THE UNIVERSITY OF HULL
Characterization of Thermal Dissipation within
Integrated Gate Bipolar Transistor (IGBT)
Layered Packaging Structure
being a Thesis submitted for the Degree of
Doctor of Philosophy
in the University of Hull
by
Dan J Lim, MEng
May 2008
i
Even if there is only one possible unified theory, it is just a set of rules and equations.
What is it that breathes fire into the equations and makes a universe for them to
describe? …The usual approach of science of constructing a mathematical model
cannot answer the questions of why there should be a universe for the model to
describe. Why does the universe go to all the bother of existing? … If we find the
answer to that, we would know the mind of God.
-- Prof. Stephen Hawking, A Brief History of Time, 1988
Š™‹™Š
He (Jesus) is the image of the invisible God, the firstborn over all creation. For by him
all things were created: things in heaven and on earth, visible and invisible, whether
thrones or powers or rulers or authorities; all things were created by him and for him.
He is before all things, and in him all things hold together. And he is the head of the
body, the church; he is the beginning and the firstborn from among the dead, so that in
everything he might have the supremacy. For God was pleased to have all his fullness
dwell in him, and through him to reconcile to himself all things, whether things on
earth or things in heaven, by making peace through his blood, shed on the cross.
Once you were alienated from God and were enemies in your minds because of your
evil behavior. But now he has reconciled you by Christ's physical body through death
to present you holy in his sight, without blemish and free from accusation—if you
continue in your faith, established and firm, not moved from the hope held out in the
gospel. This is the gospel that you heard and that has been proclaimed to every
creature under heaven, and of which I, Paul, have become a servant.
-- Paul the Apostle, The Bible (NIV), 1st Century AD
Š™‹™Š
He is no fool who gives up what he cannot keep, to gain what he cannot loose.
-- Jim Elliot, Missionary, Martyr, 1949
ii
Acknowledgements
There are many people whom I would like to thank. These are the ones who were
there at different stages of this journey, and who contributed and helped me in often
very different ways. Firstly I would like to thank Dr Susan Pulko and Dr Antony
Wilkinson, who got me into the PhD program, showed me the weird and wonderful
world of academia and played a big part in making me seriously consider where God
wanted me in life. I also want to thank Dr David Stubbs, blues man and my dear
colleague, who strode the path before me, helped me with the minutiae, explained
TLM in a way that I could understand, and showed incredible patience in everything
he ever did.
There are a whole list of names I would like to mention from St John’s Church,
Newland, Hull, but space dictates that I limit it to a few. In no particular order, I want
to thank Melvin Tinker, Nathan Buttery, Derek French, Dave Lynch, Dan Bryant,
Matt Tarling, Lee McMunn, Dave Crick and Family, the students at UCU and many,
many more. Each of you prayed for me, showed me what God was doing in your
lives, encouraged, inspired and truly helped me put some definition and detail on the
call God had placed upon me. Additionally, Pete Woodcock, Hugh Palmer, Steve
Timmis, Tim Chester, Roger Carswell all helped me to look beyond the PhD when
tunnel vision was setting in. I wish I had the space to thank you all fully.
Then there are all the folks from Lighthouse Community Church, who have been so
supportive in welcoming me into their fold, praying for me constantly, encouraging
and just being concerned. My thanks go out to the Elders, Jeff Silva, Dave Lee, Alton
To, and many others who have offered to help whenever help was needed. Thank you
iii
for being the Body of Christ. Thanks also go to Rick Franklin, Mick Boersma, John
Hutchison, Pr Ben Shin and the various members of faculty of Talbot School of
Theology, who have been incredibly supportive, interested, encouraging and
sympathetic to the struggles of trying to get a thesis out.
A very special thanks goes to my wife, Jessica, who bore with me when I was writing
the thesis, travelled back to Hull with me in the first attempt at the viva that was
cancelled on account of flooding, prayed for me throughout the process, all at great
cost and sacrifice to herself. Thank you for taking on more than you initially
bargained for, and for sticking with me through it all.
Finally, most of all and more than all, I, with all my heart, want to thank my Great
Friend, Brother, Father, Master, Lord, Saviour and God. His purposes are perfect, and
nothing happens without His allowing it to happen. This was part of His plan for me,
and therefore I call it good. I thank Him supremely for sending Jesus His Son to take
my place, suffer the right punishment for my sin, and rise again so that I have surety
of eternal life beyond this temporal coil. I thank Him for being with me through every
struggle, ever late night, every sorrow and every joy. You have sustained me, my
Father, and abundantly so. All that words in the world and in eternity could not begin
to thank You, praise You and glorify You enough. My times are in Your hands, and it
is well with my soul.
You are worthy, our Lord and God, to receive glory and honor and power, for you
created all things, and by your will they were created and have their being.
— The Revelation to John, The Bible (NIV), 1st Century AD
iv
Table of Contents
Table of Symbols
vi
Abstract
viii
1.0
Introduction
1-1
2.0
The Transmission Line Matrix (TLM) Method and The
Integrated Gate Bipolar Transistor
2-1
2.1
TLM and the Wave Equation
2-2
2.2
TLM and the Diffusion Equation
2-7
2.2.1
2.3
2.3.1
2.3.1.1
2.3.2
2.3.2.1
Heat Flow and the Diffusion Equation
2-8
The Lumped Network Model
2-10
The TLM Network Model
2-12
Scatter and Connect
TLM Stub Node
Impedance Matching and Nonlinearities
2-14
2-20
2-22
2.3.3
Boundaries and Boundary Conditions
2-25
2.3.4
Variable Meshing
2-27
2.3.4.1
2.4
2.4.1
Spatial Sub-structuring
Insulated Gate Bipolar Transistors (IGBTs)
IGBT Structure
2-29
2-32
2-33
3.0
TLMVIS and the IGBT Simulation Models
3-1
3.1
TLMVIS
3-1
3.1.1
Stub Handling in TLMVIS
3-2
3.1.2
Boundary Handling in TLMVIS
3-3
3.1.3
1D Versus 3D Models in TLMVIS
3-7
3.2
Simulation Models
3.2.1
1D “Apple Core” Model
3.2.2
3D Spreader Model
3-8
3-9
3-11
4.0
Heat Spreaders
4-1
4.1
Simulation Results and Observations
4-3
v
4.2
Discussion
4-10
5.0
Substrates
5-1
5.1
Simulation Results and Observations
5-1
5.2
Discussion
5-9
6.0
The 3D Model, Base Plates and Heat Pipes
6-1
6.1
1D Model and 3D Model Similarities and Differences
6-2
6.2
Simulation Results and Observations
6-4
6.3
Base Plate and Heat Pipes
6-13
6.4
Discussion
6-26
7.0
Conclusions
7-1
7.1
Summary of Heat Spreader Observations
7-1
7.2
Summary of Substrate Observations
7-2
7.3
Summary of 3D Model, Base Plate and Heat Pipe
Observations
7-4
7.4
Overall Observations
7-6
7.5
Future Work
7-7
vi
Table of Symbols
Symbol
Description
μ
Electrical permittivity of the material (F.m-1)
ε
Magnetic permeability of the material (H.m-1)
φ
Nodal potential (V or K)
ρ
Resistivity (Ωm)
ρ
Density of the material (kg.m-3)
φb
Potential at boundary node
δl
A short distance (m)
δt
A short time (s)
A
Cross sectional area of the material (m2)
AlN
Aluminium Nitride (Alumina), substrate material
C
Capacitance (J.K-1)
Cd
Distributed capacitance
Clink
Link line capacitance
CTE
Coefficient of Thermal Expansion (ppm.K-1)
Ctotal
Total capacitance
Cu
Copper, heat spreader material
CuMo
Copper-Molybdenum alloy, heat spreader material
D2K
CVD Diamond, substrate material
E
Electric flux density (C.m2)
H
Magnetic field intensity (A.m-1)
ht
Heat transfer coefficient (W.K-1.m-2)
Hz
Hertz (s-1)
I
Current (A)
J
Heat flux density (J.m-2.s-1)
kt
Thermal conductivity (W.m-1.K-1)
L
Inductance (H)
l
Length of a material (m)
l
Branch number
Ld
Distributed inductance
vii
m
Dimensions of a node
n
Branch number
Q
Charge (C)
R
Resistance (Ω)
Rb
Boundary resistance
Rd
Distributed resistance
Rstub
Stub resistance
Sp
Specific heat capacity (J.K-1.kg-1)
t
Time (s)
T
Temperature (K)
Vi
Incident pulse
Vistub
Incident pulse on the stub branch
r
Reflected pulse
r
V stub
Reflective pulse on the stub branch
Y
Total admittance of a node
Z
Impedance (Ω)
Zstub
Stub impedance
V
viii
Abstract
Integrated Gate Bipolar Transistors (IGBTs) generally have a high output power and
generate significant amounts of heat, which needs to be removed from the chip to
ensure continued operation. Since IGBT chips are commonly mounted on a layered
assembly structure which is in turn mounted onto a heat sink assembly, the thermal
dissipation properties of the layered structure are crucial in keeping temperatures
within operational boundaries. Traditionally, the selection of materials for the layered
structure has been largely influenced by the thermal conductivity (kt) for heat
dissipation, the similarity of the coefficient of thermal expansion (CTE) for physical
integrity of the structure and to a lesser extent, the weight of the material. These
principles of material selection are indeed adequate for steady state operation of
IGBTs. However, IGBTs are often installed in applications where they are subjected
to pulsed operation, which is predominantly transient. During transient operation, it
was found that thermal conductivity (Kt) was not necessarily the best criterion to use
for material selection within the layered structure. In certain instances, materials that
absorbed heat rather than conducting it yielded lower temperatures and higher cooling
rates, which in turn resulted in lower start temperatures in the next pulse. This study
therefore proposes an additional material selection criterion, one based on the densityspecific heat capacity (ρSp) product that should be used in conjunction with thermal
conductivity (Kt) to guide the material selection process, opening the door to material
combinations for specific applications that could enhance chip lifespan and reduce
deliamination. Materials with high density-specific heat capacity (ρSp) products could
also potentially be used to compensate for the thermal “bottlenecking” effect. This
study was conducted with numerous simulations based on the well validated
Transmission Line Matrix (TLM) Modelling method.
Chapter I: Introduction
Page 1-1
1.0 Introduction
Insulated Gate Bipolar Transistors (IGBTs) are high power semiconductor devices
that are used in various industries including motor control, inverter and laser welding
applications 1,2,3,4,5,6 . IGBTs have become increasingly popular over the last two
decades among system designers, due to the IGBT's unique ability to handle similar
high voltage and current levels to a bipolar transistor while retaining the ease of
operation, via voltage-control, which is normally associated with a MOS-Field-EffectTransistor (MOSFETs). Although the IGBT typically has a low switching frequency
(~50kHz) compared to a MOSFET, the IGBT's other characteristics make it apt for
use in high power, low frequency applications. It is this capacity to handle large
voltages (>1000V), and the ability to function even with a high junction temperature
(slightly above 100ºC), coupled with ease-of-use akin to that of a MOSFET, which
have made the IGBT so popular with designers of traction drives, welding laser
assemblies and other high voltage switching applications.
Output powers of IGBTs vary vastly, ranging from low powered (~50W) components,
to high performance, kilowatt ranged components used in traction engine control and
other similar high powered systems. IGBTs generally have a high output power and
generate correspondingly large amounts of heat 7 . This heat must be managed
adequately if chip damage is to be avoided. Furthermore, since IGBT input tends to be
in the form of a pulsed wave, rapid heating and cooling of the structure can result in
delamination which in turn leads to catastrophic failure of the device 8 .
D.J.Lim
Chapter I: Introduction
Page 1-2
It is therefore critically important to manage the heat generated by the IGBT during its
operation. To this end, finned heat sinks with large surface areas are installed on the
side remote to the IGBT chip, and are standard fixtures in IGBT packaging. However,
the heat generated at the IGBT chip must travel through the layered assembly to take
advantage of the heat dissipation capabilities the finned heat sink provides. Each layer
in the IGBT assembly has its own thermal properties and thus its own thermal
behaviour. Pulsed input common in many IGBT applications further complicates the
thermal behaviour within the assembly, as it causes the assembly to be in a constant
state of thermal flux. The thermal dissipation within and the interaction between these
layers results in much more complex thermal behaviour than one would initially
expect, particularly within the transient period.
As material technology advances, various materials have been introduced as
alternatives for the different layers. For example, Copper (Cu) base plates have given
way to lighter Aluminium-Silicon-Carbide (AlSiC) structures, and Alumina (AlN)
substrate layers are being replaced by modern Chemical Vapour Deposited (CVD)
Diamond or carbon fibre layers in high performance IGBT assemblies. “Traditional”
materials are still widely used as some of the more modern materials are still
comparatively expensive to produce. However, as manufacturing technology
advances, economic limitations will be overcome, and newer, more advanced
materials will become more feasible. Each material has its own distinct thermal
properties and behaviour and will change the thermal dissipation characteristics of an
IGBT assembly. In view of the many choices available in terms of material selection,
and the complexities inherent within the multi layered assembly, this study
D.J.Lim
Chapter I: Introduction
Page 1-3
systematically explores the influence of layer material choice on the on the
development and behaviour of thermal fields in these devices in the transient period.
This study is mainly conducted with the use of a Transmission Line Matrix (TLM)
modelling and simulation package, which, once a model is constructed, allows
changes to material properties to be easily made. TLM is an explicit, unconditionally
stable, one step technique that is used to model various forms of heat transfer. It is
based on the heat diffusion equation and uses electrical analogies to model heat
dissipation, transfer and behaviour. The unconditionally stable nature of the TLM
method allows the timestep in the thermal simulation to be modified to suit the level
of accuracy required by the application. This is precisely what is needed for the study
of thermal behaviour within the IGBT assembly, as steady state simulations that do
not require good representation of the transient can be run as well as high precision
transient simulations. The implementation of the TLM simulation technique that is
used, a bespoke application called TLMVIS, allows the implementation of
simplification techniques, such as the use of reflective boundaries to cut down
simulation time. TLMVIS was used as is, and no modifications to the program were
necessary even when applying the more advanced processing simplification
techniques.
It is hoped that this study will shed some light on the highly complex thermal
behaviour within the IGBT package structure, as well as yield a better understanding
of the part played by the thermal properties of materials used. This could in turn allow
manufacturers to optimise material choice for IGBT packages, selecting material
combinations that will be best suited for a given application in order to maximise chip
D.J.Lim
Chapter I: Introduction
Page 1-4
cooling and/or lifespan. This study is presented in seven parts, the first of which is
this introduction. The second chapter covers some of the relevant the theory behind
TLM as well as background information on IGBTs. The third chapter describes the
TLMVIS software and the models used. The chapters 4, 5 and 6 present the
simulation results for the three major elements of the IGBT structure, namely, the heat
spreaders, the substrate and the baseplate. These chapters will also discuss the
implications of those results. The final chapter is a summary of the findings and an
overview of the implications of the results as a whole.
1
Baliga BJ, Adler MS, Love RP, Gray PV, Zommer ND: The Insulated Gate Bipolar Transistor: A
New Three-Terminal MOS-Controlled Bipolar Power Device, IEEE Trans. Electron Dev., Vol ED-31,
No 6, 1984, pp 821-828.
2
Blake C, Bull C, IGBT or MOSFET: Choose Wisely, International Rectifier Corporation, El Segundo,
USA, www.irf.com/technical-info/whitepaper/choosewisely.pdf (accessed June 26 2007)
3
Francis R, Soldano M, A New SMPS Non Punch Through IGBT Replaces MOSFET in SMPS High
Frequency Applications, International Rectifier Corporation, El Segundo, USA, presented at APEC 03,
www.irf.com/technical-info/whitepaper/apec03nptigbt.pdf (accessed June 26 2007)
4
Herzer R, Schimanek E, Bokeloh CH, Lehmann J, A Universal Smart Control IC for High Power
IGBT Applications, Electronics, Circuits and Systems, 1998 IEEE Int. Conf. on Electronics, Vol 3, pp
467-470.
5
Brown AR, Asenov A, Barker JR, Jones S, Waind P, Numerical Simulation of IGBTs at Elevated
Temperatures, Proc. Int. Workshop on Computational Electronics, ed. CM Snowdon, University of
Leeds Press, 1993, pp 50-55.
6
Zehringer R, Stuck A, Lang T, Material Requirements for High Voltage, High Power IGBT Devices,
Solid-State Electronics, Vol 42, No. 12, pp 2139-2151
7
Sheng K., Williams BW, He X, Qian Z, Finney SJ, Measurement of IGBT Switching Limits, IEEE
Power Electronics Specialists Conference, PESC 1999, Vol 1, pp 376-380
D.J.Lim
Chapter I: Introduction
8
Page 1-5
Lefranc G, Licht T, Mitic G, Properties of solders and their fatigue in power modules,
Microelectronics Reliability,Vol 42, No. 1, 2002, pp 1641-1646
D.J.Lim
Chapter II: The TLM Method and The IGBT
Page 2-1
2.0 The Transmission Line Matrix (TLM) Method and The
Integrated Gate Bipolar Transistor (IGBT)
The Transmission Line Matrix (TLM) method is a well established technique for
modelling diffusion problems 1,
2, 3, 4
and has been in use for more than 35 years; it
was first devised by P.B. Johns and R.L. Buerle in 19715 . Today, it is not only used to
model electromagnetic and thermal diffusion problems 6,7,8 , but has found many
applications in numerous industries 9 including food production and distribution 10, 11 ,
glass lens pressing 12 , thermal management of electronic networks and devices 13
ceramic drying 14 and acoustic modelling 15 . One advantage of the TLM method over
other modelling techniques like finite element analysis (FEA) lies in the fact that
TLM is single-step. This means that each TLM node only requires the data from its
neighbouring nodes from the previous timestep for its calculations, and not from other
parts of the network. This translates to reduced processing and storage requirements
and increased simulation speed when compared with two step techniques like the Du
Fort-Frankel method 16 . TLM simulation models are explicit, allowing simple and
controlled manipulation of model and material properties, regardless of whether those
properties are linear or non-linear. Furthermore, TLM is unconditionally stable.
Unconditional stability means that the results of the simulation will not tend towards
infinity, regardless of the timestep used, although there is loss in accuracy as the
timestep increases. However, this permits high precision, short timestep simulations
for situations with fast transients as well as low precision, long timestep simulations
for slow transient or steady state situations 17,
18, 19
. In other words, when the transient
is slow, the timestep can be increased (usually to values far exceeding the stability
threshold of other simulation techniques), shortening the run time of the simulation.
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-2
Similarly, when precision is required, the timestep can be reduced. As the simulations
in this study require both these extremes, TLM is well suited for this endeavour.
Finite element analysis (FEA) is also a well established modelling technique that has
a wide range of applications, including thermal diffusion 20 and stress analysis 21 . It
uses a triangular mesh which excels at modelling objects of complex geometry. The
mesh can also be resized when more precision is required. However, FEA is a twostep method, which means that data the whole of the network must be considered for
every time step, which can result in significant processing and storage requirements,
especially if the transient is being examined, as is the case with this study. In contrast,
TLM only requires the data from surrounding nodes for each timestep. Additionally,
the simulation models required for this study were simple, orthogonal, block-like
shapes and would not have benefited from FEA’s triangular mesh technique.
2.1
TLM and the Wave Equation
Huygens’ Principle states that apart from a wave source, every successive wave front
is formed by secondary radiators in the previous wave front (Figure 2.1). TLM was
first conceived as a way to describe the physics of wave propagation by exactly
solving the wave equations based upon Huygens’ Principle.
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-3
Source
Primary Wave Front
Secondary Wave Front
Tertiary Wave Front
Quarternary Wave Front
(a)
(b)
Figure 2.1: Diagram Illustrating Huygens’ Principle. (a) denotes the successive wave fronts being
resultant from the previous wave fronts. (b) Shows how a wave front can be formed by multiple
sources along a smaller (previous) wave front
Considering wave propagation according to Huygens’ Principle, the propagation of
waves through a medium can be separated into a series of discrete events or sources.
By overlaying a Cartesian mesh over these sources, thus giving each of the sources a
unique coordinate, then connecting these “nodes” via imaginary loss free transmission
or link lines of length δl, a matrix can be formed in 1D, 2D and 3D. This basic node
design is easily modified to accommodate lossy cases by adding resistances at each
end of the transmission line. In this way, space is descretised.
A wave needs time to propagate from one point in space to another. A continuous
wave can also be treated as the sum of many pulses, not unlike the way in which a
line on a monitor comprises multiple dots or pixels. These pulses take a short time, δt,
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-4
to reach a point near their previous location in space. Once there, the pulse will
interact (constructively or destructively, according to the phase difference and the
magnitude of the pulse at that moment in time) with other pulses that happen to be at
that location in space before scattering to other points in space. By using many very
small steps in time (timesteps) to represent a continuous time frame, time is
descretised.
