Heat Transfer in Solid and Fluids

8/18/2019 Heat Transfer in Solid and Fluids

1/49

Heat Transfer in Solid and Fluids

John Dunec

COMSOL

© 2013 COMSOL. COMSOL, COMSOL Multiphysics, Capture the Concept and COMSOL Desktop are registered trademarks ofCOMSOL AB. LiveLink is a trademark of COMSOL AB. Other product or brand names are trademarks or

registered trademarks of their respective holders.

Jon Ebert

SC Solutions


2/49

Agenda

• Multiphysics and the Power of COMSOL

• An Overview of Heat Transfer with COMSOL

–

Conduction / Convection / Radiation – Coupling Heat Transfer with other Physics

• Thermal Modeling of a CVD Reactor

–

Video Demo

• Q&A Session


3/49

Multiphysics: Multiple Interacting Phenomena

Could be simple

• Heat convected by Flow

Could be complex

• Local temperature sets

reaction rates

• Multiple exothermic reactions

• Convected by flow in pipes

and porous media

• Viscosity strongly temperature

dependent


4/49

COMSOL Multiphysics® Solves These!

• Multiphysics – Everything can link to everything

• Flexible – You can model just about anything

• Usable – You can keep your sanity doing it

• Extensible – If its not specifically there…add it!


5/49

All Inclusive Interactive Modeling Environment

Model Builder

Provides instant

access to any part of

the model settings

• CAD/Geometry• Materials

• Physics

• Mesh

• Solve

• Results

Graphics

Ultrafast graphic presentation, stunning

visualization, and multiple plots

COMSOL Desktop®Straightforward to

use, it gives full

insight and control

over the modeling

process


6/49

Product Suite


7/49

Anywhere you can type a number or an equation

• …Or an interpolation function

• And it can depend on anything known in your problem

•

Example: Concentration-dependant viscosity

221001.0 c

Low concentration,

High velocity

High concentration,

Low velocity


8/49

Add Your Own Equations to COMSOL’s

Don’t see what you need?

Add your own equation

•

ODE’s • PDE’s

• Weak form PDE’s

Just type them in

• No Recompiling

• No Programming


9/49

Interface with CAD, Excel and MATLAB

• CAD import

• LiveLink for CAD softwares

• LiveLink for Excel

•

LiveLink for MATLAB

Pacemaker Electrode Modeled with LiveLink™ for SolidWorks®


10/49

Support for High-Performance Computing

Multi-Core Parallel Computing

• No Extra Charge

• Fully Supported on all Licenses

Cluster Parallel Computing

• No Extra Charge

• Requires Floating Network License

• Freq Sweep / Parametric Sweep

• Distributed Single Large Problem

Solvers

• Direct / Iterative - Fully Coupled / Segregated


11/49

Conjugate heat transfer around an

aluminum heat sink

Heat Transfer in COMSOL Multiphysics

Used on its Own

• Conduction

• Thermal Radiation

• Thin Conductive Media and Resistive Layers

Linked to Flow• Conduction-Convection

• Laminar / Turbulent

• Porous Media

• Bioheat Equation

Linked to Other Physics

• Structural mechanics

• Electromagnetics

• …

Temperature of a disc brake of a car in brake-

and-release sequence


12/49

Light Bulb: All Forms of Heat Transfer

• 60 W filament heats rapidly over the first seconds

• Induces a flow driven by natural convection

• Conduction / Convection / Radiation

t=0.1 sec t=6 sec t=60 s

Temperature Velocity Temperature Velocity Temperature Velocity


13/49

Laser Heating: Surface Heating

• Define Surface Flux hf(x,y)

• Multiply by emissivity

Laser Intensity - Gaussian

Wafer spinning,

Laser moving back

and forth


14/49

Phase Change:

Boiling

• Two Phase Flow with Heat Transfer

• Use Phase Field for 2-Phase Flow

Heat: 105 W/m3

1

1


15/49

Heat Transfer Linked to Other Physics

• Electrical, Mechanical, Fluid, Chemical, Acoustic

• Anything can link to anything!

