of the Wafer Temperature

ℎ𝑎

Maxwell’s stress tensor

ℎ𝑔

Cooper-Mikic-Yovanovich Correlation

Theory

Excerpt from the Proceedings of the 2014 COMSOL Conference in Shanghai

Boundary Conditions

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Geometry of electrode pairs (Bipolar)

Boundary conditions setting up

Silicon AlN 𝐀𝐥𝟐𝐎𝟑 Air

Dielectric

constant11.7 9 9 1

Excerpt from the Proceedings of the 2014 COMSOL Conference in Shanghai

Result for Electric Field

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Excerpt from the Proceedings of the 2014 COMSOL Conference in Shanghai

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Boundary Conditions Assumptions:

i. Stationary stateii. Thermal insulation in the chamberiii. Neglect the heat radiation effectiv. Uniform heat source to the wafer from plasmav. Neglect the heat of chemical reaction on wafers

ℎ𝑓 =𝑞

𝐴∆𝑇=

𝐶

𝑝𝛼𝑎+𝑑

𝜅+

𝐶

𝑝𝛼𝑏

−1

hs = 1.25 kmasp

σasp

p

Hc

0.95

Maxwell’s stress tensor

Navier-Stokes Equation

Principal Dependencies of the Wafer Temperature

Cooper-Mikic-Yovanovich Correlation

Excerpt from the Proceedings of the 2014 COMSOL Conference in Shanghai

Simulation Result

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AlN ceramic body Al2O3 ceramic body

From the result of simulation, the deep blue is near to the cooling inlet. It meansthe temperature distribution largely depends on the geometry of cooling liquid.Due to the high thermal conductivity for AlN, most of the heat goes throughceramic material and is transferred to cooling liquid.

Excerpt from the Proceedings of the 2014 COMSOL Conference in Shanghai

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Simulation Result

AlN ceramic body Al2O3 ceramic body

Excerpt from the Proceedings of the 2014 COMSOL Conference in Shanghai

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Simulation Result

Temperature uniformity Top Temperature

For Al2O3 ceramic, most of the heat energy is transferred to backside heliumdue to low thermal conductivity.For AlN ceramic, most of the heat energy is transferred to cooling liquid due tohigh thermal conductivity.

Excerpt from the Proceedings of the 2014 COMSOL Conference in Shanghai

Conclusion

I. The AlN ceramic body significantly reduces the wafer temperatureand non-uniformity than Al2O3 does.

II. The non-symmetrical temperature distribution mainly results fromthe geometric design of cooling water channel.

III. The electrostatic voltage is a principal factor of the wafertemperature and the distribution.

IV. The top temperature slightly increases as backside pressure due tothe less contact force of ESCs to the wafer.

V. Relationship between the electrostatic force and potential voltageis built up.

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Excerpt from the Proceedings of the 2014 COMSOL Conference in Shanghai

Thank You for Your Attention!

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Kuo-Chan HsuAerodynamics Design & Analysis LaboratoryR007, Institute of Applied Mechanics, National Taiwan UniversityNo.1, Sec.4, Roosevelt Road, Taipei 106, TaiwanEmail: r02543025@ntu.edu.tw

The authors gratefully acknowledge the funding by National Chung-ShanInstitute of Science & Technology (NCSIST) and assistance of LeadingPrecision Inc. (LPI).

Excerpt from the Proceedings of the 2014 COMSOL Conference in Shanghai