(a)
(b)
(c)
(d)
Figure 2.2: Illustration of pulse scattering: (a) the initial source pulse, t = 0 (b) the wave front reaching
the neighbouring nodes, converting them into weaker sources. (c) the new sources scatter, t=1. (d) the
sources after t=1. The lighter circles denote weaker pulses, and the darker circles show the wave fronts
that are formed from the constructive effect of the weaker fronts.
By way of illustration, consider a hypothetical wave which is frozen in time. This
wave can be broken down, according to Huygens’ Principle, into multiple smaller
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-5
waves, which then act as pulses, one following closely behind another to form the full
wave. Each of these pulses occupies a point in space, called a node. These pulses are
then allowed to propagate for a very short time, δt. In that time, the pulse travels a
small distance, δl, to a new node. Once at this new location, δl distance away from its
starting position, and δt time in the future, the pulse interacts with other pulses present
at that point in space at that point in time, forming a new pulse. This new pulse then
scatters, going to other neighbouring nodes. The paths that the pulses take can be
treated as transmission lines or link lines, so forming a grid or mesh. Thus, both time
and space are descretised.
For a 2D problem, the TLM calculations are carried out on a 2D Cartesian mesh of
open two-wire transmission lines which run parallel to the x and y axes. An
impedance discontinuity exists in each transmission line, as each node corresponds to
a transmission line junction, as illustrated in Figure 2.3. For convenience of reference,
each branch of transmission line emanating from the central node is numbered.
4
1
3
y
x
2
Figure 2.3: Transmission line junction pair
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-6
Iy4
4
Lδl
Lδl
Ix3
Lδl
2
2
3
2
1
Ix1
y
Lδl
2
Iy2
Vz
2Cδl
2
x
δl
δl
2
δ ly
2
δ lx
Figure 2.4: Equivalent electrical network for 2D.
An equivalent electrical network for Figure 2.3 is shown in Figure 2.4, where L and C
are the inductance and capacitance per unit length, respectively, and δl the elemental
length of the node. For a distance δl,
δV
− δ (I x1 − I x 3 ) − δ (I y 2 − I y 4 ) = 2C z
δx
δy
δt
Equation 2-1
−
δV z
= L δ (I x1 − I x 3 )
δx
δt
Equation 2-2
−
δVz
= L δ (I y 2 − I y 4 )
δy
δt
Equation 2-3
The capacitance, C, is doubled to account for the fact that there are two transmission
lines (one each for the x and y directions) intersecting at the node. Equations 2-1, 2-2
and 2-3 can be combined to form
δ 2V z δ 2V z
δ 2V z
+
= 2 LC 2
δx 2
δy 2
δt
Equation 2-4
For an Hm0 mode with field components Hx, Hy and Ez, Maxwell’s Curl Equations can
be written as
D. J. Lim
Chapter II: The TLM Method and The IGBT
−
δH x δH y
δE
−
=ε z
δy
δt
δx
Page 2-7
Equation 2-5
Hy
δ 2 Ez
μ
=
−
δt
δx 2
Equation 2-6
H
δ 2 Ez
= −μ x
2
δt
δy
Equation 2-7
The left hand terms from Equations 2-6 and 2-7 can be substituted into their
respective terms in Equation 2-5 to yield
δ 2 Ez δ 2 Ez
δ 2 Ez
+
=
με
δx 2
δy 2
δt 2
Equation 2-8
By comparing the equations from the electrical equivalent network (Equations 2-1 to
2-4) to the electromagnetic equations (2-5 to 2-8), it is observed that Ez≡Vz, -Hx≡(Iy2Iy4), -Hy≡(Ix1-Ix3), μ≡L and ε≡2C. With these equivalences and the network element
shown in Figure 2.4, it is therefore possible to construct a mesh to exactly solve the
wave equation in 2-dimensions using electrical analogies.
2.2
TLM and the Diffusion Equation
Using a similar method as that described in Section 2.1, Maxwell’s curl equations can
be combined to give
δ 2V + δ 2V + δ 2V = L C δ 2V + R C δV
d d
d d
δt
δx 2 δy 2 δz 2
δt 2
D. J. Lim
Equation 2-9
Chapter II: The TLM Method and The IGBT
Page 2-8
where V is the voltage, Rd represents the distributed resistance ( δRl ), Cd the distributed
capacitance( δCl ) and Ld the distributed inductance ( δLl ).
This equation describes
propagation in a lossy medium, and is also known as the Telegrapher’s Equation.
Equation 2-9 will model results in either a wave or diffusion model depending on the
value of δt chosen. The first term on the right can be suppressed using a small
timestep so that
d 2V
dt 2
becomes negligible 22 , resulting in a diffusion equation:
δ 2V + δ 2V + δ 2V = R C δV
d d
δt
δx 2 δy 2 δz 2
Equation 2-10
It is also in this equation where the unconditional stability of TLM lies. If the timestep
is increased, the first term on the right of Equation 2-9 comes back into play. This
causes the output to acquire an oscillating wave component. However, as the model
reaches a steady state, this wave component will decrease and finally die away.
2.2.1 Heat Flow and the Diffusion Equation
There are two basic laws which describe the diffusive flow of heat through a body.
The first is that the heat flux density across a body is related to the gradient of the
temperature across it. This is illustrated for the one dimensional case in Figure 2.5a
and expressed mathematically as
J = − k t δT
δx
Equation 2-11
where J is the heat flux density in Jm-2s-1, T is the temperature of the body in Kelvin
(K) and kt is the thermal conductivity in Wm-1K-1.
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-9
T
T+δT
J
δx
(a)
T
J+δJ
J
δx
(b)
Figure 2.5: Illustrations of the basic diffusion laws. (a) First rule. (b) Second rule.
The second rule states that the accumulation of heat corresponds to an increase in
temperature with time, as illustrated for the one dimensional case in Figure 2.5b. It is
expressed mathematically as
δT = 1 ⋅ δJ
δt S p δx
Equation 2-12
where Sp is the specific heat capacity of the material in JK-1kg-1.
Combining equations 2-11 and 2-12 yields
δT = k t ⋅ δ 2T
δt S p δx 2
Equation 2-13
which is the one dimensional diffusion equation for heat transfer. Equation 2-13 can
also be extended into the more general three dimensional form
δ 2T + δ 2T + δ 2T = S p ⋅ δT
k t δt
δx 2 δy 2 δz 2
D. J. Lim
Equation 2-14
Chapter II: The TLM Method and The IGBT
Page 2-10
By comparing Equation 2-14 to Equation 2-10, it is apparent that the equations are
analogues:
δ 2T + δ 2T + δ 2T = S p ⋅ δT
k t δt
δx 2 δy 2 δz 2
δ 2V + δ 2V + δ 2V = R C δV
d d
δt
δx 2 δy 2 δz 2
≡
It is also observed that
Rd C d ≡
2.3
Sp
kt
Equation 2-15
The Lumped Network Model
An electrical analogy cannot yet be built from the equations derived in the previous
section since the resistance and capacitance of the material are still in their distributed
forms. This can be resolved by considering a cube of material, of thermal conductivity
kt and specific heat capacity Sp, the lumped network representation of which is shown
in Figure 2.6.
R
R
δ lz
R
R
C
R
R
δ ly
δ lx
Figure 2.6: Lumped network element.
The centroid of the cube, which is also the nexus for the branches, is treated as the
calculation point or node. The heat flow through the cube, which is analogous to
current, in the x, y or z direction is given by
D. J. Lim
Chapter II: The TLM Method and The IGBT
I x = J ⋅ (δl x )
2
I y = J ⋅ (δl y )
2
I z = J ⋅ (δl z )
Page 2-11
Equation 2-16
2
where Ix, Iy and Iz denote the heat flow or current (W) in the x, y and z directions
respectively, J denotes the heat flux density (J.m-2.s-1), and δlx, δly and δlz denote the
elemental distance (m) for the corresponding axis. For a given direction the heat flow
occurs through two resistors, the resistance of which can be calculated with the basic
equation of resistance
R=
ρL
A
Equation 2-17
where R is the resistance, ρ denotes the resistivity (not to be confused with the density
of a material, which also uses the symbol ρ and is the mass per unit volume of a given
material), L, the length of the material and A, the cross sectional area. For a cube,
2R = 1
k t δl
Equation 2-18
or, if δlx ≠ δly ≠ δlz
2Rx =
δl x
k t δl y δl z
2Ry =
δl y
k t δl x δl z
2 Rz =
δl z
k t δl x δl y
D. J. Lim
Equation 2-19
Chapter II: The TLM Method and The IGBT
Page 2-12
the doubled R reflecting the fact that there are two resisters per direction on the node.
The nodal capacitance represents the amount of energy (in the form of heat or
voltage) that will be stored by the node (J.K-1), and thus is the heat capacity of the
material. The specific heat capacity (Sp) of a material denotes the amount of energy
required to raise the temperature of a kilogram of a material by 1°C (J.K-1.kg-1).
Therefore, the heat capacity of a material is the product of the specific heat capacity
and the mass of the material. The said mass can be found by multiplying the density
(ρ) of the material with the volume, since density is the mass per unit volume of a
given material (kg.m-3). Hence, the nodal capacitance, C, can be represented as
C = S p ⋅ ρ (δl x ⋅ δl y ⋅ δl z )
Equation 2-20
when δlx ≠ δly ≠ δlz. If δlx = δly = δlz = δl (a perfect cube), then Equation 2-20 can be
simplified to
C = S p ⋅ ρ (δl )
3
Equation 2-21
2.3.1 The TLM Network Model
The lumped network element presented in the previous section can be modified to
form a TLM network element by replacing the branches with lossless transmission
lines, which have an impedance, Z, corresponding to the capacitance of the block, as
illustrated in Figure 2.7.
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-13
Z
R
R
δ lz
R
R
Z
Z
R
Z
R
Z
δ ly
Z
δ lx
Figure 2.7 : A standard 3D TLM node with resistors and impedances on each branch.
Using Ohm’s Law along the transmission line,
Z =V
I
Equation 2-22
where Z is the transmission line impedance in Ω and I is the current along the line in
A and is calculated by
I=
δQ
δt
Equation 2-23
where δt is the elemental timestep in s and Q denotes charge and is measured in C
(Coulombs). The basic network equation for a capacitor is given by
C=
Q
V
Equation 2-24
Z, therefore, can be written as
Z = δt
C
Equation 2-25
From the 3D case in Equation 2-21 for heat,
Z=
δt
3
S p ρ (δl )
D. J. Lim
Equation 2-26
Chapter II: The TLM Method and The IGBT
Page 2-14
Each branch of the 3D network is connected to adjacent blocks by half a transmission
line. Therefore the total capacitance is divided between 3 full transmission lines,
rendering Equation 2-25
Z = δCt
3
Z = 3δt
C
Equation 2-27
which results in the 3D TLM elemental node depicted in Figure 2.7.
2.3.1.1
Scatter and Connect
Now that the generalised TLM network node has been established, the passing of
pulses along a TLM mesh can be investigated. A pulse that is present at a node at a
given instance in time is designated incident, commonly denoted Vi. An incident pulse
will travel outwards from the node as time elapses becoming a reflected pulse (Vr). In
order to derive the governing equations for the incident and reflected pulses, and most
importantly the nodal potential, φ, which is usually the output value of the simulation,
the generalised TLM node (Figure 2.7) is converted into a Thévenin equivalent
circuit. This is illustrated in Figure 2.8, which depicts the pulses for the specific
instance at which the incident pulse is reflected back from the node.
D. J. Lim
Page 2-15
R2
Rn
Z1
Z2
Zn
V2 i + V2r
Vn i + Vnr
R1
V1 i + V1r
φ
Chapter II: The TLM Method and The IGBT
2V1i
2V2i
2Vni
Figure 2.8: Thévenin equivalent circuit for a generalised TLM node.
The n in Figure 2.8 denotes the branch number of the node, so n is twice the value of
the dimensions of the node (for an m dimensional node, n = 2m). φ denotes the nodal
potential, 2Vbi and 2Vbr are the incident and reflected voltages on the relevant branch
b (for the 3d case, b would range from 1 to 6).
Applying Kirchoff’s Current Law (KCL) to the node,
2Vni − φ
2V1i − φ 2V2i − φ
+
+L+
=0
R1 + Z 1 R2 + Z 2
Rn + Z n
Equation 2-28
Equation 2-28 can also be written as
2Vni
2V1i
2V2i
φ
φ
φ
+
+L+
=
+
+L+
R1 + Z 1 R2 + Z 2
Rn + Z n R1 + Z 1 R2 + Z 2
Rn + Z n
Equation 2-29
which, to find the nodal potential, can be written in terms of φ
n
φ=
∑
2Vli
Rl + Z l
∑
1
Rl + Z l
l =1
n
l =1
D. J. Lim
Equation 2-30
Chapter II: The TLM Method and The IGBT
Page 2-16
or
⎡
Vi
n
⎤
1
l
φ = ⎢ 2∑
⎥⋅Y
R
Z
+
l ⎦
⎣ l =1 l
Equation 2-31
and
n
Y =∑
l =1
1
Rl + Z l
Equation 2-32
where φ represents the potential of the node and Y is the total admittance of the node.
In order to calculate the reflected pulse, Vr, for the node, consider the current down a
single branch, Il, where l is the branch number.
Il =
(
) (
)
V i − Vl r − φ
2Vl i − Vl i − Vl r
= l
Zl
Rl
Equation 2-33
Rearranging Equation 2-33 and isolating Vr yields
Vl r Vl r Vl i Vl i − φ
+
=
−
Rl Z l
Zl
Rl
Vl =
r
Vli
Zl
+ φ −RVl l
Equation 2-34
i
Rl Z l
Rl + Z l
Equation 2-35
and can be simplified into
Vl r =
Rl − Z l i
Zl
φ
Vl +
Rl + Z l
Rl + Z l
Equation 2-36
Equation 2-36 yields the magnitude of the reflected pulse along a given branch as the
pulse scatters into adjacent nodes, and is thus sometimes known as the TLM
scattering equation.
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-17
5
Z
4
R
R
Z
Z
R
z
Z
R
3
y
1
R
2
R
x
Node (x, y, z)
Z
Z
6
Figure 2.9: TLM node (x, y, z) with numbered branches
Information must be passed between elements within a mesh. For a continuous,
homogenous, 3D mesh (i.e. all elements within the mesh have exactly the same
parameters), the process of connecting the transmission lines so that information can
flow between the elements for a node with branches numbered as per Figure 2.9 can
be achieved by
V1i (x, y, z ) = V3r ( x + 1, y, z )
V2i (x, y, z ) = V4r ( x, y + 1, z )
V3i ( x, y, z ) = V1r ( x − 1, y, z )
V4i (x, y, z ) = V2r ( x, y + 1, z )
Equation 2-37
V5i (x, y, z ) = V6r ( x, y, z + 1)
V6i ( x, y, z ) = V5r ( x, y, z − 1)
Equations 2-30 (and therefore, by extension, Equations 2-31 and 2-32), 2-36 and 2-37
form the core equations for tracking the passage of pulses within a TLM mesh. By
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-18
way of illustration of the scatter and connect process, consider a simple 1D mesh
where R=Z. From Equations 2-30, 2-36 and 2-37, φ, Vr and Vi are
φ = V1i (n ) + V2i (n )
V1r (n ) =
V2r (n ) =
φ (n )
2
φ (n )
Equation 2-38
2
V1i (n ) = V2r (n − 1)
V2i (n ) = V1r (n + 1)
where n is the node designation as illustrated in Figure 2.10.
R
Z
R
1
n-1
R
Z
2
1
R
n
Z
2
R
1
R
n+1
Z
2
Figure 2.10: Simple 1D mesh with matching impedance and numbered branches
Let there be an excitation pulse of arbitrary magnitude, P, at time t=0, incident on
node n. The resultant reflected pulses will be of magnitude
P
2
and will propagate
towards nodes n+1 and n-1 (Figure 2.11a). At t=δt, reflected pulses from t=0 with
magnitude
magnitude
P
2
P
4
are incident on nodes n+1 and n-1 and in turn reflect a pulse of
, which is half the magnitude of the incident pulse, and a quarter of the
magnitude of the original pulse (Figure 2.11b). At the next timestep, t=2δt, the
reflected pulses from n+1 and n-1 are once again incident on node n, as well as on
nodes n+2 and n-2 (Figure 2.11c). The two pulses of magnitude
D. J. Lim
P
4
incident on node n
Chapter II: The TLM Method and The IGBT
Page 2-19
result in a total incident pulse magnitude of
of
P
2
, which is then reflected at magnitudes
back towards n+1 and n-1. Given that there are no external or extraneous
P
4
incident pulses in play, nodes n+2 and n-2, which are beyond the scope of Figure
2.11, will reflect pulses of magnitude
result of the incident
P
8
towards nodes n+3, n+1, n-3 and n-1 as a
pulses from n+1 and n-1.
P
4
P
R
Z
1
R
R
Z
1
2
n-1
R
Z
2
n
P
2
R
R
1
Z
2
n+1
P
2
(a)
P
2
R
Z
1
P
2
R
R
Z
1
2
n-1
P
4
R
Z
2
n
R
1
P
4
R
Z
2
n+1
P
4
P
4
(b)
P
2
P
4
P
4
R
Z
1
R
n-1
R
Z
2
1
P
4
R
n
(c)
Z
2
R
1
R
n+1
Z
2
P
4
Figure 2.11: Pulse propagation in simple 1D mesh. (a) t=0. (b) t=δt. (c) t=2δt.
The pulses will continue to propagate for the rest of the simulation, thus giving a
transient solution for every timestep. The mesh will eventually reach equilibrium,
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-20
pursuant to the boundary conditions and external inputs. As the pulses are only used
to calculate the next timestep, the simulation only needs to store mesh data for one
iteration, thus minimising the memory (and in some cases, processing) requirements
for a TLM mesh simulation.
2.3.2 TLM Stub Node
The nodal structure for a TLM node presented in Section 2.3.1 is a basic structure,
and only works for instances where the capacitance throughout the mesh is constant,
thereby rendering the impedance of the transmission line constant as well. For
situations where this is not the case, a stub branch can be introduced. A stub consists
of an open circuit transmission line that is connected to a single node and is modelled
as a half length transmission line with an open circuit impedance, as illustrated in
Figure 2.12. A convenient value of capacitance is chosen so that a common
impedance can be used throughout the network. The stub branch can then be used to
match elements within multi-capacitance or irregular elemental volume mesh models6
or to incorporate non-linear properties within a mesh7.
5
Z
R
R
Z
4
Z
R
z
Z
R
3
1
R
R
Rstub
Zstub
2
Z
Z
6
Figure 2.12: 3D TLM node with stub.
D. J. Lim
y
x
Chapter II: The TLM Method and The IGBT
Page 2-21
The stub branch is easily incorporated into the core TLM equations. Since the stub
branch is modelled as a half length open circuit transmission line, as a pulse travels
down the stub line from the node to the open circuit during a timestep, δt, the stub
acts like a mirror, reflecting the pulse (without a phase change) back to the node so
that it is incident one timestep into the future. Since the pulse is reflected at 12 δt , the
stub impedance, Zstub can be calculated, from Equation 2-25, as
Z stub =
δt
2C stub
Equation 2-39
i
and Vstub
, the voltage incident on the stub branch, can be described via
i
r
(t ) = Vstub
(t − δt )
Vstub
Equation 2-40
i
r
(t ) is the incident voltage on the stub branch at time t, and Vstub
(t − δt ) is
where Vstub
the reflected voltage from the stub branch from the previous (t-δt) timestep.
The nodal potential, φ, can then be calculated from Equation 2-30, as
n
φ=
∑
2Vli
Rl + Z l
+
∑
1
Rl + Z l
+
l =1
n
l =1
i
2Vstub
Rstub + Z stub
Equation 2-41
1
Rstub + Z stub
and by extension, Equations 2-31 and 2-32 expand into
⎡
n
Vi
Vi
⎤
l
stub
+
φ = ⎢ 2∑
⋅1
⎥
⎣ l =1 Rl + Z l Rstub + Z stub ⎦ Y
Equation 2-42
and
n
Y =∑
l =1
D. J. Lim
1 +
1
Rl + Z l Rstub + Z stub
Equation 2-43
Chapter II: The TLM Method and The IGBT
Page 2-22
i
respectively, where Vstub
is the voltage incident on the stub branch, Rstub is the stub
resistance and Zstub denotes the stub impedance. Rstub is only included for generality
and has a value of Rstub=0 for most practical situations. This means that the equation
for Vr (as applied to the stub line from Equation 2-36),
Vl r =
Rstub − Z stub i
Z stub
φ
Vstub +
Rstub + Z stub
Rstub + Z stub
Equation 2-44
can be simplified to
r
i
Vstub
= φ − Vstub
2.3.2.1
Equation 2-45
Impedance Matching and Nonlinearities
When two nodes are connected to each other in a TLM mesh, there are instances
where they might have different impedances, as illustrated in Figure 2.13. This tends
to occur at the intersection point of materials with different thermal properties or
within materials that have nonlinear properties. It results in a discontinuity in the
connection between the nodal elements, causing secondary reflections halfway along
the transmission line, which in turn gives rise to numerical error, if not taken account
of.