•

Microwave heating in a waveguide – Skin depth heating of copper plated waveguide

– Volumetric heating of dielectric block

– Properties of block are temperature dependent


16/49

Joule Heating

• Volts x Amps = Power

• Power goes to heat

• Heat expands metal

Current Direction, Isotherms

Temperature [C], Deformation (10x)Current Density from 0.2 volts across resistor


17/49

Magnetic Induction Heating

• Furnace reactor that heats a susceptor of graphite, using an 8

kW RF signal at 20 kHz

• Used in the fabrication of semiconductors to grow layers on

wafers

Surface Plot

• Temperature

Contours

• Temperature

Arrow Plot

• B-field


18/49

Exothermic / Endothermic Reactions

Three Physics: Flow / Heat / Convection-Diffusion with Reactions

• Flow

• Temperature WITHOUT exothermic reaction

•Temperature WITH exothermic reaction

Heater lifts T over activation energy Higher Temperature speeds reaction


19/49

Chemical Heating

Heat from Curing Reaction After 700 sec

Temperature Profile After 750 sec

P M M A C e m e

n t


20/49

SC SOLUTIONS

Thermal Modeling of a CVD Reactor

Case Study: Temperature Control of a Cold-wall Vertical

CVD Reactor with Rotating Susceptor

Jon Ebert

SC Solutions, Inc.

1261 Oakmead Pkwy., Sunnyvale, CA 94085

Email: [email protected]

COMSOL Webinar

March 7, 2013

Copyright© 2013, SC Solutions, Inc. All Rights Reserved 20

SC S l ti

mailto:[email protected]:[email protected]


21/49

SC SOLUTIONS

SC Solutions

Engineering firm in Silicon Valley – 40 employees

Structural Division Founded in 1989

Control Division Founded in 1996

o Engineering Consulting

Using models for equipment design

o Feedback Control Software for Semiconductor Industry

Using models for equipment control

o Contract Research

COMSOL® Certified Consultant, MathWorks® Partner.


MATLAB is a registered trademark of The MathWorks, Inc.

O i

http://www.mathworks.com/products/connections/product_detail/service_35810.html


22/49

SC SOLUTIONS

Overview

Overview of Chemical Vapor Deposition (CVD)

o Chemical process for growing thin solid films

Metal-organic Chemical Vapor Deposition (MOCVD)

o CVD with metal-organic precursors (e.g., tri-methyl Gallium)

o Used to manufacture Light Emitting Diodes (LEDs)

A Case Study of Temperature Control of a Rotating Susceptor CVD Reactoro Show how we use COMSOL and Livelink for Matlab in concert with optimization and

control tools.

o Evaluate design limits for a range of operating conditions.

Summary


Ch i l V D iti


23/49

SC SOLUTIONS

Chemical Vapor Deposition

Process by which a thin solid film is formed on a surface (e.g., wafer) from gas-

phase precursors via chemical reactions.

Used for growing high-purity crystalline layers, typically semiconductor

multilayers.


Susceptor

Wafer Wafer

Wafer

Heater Coils

Heater Coils

Gas flow

Wafer Wafer

Wafer Wafer

Process Gas Entry

Rotating HeatedSusceptor

Process Gas Entry

Wafer

Rotating HeatedSusceptor

Gas Exit

Horizontal Reactor

Vertical Reactor

Pancake Reactor

MOCVD for LEDs


24/49

SC SOLUTIONS

MOCVD for LEDs

MOCVD is used to produce Light Emitting Diodes (LEDs) by

reacting metal-organic precursors (e.g.,tri-methyl Gallium, tri-

methyl Indium, etc.).

Increasingly important for many applications (LED TV’s,

Lighting, etc.) due to potential for high efficiency.

InGaN/GaN multiple quantum well (MQW) structures are

grown on sapphire substrates for green, blue, and white LEDs.


Studies* have shown that LED properties such as photoluminescence and

electroluminescence can vary by a factor of two if the substrate temperature is

changed from 1000°C to 1030°C.

Involves many process steps over a wide temperature range (500-1100°C).

As a result, real-time control of substrate temperature to within 1°C or less is

essential for repeatable manufacturing of LEDs with desired color .

* For example, see J. W. Ju, et al., “Effects of p-GaN Growth Temperature on a Green InGaN/GaN Multiple Quantum

Well,” Journal of the Korean Physical Society, Vol. 50, No. 3, March 2007, pp. 810-813.

Wikipedia


25/49

SC SOLUTIONS

A Case Study

Temperature Control of a Rotating Susceptor, Cold-wall

MOCVD System


COMSOL Model


26/49

SC SOLUTIONS

COMSOL Model


CVD Surface

A vertical reactor with top-side showerhead and rotating susceptor.