Change over point
Figure 2.13: Varied impedance at elemental boundary
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-23
A stub can be used to rectify the error. A minimum capacitance is chosen for the
transmission line and the extraneous capacitance is stored in the stubs. The stub
impedance for each node can be represented mathematically as
Z stub =
δt
2(Ctotal − C link )
Equation 2-46
where Ctotal is the total capacitance for the node and Clink is the capacitance for the link
lines (without the stub). The
δt
2
term occurs because the stub is modelled as a half
length transmission line and the reflection of the pulse at the end of the stub line
means that its effect acts twice.
Za
Node a
Zb
Ctotal_a=5 Ctotal_b=10
Node b
Figure 2.14: Varied impedances
By way of illustration, consider the 1D situation presented in Figure 2.14, where the
nodal impedances Za and Zb are linked and the nodes have the arbitrary total
capacitance values of 5 and 10 for nodes a and b respectively. The nodal impedances
can be represented as
Z a = δt
5
Equation 2-47
and
Z b = δt
10
D. J. Lim
Equation 2-48
Chapter II: The TLM Method and The IGBT
Page 2-24
For this situation, a minimum value of capacitance on the link lines of 4 can be
chosen, while the rest of the capacitance is placed into the stub, resulting in
Z stub _ a =
δt
= δt
2(5 − 4 ) 2
Z stub _ b =
δt
= δt
2(10 − 4) 12
Equation 2-49
Z a = Z b = δt
4
as illustrated in Figure 2.15.
Cstub_b=6
Cstub_a=1
Za
Zb
Zstub_b
Zstub_a
Node a
Clink_a=4
Clink_b=4
Node b
Figure 2.15: Stub enhanced, impedance matched link line
For a nonlinear case, a minimum capacitance for the network can be chosen. Any
changes in the nodal capacitance during the simulation can be placed into the stub,
thus maintaining a stable (and uniform) link line capacitance throughout the network,
even though the total capacitance of the node fluctuates7. As long as the stub
impedances are recalculated at every iteration to match the changing total capacitance
of the nodes, the mesh-wide link line capacitance, and by extension the link line
impedance, will remain unchanged.
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-25
2.3.3 Boundaries and Boundary Conditions
For TLM meshes to simulate anything more than the most basic of problems, the
mesh needs to represent more than just an infinitely large block of homogenous
material. Therefore, a method must be found to define mesh boundaries or edges that
is consistent with the core TLM equations (Equations 2-31, 2-32, 2-36 and 2-37).
Mesh boundary
Z
R
R
Vi
R
R
Z
Z
z
R
Z
R
Z
Rb
Vr
y
x
Z
Z
Figure 2.16: Boundary node connected to TLM mesh.
Attaching a node to the outside wall of the mesh boundary, as illustrated in Figure
2.16, not only provides a way to preserve consistency with the core TLM equations,
but also constitutes a convenient method to represent external input into the mesh.
The node is connected to the mesh by a boundary resistor, Rb. If the nodal potential of
this boundary node, φb, is controlled and held steady by the user, it will be unaffected
by pulses passed to it from the mesh. The nodal temperature is therefore unchanging
and the heat transfer is adiabatic. The reflected voltage, Vr, from the boundary node,
which also forms the external input to the mesh, is given by
Vr =
Rb − Z i
V + Z φb
Rb + Z
Rb + Z
D. J. Lim
Equation 2-50
Chapter II: The TLM Method and The IGBT
Page 2-26
and is dependant upon both the incident voltage from the mesh, Vi, and the user
controlled boundary node potential, φb. An external sink or source can therefore be
simulated by modifying the boundary node.
In addition, the extent to which the boundary node affects the reflected pulse can also
be controlled by changing the boundary resistance, Rb. One extremely useful
application of this principle is to set Rb to infinity, thereby rendering the impedance
and boundary potential terms in Equation 2-50 negligible and rendering Vr=Vi. This
creates a perfectly insulating or reflective boundary, which can be used to “mirror” a
mesh, cutting the processing requirements to a fraction of what would be needed if the
complete object were to be simulated. This effect is used to great benefit for the
simulations in this study.
For heat transfer processes, such as when modelling the diffusion of heat from an
object into the surrounding ambient, the boundary resistance, Rb can be calculated
according to
Rb = 1
ht A
Equation 2-51
where ht is the heat transfer coefficient in W.K-1m-2, and A is the area of contact
between the boundary node and the mesh node. From Equation 2-51, the boundary
resistances for the x, y and z directions (as per the axis orientations in Figure 2.16)
are, respectively,
D. J. Lim
Chapter II: The TLM Method and The IGBT
Rbx =
1
ht δyδz
Rby =
1
ht δxδz
Rbz =
1
ht δxδy
Page 2-27
Equation 2-52
2.3.4 Variable Meshing
Variable meshing is a TLM simulation technique that can be used in situations where
objects of complex geometries need to be simulated6. It increases computing
efficiency by using an irregular mesh, varying the density of the mesh according to
the anticipated or required output. In other words, smaller elements are used where
points of interest are anticipated, while areas where less accuracy is required are
simulated with a coarser mesh, which in many cases results in a lower element count.
When modelling using the TLM method, it is required that all the pulses arrive at all
nodes within a mesh simultaneously. If transmission line lengths are not uniform, the
synchronicity required by the method would be disrupted. However, it is possible to
vary the inductances of the transmission lines, and thereby vary the velocities of the
pulses that travel along those lines, forcing them to arrive simultaneously. This is
done by reintroducing the inductance term from Equation 2-9 that is suppressed for
diffusion problems to yield Equation 2-10. Considering a transmission line of length
δl, with distributed capacitance and inductance, Cd and Ld respectively, the impedance
of the transmission line is
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-28
Ld
Cd
Z=
Equation 2-53
Given that pulses travel a distance δl in time δt,
δl = 1
δt
Ld C d
rearranging for
Equation 2-54
Ld and substituting into Equation 2-53 yields
Z = δt = δt
C d δl C
Equation 2-55
which is equivalent to Equation 2-25. If δt is fixed for the network while δl and Cd are
variable, Ld can be controlled so that pulse synchronicity is maintained.
For a Cartesian mesh where the elements are not a cube (δlx ≠ δly ≠ δlz), Equation
2-19 applies for the nodal resistances. The nodal capacitance, C, is calculated for each
node with Equation 2-20, keeping the δlx,δly and δlz terms distinct. Given the axis
orientation and branch numbering in Figure 2.12, the nodal potential, φ, can be
calculated with
⎡ 2(V i + V i )
2(V i + V i )
2(V i + V i )
2V i
⎤
1
3
5
6
stub
2
4
+
+
+
φ=⎢ 1
⎥⋅Y
+
+
+
+
R
Z
R
Z
R
Z
R
Z
y
z
stub
stub ⎦
⎣ x
Y=
2 + 2 + 2 +
1
R x + Z R y + Z RZ + Z Rstub + Z stub
Equation 2-56
Equation 2-57
The boundary resistors are similarly calculated with distinct δlx,δly and δlz terms, as in
Equation 2-52. Reflected pulses are calculated normally, according to Equation 2-37.
Additionally, the nodal inductance, L, can be calculated from Equation 2-54 so that
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-29
L = δt
C
2
Equation 2-58
In a stub enhanced TLM node, the stub functions as an open circuit capacitor, as
explained in Section 2.3.2. From Equation 2-58, it is possible to deduce that if a node
is too heavily weighted towards the stub by having a large nodal capacitance and a
sufficiently large timesstep, the inductance term is reintroduced into Equation 2-10,
bringing back the wave term so that Equation 2-9 is reinstated. However, if the δt2
and C terms in Equation 2-58 are sufficiently controlled so that L remains negligible,
the wave component can still be ignored.
2.3.4.1
Spatial Sub-structuring
Area requiring fine
mesh
(a)
(b)
Figure 2.17: Varied meshing. (a) Continuous mesh lines. (b) discontinuous mesh lines.
Traditional variable meshes make use of continuous mesh lines, as depicted in Figure
2.17a. The disadvantage of this form of variable meshing is that once the elemental
dimensions are set for the area where the higher mesh resolution is required, other
sections of the mesh will also have these dimensions imposed upon them. This in turn
leads to a higher number of nodes than is strictly necessary, which results in longer
simulation times and increased processing requirements.
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-30
The use of discontinuous mesh lines, as illustrated in Figure 2.17b, offers a reduction
of the total node number, resulting in a more efficient, fast running mesh. This
meshing approach, known as spatial sub-structuring 23 , requires that two or more
smaller elements be “fitted” to a larger element, as illustrated in the two dimensional
case in Figure 2.18.
δlya
δlyb
δlxa
Section A
δlxb
Section B
Figure 2.18: 2D spatially substructured mesh.
For the situation illustrated in Figure 2.18, sections A and B have different elemental
dimensions, leading to different nodal resistances and capacitances. The individual
nodal resistances for the connected branches (in this case, the branches on the x-axis)
can be calculated from Equation 2-19 so that
2 R xA =
1
k tAδl yA
Equation 2-59
for section A and
2 R xB =
1
k tB δl yB
Equation 2-60
for section B, where ktA and ktB are the thermal conductivities for the relevant sections.
If the object being modelled is homogeneous, then ktA will equal ktB. Similarly, the
nodal capacitances can be calculated from Equation 2-20 so that
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-31
C A = S pA ρ A (δl xA ⋅ δl yA )
Equation 2-61
and
C B = S pB ρ B (δl xB ⋅ δl yB )
Equation 2-62
where each term in the equation refers to its value for the relevant section. Even if the
thermal conductivity, specific heat capacity and density of the material are the same
for both sections, the resultant nodal resistances and capacitances will vary because of
the different elemental lengths involved.
The resulting impedance discontinuity can be dealt with by the introduction of a
secondary node (calculation point) on the elemental boundary between the two
sections, as illustrated in Figure 2.19. The scattering event for this node occurs at
δt
2
to maintain temporal continuity.
Section A
Section B
ZB1
RA
RB1
Primary
Node B1
ZA
Primary
Node A
Secondary
Node
ZB2
RB2
Primary
Node B2
Elemental
Boundary
Figure 2.19: Secondary scattering node on elemental boundary.
The secondary node is treated in a similar manner to a normal node, with the extra
consideration that there are two transmission lines for section B, and that there is no
nodal resistance (Rsec=0). The nodal potential for the secondary node, φsec, is the sum
of the reflected pulses from all three connected branches, and is expressed by
D. J. Lim
Chapter II: The TLM Method and The IGBT
⎡ 2V r
2V r
2V r ⎤
φsec = ⎢ A + B1 + B 2 ⎥ ⋅ 1
ZB
ZB ⎦ Y
⎣ ZA
Page 2-32
Equation 2-63
where
Y= 1 + 2
ZA ZB
Equation 2-64
The reflected pulses from the scattering process in the secondary node then become
incident on the primary nodes at the next primary scattering event, so that
V Ai = φsec − V Ar
V Bi1 = φsec − V Br1
Equation 2-65
V Bi 2 = φsec − VBr2
2.4
Insulated Gate Bipolar Transistors (IGBTs)
IGBTs are usually packaged in a layered structure with a finned heat sink 24 on the
side remote from the device. These devices generally have a very high output power,
often in excess of 5kW, and generate correspondingly large amounts of heat. This can
result in temperatures far in excess of 100ºC 25 which can cause device damage in
various forms. The input of an IGBT is often in the form of a pulsed wave. The rapid
repeated heating and cooling of the chip and the surrounding packaging resulting from
pulsed input cause physical stresses, which can eventually lead to breakdown. In some
cases, the solder which holds the connections in place either melts, cracks, or lifts
from the base-plate 26 . This process, which is known as delamination, is a major
concern of IGBT packaging manufacturers. Delamination also occurs between the
IGBT and the cooling structure, which is normally in the form of multiple layers of
thermally conductive material bonded to the chip18,20. When delamination occurs, the
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-33
temperature in the chip increases further, since the chip now has reduced thermal
contact with the heat sink assembly. Ultimately, the whole physical structure of the
silicon may break down as the increased temperature changes the electrical and
physical properties of the materials, causing thermal runaway 27 . The end result of this
is usually a catastrophic failure of the IGBT. Effective dissipation of generated heat is
therefore crucial to the lifetime of devices.
However, transient heat transfer within the device and its analysis are complicated by
the different thermal properties of the materials in the multilayer structure. Materials
used in IGBT construction tend to vary significantly in their thermal properties, the
choices being constrained by factors including their electrical properties and
manufacturing costs. During IGBT operation, thermal energy travels through the
device as the heat dissipates into the system and eventually out of the device primarily
through the finned heat sink structure. Each layer of the device has its own thermal
properties, but cannot be considered independently of the other layers in the device, as
the transient heat flow in one material affects the thermal state in other layers.
2.4.1 IGBT Structure
Baseplate
Figure 2.20: IGBT module layout
D. J. Lim
IGBT Chips
Chapter II: The TLM Method and The IGBT
Page 2-34
Figure 2.21: IGBT Module in 3x2 matrix layout.
Many common IGBT modules have six subassemblies, arranged in a 3x2 matrix
structure 28,29 , as illustrated in Figure 2.20 and Figure 2.21. Each subassembly is a
layered structure, which contains an IGBT chip and a heat sink assembly.
Top Plate
Solder
Silicon Chip (Active Region)
Heat Spreader
Substrate
Base Plate
Heat Sink (Fin Structure)
Figure 2.22: Generic IGBT layered heat sink assembly structure
The heat sink assembly of an IGBT package is depicted in Figure 2.22. The chip,
which is the active region of the IGBT, comprises a small fraction of the physical
volume of an IGBT assembly. The materials are brazed together by Direct Bond
Copper (DBC) or other similar methods. Most IGBT assemblies have two heat
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-35
spreader layers that are made of copper or other similar materials. The ceramic
substrate, which is typically about 300µm thick28, is sandwiched between these heat
spreaders. The top plate and the chip are soldered onto the heat spreader-substrate
sandwich, and the whole structure is then brazed onto the base plate. This whole
structure is in turn secured to the heat sink fin structure, which has a high surface area
per unit volume for high heat transfer to ambient. A heat sink compound is used to
provide thermal contact between the base plate and the fin structure. The active
components, which are individually wire bonded for top-connect operation, are
electrically isolated from the base plate by the substrate layer, as shown in Figure
2.23. There are hotspots within the IGBT chip, centred around the wire bonded
connections 30 , but that is outside of the scope of this study and the simulations do not
take account of this.
Solder bead
Bond wire
Solder
Silicon Chip (Active Region)
Heat Spreader
Substrate
Base Plate
Heat Sink (Fin Structure)
Figure 2.23: IGBT Structure showing wire bond connection
For the IGBT to function the chip must be kept within operational temperatures. To
ensure this, it is important that the heat generated by the chip be removed from the
active region. However, if the heat is removed into the surrounding area, even if it is
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-36
conducted out of the chip itself early in the transient, it will cause the heat flow out of
the chip to slow later in the transient. Therefore, it is not only important to conduct the
heat away from the chip itself, but also to retain a low temperature in the area
surrounding the chip. In order to explore the possibilities and practicalities of
designing such a system, the thermal simulations in this study focus on the transient
profiles of the IGBT assembly as a whole, representing, explicitly, the different
thermal properties of components of the layered structure.
Table 2.1 shows a range of materials commonly used in the construction of IGBT
assemblies. These materials are normally chosen based on their thermal diffusivity or
their thermal conductivity (Kt).
Material
Density
(ρ),
kg.m-3
AlN
Diamond 2K
3260
3510
Cu
CuMo
8960
9985
Silicon
Solder
Top Plate
Base Plate
2320
7400
10220
2980
Specific Heat
Thermal
Capacity (Sp),
Conductivity (Kt),
J.kg-1.K-1
W.m-1.K-1
Substrate
669
170
620
2000
Spreader
276
393
678
197
Other Materials
700
148
160
40
255
138
722
180
RhoSp
Diffusivity
2.18E+06
2.18E+06
7.79E-05
9.19E-04
2.47E+06
6.77E+06
1.59E-04
2.91E-05
1.63E+06
1.18E+06
2.16E+06
2.15E+06
9.11E-05
3.38E-05
5.30E-05
8.37E-05
Table 2.1: Material properties of IGBT heat sink assembly structure materials
Common heat spreaders are made of copper (Cu) or a copper molybdenum alloy
(CuMo)23. These two materials are a contrast of properties. While Cu is a standard
heat spreader material and has a high thermal conductivity, a low specific heat
capacity and a high density, CuMo has a similar density to Cu, but only about half the
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-37
Kt and about double the specific heat capacity (Sp). This means that Cu has a higher
thermal diffusivity than CuMo, as noted in Table 2.1.
The IGBT substrate is typically a Metal Matrix Composite (MMC) material23,31 .
Aluminium Nitride or Alumina (AlN), is a low density material with a high Sp and a
low Kt. Chemical Vapour Deposited (CVD) Diamond is a substrate material which
has a much higher thermal conductivity than AlN while retaining a similar specific
heat capacity and density. In this study, CVD Diamond with a Kt of 2,000W.m-1.K-1,
denoted D2K, will be considered. These two materials are used for this study as their
thermal properties are different enough to show the effects of changes in Kt in the
substrate, yet similar in terms of density and Sp, thereby allowing clearer examination
of thermal transients within the layers in the IGBT assembly. This study also assumes
an AlSiC base plate, which is light, cheap, easily processed and has a comparable
CTE to Silicon, albeit with a lower Kt than the traditional Cu base plates26. The
thermal properties of the various materials used in this investigation are shown in
Table 2.124.
In this chapter, some of the relevant theory describing the Transmission Line Matrix
modelling method has been presented. An overview of the basic IGBT structure has
also been described. In the next chapter, the discussion will shift to issues that are
specifically linked to this study, namely the TLMVIS software and the models that
were used for the simulations found in this study.
D. J. Lim
Chapter II: The TLM Method and The IGBT
Page 2-38
Johns PB, A Simple Explicit and Unconditionally Stable Numerical Routine for the Solution of the
1
Diffusion Equation, Int. J. Numer. Methods Eng., Vol 11, No. 8, 1977, pp 1307-1328.
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Ait-Sadi R, Naylor P, An Investigation of the Different TLM Configurations Used in the Modelling of
Diffusion Problems, Int. J. Numer. Model., Vol 6, No. 4, 1993, pp 253-268.
Gui X, Webb PW, A Comparative Study of Two TLM Networks for Modelling Diffusion Processes,
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Int. J. Numer. Model. Vol 6, No. 2, 1993, pp 161-164.
4
Enders P, De Cogan D, The Efficiency of Transmission Line Modelling – A Rigorous Viewpoint, Int.
J. Numer. Model., Vol 6 , No. 2, 1993, pp 109-126.
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Johns PB, Beurle RL, Numerical Solutions of 2D Scattering Problems Using a TLM Model, Proc IEE,
Vol 118, No. 9, 1971, pp 1203-1208.
Pulko SH, Mallik A, Johns PB, Application of Transmission Lime Modelling (TLM) to Thermal
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Diffusion in Bodies of Complex Geometry, Int. J. Numer. Methods Eng., Vol 23, No. 12, 1986, pp
2303-2312.
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Pulko SH, Johns, PB, Modelling of Thermal Diffusion in Three Dimensions by the Transmission Line
Matrix Meathod and the Incorporation of Non-linear Thermal Properties, Communications in Applied
Numerical Methods, Vol 3, No. 6, 1987, pp 571-579.
Righi M, Eswarappa C, Hoefer WJR, Analysis of Passive Components for Wireless Applications
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Using TLM Electromagnetic Simulations, Wireless Applications Digest, 1997, IEEE MTT-S
Symposium on Technologies for Wireless Applications, Feb 23-26 1997, pp 143-146
9
Hoefer WJR, The Transmission Lime Matrix Method – Theory and Applications, IEEE Transactions
on Microwave Theory and Techniques Vol 33, No 10, Oct 1985, pp 882 - 893.
10
Johns PB, Pulko SH, Modelling of Heat and Mass Transfer in Foodstuffs, Food Structure and
Behaviour: Equilibrium and Non-Equilibrium Aspects, ed. Blanchard J, Lillford P, Chapter 12,
Academic Press, 1987, ISBN 0121042308, pp 199-218.
11
Hendricx M, Engles C, Tobback P, Two Dimensional TLM Models for Water Diffusion in White
Rice, J Food Engng., Vol 6, No. 3, 1987, pp 187-197.
12
Phizacklea, C.P., Pulko, S.H.: Modelling Heat Transfer in Cyclic Glass Lens Pressing Processes by
Transmission Line Matrix Method, Proc. IASTEAD MIC, 1988, pp 146-149.
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Chapter II: The TLM Method and The IGBT
13
Page 2-39
Pulko, S.H., DeCogan, D.: Computer Aided Thermal Management of Electronic Networks and
Devices Using TLM, Computer Aided Engineering Journal, Vol 8, No. 3, June 1991, pp 91-96.
14
Pulko, S.H., Hurst, A.I., Newton, H.R., Gilbert, J.M., Wilkinson, A.J.: Simulation of Ceramic Firing,
Computing & Control Engineering Journal, Vol 10, No. 1, Feb 1999, pp 23-27.
15
Saleh AHM, Blanchfield P, Analysis of acoustic radiation patterns of array transducers using the
TLM Method, Int. Journ.Numer. Model. , Vol 3, No. 1, 1990, pp. 39-56.
16
Moin P, Fundamentals of Engineering Numerical Analysis, Cambridge University Press, 2001.
17
DeCogan, D.: Transmission Line Matrix (TLM) Techniques for Diffusion Applications, Gordon &
Breach Publishing Group, 1998, ISBN 9056991299.
18
Christopoulos, C.: The Transmission Line Modeling (TLM). Method, Electromagnetic Wave Theory,
IEEE Press, 1995, ISBN 0780310179.
19
Johns, P.B.: A Symmetrical Condensed Node for the TLM Method, IEEE Transactions on Microwave
Theory and Techniques, Vol 35, No. 4, April 1987, pp 370-377.
20
Shammas NYA, Rodriguez MP, Plumpton AT, Newcombe D, Finite Element Modelling of Thermal
Fatigue Effects in IGBT- Modules, IEE Proceedings Circuits, Devices and Systems, Vol 148. No. 2,
ISSN 1350-2408, April 2001, pp 95-100.
21
Cook RD, Finite Element Modelling for Stress Analysis, John Wiley, 1995, ISBN 0471107743.
22
Pulko SH, Mallik A, Allen R, Johns PB, Automatic Timestepping in TLM Routines for Modelling of
Diffusion Processes, Int. J. Numer. Model., Vol 3, No. 2, 1990, pp 127-136.
23
Pulko SH, Halleron IA, Phizacklea CP, Substructuring of Space and Time in TLM Diffusion
Applications, Int. J. Numer. Model: Electronic Networks, Devices and Fields, Vol 3, No. 3, 1990, pp
207-214.
24
Gillot, C., Shaeffer, C., Massit, C., Meysenc, L.: Double Sided Cooling for High Power IGBT
Modules Using Flip Chip Technology, IEEE Transactions on Components and Packaging
Technologies, Vol 24, No. 4, Dec 2001, pp 698-704.
25
Sheng, K., Williams, B.W., He, X., Qian, Z., Finney, S.J.: Measurement of IGBT Switching Limits,
IEEE Power Electronics Specialists Conference, PESC 1999, Vol 1, 1999, pp 376-380.
26
Berg, H., Wolfgang, E.: Advanced IGBT Modules for Railway Traction Applications: Reliability
Testing, Microelectronics Reliability, Vol 38, No. 6, 1998, pp 1319-1323.
D. J. Lim
Chapter II: The TLM Method and The IGBT
27
Page 2-40
Fratelli, L., Cascone, B., Giannini, G., Busatto, G.: Long Term Reliability Testing of HV-IGBT
Modules in Worst Case Traction Operation, Microelectronics Reliability, Vol 39, No. 6, 1999, pp
1137-1142.
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Hocine R, Boudghene Stambouli A, Saidane A, A Three-dimensional TLM Simulation Method for
Thermal Effect in High Power Insulated Gate Bipolar Transistors, Microelectronic Engineering, Vol
65, No. 3, 2003, pp 293-306.
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Hocine R, Lim D, Pulko SH, Boudghene Stambouli A, Saidene A, A Three Dimensional
Transmission Line Matrix (TLM) Simulation Method For Thermal Effects In High Power Insulated
Gate Bipolar Transistors, Circuit World, 2003, Vol 29, No. 3, pp 27-32.
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Ishikoa M,Usuia M, Ohuchib T, Shiraib M, Design Concept for Wire-Bonding Reliability
Improvement by Optimizing Position in Power Devices, Microelectronics Journal, Vol 37, No. 3,
March 2006, pp 262-268
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Occhionero MA, Hay RA, Adams RW, Fennessy KP, Cost Effective Manufacturing of Aluminium
Silicon Carbide (AlSiC) Electronic Packages, IMAPS Advanced Packaging Materials Symposium,
March 1999, Ceramic Process Systems Corp.
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
Page 3-1
3.0 TLMVIS and The IGBT Simulation Models
The mathematical equations of the Transmission Line Matrix (TLM) Method describe
a physical model built from a mesh of transmission lines. This is of great benefit
when representing and simulating physical processes like heat transfer or diffusion as
the method itself provides a conceptual model that can be reproduced with great
accuracy on a computer 1 .
3.1
TLMVIS
TLMVIS is a thermal transient modelling and simulation package that was developed
at the University of Hull. It uses a TLM core for processing the thermal transient, and
incorporates a full suite of features, including stub handling and the processing of
nonlinearities. The package also handles 1-, 2-, and 3-dimensional models, and is
capable of handling objects of fairly complex geometry. Additionally, because of the
way the geometry is entered into the system and treated by the TLM core, it is able to
accommodate inhomogeneous systems. TLMVIS also has specific subroutines that
enable the use of adiabatic sink and source nodes, reflective boundaries and even time
dependant nonlinear inputs. Of particular interest is the ability of TLMVIS to handle
meshes where the elements are non-cubic, as greater accuracy (and hence, a higher
resolution) is required on the vertical axis of the proposed mesh to provide sufficient
detail of thermal transients within the layers of the IGBT assembly. Since the
proposed application requires many of the aforementioned features, TLMVIS is a
logical choice as the simulation package for this study.
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
Page 3-2
A TLMVIS model is constructed from geometrical shapes, then descretised using a
meshing tool. This tool breaks the model volume down into TLM nodes, which can
then be assigned material properties. Specific elements can then be designated as
probes. TLMVIS will then record the temperature of these probe elements for every
timestep of the simulation, yielding the transient conditions of the material in that
element. By designating probes in the appropriate places within the model, it is then
possible to reconstruct a fairly detailed thermal profile of the object simulated for both
its transient and steady states.
3.1.1 Stub Handling in TLMVIS
The use of stub branches in the TLM node adds considerable flexibility to the
algorithm 2 . This is particularly true when dealing with inhomogeneous problems
where the material in one region has a higher heat capacity than that in another (as is
the case with IGBTs), and non linear problems where the heat capacity of a given
material varies with time or temperature. In these situations, the additional heat
capacity of a certain material relative to other associated materials is stored in the
stub. Additionally, stubs are used for their smoothing effect on the simulation 3 .
However, the more the heat capacity of a node is weighted towards the stub, the more
the second order term of the TLM equation (Equation 2-9), will come into play,
resulting in a wave component that distorts the diffusion transient, as described in
Section 2.3.4.
TLMVIS deals with this problem by surveying all the material properties in a given
model to find the smallest link line impedance, then proposing a timestep based on
that impedance. A general rule of thumb is that the timestep used in a given
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
Page 3-3
simulation will be one tenth of the RC time constant. This is because the material with
the smallest link line impedance is, in almost all cases, the material with the fastest
thermal response time and must therefore be simulated with the smallest timestep to
maintain accuracy. It then follows that all other materials in the simulation model are
slower to react to heat and will be simulated with sufficient accuracy. Hence, the
timestep for the whole simulation must be determined by this shortest timestep if the
same timestep is to be used throughout the network.
There is more recent work that uses TLM state-space representations to solve the
hyperbolic or second order TLM equations 4 . However, these theories only apply
when there is both a diffusion and wave component to the TLM equation, which are
usually situations where very rapid and intense heating occurs. This situation does not
apply to the IGBT models in question. The timestep used for the models was small
enough to eliminate the wave component of the TLM equation, as seen from the fact
that there is no visible wave component in the transients presented in the following
chapters. Additionally, neither the rate of change of the thermal transient nor the
amount of heat injected into the system are in the same order of magnitude as those
for which the hyperbolic representation is needed and recommended4.
3.1.2 Boundary Handling in TLMVIS
There are three types of boundary conditions used in the simulation models for this
study, and these will be the ones considered in this section. The first is an intermaterial boundary as described in Section 2.3.2.1. TLMVIS handles the differences in
impedance at material interfaces by loading the stub nodes with the heat capacitance
accordingly. In this way, intermediate scatter is avoided.
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
Page 3-4
The interface between materials and ambient blocks, which is the second type of
boundary, is handled by defining the resistance of the relevant branch in the form of a
heat transfer coefficient, ht, as described in Section 2.3.3. The higher the value of the
heat transfer coefficient, the more easily heat flows into or out of the ambient block.
A typical object-to-still air heat transfer coefficient is between 7 and 10. By defining a
heat transfer coefficient that is higher than these “normal” heat transfer coefficients,
heat sinks can be modelled. Increasingly more effective heat sinks are modelled by
simply increasing the value of ht. For example, if the installation of a heat sink to a
system results in twice the amount of heat being dissipated, the heat sink can be
modelled with a ht of about 20, while a more efficient, very high surface area, crystal
alloy, liquid cooled, force convection assisted heat sink may have a ht approaching
100. Since the resistance on a link-line is bound to the thermal conductivity, kt, the
thermal conductivity is not defined for an ambient block as it is already defined by the
heat transfer coefficient.
The third type of boundary used in this study is the reflective boundary, which is also
described in Section 2.3.3. This boundary can be defined as having an infinitely high
resistance in the link line, or by a heat transfer coefficient of 0. Both of these
situations have the net effect of rendering Vi = Vr, where i denotes the incident pulse
and r denotes the reflective pulse. This means that the pulse that is passing out of the
boundary node of the material into this reflective boundary meets an infinitely high
resistance and is reflected back without loss. There are two ways for this type of
boundary to be defined in TLMVIS. The first way is by assigning the boundary a heat
transfer coefficient that approaches 0. As the heat transfer coefficient approaches 0,
the resistance of the link line approaches infinity, rendering the boundary effectively
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
Page 3-5
reflective. The second method is to actually set the heat transfer coefficient of the
boundary to 0. The reason this second method is not the default choice in the
implementation of a reflective boundary is an artefact of the TLMVIS kernel.
Recalling Equation 2-51, the software cannot inherently calculate a heat transfer
coefficient of 0, as it would involve a division by 0. However, a subroutine has been
added to the latest version of TLMVIS to account for this, and both methods are now
available for use. If appropriately implemented, reflective boundaries can be used to
increase computational efficiency and reduce the computational requirements of a
given simulation model, as will be seen in Section 3.1.3.
Imagine a simulation model where there is thermal excitation is in the middle of a
square of homogeneous material (Figure 3.1a). The heat from the excitation would
diffuse equally in all directions so that at a given time after the initial excitation, all
the corners of the square would have the same temperature, each corner being a
reflection of the others. Suppose then that a perfectly reflecting mirror was placed in
the middle of the square, halving it, and that the transient thermal profile was also
reflected perfectly. It would then be possible to simulate only half of the area of the
square, since the results on one side would be exactly the same as the results on the
other, mirrored side, as depicted in Figure 3.1b. Furthermore, since the remaining two
corners have the same thermal profile, the half square can be halved again with a
second mirror placed perpendicular to the first (Figure 3.1c), thereby quartering the
square and the resources used to simulate it. Therefore, if a model, such as the one
shown in Figure 3.1a, has a uniform pattern of excitation where the transient heat flow
can be mirrored at certain points throughout the structure, only the smallest possible
repeatable section needs to be simulated (Figure 3.1c).
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
Page 3-6
Reflective
Boundary
Simulated
Area
Active region
(Heat Source)
(a)
(b)
Simulated
Area
Reflective
Boundary
(c)
Figure 3.1: Use of reflective boundaries in simulation. (a) Original model. (b) Only a quarter of the
original model is simulated.
Since the IGBT assemblies are typically arranged in the 3x2 matrix, the question
arises of whether the use of reflective boundaries is valid, as there is the issue of the
thermal interaction between the simulated chip and other chips on the assembly. This
would indeed be a concern if the simulations were for a longer period of time. As it
will be proved in Chapter 6, the thermal footprint of the chip barely extends beyond
the physical footprint of the chip itself for the simulation time considered. There is,
therefore, no thermal interaction at this stage.
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
Page 3-7
3.1.3 1D Versus 3D Models in TLMVIS
Another method to increase computational efficiency and reduce simulation time is to
render simulation models in one dimension. 1D models can be simulated much faster
than their 3D equivalents since only two branches per node require calculation
compared to the six branches of a 3D model. Additionally, 1D models will invariably
have fewer nodes than their 3D equivalents. However, this treatment of simulation
models can only be used under certain conditions and with certain presuppositions.
Imagine an arbitrary cube of material measuring 5m in all dimensions. Imagine also a
heat source that covered the top of the cube, with perfect contact on the whole of the
top surface. Now suppose that the vertical thermal profile was required for only a
small 5cm x 5cm section from the middle of the block, as illustrated in Figure 3.2 (a)
and (b). The 5cm x 5cm x 5m tube can be simulated without the surrounding material
by placing reflective boundaries around the four sides of the tube (Figure 3.2 (c) and
(d)). This would represent the tube as being part of an infinitely large area that is 5m
thick, but since the edges of the cube (where there would be temperature changes as a
result of ambient conditions) are relatively distant from the boundaries in question,
the thermal loss is negligible. By rendering the tube one dimensional in the zdirection, as in Figure 3.2(e) and (f), the need for reflective boundaries is removed,
thereby further streamlining the simulation model and further increasing
computational efficiency.
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
Page 3-8
Heat
Source
Implied
Infinite
Area
Required
area
(a)
(c)
(b)
(d)
Reflective
Boundary
Heat
Source
Simulated
Area
(e)
(f)
Figure 3.2: Example of 3D to 1 D model simplification. (a) Top view of 3D object. (b) side view of 3D object. (c) top view of
simplified simulation area with reflective boundaries. (d) side view of simplified simulation area with reflective boundaries. (e)
top view of 1D object. (f) side view of 1D object. Object not to scale.
3.2
Simulation Models
The models used in this study need to enable the detailed study of the transient
behaviour of these layers as well as facilitate the investigation of their interaction and
effect on the rest of the IGBT assembly. The models must therefore support sufficient
detail to yield an adequate simulation of the thermal transient while at the same time
retaining reasonable computational efficiency.
In order to achieve this, two models were constructed. The first is a 1D model which
represents a small section within an IGBT assembly. This model facilitates the study
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
Page 3-9
of the vertical heat transfer process for various materials. The second model is a 3D
representation that allows the investigation of the lateral or horizontal heat dissipation
process. It also enables the study of the effect of the spreader layer extending beyond
the footprint of the IGBT chip on the assembly as a whole. Both models were
constructed with much more vertical resolution than horizontal, as the heat transfer
process was found to occur in a predominantly vertical direction. Furthermore, the
IGBT assembly is very thin, being only about one tenth the width and length of a
single subassembly. It was therefore important to have sufficient resolution in the zdirection to adequately observe the vertical thermal transient. As a result, the nodal
elements for both models have a δlx and δly of 0.2cm and a δlz of only 0.005cm. The
observations gleaned from both these models can then be combined to give a synergic
picture of the complex transient heat transfer processes within the IGBT assembly.
3.2.1 1D “Apple Core” Model
Simulated Section
Figure 3.3: Simulated section of IGBT module in 1D “Apple Core” model
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
Page 3-10
As stated in Section 2.4.1, IGBT modules comprise six subassemblies, arranged in a
3x2 matrix. Each of these subassemblies is usually around 6.8cm by 6.2cm in area
with a thickness of 0.64cm 5,6 , as illustrated in Figure 3.3. In the interests of
computational efficiency, the model presented in this section is a simplified
representation of an IGBT assembly, representing a small section of the IGBT cross
section from the middle of a subassembly. It is constructed as a 1D model in the zdirection with 0°C ambient conditions on the upper and lower surfaces. A heat
transfer coefficient is used to represent a high surface area fin structure. The active
region is subjected to three 85W pulses of 0.1s each, at a 50% duty cycle followed by
cooling time of 0.1s. The temperature rise is plotted at various points along the central
axis through the assembly.
Top Plate
Solder
Silicon Chip (Active Region)
Heat Spreader
Substrate
Base
Ambient
Figure 3.4: 1D "Apple Core" Model
This 1D "Apple Core" model (thus named for its similarity to an extracted apple core)
provides a fast running model which allows structural or material changes to be made
and simulated within a reasonable timeframe. The "Apple Core" model represents a
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
Page 3-11
cross-section measuring 0.6cm by 0.6cm in area with a thickness of 0.64cm that
consists of only approximately 130 nodes, but is detailed enough to have a layered
structure as illustrated in Figure 3.4.
Four material combinations are simulated in this study. Two types of heat spreader
material, Cu and CuMo, and two types of substrate material, AlN and D2K, are
considered. All other materials are as noted in Table 2.1 in Chapter 2. For ease of
reference, the models will be referred to by the heat spreader material first, followed
by the substrate material. For example, a model with Cu heat spreaders and an AlN
substrate will be denoted Cu/AlN.
3.2.2 3D Spreader Model
(b)
(a)
Top Plate
Heat Spreader
Ambient
Solder
Substrate
Base Plate
Reflective Boundary
Silicon Chip (Active Region)
Figure 3.5: 3D Spreader Model. (a) Top view. (b) Side view.
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
Page 3-12
The second model used in this study represents a quarter of an IGBT subassembly
with the spreader and substrate layers extending 3cm beyond the area of the IGBT
chip, as illustrated in Figure 3.5. This whole structure is surrounded on all four sides
by reflective boundaries. The model is thus equivalent to a full sized IGBT
subassembly with the surrounding spreader, substrate and base plate material, as
depicted in Figure 3.6. This translates to a much more complex model, consisting of
about 120,000 nodes, excluding the surrounding ambient areas.
Equivalent Simulated Section
Simulated Section
Figure 3.6: Simulated section of IGBT module in 3D Spreader Model
Like the “Apple Core” model, the active region is subjected to a 85W, 50% duty cycle
pulse for 0.1s, the same time as the 1D “Apple Core” model. The material
combinations used for the spreader and substrate layers are the same as those used for
the “Apple Core” model and will be referred to in the same way. The 3D Spreader
model has 0°C ambient conditions on the top and bottom faces. The thermal transient
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
Page 3-13
for this model is recorded in the same places within the layers as the 1D “Apple Core”
model as well as in the regions beyond the IGBT chip footprint. This will allow a
thermal profile to be constructed that will detail the lateral heat dissipation within the
IGBT assembly.
There is, admittedly, very little external validation for this study. This is mainly due to
the difficulty in measuring the transient within the IGBT assembly to the degree of
detail that is undertaken in this study. As such, most studies tend to focus on the
thermal behaviour in the steady state. However, there are some published articles that
present sufficient information to show that the results of the simulations are within
reasonable parameters 7 .
Additionally, in order to ensure that there were minimal artefacts of the simulation
technique, very small timestep values of 6.8x10-6s were used. This translates to
approximately 15,000 timesteps for every 0.1 seconds of simulated time, providing
excellent resolution and complete suppression of any potential spurious results. With
the 3D model, each timestep could take between 10 to 15 seconds, resulting in
simulation runs that required up to 8 days or real time.
An overview of the TLMVIS simulation software, including specific features that
were useful for the simulations required have been presented in this chapter along
with descriptions of the models that were constructed for this study. The next chapter
will transition into presenting the simulation data and discussing the implications
thereof, beginning with the heat spreader layers of the IGBT package assembly.
D. J. Lim
Chapter III: TLMVIS And The IGBT Simulation Models
1
Page 3-14
Johns PB, On the Relationship Between TLM and Finite Difference Methods for Maxwell’s
Equations, IEEE Transactions on Microwave Theory and Techniques, Vol MTT-35, No. l, Jan 1987,
pp 60-61
2
Gilbert JM, Wilkinson AJ, Pulko SH, The Effect of Stubs on the Dynamics of TLM Diffusion
Modelling Networks, Numerical Heat Transfer B, 2000, Vol 37, No. 2, pp 165-184
3
Pulko SH, Wilkinson AJ, Gallagher, Redundancy and Its Implications in TLM Diffusion Models, In. J.
Numer. Modelling, Vol 6, No. 2, 1987,pp. 135-144,
4
Pulko SH, Wilkinson AJ, Saidane A, TLM Representation of the Hyperbolic Heat Conduction
Equation, Int. J. Numer. Modell., March/April 2002, Vol 15, No. 3, pp. 303-315,
5
Hocine R, Boudghene Stambouli A, Saidane A, A Three-dimensional TLM Simulation Method for
Thermal Effect in High Power Insulated Gate Bipolar Transistors, Microelectronic Engineering, 2003,
Vol 65, No. 3, pp 293-306
6
Hocine R, Lim D, Pulko SH, Boudghene Stambouli MA, Saidene A, A Three Dimensional
Transmission Line Matrix (TLM) Simulation Method For Thermal Effects In High Power Insulated
Gate Bipolar Transistors, Circuit World, 2003, Vol 29, No 3, pp. 27-32.