The temperature on the CVD Surface is critically important

Cold walls

“Showerhead”

2D Axisymmetric COMSOL model – Non-isothermal flow, with swirl and buoyancy.

Example Operating Conditions


27/49

SC SOLUTIONS

Example Operating Conditions


Hydrogen is the main carrier gas (no reactions, only heat transfer).

Nominal operating temperature is 1100°C.

Susceptor rotation rate = 100 RPM

Operating pressure range is 100 Torr ≤ p ≤ 500 Torr (1 Atm = 760 Torr)

Operating flow rate range is 5 slm ≤ Q ≤ 50 slm (slm = standard liters per minute)

Required temperature uniformity of ± 0.5°C (over widest possible area of susceptor)

The goal is to adjust the control flux, q(r), to get good temperature

uniformity on the CVD Surface.

Pressure (Torr)

F l o w r a t e ( S L M )

5

50

100 500

Process

Window

Heat Transfer


28/49

SC SOLUTIONS

Heat Transfer

Gas Convection and Conduction

o The cold gas (27°C) is injected at the showerhead

o Convective cooling flux of the susceptor is of order 10 4 W/m2

o qc = h(T sus-T wall ), h is of order 10-100 W/m2°C

Radiation

o qr = (T sus4 – T wall

4 ), = effective emissivity, = Stefan-Boltzmann constant.

o Radiation losses are of order 10 5 W/m2

o Radiation does not vary with flow rate or pressure.

Conduction

o Gas conduction is fairly high for Hydrogen (compared to other gases)

o Solid conduction in susceptor is important, especially if we heat from backside.

The distribution of heat transfer at the CVD surface varies with flow rate and

pressure due to changes in convection heat transfer.


Heater Zone Definition


29/49

SC SOLUTIONS

Heater Zone Definition

It is common to divide the control flux into a number of independently controlled

“zones”.

Here we divide the control flux into six independent zones.

o Uniformly divided along the radius

o Heaters can be made in many ways

Resistive films

Lamp arrays

Hot filaments

RF Inductive elements


This is the system to be controlled

Surface temperature

Heater zones

Gas inflow

A x

i s o f R o t a t i o n

CVD Surface

The Control Problem


30/49

SC SOLUTIONS

The Control Problem

The controller, C, adjusts the flux, q, to make the temperature T on the CVD

surface uniform at the reference temperature, Tref .

This is a form of the “inverse problem”.

(What inputs do I need to produce a given output?)

Real-time feedback is a common method of dynamically solving this problem.


Controller CVD System

Feedback

(1100°C)

For this demo, we will focus on steady-state, but the same methods are used to solve the time-

varying dynamic control problem (e.g., uniformity during temperature ramp, stabilization, etc).

COMSOL®Matlab®LiveLink for Matlab

Baseline System Performance


31/49

SC SOLUTIONS

Baseline System Performance


Normalized power commands

100 Torr, 50 slm 32 degC

5 x p o w e r o

nz o n e 6

Temperature on CVD Surface

Edge cold, can

we do better?

Optimal Control


32/49

SC SOLUTIONS

Optimal Control


In words:

Find the input control flux, q, for each heater that produces the besttemperature uniformity.

subject to the constraint that q ≥ 0

the uniformity is optimized over limited radius (r < Rmax).

Mathematically:

How Many Independent Heaters do we Need?


33/49

SC SOLUTIONS

How Many Independent Heaters do we Need?

In practice, for each independent heater we need an another power supply and

an another temperature sensor – adding heaters is expensive.

We want as few as possible.

We also want uniformity over the largest possible radius (Rmax).

Can we make ONE heater work for the entire operating range of pressure andflow rate?

Strategy: fix the ratio of each heater power from baseline optimal result (100Torr,

50slm) and scale this power distribution up and down with one input scaling.

o This ratio can be done in hardware (e.g., filament density distribution, or resistancevariation, etc.)

o One zone control requires only one temperature sensor.


Optimizing Rmax (6-zone control)


34/49

SC SOLUTIONS

Optimizing Rmax (6 zone control)


It is only possible to get

the inner 0.13m radius

within the design limits.

Rmax = 0.13 m

Rmax = 0.15m

If we try to optimize T for the

whole radius (0


35/49

SC SOLUTIONS

One zone Control

We found the “optimal” Rmax to produce the largest area of temperature within

design limits.