7
Yun CS, Regli P, Waldmeyer J, Fichtner W, Static and Dynamic Characteristics of IGBT Power
Modules, ISPSD'99, Toronto, Ontario, CAN, May 25-28, 1999.
D. J. Lim
Chapter IV: Heat Spreaders
Page 4-1
4.0 Heat Spreaders
Although relatively thin compared to other layers in the IGBT assembly, the heat
spreader layer has a significant impact on the overall thermal profile of the module.
Figures 4.1, 4.2 and 4.3 show the temperature profile through the centre of an IGBT
assembly early in the transient, specifically at 1x10-3s, 1x10-2s and 1x10-1s, for the
Cu/D2K and CuMo/D2K 3D models. Ambient conditions are set at 0°C. All profiles
show the highest temperature in the chip and the lowest temperature in the base plate.
In the earliest profile, which is 1x10-3s into the transient, there is barely any
temperature change in the base plate. This changes as time passes, as seen in Figure
4.3, and the heat diffuses into the base plate, raising its temperature. It is evident that
the layer with the largest thermal gradient per unit thickness in the IGBT heat sink
assembly is the solder layer that links the IGBT chip to the upper heat spreader. There
are many thermal, chemical and electrical restrictions which prevent the type and
composition of the solder used being modified at will 1 .
However, the region with the second highest heat gradient, the upper heat spreader,
does not have as many restrictions. From Figures 4.1, 4.2 and 4.3, the upper heat
spreader layer is seen to have the largest temperature drop per unit thickness in the
heat sink assembly after the solder layer, discounting the IGBT chip itself. Comparing
the layers at 1x10-1s, the difference in rate of temperature drop per unit thickness in
the upper spreader layer for both the Cu/D2K and CuMo/D2K models is about twice
that in the lower layer, and more than ten times that in the substrate. Thus, it is the
effect this layer has on the rest of the IGBT assembly that is further investigated in
this section of the study.
D J Lim
Chapter IV: Heat Spreaders
Page 4-2
Temp Profile Through Model T=1e-3s
Solder
0.03
IGBT Device
Upper
Spreader
Substrate
Low er
Spreader
Baseplate
0.02
0.01
Temp (C)
0.02
0.01
0.00
8
7
6
5
4
3
2
1
0
-0.01
Distance into assem bly (m m )
Cu Spreader
CuMo Spreader
Figure 4.1: Temperature profile through IGBT assembly (1x10-3s)
Temp Profile Through Model T=1e-2s
Solder
0.08
IGBT Device
Upper
Spreader
Substrate
Low er
Spreader
Baseplate
0.07
0.06
0.04
0.03
0.02
0.01
0.00
8
7
6
5
4
3
2
1
0
-0.01
Distance into assem bly (m m )
Cu Spreader
Figure 4.2: Temperature profile through IGBT assembly (1x10-2s)
D J Lim
CuMo Spreader
Temp (C)
0.05
Chapter IV: Heat Spreaders
Page 4-3
Temp Profile Through Model T=1e-1s
Solder
IGBT Device
0.30
Upper
Spreader
Substrate
Low er
Spreader
Baseplate
0.25
0.15
0.10
0.05
0.00
8
7
6
5
4
3
2
1
0
Distance into assem bly (m m )
Cu Spreader
CuMo Spreader
Figure 4.3: Temperature profile through IGBT assembly (1x10-1s)
4.1
Simulation Results and Observations
Figure 4.4 compares the temperature in the centre of the chip for Cu, CuMo and
AlSiC heat spreaders for 85W of uniform heat generation throughout the chip over
1x10-1s. As is seen from Figure 4.4a, AlSiC is less thermally favourable than Cu or
CuMo and is associated with higher temperatures both in the chip and in the solder
layers.
D J Lim
Temp (C)
0.20
Chapter IV: Heat Spreaders
Page 4-4
1D 1st Pulse
0.20
0.18
0.16
0.14
Temp, C
0.12
0.10
Crossover section
0.08
0.06
0.04
0.02
0.00
0.00E+00
5.00E-03
1.00E-02
1.50E-02
2.00E-02
2.50E-02
3.00E-02
3.50E-02
4.00E-02
4.50E-02
5.00E-02
Time, s
Cu
CuMo
AlSiC
(a)
1D 1st Pulse
0.1000
0.0950
Temp, C
Crossover section
0.0900
0.0850
0.0800
1.50E-02
1.60E-02
1.70E-02
1.80E-02
1.90E-02
2.00E-02
Time, s
Cu
CuMo
AlSiC
(b)
Figure 4.4: (a) Top. Comparison of chip temperatures between IGBT assemblies with Cu and CuMo heat spreaders at 5x10-2s.
D2K substrate. (b) Bottom. Detail of thermal crossover of Fig 4.4a.
As far as the Cu and CuMo heat spreaders are concerned, it is apparent that the effect
the heat spreader material has on the thermal response of the IGBT chip is not as
straightforward as might be expected. This is evident in the thermal transients
D J Lim
Chapter IV: Heat Spreaders
Page 4-5
presented in Figures 4.4a and 4.5a, where the models with Cu and CuMo heat
spreaders have points where the thermal transients "cross-over". This "cross-over"
point occurs at different points in time in the different layers of the assembly, as
Figures 4.4a and 4.5a show. The model with the Cu heat spreader has a slightly higher
temperature very early in the transient, both in the chip and in the solder layer
between the chip and the upper spreader layer. This occurs even though Cu has a
higher thermal conductivity than CuMo. However, at approximately 2.0x10-3s, the
thermal transients converge and cross over, the CuMo/D2K model now showing
slightly higher temperatures in the chip, as shown in the detailed transient in Figure
4.4b. At approximately 2.0x10-2s, the temperature trends reverse again, with the
Cu/D2K model now showing the higher temperature. Much further into the transient,
and beyond the scope of Figures 4.4a and 4.5a, the thermal profiles cross over yet
again and continue into steady state, with the CuMo spreader model having the higher
steady state temperature, as would be expected of a material with a lower thermal
conductivity than Cu, as evidenced in Figure 4.6.
D J Lim
Chapter IV: Heat Spreaders
Page 4-6
1D 1st Pulse
0.20
0.18
0.16
0.14
Temp, C
0.12
0.10
0.08
0.06
Crossover section
0.04
0.02
0.00
0.00E+00
5.00E-03
1.00E-02
1.50E-02
2.00E-02
2.50E-02
3.00E-02
3.50E-02
4.00E-02
4.50E-02
5.00E-02
Time, s
Cu
CuMo
AlSiC
(a)
1D 1st Pulse
0.0700
Temp, C
0.0650
0.0600
Crossover section
0.0550
0.0500
1.50E-02
1.55E-02
1.60E-02
1.65E-02
1.70E-02
1.75E-02
1.80E-02
Time, s
Cu
CuMo
AlSiC
(b)
Figure 4.5: (a) Top. Comparison of upper spreader solder temperatures between IGBT assemblies with Cu and CuMo heat
spreaders at 5x10-2s. D2K substrate. (b) Bottom. Detail of thermal crossover of Fig 4.5a.
D J Lim
Chapter IV: Heat Spreaders
Page 4-7
700.00
600.00
Temp (C)
500.00
400.00
300.00
200.00
100.00
0.00
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Time (s)
Cu
CuMo
Figure 4.6: Comparison of chip temperature of Cu and CuMo heat spreader models as they approach steady state
1D 1st Pulse
0.18
0.16
0.14
Temp, C
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0.00E+00
1.00E-02
2.00E-02
3.00E-02
4.00E-02
5.00E-02
6.00E-02
7.00E-02
Time, s
Cu
CuMo
Figure 4.7: Thermal transient comparison of first pulse in an IGBT chip with Cu and CuMo spreaders
D J Lim
8.00E-02
9.00E-02
1.00E-01
Chapter IV: Heat Spreaders
Page 4-8
1D 2nd Pulse
0.18
0.16
0.14
Temp, C
0.12
0.10
0.08
0.06
0.04
0.02
0.00
1.00E-01
1.10E-01
1.20E-01
1.30E-01
1.40E-01
1.50E-01
1.60E-01
1.70E-01
1.80E-01
1.90E-01
2.00E-01
Time, s
Cu
CuMo
Figure 4.8:Thermal transient comparison of second pulse in an IGBT chip with the start point of pulses normalised to 0 for
comparison. Cu and CuMo spreaders
1D 3rd Pulse
0.18
0.16
0.14
Temp, C
0.12
0.10
0.08
0.06
0.04
0.02
0.00
2.00E-01
2.10E-01
2.20E-01
2.30E-01
2.40E-01
2.50E-01
2.60E-01
2.70E-01
2.80E-01
2.90E-01
3.00E-01
Time, s
Cu
CuMo
Figure 4.9: Thermal transient comparison of third pulse in an IGBT chip with the start point of pulses normalised to 0 for
comparison. Cu and CuMo spreaders.
D J Lim
Chapter IV: Heat Spreaders
Cu
st
1 Pulse
nd
2 Pulse
rd
3 Pulse
CuMo
st
1 Pulse
nd
2 Pulse
rd
3 Pulse
Page 4-9
Pulse Peak
(°C)
Pulse Trough
(°C)
% drop (from peak)
% Rise (Pulse 1 to 2)
% Rise (Pulse 2 to
3)
0.1673
0.1522
0.1516
0.0924
0.0729
0.0705
44.75
52.08
53.50
-9.05
--
--0.38
0.1597
0.1465
0.1458
0.0813
0.0640
0.0615
49.11
56.30
57.85
-8.38
--
--0.45
Table 4.1: Temperature rise and fall percentages for three pulses in models with Cu and CuMo heat spreaders, Diamond 2K
substrate. Temperatures show normalised values for 2nd and 3rd pulse.
Figures 4.7, 4.8 and 4.9 show the transient temperature of three consecutive pulses,
each having a 50% duty cycle, for models with Cu and CuMo heat spreaders. For the
sake of comparison, the results from the second and third pulses have been normalised
so that they start from 0°C. From the simulation results, which have been tabulated in
Table 4.1, it is evident that the rate of temperature rise is slower with each
consecutive pulse, while the rate of temperature drop (i.e. the rate at which the
temperature in the chip falls after the pulse ends) is greater. Comparing the relative
temperature rise for the duration of the pulses at the chip at 0.1s and 0.2s (the end of
the first and the second pulse, Figure 4.7 and 4.8 respectively), the temperature rise
caused by the first pulse (Figure 4.7) is about 7.25% higher than the temperature rise
caused by the second pulse (Figure 4.8) in both models (Cu and CuMo heat
spreaders), while the relative temperature rise caused by the second pulse is about
8.75% higher than that caused by the third pulse (Figure 4.9) at 0.3s. By contrast, the
peak of the second pulse is approximately 8.65% lower than the first, while the peak
of the third pulse is only 0.42% lower than the second pulse. The faster drop in
temperature, combined with the slower pulse rises has a cumulative effect of causing
the temperature in the assembly with the CuMo heat spreader to be consistently lower
than the one with the Cu heat spreader with each consecutive pulse (other than for a
D J Lim
Chapter IV: Heat Spreaders
Page 4-10
very short time in the initial rise, as detailed in the beginning of this section), as is
evidenced in Figure 4.10.
1D 3 Pulse
0.35
0.30
Temp, C
0.25
0.20
0.15
0.10
0.05
0.00
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
3.00E-01
3.50E-01
4.00E-01
Time, s
Cu
CuMo
Figure 4.10:Graph depicting the thermal transient in the IGBT chip of three consecutive pulses for a heatsink with a Cu and
CuMo spreader
4.2
Discussion
The main differences between Cu and CuMo in terms of thermal properties is that Cu
has a significantly higher thermal conductivity and a higher thermal diffusivity than
CuMo (as shown in Table 2.1). On the other hand, for CuMo the product of specific
heat capacity and density is higher than is the case for Cu, so it must absorb more heat
before its own temperature rises. Thus, while the CuMo heat spreader cannot perform
as well as Cu in removing the heat from the entire region in the steady state, the
situation is more complex in the transient. The results presented in Figures 4.4 and 4.5
suggest that at some stages during the transient lower chip and solder temperatures are
associated with the use of a CuMo spreader as the high specific heat capacity and
D J Lim
Chapter IV: Heat Spreaders
Page 4-11
density product act as a buffer of sorts against the temperature rise that should result
from the heat coming from the chip.
Temperature differences are larger in the case of the AlSiC spreader which is
associated with higher chip and solder temperatures throughout the early transient as
shown in Figures 4.4 and 4.5. Although the thermal diffusivity of AlSiC falls between
that of Cu and that of CuMo, its thermal conductivity is less than a half of that of Cu
and its specific heat capacity-density product is only a third that of CuMo. The
cumulative result of these properties is that AlSiC is thermally inferior to the other
two materials. Although steady state chip temperatures were found to be lowest with a
Cu spreader and highest with an AlSiC spreader with CuMo yielding intermediate
values (which is consistent with the respective thermal conductivity values), the
“crossover phenomenon” evidenced in Figures 4.4 to 4.10 suggests that much more
detail of consideration is needed to ascertain which spreader will yield lowest
temperatures in the transient.
"Crossover phenomenon", shown in Figures 4.4 to 4.10, indicate that the choice of
heat spreader material should be made with consideration to the duty cycle of the
IGBT in question. From Figure 4.4, it is clear that the thermal response can be
separated into three distinct ranges. The same is even more evident in the solder layer
between the chip and the upper spreader (Figure 4.5), where the crossover occurs
slightly earlier (approximately at 1.75x10-3s into the transient) resulting in a
marginally larger discrepancy between the models for Cu and CuMo heat spreaders. It
is evident that, within the transient period, any application with an operational
frequency between 50Hz and 500Hz, with a duty cycle around 50%, would benefit
from a Cu heat spreader, while any application with frequencies falling outside this
D J Lim
Chapter IV: Heat Spreaders
Page 4-12
range would benefit from a CuMo heat spreader. This is contrary to the normal
“expected” results, where a higher thermal conductivity is almost synonymous with
lower temperatures. While this is indeed the case in the steady state, it is not
necessarily true in the transient.
The materials used in the heat sink assembly typically have different magnitudes of
thermal expansion and contraction for a given temperature change, which is
numerically expressed as the Coefficient of Thermal Expansion or CTE. Since the
assembly is a layered structure, materials with different CTE can cause the layers of
the assembly to warp when subjected to rapid thermal excitation, which may then lead
to delamination. As this occurs, the efficiency of thermal dissipation from the active
region deteriorates rapidly, leading to a critical failure as the chip overheats.
Furthermore, even after the initial thermal pulse, heat dissipates through the assembly,
causing different locations in different layers to expand or contract. For example,
given a stable heat source at the chip, heat dissipates into the assembly. The upper
layers, which are closer to the heat source, will be hotter than the lower layers which
are further away from the heat source. These will expand at a certain rate, given the
CTE of each material. Lower into the assembly and further from the heat source, the
temperature will be lower. These areas will thus expand at a slower rate than the
materials closer to the chip. Stresses will therefore build up between the upper and
lower regions of the assembly. One way to help alleviate this is by having materials
with lower CTE values at the upper, hotter part of the assembly, and materials with
larger CTE values in the lower, cooler parts. This should then result in the upper parts
expanding less as temperature rises, and the lower parts expanding more even with
minor rises in temperature. The intended net result would be that the whole assembly
D J Lim
Chapter IV: Heat Spreaders
Page 4-13
expands and contracts at almost the same rate. It is, however, very difficult to match
materials with sufficient precision, as there are many external and operational factors
which will render such an arrangement at best ineffective, at worst the cause of
stresses within the assembly. One such “worst case” occurs if the chip is turned off as
the assembly saturates with heat. The top part of the assembly would start to cool and
contract while the lower regions of the assembly would still contain residual heat,
causing it to expand. If the materials at the top have a small CTE and the materials at
the bottom have a larger CTE, as previously suggested, the stresses already present
would be compounded by the contracting top part and the expanding lower part of the
assembly. To avoid this, materials that are fairly close in terms of their CTE values
can be used to minimise stresses.
In view of these considerations, component design should not only take into account
the thermal and physical problems inherent in the chip-to-heat sink assembly
connection, but also of the interaction issues between the layers of the heat sink
assembly itself. Cu and AlSiC have much higher CTE values (17.2 ppm.K-1 and 12.6
ppm.K-1 respectively) making them less favourable compared with CuMo (7.0
ppm.K-1) if coupled with a D2K substrate, which has a CTE between 0.8 and 2.0.
It was also observed in Figure 4.10 that the cooling rates associated with the models
with the CuMo heat spreaders were higher with each consecutive pulse. This is due to
the combination of residual heat effects and CuMo’s high specific heat capacity. As
the input pulse ends for all models, there is still residual heat within the chip that
needs to be dissipated. This heat is still transferred into the heat spreaders, but at a
reduced rate. Cu has a lower specific heat capacity than CuMo, which means that it
D J Lim
Chapter IV: Heat Spreaders
Page 4-14
takes less energy to raise, or in this case, maintain a slower fall of temperature within
the Cu heat spreader. The CuMo heat spreader, on the other hand, is also absorbing
the residual heat, but because of its higher specific heat capacity, does not show as
large a temperature rise as the Cu heat spreader. The net result is a faster cooling rate
for the model with the CuMo heat spreader.
This implies that as there are more pulses, the cooling rates of the heat sink assembly
will play a more important role in ensuring an acceptable overall temperature
compared to the maintenance of a lower peak temperature, as more heat will be
dissipated with each successive pulse. Interestingly, while the model with the Cu heat
spreader has larger differences in the relative pulse peak temperatures, i.e. that each
consecutive pulse has a relatively lower temperature compared to the CuMo spreader
model (~0.76%), the CuMo model has a significantly larger temperature drop (4.28%)
compared to the Cu spreader model (refer to Figure 4.10 and Table 4.1). This means
that the model with the CuMo heat spreader always starts each successive pulse at a
lower temperature than the model with a Cu heat spreader. As Figure 4.10 shows, this
phenomenon causes the model with the CuMo heat spreader to have a progressively
lower temperature compared to that with the Cu heat spreader. This is contrary to the
traditional expectations based on the material properties, where Cu, which is more
thermally conductive, would be expected to have a lower temperature. Although this
is indeed the case once the chip has reached steady state temperatures, it is not true for
the transient, or pulsed transient operation where the input is in a series of repeated
pulses. In pulsed transient operation, the temperatures within the chip are always
changing. Even when the assembly has reached a general steady state, the chip is still
D J Lim
Chapter IV: Heat Spreaders
Page 4-15
thermally transient. Therefore, the effect of the RhoSp product still has a significant
effect on the thermal profiles within the assembly.
AlSiC was also considered for this study and was found to have consistently and
significantly higher temperatures at both transient and steady state compared to Cu
and CuMo. The results of the simulations show that although selecting heat spreader
material can be based on the Kt value in certain situations, this value alone cannot be
used as a definitive measure of a heat spreader material's suitability or efficiency, as
seen in the more favourable transients of the CuMo model compared to the model
with the Cu spreader. Furthermore, diffusivity alone is not a wholly valid parameter
by which to select materials for use in transient applications. Since material
combinations within the layered structure will give varied thermal responses, an
analysis of operational behaviour of these components, with attention given to the
input frequency as well as duty cycle would provide a guide to designing better and
more suitable packaging assemblies and heat sinks.
Various aspects of the thermal dissipation within the heat spreader layers of the IGBT
package assembly were discussed in this chapter. This includes the “crossover
phenomenon”, which shows the effect that the product of the specific heat capacity
and density of the material has on the thermal dissipation within the system, as well as
the importance of cooling rates to the overall thermal transient. In the next chapter,
the simulation results for the substrate layer of the IGBT package assembly will be
presented and discussed.
1
LeFranc G, Licht T, Mitic G, Properties of Solders and Their Fatigue in Power Modules,
Microelectronics Reliability, 2002, Vol 42, No. 9, pp 1641-1646
D J Lim
Chapter V: Substrates
Page 5-1
5.0 Substrates
As mentioned in Section 2.4.1, the substrate layer of an IGBT assembly is commonly
constructed from a Metal Matrix Composite (MMC) material like AlN. D2K is a more
expensive alternative which has a very high thermal conductivity as opposed to AlN’s
high specific heat capacity (as shown in Table 2.1). These differences in the thermal
properties of the two materials enable the study of the effects of the interaction
between thermal conductivity and specific heat capacity. The substrate layer is also
the second largest segment of a device, second only to the base plate. This chapter
will focus on the effects of different substrate materials on the thermal profile of the
IGBT assembly. The effects of Cu and CuMo heat spreaders in relation to the
different substrates will also be examined.
5.1
Simulation Results and Observations
4.50E-01
4.00E-01
3.50E-01
Temp, C
3.00E-01
2.50E-01
2.00E-01
1.50E-01
1.00E-01
5.00E-02
0.00E+00
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
3.00E-01
1.50E 01
2.00E 01
2.50E 01
3.00E 01
Time, S Cu/D2K
Cu/AlN
CuMo/AlN
CuMo/D2K
Cu/AlN
CuMo/AlN
Cu/D2K
CuMo/D2K
3.50E-01
Figure 5.1: Comparison of temperatures for all material combinations in IGBT chip
D. J. Lim
4.00E-01
4.50E-01
Chapter V: Substrates
Page 5-2
4.00E-01
Temp (C)
3.50E-01
3.00E-01
2.50E-01
2.00E-01
1.50E-01
Pulse 1
Pulse 2
Pulse 3
Pulse 2
Pulse 3
(a)
1.10E-01
Temp (C)
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
Pulse 1
(b)
Cu/AlN
CuMo/AlN
Series Cu/D2K
CuMo/D2K
Figure 5.2: (a) Peak temperatures at chip for all pulses, all material combinations, (b) Difference in
peak to trough temperatures (highest temperature during pulse vs lowest temperature after pulse) for all
pulses, all material combinations
Figure 5.1 depicts the transient temperatures in the centre of the chip for three
consecutive, 50% duty cycle pulses for the models Cu/AlN, CuMo/AlN, Cu/D2K and
CuMo/D2K. These pulses are followed by an extended cooling period equal to one
complete pulse length from 0.3s to 0.4s. Figure 5.1 shows that Cu/AlN has the highest
temperature throughout the simulation period. CuMo/AlN follows the same transient
shape as Cu/AlN, but at a slightly lower temperature. Cu/D2K and CuMo/D2K have
even lower temperatures but do not cool as quickly as Cu/AlN or CuMo/AlN, as seen
most clearly in the cooling period after the third pulse. It is also observed in Figure
5.2a that the models with an AlN substrate maintain higher temperatures throughout
the simulated period than the models with the D2K substrate. The differences in
D. J. Lim
Chapter V: Substrates
Page 5-3
temperature between the Cu/AlN and CuMo/AlN models are also larger than the
differences in the corresponding models with the D2K substrate. This is seen most
clearly at the first pulse in Figure 5.2a, where the temperature difference of the
models with the D2K substrate are only 36.8% of the difference displayed by the
models with the AlN substrate. Furthermore, Figure 5.2b shows that AlN substrate
models maintain a higher peak to trough temperature difference compared to models
with D2K substrates. Additionally, the amount of heat dissipated with each
consecutive pulse increases in the AlN substrate pair and decreases in the D2K
substrate pair, as seen in the rising and falling gradients of the corresponding plots in
Figure 5.2b. This indicates that the cooling rate for Cu/AlN and CuMo/AlN are higher
than Cu/D2K and CuMo/D2K. This also shows that the substrates have a greater
effect on the chip temperature than the heat spreaders, and form two distinct bands
with the AlN substrate models (Cu/AlN and CuMo/AlN) forming a hotter band, while
the models with the D2K substrate (Cu/D2K and CuMo/D2K), form a cooler band.
Within both of these bands, the Cu spreader shows higher temperatures throughout
the transient. Substrate materials also seem to have an effect on the shape of the
transient (as evidenced by the differences in cooling rates), while the heat spreader
materials influence the temperatures within the given band.
D. J. Lim
Chapter V: Substrates
Page 5-4
4.50E-01
4.00E-01
3.50E-01
Temp, C
3.00E-01
2.50E-01
2.00E-01
1.50E-01
1.00E-01
5.00E-02
0.00E+00
0.00E+00
5.00E-02
1.00E-01
1.50E-01
1.50E 01
Cu/AlN
Cu/AlN
2.00E-01
2.50E-01
2.00E 01
2.50E 01
Time, S Cu/D2K
CuMo/AlN
CuMo/AlN
Cu/D2K
3.00E-01
3.50E-01
4.00E-01
4.50E-01
3.00E 01
CuMo/D2K
CuMo/D2K
Figure 5.3: Comparison of temperatures for all material combinations at bottom of substrate
However, these transient patterns do not continue uniformly throughout the structure.
A comparison of Figure 5.1 with Figure 5.3 and Figure 5.7 to 5.10, which are
temperature profiles from deeper into the structure, shows that there are significant
changes in the transients, both in terms of shape and order. In the chip, Figure 5.1,
Cu/AlN is the hottest material combination, but in Figure 5.3, Cu/D2K is the hottest
material. At the bottom of the substrate layer, (Figure 5.3) for all cases, it is observed
that the transients appear to have a slower response to changes in the input, resulting
in more gentle curves in the transient responses. More significant, however, is the fact
that the models with the AlN substrate, Cu/AlN and CuMo/AlN, which are at higher
temperatures than Cu/D2K and CuMo/D2K at the chip (Figure 5.1), are cooler than
their D2K counterparts at the bottom of the substrate layer.
D. J. Lim
Chapter V: Substrates
Page 5-5
Baseplate
Bottom Spreader
Substrate
Chip
Top Spreader
4.50E-01
T=0.25
4.00E-01
3.50E-01
2.50E-01
2.00E-01
Temp (C)
3.00E-01
1.50E-01
1.00E-01
5.00E-02
0.00E+00
7
6
5
Solder
8
4
3
2
1
0
Distance into assembly (mm)
Cu AlN
CuMo AlN
Cu D2K
CuMo D2k
Figure 5.4: Comparison of temperature profiles for all material combinations at T=0.25s.
3.00E-01
T=0.3
2.50E-01
1.50E-01
Bottom Spreader
5.00E-02
Baseplate
Substrate
Chip
Top Spreader
1.00E-01
0.00E+00
7
6
5
Solder
8
4
3
2
1
Distance into assembly (mm)
Cu AlN
CuMo AlN
Cu D2K
CuMo D2k
Figure 5.5: Comparison of temperature profiles for all material combinations at T=0.3s
D. J. Lim
0
Temp (C)
2.00E-01
Chapter V: Substrates
Page 5-6
2.50E-01
T=0.4
2.00E-01
Temp (C)
1.50E-01
Bottom Spreader
5.00E-02
Baseplate
Substrate
Chip
Top Spreader
1.00E-01
0.00E+00
7
6
5
Solder
8
4
3
2
1
0
Distance into assembly (mm)
Cu AlN
CuMo AlN
Cu D2K
CuMo D2k
Figure 5.6: Comparison of temperature profiles for all material combinations at T=0.4s
The transient temperature profiles in Figures 5.4 to 5.6, which show the progression
of temperatures from 0.25s (the peak of the third pulse) to 0.4s, confirm the case
presented in Figures 5.1 and 5.3 and show that the distribution of heat within the
device varies significantly throughout the transient. The gradient in the AlN substrate
reveals a distinct fall in temperature as the heat dissipates away from the active
region, while the D2K substrate conducts the heat through with minimal reduction in
temperature, as shown by the steeper gradients in the AlN substrates in Figures 5.4 to
5.6 as compared to the temperatures in the D2K substrates, which remain relatively
unchanged. At 0.4s, the temperature is almost uniform throughout the device, as
observed in Figure 5.6.
D. J. Lim
Chapter V: Substrates
Page 5-7
4.50E-01
4.00E-01
3.50E-01
Temp, C
3.00E-01
2.50E-01
2.00E-01
1.50E-01
1.00E-01
5.00E-02
0.00E+00
0.00E+00
5.00E-02
1.00E-01
1.50E-01
1.50E 01
Cu/AlN
Cu/AlN
2.00E-01
2.50E-01
2.00E 01
2.50E 01
CuMo/AlN
Time, S Cu/D2K
CuMo/AlN
Cu/D2K
3.00E-01
3.50E-01
4.00E-01
4.50E-01
4.00E-01
4.50E-01
3.00E 01
CuMo/D2K
CuMo/D2K
Figure 5.7: Comparison of temperatures for all material combinations at top of base plate
4.50E-01
4.00E-01
3.50E-01
Temp, C
3.00E-01
2.50E-01
2.00E-01
1.50E-01
1.00E-01
5.00E-02
0.00E+00
0.00E+00
5.00E-02
1.00E-01
1.50E-01
1.50E 01
Cu/AlN
Cu/AlN
2.00E-01
2.50E-01
2.00E 01
2.50E 01
Time, S Cu/D2K
CuMo/AlN
CuMo/AlN
Cu/D2K
3.00E-01
3.50E-01
3.00E 01
CuMo/D2K
CuMo/D2K
Figure 5.8: Comparison of temperatures for all material combinations at bottom of base plate
It is also observed from Figures 5.3, 5.7 and 5.8 that models with the same heat
spreader material tend towards the same temperature in the cooling cycle (after 0.3s).
The transients for the Cu/AlN and CuMo/D2K models converge, as do those for the
CuMo/AlN and CuMo/D2K models. Moreover, the temperature profiles in the base
D. J. Lim
Chapter V: Substrates
Page 5-8
plate (Figures 5.7 and 5.8) show that the transients of the models with lower
temperatures rise, tending towards a convergence of the bands. From Figures 5.3, 5.9
and 5.10, it is seen that as the transients converge, they also crossover, resulting in the
models with the AlN substrates once again having a fractionally higher temperature
than their D2K counterparts. The models then cool at similar rates, with only small
differences, which is unexpected since thermal conductivities of the AlN and D2K
substrates are vastly different.
4.50E-01
4.00E-01
3.50E-01
Temp, C
3.00E-01
2.50E-01
2.00E-01
1.50E-01
1.00E-01
5.00E-02
0.00E+00
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
3.00E-01
1.50E 01
2.00E 01
2.50E 01
3.00E 01
Time, S
Cu/AlN
CuMo/AlN
Cu/D2K
CuMo/D2K
Cu/AlN
CuMo/AlN
Cu/D2K
CuMo/D2K
3.50E-01
4.00E-01
Figure 5.9: Comparison of temperatures for all material combinations at top of bottom heat spreader
D. J. Lim
4.50E-01
Chapter V: Substrates
Page 5-9
4.50E-01
4.00E-01
3.50E-01
Temp, C
3.00E-01
2.50E-01
2.00E-01
1.50E-01
1.00E-01
5.00E-02
0.00E+00
0.00E+00
5.00E-02
1.00E-01
1.50E-01
1.50E 01
2.00E-01
2.50E-01
2.00E 01
2.50ECu/D2K
01
Cu/AlN
CuMo/AlN
Time, S
Cu/AlN
CuMo/AlN
Cu/D2K
3.00E-01
3.50E-01
4.00E-01
4.50E-01
3.00E
01
CuMo/D2K
CuMo/D2K
Figure 5.10: Comparison of temperatures for all material combinations in middle of bottom heat
spreader
5.2
Discussion
Material
Density
(ρ),
kg.m3
AlN
Diamond 2K
3260
3510
Cu
CuMo
8960
9985
Silicon
Solder
Top Plate
Base Plate
2320
7400
10220
2980
Specific Heat
Thermal
Capacity (Sp),
Conductivity (Kt),
J/kg.K
W/m.K
Substrate
669
170
620
2000
Spreader
276
393
678
197
Other Materials
700
148
160
40
255
138
722
180
RhoSp
Diffusivity
2.18E+06
2.18E+06
7.79E-05
9.19E-04
2.47E+06
6.77E+06
1.59E-04
2.91E-05
1.63E+06
1.18E+06
2.16E+06
2.15E+06
9.11E-05
3.38E-05
5.30E-05
8.37E-05
Table 5.1: Material properties of IGBT heat sink assembly structure materials
Considering the heat spreader materials as noted in Table 2.1, reproduced here as
Table 5.1, Cu has a much higher thermal conductivity than CuMo, and CuMo has
about 3 times the specific heat capacity of Cu. Cu will, therefore, conduct heat faster
than CuMo, but CuMo absorbs more heat than Cu before its temperature rises. This is
consistent with the higher value of the product of the specific heat capacity and the
D. J. Lim
Chapter V: Substrates
Page 5-10
density of CuMo, as shown in Table 5.1. For substrate materials, D2K has a thermal
conductivity which is more than ten times that of AlN. The AlN substrate does not
conduct heat through the device as quickly as the D2K, so that higher internal
temperatures develop in the upper regions of the device, nearer to the chip. However,
when heat reaches the base plate, the relatively low thermal conductivity associated
with the base plate materials mean that it diffuses out of the device more slowly. This
is further compounded by the high product of specific heat capacity and density,
which leads to the heat that is transmitted into the base plate being retained there, and
this in turn causes a reduction in the temperature gradient within the device, as is
particularly evident in Figure 5.6.
Higher internal temperatures also mean that there is a larger difference between the
resulting temperature in the base plate and the peak temperatures in individual
materials. For example, a model with the AlN substrate would have a higher peak
temperature in the substrate than a model with a D2K substrate, as seen in Figure 5.1.
However, both these models tend towards a similar temperature in the cooling period
and, therefore, display a similar rate of heat flow out of the system (Figures 5.9 and
5.10). The larger differences between these temperatures and the peak temperatures in
individual materials for models with AlN spreaders also cause higher cooling rates
within the devices. This is evident in Figure 5.2b where the Cu/AlN and CuMo/AlN
models have a larger difference in the amount of heat lost between pulses than the
Cu/D2K and CuMo/D2K models. D2K maintains a relatively stable rate of heat
throughput, as expected from the high thermal conductivity of the material. However,
the amount of heat dissipated from the chip in each consecutive pulse is declining.
Not as much heat is passed into the base plate by the AlN substrate as by the D2K
D. J. Lim
Chapter V: Substrates
Page 5-11
substrate, resulting in lower temperatures there as seen in Figure 5.5. In the AlN
model pair, the amount of heat being dissipated from the chip after each pulse is
rising, as shown in Figure 5.2b. By the time the device is left to cool down at 0.25s to
0.4s, more heat has been passed through the device with a D2K substrate than a
device with an AlN substrate. However, this heat has not necessarily been passed out
of the body. Although there are different rates of heat loss from the system, it is
observed that the transients tend towards a very similar temperature in their own band,
i.e. those having the same substrate material (Figures 5.3, 5.7 and 5.8). Both sets of
transients with the same spreader materials tend towards similar temperatures in the
base plate, indicating that there is a certain maximum rate of heat flow. This indicates
that the base plate, which has low thermal conductivity and high specific heat capacity
values, forms a bottleneck for the heat flow in the structure, limiting cooling rates.
This is most apparent in Figure 5.6, where the heat within the device is almost evenly
distributed. This distribution occurs as the heat saturates the base plate, in turn
causing saturation in the rest of the device.
In the case of the model with the AlN substrate, the heat flow is slower through the
body, resulting in lower temperatures in the base plate, as seen in Figures 5.7 and 5.8,
where the transients for Cu/AlN and CuMo/AlN are at a lower temperature than the
transients for Cu/D2K and CuMo/D2K. However, since the same amount of heat has
been put into the system for all models, and the thermal energy has not dissipated via
other means, there is, in the models with the AlN substrate, more residual heat still to
be transferred out of the system as compared to the models with the D2K substrate.
The rate of heat flow is related to the difference between the current temperature of
the device in question and the external ambient temperature, in that the larger the
D. J. Lim
Chapter V: Substrates
Page 5-12
difference, the faster the heat would flow from the hotter area to the colder area until
thermal equality is achieved. Therefore, the model with D2K, which is hotter at the
base plate than the models with the AlN substrate (since the D2K has conducted more
heat through itself into the lower regions of the device), will cool faster at the base
plate by losing more heat into the ambient than the AlN model. However, because the
AlN substrate has a higher specific heat capacity and therefore absorbs more energy
before it raises its temperature, it will take longer to heat up to the same temperature
as the model with the D2K substrate.
The main objective of the whole structure is to prevent the chip from overheating, and
both the D2K and AlN substrates achieve this, but in slightly different ways.
According to Figure 5.1, the D2K substrate is marginally better for this particular
application. On the other hand, if there is a shorter cooling period in between pulses,
the AlN substrate could be better since it has a higher cooling rate. The D2K substrate
can indeed conduct heat to the base plate faster, but the base plate will bottleneck this
transfer. Once this occurs, which will be comparatively sooner than in the model with
the AlN substrate, it will heat up faster, although only marginally so, given the small
difference in the specific heat capacity and density product. This in turn results in a
rise in the chip temperature as well. However, AlN, with its slower transference of
heat, results in a more gradual but steady transfer of heat out of the system via the
base plate, and delays the base plate saturation, and therefore the saturation of the
substrate and the rise of temperature in the chip. However, in both cases, the base
plate will eventually bottleneck the whole system. Therefore, the best solution to the
problem would be to make sure that the base plate material is capable of conducting
heat out of the system and is able to take full advantage of whatever dissipation
D. J. Lim
Chapter V: Substrates
Page 5-13
capabilities the finned heat sink is able to offer. This will be further investigated in the
next chapter.
Given the situations presented, it is proposed that it could still sometimes be
beneficial to use materials like AlN that absorb heat rather than conducting it through
to the next layer. Since materials like AlN, which have a high specific heat capacitydensity product, are able to retain heat without a large temperature rise, the residual
heat after a pulse has a smaller influence on the overall temperature within the
assembly. This has the net effect of a faster temperature fall off within the assembly,
which could be interpreted as a “cooling rate”. This could result in a lower starting
temperature for the next series of pulses, given a long enough cooling time.
It is also shown that some materials will bottleneck the heat transfer, negating any and
all benefit associated with materials on each side of it in a layered structure. For
example, the base plate, with its low thermal conductivity and high specific heat
capacity will negate the benefits of having a highly efficient D2K substrate once the
system saturates. It also has a maximum rate of heat flow, which could be less than
that which a good fin structure is capable of dissipating. In this situation, materials
with very high specific heat capacity values could theoretically be used to compensate
somewhat for this during transient operation.
It is evident that the dynamics of heat flow within a layered structure are complex.
The choice of materials for the optimisation of heat flow, likewise, cannot be reduced
to a simple selection using only one or two parameters like thermal conductivity,
specific heat capacity or even diffusivity as guidelines. Material selection needs to
D. J. Lim
Chapter V: Substrates
Page 5-14
take into account the whole of the system, from the individual material properties to
the thermal dynamics within the model. The likely heat input patterns also need to be
taken into account, as a system with many successive but small pulses and short
cooling period would require different materials from a system with fewer, larger
pulses that are followed by a longer cooling period. There are a myriad of
considerations that need to be taken into account to fine tune thermal dissipation rates
of devices with the materials used, and each must be carefully considered if an
optimal solution is to be achieved for a given application.
The effects of substrate materials with very different thermal conductivity values have
been presented in this chapter. The added consideration of cooling rates as well as the
issue of thermal bottlenecking has also been described, demonstrating the complexity
of the thermal dissipation within the layered structure. The next chapter will
investigate this further, and will present simulation data and discussions pertaining to
the baseplate of the IGBT assembly.
D. J. Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-1
6.0 The 3D Model, Base Plates and Heat Pipes
The case has already been made in the previous chapter that the thermal properties of
the base plate can cause a bottleneck in the heat transfer process throughout the IGBT
assembly, and that this situation can be alleviated by ensuring that the base plate is
capable of transferring heat out of the system in an efficient manner. It is the aim of
this chapter to examine this in more detail. The “Apple Core” model is insufficient for
this task, as the best it can hope to represent is a small section of a much larger,
uniform structure, as detailed in Section 3.2.1.
An IGBT module is not uniform, being devices arranged in a 3x2 matrix, as detailed
in the Section 3.2.1. As has been suggested in the last two chapters, adequate
examination of the IGBT heat transfer process should be conducted in a wholistic
manner, taking into account all the material types in use. This can and should also be
extended to the physical structure of the IGBT assembly, where a 3D representation
(such as the one detailed in Section 3.2.2) is superior to a 1D representation. The 3D
model allows the examination of the heat distribution within the various layers,
enabling the identification and observation of hot spots within a given layer, as well
as thermal distribution at the edges of the exposed chip (Refer to Figure 3.5).
The value of the 1D representation should still be acknowledged, but must be
tempered with the recognition of its limitations. In this specific case, the 1D “Apple
Core” model has been instrumental in yielding information about the vertical thermal
dynamics of both the heat sink and the substrate, as well as giving hints as to the
problem of the thermal bottleneck cause by the base plate material. However, it is in
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-2
the examination of the 3D model that a better analysis can be conducted and more
pertinent proposals presented. Furthermore, there are slight differences between the
1D and 3D models, as will be addressed in the following section.
6.1
1D and 3D Model Similarities and Differences
2.50E-01
2.00E-01
Temp (C)
1.50E-01
1.00E-01
5.00E-02
0.00E+00
0
0.01
0.02
0.03
0.04
0.05
0.06
Time (s)
Cu/AlN 1D
CuMo/AlN 1D
Cu/D2K 1D
CuMo/D2K 1D
Cu/AlN 3D w/Baseplate
CuMo/AlN 3D w/Baseplate
Cu/D2K 3D w/Baseplate
CuMo/D2K 3D w/Baseplate
Figure 6.1: Comparison of 1D and 3D simulation models for all material combinations
A quick comparison of the 1D and 3D models, presented here as Figure 6.1 reveals
that the 3D model is between 2.85% and 2.9% cooler in the chip for all material
combinations. This is easily accounted for by the fact that the 3D model used for the
simulations has an area surrounding the chip (as shown in Figure 3.5) which allows
the heat to dissipate laterally into the structure. It is interesting to note, however, that
while the 3D model has 3 times the amount of spreader, substrate and base plate area
outside the chip foot print compared to the 1D model, there is barely a 3% drop in
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-3
temperature, indicating that most of the thermal energy travels vertically through the
structure.