Next we want to optimize the input flux distribution for different operating

conditions.

First we look at 1-zone control, then look at the improvement of increasing the

number of independent control zones.


One Zone Control


36/49

SC SOLUTIONS

One Zone Control


In all cases the mean

temperature optimized for

r


37/49

SC SOLUTIONS

Lower Pressure Flow fields (100 Torr)


100 Torr, 50 slm

Baseline case.

100 Torr, 5 slm

For slower flow we start to see

some “lift” of the streamlines

at larger radius.

Higher Pressure Flow fields (500 Torr)


38/49

SC SOLUTIONS

Higher Pressure Flow fields (500 Torr)


500 Torr, 50slm

Buoyancy driven recirculation is

causing a significant

redistribution of the convective

losses.

500 Torr, 5slm

Buoyancy driven recirculation

even more complex here.

1-zone control cannot work

for this range of operating

conditions.

Two-zone Control


39/49

SC SOLUTIONS

Two zone Control


Group q1-q5 as one zoneq6 is second zone

Much better, but still

not within design

limits.

Both 100 Torr

processes are close to

being within the design

limits.

Temperature 2-zone Control

Six-zone Control


40/49

SC SOLUTIONS

Six zone Control


Temperature Uniformity vs Number of Control Zones


41/49

SC SOLUTIONS

e pe atu e U o ty s u be o Co t o o es


Summary


42/49

SC SOLUTIONS

y

This case study illustrates how COMSOL can be used in concert with SC control

tools to evaluate optimal closed-loop performance of a system.

In this particular case study, the results point to a need to eliminate “roll cells” in

the flow, either by changing the geometry, increasing the flow rate, or increasing

the rotation rate.

Demo will show:

o Livelink for Matlab is a very powerful feature of COMSOL, allowing use of control tools

that have been developed over many years.

o The “swirl” feature in COMSOL is very important for these types of problems where

models must be run many times.



43/49

Video Demo

• Please wait while the content is

loading…

• Applications shown in the demo

– 3D swirling flow over a hot susceptor

– 2D swirling flow over a hot susceptor


44/49

SC SOLUTIONS

Thermal Modeling of a CVD Reactor

Case Study: Temperature Control of a Cold-wall Vertical

CVD Reactor with Rotating Susceptor

Jon Ebert

SC Solutions, Inc.

1261 Oakmead Pkwy., Sunnyvale, CA 94085

Email: [email protected]

COMSOL Webinar

March 7, 2013


mailto:[email protected]:[email protected]


45/49

Product Suite


46/49

Try COMSOL Multiphysics®

• North America – Calgary, AB

– San Diego, CA

– Sacramento, CA

– Oak Brook, IL

– Markham, ON

– San Jose, CA

– Spring, TX

– Toronto, ON

– Cambridge, ON

– East Syracuse, NY

– Richardson, TX

• Europe – Nürnberg-Erlangen, Germany – Saint Martin d'Hères, France – Brno, Czech Republic – Uppsala, Sweden – Helsinki, Finland – London, United Kingdom – Wien, Austria – Trondheim, Norway – Cranfield, United Kingdom – Zilina, Slovakia

• Register to our free hands-onworkshops at

www.comsol.com/events

http://www.comsol.com/eventshttp://www.comsol.com/events


47/49

Try COMSOL Multiphysics®

• North America – Calgary, AB

– San Diego, CA

– Sacramento, CA

– Oak Brook, IL

– Markham, ON

– San Jose, CA

– Spring, TX

– Toronto, ON

– Cambridge, ON

– East Syracuse, NY

– Richardson, TX

• Europe – Nürnberg-Erlangen, Germany – Saint Martin d'Hères, France – Brno, Czech Republic – Uppsala, Sweden – Helsinki, Finland – London, United Kingdom – Wien, Austria – Trondheim, Norway – Cranfield, United Kingdom – Zilina, Slovakia

• Register to our free hands-onworkshops at

www.comsol.com/events

http://www.comsol.com/eventshttp://www.comsol.com/events


48/49

Contact Us

• Questions?

www.comsol.com/contact

• www.comsol.com

– User Stories

– Videos

– Model Gallery

– Discussion Forum

– Blog

– Product News

http://www.comsol.com/contacthttp://www.comsol.com/http://www.comsol.com/http://www.comsol.com/http://www.comsol.com/contact


49/49

Q&A Session

Documents

Heat Transfer in Solid and Fluids