2.50E-01
2.00E-01
Temp (C)
1.50E-01
1.00E-01
Crossover Section
5.00E-02
0.00E+00
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Time (s)
Cu/AlN 3D w/Baseplate
CuMo/AlN 3D w/Baseplate
Cu/D2K 3D w/Baseplate
CuMo/D2K 3D w/Baseplate
Figure 6.2: Transients for 3D model, at the centre of chip, all material combinations
Closer examination of the 3D transients also reveals the same “crossover
phenomenon” described in Chapter 4, presented here as Figure 6.2. The crossover
occurs slightly later in the transient compared to the 1D model, but is also slightly
more distinct. These slight discrepancies are hardly surprising since the added lateral
component of the thermal flow in the 3D model would slightly damp (leading to a
later crossover) and enhance (hence a slightly better defined difference in
temperatures) the result, bringing it closer to a “real” representation rather than a mere
1D simulation. Nevertheless, these observations further confirm that the “crossover
phenomenon” does indeed occur. The implications of this have already been
discussed in Chapter 4.
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
6.2
Page 6-4
Simulation Results and Observations
Both AlN and D2K have similar density and specific heat capacity values, the main
distinction between the two materials being the vast difference in their thermal
conductivity. The Cu heat spreader has a high thermal conductivity, and when paired
with either of the substrate materials, forms in effect a thermal conduit with slightly
different thermal flow rates on the two ends. However, CuMo heat spreaders, with
their high specific heat capacity (Sp), display much more interesting dynamics.
Furthermore, the models with CuMo heat spreaders are the models with the lower
transient temperatures in both temperature bands, as discussed in the previous chapter.
Because of this, only the CuMo/AlN and CuMo/D2K material combinations will be
considered here.
3
4
2
1
5
(a)
(b)
Top Plate
Heat Spreader
Ambient
Solder
Substrate
Base Plate
Reflective Boundary
Silicon Chip
(Active Region)
Position Marker
Figure 6.3: Positional references for 3D model. (a) Top view showing the positional markers as refered to in the text. (b) Side
view showing where these markers are located within the layers of the IGBT assembly.
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-5
For ease of reference, positions of interest are marked and labelled in Figure 6.3. The
layers are designated Chip for the IGBT chip, USpr for the upper heat spreader layer,
Subst for the Substrate layer and LSpr for the lower heat spreader layer. References
will be made in the form [Position]/[Layer]. For example, a point in Position 2 in the
upper spreader layer will be denoted 2/USpr.
0.25
0.2
Temp (C)
0.15
0.1
0.05
0
Chip
Uspr
Subst
CuMo/AlN
LSpr
CuMo/D2K
Figure 6.4: Temperature comparisons of 3D CuMo/AlN and CuMo/D2K models at Position 1. T=0.05s.
Figure 6.4 shows the temperature at various layers of the IGBT assembly at a point
corresponding to position marker 1 in Figure 6.3. These temperatures are taken at the
peak of the first pulse, 0.05s into the transient. As is evident, the model with the D2K
substrate displays lower temperatures in the Chip (1/Chip) but higher temperatures in
the lower heat spreader layer (1/LSpr), with the AlN model being at only 42.10% of
the temperature of the D2K model.
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-6
2.00E-01-2.10E-01
1.90E-01-2.00E-01
1.80E-01-1.90E-01
1
6
11
10
19
16
1.50E-01-1.60E-01
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
28
25
1.60E-01-1.70E-01
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
y-axis
1
4
7
26
13
21
22
16
x-axis
1.70E-01-1.80E-01
Temp (C)
2.10E-01
2.00E-01
1.90E-01
1.80E-01
1.70E-01
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
Figure 6.5: Contour of temperature rise of CuMo/AlN model at chip, T=0.05s.
1
6
11
10
19
28
25
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
1
4
7
26
16
21
13
x-axis
22
16
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
y-axis
Figure 6.6: Contour of temperature rise of CuMo/D2K model at chip, T=0.05s.
The 3D thermal contours presented in Figure 6.5 onwards are displayed on a 30x30 xy grid, with (1,1) corresponding to Position 1 in Figure 6.3. The chip footprint extends
to (15,15), which is Position 3 in Figure 6.3. Examination of the thermal contours of
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-7
the CuMo/AlN and CuMo/D2K models reveals some more subtle but significant
differences between them. The first thing to note is that the AlN model (Figure 6.5)
has a much “flatter” thermal contour, in that the surface area of the chip is of almost
uniform temperature, except for a small rise in temperature that is centred on the
middle of the simulated section of the chip, marked Position 2 in Figure 6.3. This is
the result of high thermal resistances on all four sides of the chip (two reflective
boundaries and two ambient boundaries) that prevent heat from escaping through
lateral transfer, thus causing the in the middle of the simulated quadrant of the chip to
be marginally higher than the surrounding area. The D2K model in Figure 6.6 shows a
more uneven thermal distribution in the chip in the form of a dome-like thermal
contour. The peak in Position 2 (refer to Figure 6.3) is more apparent, as is the drop in
temperature at the corner of the chip, marked Position 3 in Figure 6.3.
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-8
1
6
11
10
22
19
16
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
28
0.00E+00-1.00E-02
y-axis
1
4
7
26
13
21
25
x-axis
16
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
1.50E-01-1.60E-01
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
y-axis
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
29
27
25
23
21
19
17
15
13
11
9
7
5
3
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1
Tem
p (C)
(a)
x-axis
(b)
Figure 6.7: Contour of temperature rise of CuMo/AlN model at upper spreader layer, T=0.05s. (a) Surface plot. (b) Contour plot.
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-9
1
6
11
10
4
7
26
19
16
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
28
25
x-axis
13
21
22
16
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
1
y-axis
1.50E-01-1.60E-01
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
y-axis
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
29
27
25
23
21
x-axis
19
17
15
13
11
9
7
5
3
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1
Tem
p (C)
(a)
(b)
Figure 6.8: Contour of temperature rise of CuMo/D2K model at upper spreader layer, T=0.05s. (a) Surface plot. (b) Contour plot.
Deeper in the structure, it is found that there is little lateral heat flow within the
structure for both material combinations. This is unexpected, and even more so with
the D2K model, since D2K has a very high thermal conductivity. Given a thermally
isotropic material, which the IGBT assembly materials are, heat should travel
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-10
outwards from the heat source equally in all directions. However, this does not
happen. As is evident in Figures 6.7a and 6.8a, which are the thermal profiles in the
upper heat spreader layers, most of the temperature rise is concentrated almost
directly under the chip. There is hardly any change in temperature in the areas
surrounding the chip’s foot print. This trend occurs throughout the structure, as a brief
examination of Figures 6.9 to 6.12 will show. Additionally, there is a more drastic
temperature drop at the edge of the chip for the model with the AlN substrate, as
evidenced in the almost vertical drop near the edge of the chip foot print (Figures 6.7b
and 6.8b), which is expected in view of the lower thermal conductivity and higher
specific heat capacity of AlN. In the model with the D2K substrate, there is evidence
of a rise in temperature a little further outwards, and more gradually than in the AlN
model. The higher temperature at Position 2 is still apparent for both models, but in
the D2K model, there is a less immediate temperature drop in the outward facing
sides of the chip foot print.
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-11
1
6
11
10
4
7
26
19
16
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
28
25
x-axis
13
21
22
16
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
1
y-axis
Figure 6.9: Contour of temperature rise of CuMo/AlN model at substrate layer, T=0.05s.
1
6
11
10
19
28
25
y-axis
1
4
7
26
16
21
13
x-axis
22
16
Figure 6.10: Contour of temperature rise of CuMo/D2K model at substrate layer, T=0.05s.
D.J.Lim
1.50E-01-1.60E-01
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-12
1
6
11
19
16
13
10
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
28
0.00E+00-1.00E-02
y-axis
1
4
7
26
25
x-axis
21
22
16
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
Figure 6.11: Contour of temperature rise of CuMo/AlN model at lower spreader layer, T=0.05s.
1
6
11
10
19
16
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
28
25
1.40E-01-1.50E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
y-axis
1
4
7
26
13
21
22
16
x-axis
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
Figure 6.12: Contour of temperature rise of CuMo/D2K model at lower spreader layer, T=0.05s.
The differences between the CuMo/AlN and CuMo/D2K models are probably most
apparent at the lower heat spreader layer. While there is a relatively large (61.95%)
drop in temperature compared to the substrate in the lower heat spreader layer of the
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-13
AlN model (Figure 6.11), the D2K model, Figure 6.12, shows only a relatively small
(17.01%) drop in temperature as it conducts most of the heat out of the upper IGBT
structure (chip, upper heat spreader, substrate and lower heat spreader) into the base
plate.
6.3
Base Plate and Heat Pipes
The previous chapter showed that thermal bottlenecking occurs at the base plate. For
structural reasons, IGBTs very seldom, if ever, have fans fitted to them for cooling
purposes. Therefore, the problem must be addressed without adding anything to the
external structure. Heat pipes are ideal for this situation, as these simple structures
have high thermal conductivity, and are represented in the simulation as rods of D2K
material that run vertically through the base plate at certain points, as illustrated in
Figure 6.13. In reality, these pipes would be made of far cheaper material. This, and
other practicalities, will be explored later in this chapter.
Two heat pipe configurations were tested, as illustrated in Figure 6.13. The first
configuration, Configuration 1, has heat pipes in the centre of the chip as well as at
the point directly under the temperature rise at Position 2. This configuration was
chosen as it should directly address the hottest parts of the IGBT assembly. The
second heat pipe configuration, labelled Configuration 2, was selected as a possible
way to reduce the temperature in the chip by “siphoning” the thermal energy out from
the system as it was spread out laterally via the substrate and heat spreader layers.
However, since there is little lateral heat transfer, even with materials that are highly
thermally conductive, the effect Configuration 2 had on the overall thermal profile
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-14
was almost negligible, as shown in Figures 6.14 to 6.17, and the temperatures reached
virtually identical, as shown in Figure 6.18.
(a)
(b)
(c)
(d)
Top Plate
Heat Spreader
Ambient
Solder
Substrate
Base Plate
Reflective Boundary
Silicon Chip
(Active Region)
Heat Pipe
Figure 6.13: Heat pipe conficurations. (a) Configuration 1, top view. (b) Configuration 1, side view. (c) Configuration 2, top
view. (d) Configuration 2, side view.
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-15
2.00E-01-2.10E-01
1.90E-01-2.00E-01
1.80E-01-1.90E-01
1
6
11
10
19
16
1.60E-01-1.70E-01
1.50E-01-1.60E-01
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
28
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
y-axis
1
4
7
26
13
21
25
x-axis
22
16
1.70E-01-1.80E-01
Temp (C)
2.10E-01
2.00E-01
1.90E-01
1.80E-01
1.70E-01
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
Figure 6.14: Contour of temperature rise of CuMo/AlN model at chip with Configuration 2 heat pipe, T=0.05s.
2.00E-01-2.10E-01
1.90E-01-2.00E-01
1.80E-01-1.90E-01
1
6
11
10
19
28
25
1.60E-01-1.70E-01
1.50E-01-1.60E-01
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
y-axis
1
4
7
26
16
21
13
x-axis
22
16
1.70E-01-1.80E-01
Temp (C)
2.10E-01
2.00E-01
1.90E-01
1.80E-01
1.70E-01
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
Figure 6.15: Contour of temperature rise of CuMo/AlN model at lower spreader layer with Configuration 2 heat pipe, T=0.05s.
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-16
1
6
11
10
22
19
16
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
28
0.00E+00-1.00E-02
y-axis
1
4
7
26
13
21
25
16
x-axis
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
Figure 6.16: Contour of temperature rise of CuMo/D2K model at chip with Configuration 2 heat pipe, T=0.05s.
1
6
11
10
19
16
28
25
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
y-axis
1
4
7
26
13
21
22
16
x-axis
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
Figure 6.17: Contour of temperature rise of CuMo/D2K model at lower spreader layer with Configuration 2 heat pipe, T=0.05s.
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-17
0.25
Temp, C
0.2
0.15
0.1
0.05
0
Chip
Uspr
CuMo/AlN
CuMo/AlN Configuration 2 Heat Pipe
Subst
Series4
CuMo/D2K
LSpr
CuMo/D2K Configuration 2 Heat Pipe
Figure 6.18: Comparison of original simulation model and model with Configuration 2 heat pipes. Temperatures shown at
Position 1, T=0.05s.
The most sizable drop in temperature for the Configuration 2 models compared to the
original models was only 1.05% at 2/LSpr and 3/LSpr, which is almost negligible. On
the other hand, models with Configuration 1 heat pipes yield persistently lower
temperatures than the original model. As seen in Figure 6.19, the heat pipe has more
of an effect in the D2K model overall, where the temperature drop is 5.65% in the
chip to as much as 36.95% in the lower spreader layer. In the AlN model, the heat
pipes have a smaller overall effect, with only a 0.51% drop in temperature at the Chip
compared to the original model. Although there is a 43.57% drop in temperature of
the lower spreader layer of the AlN model compared to the D2K model (36.95%), the
quantitative temperature drop in the AlN model is only about 50% that of the D2K
model.
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-18
0.25
0.2
Temp (C)
0.15
0.1
0.05
0
Chip
CuMo/AlN
Uspr
CuMo/AlN Config 1 Pipe
Subst
CuMo/AlN Config 2 Pipe
Series4
CuMo/D2K
LSpr
CuMo/D2K Config 1 Pipe
CuMo/D2K Config 2 Pipe
Figure 6.19: Comparison of original simulation model and model with Configuration 1 and 2 heat pipes. Temperatures shown at
Position 1, T=0.05s.
2.00E-01-2.10E-01
1.90E-01-2.00E-01
1.80E-01-1.90E-01
1
6
11
10
19
1.50E-01-1.60E-01
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
28
25
1.60E-01-1.70E-01
y-axis
1
4
7
26
16
21
13
x-axis
22
16
1.70E-01-1.80E-01
Temp (C)
2.10E-01
2.00E-01
1.90E-01
1.80E-01
1.70E-01
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
Figure 6.20: Contour of temperature rise of CuMo/AlN model at chip with Configuration 1 heat pipe, T=0.05s.
D.J.Lim
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-19
1
6
11
19
16
13
10
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
28
0.00E+00-1.00E-02
y-axis
1
4
7
26
25
x-axis
21
22
16
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
Figure 6.21: Contour of temperature rise of CuMo/AlN model at upper spreader layer with Configuration 1 heat pipe, T=0.05s.
1
6
11
10
19
16
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
28
25
1.40E-01-1.50E-01
y-axis
1
4
7
26
13
21
22
16
x-axis
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
Figure 6.22: Contour of temperature rise of CuMo/AlN model at substrate with Configuration 1 heat pipe, T=0.05s.
D.J.Lim
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-20
1
6
11
19
16
13
10
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
28
0.00E+00-1.00E-02
y-axis
1
4
7
26
25
x-axis
21
22
16
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
1.50E-01-1.60E-01
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
y-axis
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
29
27
25
23
21
x-axis
19
17
15
13
11
9
7
5
3
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1
Tem
p (C)
(a)
(b)
Figure 6.23: Contour of temperature rise of CuMo/AlN model at lower spreader layer with Configuration 1 heat pipe, T=0.05s.
(a) Surface plot. (b) Contour plot.
An examination of Figures 6.20 to 6.23 further reveals that while, in the AlN substrate
model, there is very little change in the shape of the thermal contour higher up in the
structure, the temperature peak at 2/LSpr in the original model has become a trough in
the model with the Configuration 1 heat pipes. The shape of the dips in temperature at
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-21
Positions 1 and 2, which are directly above the heat pipes, also show that there is very
little lateral heat flow, as the areas surrounding the area immediately above the pipes
show almost no change in temperature (Figure 6.23b).
1
6
11
10
19
16
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
28
0.00E+00-1.00E-02
y-axis
1
4
7
26
13
21
25
x-axis
22
16
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
Figure 6.24: Contour of temperature rise of CuMo/D2K model at chip with Configuration 1 heat pipe, T=0.05s.
1
6
11
1
4
10
7
26
19
16
28
25
21
13
x-axis
22
16
1.50E-01-1.60E-01
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
y-axis
Figure 6.25: Contour of temperature rise of CuMo/D2K model at upper spreader layer with Configuration 1 heat pipe, T=0.05s.
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-22
1
6
11
10
19
16
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
28
25
1.40E-01-1.50E-01
y-axis
1
4
7
26
13
21
22
16
x-axis
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
Figure 6.26: Contour of temperature rise of CuMo/D2K model at substrate with Configuration 1 heat pipe, T=0.05s.
D.J.Lim
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-23
1
6
11
19
16
13
10
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
28
0.00E+00-1.00E-02
y-axis
1
4
7
26
25
x-axis
21
22
16
1.50E-01-1.60E-01
Temp (C)
1.60E-01
1.50E-01
1.40E-01
1.30E-01
1.20E-01
1.10E-01
1.00E-01
9.00E-02
8.00E-02
7.00E-02
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
1.50E-01-1.60E-01
1.40E-01-1.50E-01
1.30E-01-1.40E-01
1.20E-01-1.30E-01
y-axis
1.10E-01-1.20E-01
1.00E-01-1.10E-01
9.00E-02-1.00E-01
8.00E-02-9.00E-02
7.00E-02-8.00E-02
6.00E-02-7.00E-02
5.00E-02-6.00E-02
4.00E-02-5.00E-02
3.00E-02-4.00E-02
2.00E-02-3.00E-02
1.00E-02-2.00E-02
0.00E+00-1.00E-02
29
27
25
23
21
x-axis
19
17
15
13
11
9
7
5
3
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1
Tem
p (C)
(a)
(b)
Figure 6.27: Contour of temperature rise of CuMo/D2K model at lower spreader layer with Configuration 1 heat pipe, T=0.05s.
(a) Surface plot. (b) Controur plot.
The thermal contours in the D2K model have slightly more dramatic changes deeper
into the structure, as seen in Figures 6.24 to 6.27. Figure 6.27, in particular, reveals
fairly drastic variances in temperatures within the lower heat spreader layer as seen in
the more “mountainous” contour. As with the AlN model, the temperature peak
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-24
displayed at Position 2 in the original model is a trough at 2/LSpr here. The area of
temperature variations caused by the heat pipes are slightly wider in the D2K model,
as is evident in Figure 6.27b.
0.18
0.16
0.14
Temp (C)
0.12
0.1
0.08
0.06
0.04
0.02
0
Chip
Uspr
CuMo/D2K
CuMo/D2K Config 1 Pipe
Subst
CuMo/D2K Config 2 Pipe
LSpr
CuMo/D2K with Cu Baseplate
Figure 6.28: Comparison of original and heat pipe enhanced models with model with Cu base plate (no heat pipes). All
temperatures shown at Position 1, T=0.05s.
Figure 6.28 shows a comparison of the aforementioned models with one equipped
with a Cu base plate. Table 2.1 shows that Cu has a higher thermal conductivity than
the base plate material, AlSiC. It is evident from Figure 6.28 that the model with the
heat pipe has temperatures as much as 28.17% lower in the lower spreader layer than
the model with the Cu base plate. However, this is only true for the area immediately
above the heat pipe, i.e. Positions 1 and 2. At Positions 3 and 4 (refer to Figure 6.3),
the temperatures are between 13.59% and 14.13% lower for the model with the Cu
base plate than the model with Configuration 1 heat pipes, as seen in Figures 6.29 and
6.30
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-25
0.18
0.16
0.14
Temp (C)
0.12
0.1
0.08
0.06
0.04
0.02
0
Chip
Uspr
CuMo/D2K
CuMo/D2K Config 1 Pipe
Subst
LSpr
CuMo/D2K with Cu Baseplate
Figure 6.29: Comparison of original and heat pipe enhanced (Configuration 1) models with model with Cu base plate (no heat
pipes). All temperatrues shown at Position 3, T=0.05s.
0.18
0.16
0.14
Temp (C)
0.12
0.1
0.08
0.06
0.04
0.02
0
Chip
Uspr
CuMo/D2K
CuMo/D2K Config 1 Pipe
Subst
LSpr
CuMo/D2K with Cu Baseplate
Figure 6.30: Comparison of original and heat pipe enhanced (Configuration 1) models with model with Cu base plate (no heat
pipes). All temperatrues shown at Position 4, T=0.05s.
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
6.4
Page 6-26
Discussion
From Figure 6.4, it is seen that the changeover of CuMo/D2K to CuMo/AlN being the
cooler model occurs somewhere in the substrate layer, demonstrating the effect of
D2K’s high thermal conductivity. This also shows the bottlenecking effects of the
base plate, as the heat from the chip is removed quickly from the area surrounding the
chip, only to collect at the area surrounding the base plate. This in turn causes the base
plate, which has poorer thermal conductivity, to saturate, resulting in the rise in
temperature seen at 1/LSpr for the D2K model. The AlN model, on the other hand,
conducts the heat through more slowly, so that the temperature in the lower heat
spreader is less than half (40.75%) that of the model with the D2K substrate. Given a
longer simulation duration, thermal saturation would occur at the base plate, raising
the temperature of the whole assembly, as the base plate is unable to dissipate the
thermal energy from the system. The use of a highly thermal conductive base plate
does result in a lower temperature, as seen with the use of a Cu base plate in Figures
6.28 to 6.30. However, since Cu is a much denser material than AlSiC, this would
result in a much heavier component assembly. This is where the heat pipes would be
of greatest effect, as they would channel the heat out of the system through the base
plate, taking advantage of the finned heat sink structure on the underside of the
structure, while allowing the use of lighter, if thermally inferior materials.
Figures 6.5 and 6.6 show the differences between the substrate materials in terms of
their horizontal thermal profile. Examination of these and other examples of the
thermal profiles of these two models reveal that the D2K model has a more widely
varying thermal contour in the area immediately under the chip, which in turn would
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-27
cause more thermal stresses to that whole area. In contrast, the AlN model has more
drastic thermal drops at the edge of the chip footprint. Both these scenarios could
cause delamination, but in different ways. The AlN model is more likely to produce
delamination around the edges of the chip footprint, as the differences in temperature
there cause the materials in that border area to expand and contract at different rates.
In the D2K model, delamination is likely to occur in a wider area under the chip
footprint, as the temperatures associated with the more varied thermal contours cause
the materials to expand and contract accordingly. Furthermore, the D2K substrate has
sharper thermal responses through the transient, as detailed in the previous chapter,
which in turn increases the likelihood of delamination.
Since most of the heat transfer is vertical, as seen in the thermal contour plots
throughout this chapter, it is prudent that the heat pipes are placed directly under the
thermally active region, as in Configuration 1. Furthermore, since the area of effect of
the heat pipes seems to be fairly limited, and since the heat transfer is mostly vertical,
it would be advantageous to consider having an area under the whole of the active
region that acts as a heat pipe, as opposed to the suggested column structures in
Configurations 1 and 2.
As mentioned in Section 6.3, D2K was used to represent a material with high thermal
conductivity that would be suitable for the heat pipes. However, it is not practical to
use D2K as heat pipe material since it is expensive and complicated to manufacture.
Additionally, there are a few considerations other than cost and manufacturing
complexity associated with the material required. One key attribute is the CTE of the
pipe material. The base plate will expand as it heats up. The base plate material used
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-28
for the simulations is AlSiC, which has a CTE of 12.6ppm.K-1. Since the columns
where the heat pipes will be housed will shrink in volume, the heat pipe material must
have a CTE that is lower than the base plate material and be fitted with a small gap
between the pipe and the housing wall to accommodate the mutual expansion of the
components. If the CTE is higher or even equal to the base plate material, or if it is
fitted inaccurately, physical stresses will occur as the base plate expands, eventually
leading to cracks and deterioration of structural integrity. The heat pipe material must,
therefore, also be highly workable, as it needs to be shaped to very specific
dimensions. Conversely, if the heat pipe is too small or loosely fitted into the base
plate housing, thermal contact will be compromised. The designer therefore needs to
consider how to best to physically join the heat pipe material to the base plate to
ensure optimal thermal transfer. Options of doing this include brazing the materials
together, securing the contact with a thermal compound of some sort, or even
manufacturing the pipes to specific dimensions so that thermal contact is achieved as
the base plate expands and reduces the volume of the pipe chamber. However, none of
these solutions is easily workable.
One possible solution to this problem is to the fill the chamber with of some sort of
thermal gel instead of a rigid heat pipe. Thermal gel is not likely to cause cracks in the
base plate structure because of differing CTE values as it is not a rigid material. It is
easy to handle, will shape itself according to the shape of the structure it is put in, and
it is a low cost material. Unlike thermal pastes or compounds that need to be
compacted to ensure optimal thermal conductivity, thermal gel can be piped into cells
in the base plate structure then permanently sealed in as part of the manufacturing
process, thus also ensuring that the gel does not dry out. Unfortunately, current
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-29
commercially available gels do not have sufficiently high thermal conductivity to be
of any practical use. The next generation of gels, which should result from current
developments in nanofluids 1,2 may offer more workable solutions.
(a)
(b)
Top Plate
Heat Spreader
Ambient
Solder
Substrate
Base Plate
Reflective Boundary
Silicon Chip
(Active Region)
Gel Cell
Figure 6.31: Suggested Gel Cell structure. Figure represents only a quarter of actual structure. (a) Top view. (b) Side view.
A possible “gel cell” structure is shown in Figure 6.28. The cell itself, as evident from
the illustration has rounded corners to avoid air pockets when piping the gel into the
cavity. There is also a thin layer of base plate material above and below the cell,
which seals the gel into the cell as well as provides some structural integrity to the
base plate. Another possibility is to manufacture the base plate with cells linked by
channels or tubes, with two access points on either side of the structure, as shown in
D.J.Lim
Chapter VI: 3D Model, Base Plates and Heat Pipes
Page 6-30
Figure 6.29. The gel can then be piped in one hole to fill the cells, while air can
escape or be extracted from the other hole to ensure the volume is filled.
Access
point
Access
point
Figure 6.32: Gel cell with piping structure.
This chapter has shown how thermal bottlenecking affects the thermal transient higher
up in the layered structure and the effect of heat pipes on the overall thermal
landscape of the layered structure. Nanofluid filed gel cells are also proposed as a
theoretical future adaptation to counter the problem. All the findings of this study will
be summarized and commented upon in the next and final chapter.
1
Keblinski P, Eastman, JA, Cahill DG, Nanofluids for Thermal Transport, Materials Today, June
2005, ISSN 1369 7021, pp 36-44.
2
Murshed SMS, Leong KC, Yang C, Enhanced Thermal Conductivity of TiO2 – Water Based
Nanofluids, International Journal of Thermal Sciences, Vol 44, No. 4, 2005, pp 367-373.
D.J.Lim
Chapter VII: Conclusions
Page 7-1
7.0 Conclusions
Over the course of this study, different parts of the IGBT assembly have been
examined and characterised. The thermal response of the heat spreader, substrate and
base plate layers were scrutinised and their individual reactions to stable and pulsed
operation of the IGBT chip were simulated, recorded and analysed. This in turn gave
rise to observations on how these components interacted with each other, forming a
complex and sometimes unexpected thermal map of the IGBT assembly.
Of particular interest was the fact that materials which were “traditionally” considered
better for thermal transfer in the steady state, i.e. those with high thermal
conductivity, did not always yield the most thermally favourable results during the
transient phases. This also brought to light the importance of cooling rates within the
IGBT structure during pulsed operation and the possibility of the selection of
assembly materials based in part on the operational phases of the IGBT.
7.1
Summary of Heat Spreader Observations
As described in Chapter 4, the models with Cu heat spreaders were noted to have
almost consistently higher temperatures compared to the models with CuMo heat
spreaders, even though Cu has around double the thermal conductivity of CuMo.
Closer examination of the initial transient (Figures 4.4 and 4.5) revealed that the
models with the Cu heat spreaders did indeed start out at lower temperatures, as was
expected. However, fairly early in the simulation, the thermal transients of the models
with the CuMo heat spreaders dropped below those of the Cu models, “crossing over”
D.J.Lim
Chapter VII: Conclusions
Page 7-2
each other to yield lower temperatures for the supposedly less thermally favourable
material.
Further investigation revealed this “crossover” phenomenon to be the result of
CuMo’s high specific heat capacity. The heat from the IGBT chip was not being
conducted away from the surrounding area, but was being absorbed by the CuMo heat
spreaders. Nevertheless, this resulted in lower temperatures at the chip, as seen in
Figure 4.9.
In pulsed operation, it was also observed that CuMo also had a faster cooling rate
compared to Cu due to CuMo’s high specific heat capacity and the effects of residual
heat dissipation, as detailed in Section 4.2. These faster CuMo cooling rates in turn
caused the next pulse in the series to start at a lower temperature compared to Cu
models. The net result of these higher cooling rates and the slowed thermal rises were
consistently lower temperatures in models with CuMo heat spreaders compared to
their Cu counterparts. This was once again contrary to “traditional” expectations.
7.2
Summary of Substrate Observations
Examination of the substrate layers, as well as comparisons of performance for AlN
and D2K substrates showed that while the different heat spreader materials had some
effect on the temperatures of the models, it was the substrates that made the biggest
difference overall. Each substrate pair formed a distinctly shaped “band”, with the
heat spreaders determining where in the band the transient lay within that band
(Figures 5.1 and 5.3).
D.J.Lim
Chapter VII: Conclusions
Page 7-3
Examination of the substrate layer also revealed that the various material
combinations did not necessarily maintain their thermal “superiority” or “inferiority”
throughout the structure. From Figures 5.1 and 5.3, it is seen that while the
CuMo/D2K model had the lowest temperature in the chip, it was CuMo/AlN that
yielded the lowest temperatures in the bottom of the substrate layer. This was because
the AlN substrate was incapable of passing heat through itself at the same rate as the
D2K substrate. While the models with the D2K substrate had shifted most of the heat
away from the chip, the models with the AlN substrate still had significantly more
thermal energy to transport. This suggests that even if there was a finned heat sink
capable of dissipating a large amount of heat, the model with the AlN substrate would
be incapable of taking advantage of it, as a thermal bottleneck would be formed
because of AlN’s lower thermal conductivity.
However, the build up of heat at the lower regions of the models with the D2K
substrates, the progression of which was shown in Figures 5.4 to 5.6, indicated that
the heat was not being completely removed from the IGBT assembly. In fact, at the
end of the simulation time, the models with the D2K substrates had almost uniform
temperatures in all the layers. While the heat was being channelled away from the
chip itself, it was still saturating at the base plate. The relatively poor thermal
conductivity of the base plate, combined with its moderate density-specific heat
capacity product also resulted in a bottleneck in the system. As the thermal energy
saturated the base plate, it would raise the overall temperature of the IGBT assembly,
effectively negating any benefit gained by the D2K substrate, eventually causing the
chip to overheat. Therefore, neither AlN nor D2K could be individually superior over
D.J.Lim
Chapter VII: Conclusions
Page 7-4
the other. These materials must therefore be considered in relation to the materials in
the other layers within the assembly. As a chain is only as strong as its weakest link,
so any material layer that causes a thermal bottleneck within the assembly could
render any thermal benefit afforded by other layers useless.
7.3
Summary of 3D Model, Base Plate and Heat Pipe Observations
The 3D model was used for most of the investigations relating to the base plate. Most
of the work up to this point was focused on the vertical thermal dynamics of the IGBT
assembly. Observations in this section followed in the same vein, but also took into
account the lateral heat flow within the IGBT body. The physical structure of the base
plate was also modified, and resulting changes to the thermal landscape observed.
The simulations showed only a small amount of lateral heat flow. The model with the
AlN substrate showed an almost immediate drop in temperature at the boundary of the
chip footprint (Figure 6.7), while the D2K substrate model had a slightly wider
thermal footprint (Figure 6.8). Considering the thermal properties of the D2K
substrate, this was quite unexpected. The thermal conductivity of D2K far exceeds
that of all the other materials, and this would, at first glance, mandate that there be
significant lateral as well as vertical heat flow. However, this is not the case, as
evidenced in the simulation results in Figures 6.8, 6.10 and 6.12. Nevertheless, the
primacy of the vertical thermal dynamic over the lateral indicates that any attempt to
siphon heat from the IGBT assembly structure via the base plate must be concentrated
on the area directly under the IGBT chip. It is expected, however, that areas further
D.J.Lim
Chapter VII: Conclusions
Page 7-5
beyond the boundaries of the chip footprint would be of interest later in the transient
as the base plate becomes increasingly thermally saturated.
The D2K substrate model also has a more uneven, dome-like thermal profile than the
AlN substrate model as the comparison of Figure 6.5 to 6.6 show. D2K is also the
more responsive of the two substrate materials, rendering it more susceptible to
stresses associated with rapid thermal changes. Heat also spreads out more in the D2K
substrate, resulting in a more varied thermal contour within the chip foot print. This
means that the IGBT assembly containing a D2K substrate will have more thermal
variation within the whole of the assembly, rendering it more susceptible to
delamination than those with AlN substrates, as the materials heat and cool more
rapidly and with greater irregularity between the material layers.
Heat Pipes were also introduced into the system as a means of siphoning heat through
the base plate, and thereby bypassing the problem of bottlenecking caused by the base
plate’s poor thermal conductivity. It was determined that this technique was indeed
effective, but only in the area directly above the pipes (Figures 6.19 to 6.27), at least
in the initial transient period. As the heat diffuses laterally outside the footprint of the
chip later in the transient, however, it is expected that heat pipes in Configuration 2
would become more effective. However, the heat pipes also caused temperature
variations within the assembly, which may contribute towards delamination.
D.J.Lim
Chapter VII: Conclusions
7.4
Page 7-6
Overall Observations
When considering the IGBT assembly as a unified whole, there are many factors that
come to light. For example, the higher cooling rates of CuMo are an advantage so
long as there is time for the system to cool down. The performance of the system is,
therefore, dependent on the pulse rate of the input. On the other hand, the D2K
substrates are excellent at transferring heat away from the chip and its surrounding
areas, but this is at the price of being more susceptible to effects that could lead to
delamination because of its sharper thermal response. The length of input pulse
cycles, i.e. how many pulses there will be before there is a long cooling or rest period
may also influence the selection of the materials for optimal heat management. It was
also shown that seemingly small effects, like residual heat after an input pulse, could
have a fairly large influence over the thermal transient, as was the case with the CuMo
cooling rates.
Material properties not only affect the amount of heat transferred, but also the way
that it spreads out during the transient, and the speed at which this process occurs. It
is, therefore, possible to utilise the knowledge of the behaviour of the thermal
dynamics within the IGBT assembly, given known operating conditions, to the
optimise heat transfer through the assembly. For example, a CuMo heat spreader
could act as a buffer, absorbing heat from the chip and compensating for slower heat
transfer of an AlN substrate. A D2K substrate could, on the other hand, compliment a
Cu spreader, as it has a higher thermal conductivity than Cu, and can therefore
transfer heat faster than the spreader. However, this does mean that the rate of heat
transfer for the whole system is limited by the Cu heat spreader. Even with high
conductivity materials in the heat spreader and substrate layers, a base plate with low
D.J.Lim
Chapter VII: Conclusions
Page 7-7
thermal conductivity will bottleneck the system as it saturates. This can be avoided, to
some extent, by the use of heat pipes to channel heat through the base plate quickly,
but even this is limited by the lack of lateral heat flow during early IGBT operation.
However, later in the transient, when the heat has spread throughout the assembly,
heat pipes will be more effective, even in the area surrounding the chip. All of this is
then tempered the fact that materials with high thermal conductivity also have sharper
thermal responses and therefore are more prone to delamination.
It is, however, clear that choosing materials based solely on their thermal conductivity
will not necessarily yield the best thermal management solution, as is the case with
the Cu and CuMo heat spreaders (Figure 4.9). Additionally, while Cu has a diffusivity
value that is an entire order of magnitude larger than CuMo, it is CuMo that
consistently yields lower temperatures in the transient (refer to Table 2.1). This calls
into question the suitability using diffusivity (which is the ratio of the density-specific
heat capacity product and the thermal conductivity of a material) as an adequate
indicator of the material’s performance.
7.5
Future Work
Current simulations provide a significant amount of data in the regions above the base
plate. However, data of the thermal dynamics within the base plate itself is somewhat
lacking, especially in regards to the 3D models. Further analysis of the 3D models
should be conducted, with particular focus on the reaction of the base plate to
prolonged stable input and pulsed input situations. Better recommendations pertaining
to heat pipes and gel cells can then be made.
D.J.Lim
Chapter VII: Conclusions
Page 7-8
There is also a need for longer simulations to show and validate current theories on
what will happen when saturation occurs in the system. As of the time of writing, the
simulations run for only 0.4s at the longest, with the 3D models simulating 0.05s into
the transient. Saturation of the assembly layers will occur much later in the transient,
and systems to deal with the saturated systems should be investigated.
Further investigation of the cooling rates associated with pulsed inputs using the 3D
model should also be undertaken. It is currently unknown how multiple pulses will
effect the lateral heat flow within the system over a longer period of time.
Additionally, there should be some investigation into the differences in thermal
dynamics between slow and fast pulse applications, with particular attention given to
the cooling rates in the heat spreader layers.
A typical IGBT assembly is arranged in a 3x2 matrix. However, all the simulations
undertaken for this study assumed an infinitely repeating pattern. While this was
adequate for the purposes of this study, further investigation into the effects of the
thermal interaction within the 3x2 matrix assembly should also be considered.
Optimal distances between devices can then be proposed, taking into account the
thermal dynamics between different devices.
Throughout the study of the IGBT assembly, the observation that no one material
layer acts independently of another has been repeatedly arrived at. It is only prudent,
therefore, to propose further study of the interactivity of the materials. This would
include the finned heat sink at the bottom of the base plate, which was only
D.J.Lim
Chapter VII: Conclusions
Page 7-9
rudimentarily represented in this series of simulations. Since most of the heat in the
early transient flows vertically, it may be worth investigating just how much heat is
dissipated by the finned heat sinks out side of the chip foot print. Of particular interest
would be the effect of static and dynamic ambient conditions around the IGBT
assembly, as IGBTs may be employed in situations where there is varying and
possibly intermittent airflow, e.g. as part of the motor control unit for an intercity tram
unit. A modified TLM model that takes into account non-infinite heat sources 1 could,
in theory, be suitable for this.
Development of more detailed design rules for material selection should also be
undertaken. As already mentioned, the “traditional” selection criteria of diffusivity
and mainly thermal conductivity are not adequate if optimal thermal management is to
be achieved for a given application.
One of the major challenges throughout this study was the balancing of adequately
detailed models with reasonable simulation run times. While the Apple Core and 3D
models were sufficient for the purposes of this study, further development of more
detailed and comprehensive models that will run within a reasonable time frame
should be undertaken. Bearing this in mind, one must be aware that the 3D model
used still falls far short of the true thermal dynamics of the actual structure, just as a
picture or photograph can never truly and fully represent its subject. Many aspects of
a real IGBT assembly were simply not investigated, including the interaction between
subassemblies and other devices, the effect of different finned heat sink structures,
and other points of interest mentioned above.
D.J.Lim
Chapter VII: Conclusions
Page 7-10
Another possible direction for investigation is the development of TLM meshes that
dynamically change size with temperature, to mimic the effects of thermal expansion
and contraction. A multi network TLM model that combines thermal simulation with
mesh warping and the associated material expansion stresses would allow much more
comprehensive analysis of the IGBT assembly structure, in particular with regards to
delaminaion and its effects. Some groundwork for multi-network TLM already exists
in the form of TLM models that couple heat and mass diffusion models 2,3 , and could
be used for this purpose.
It is hoped that this study will provide a springboard for more detailed examination of
the reasons behind the selection of materials for IGBT packaging. As is evident from
the findings, the thermal dissipation within the layered structure is indeed more
complex than would be initially suspected. As such, the “traditional” choices for
materials based solely upon the thermal conductivity or the coefficient of thermal
expansion alone are not necessarily always the best choices for a given application. A
more holistic approach is needed if full advantage is to be taken of the many materials
currently available for use, as well as materials that will become available in time.
1
Pulko S, Green WA, Johns PB, An Extension of the Application of Transmission Line Modelling
(TLM) To Thermal Diffusion To Include Non-Infinite Heat Sources, International Journal for Numerical
Methods in Engineering, Vol 24, No. 7, 1987, pp 1333-1342.
2
Newton HR, Pulko SH, A TLM Model for Drying Processes, Proc MIC, 1991, IASTED, Innsbruk, pp
339-343.
3
Newton HR, Pulko SH, A Coupled Model of Drying Processes Involving Evaporation and
Recondensation, Proc of Modeling and Simulation, 1991, IASTED, Calgary, pp 132-136.
D.J.Lim
Other Relevant Publications by the Author
Hocine R, Lim D, Pulko SH, Boudghene Stambouli MA, Saidene A, A Three
Dimensional Transmission Line Matrix (TLM) Simulation Method For Thermal
Effects In High Power Insulated Gate Bipolar Transistors, Circuit World, Vol 29, No
3, 2003, pp 27-32.
Lim D, Pulko SH, The Effect of Spreader Material on Chip Temperatures in IGBTs
Under Pulsed Operation, IET Circuits, Devices and Systems, Vol 1, No. 2, 2007, pp
126-136.