Aalborg Universitet
A Temperature-Dependent Thermal Model of IGBT Modules Suitable for Circuit-Level
Simulations
Wu, Rui; Wang, Huai; Ma, Ke; Ghimire, Pramod; Iannuzzo, Francesco; Blaabjerg, Frede
Published in:
Proceedings of the 2014 IEEE Energy Conversion Congress and Exposition (ECCE)
DOI (link to publication from Publisher):
10.1109/ECCE.2014.6953793
Publication date:
2014
Document Version
Early version, also known as pre-print
Link to publication from Aalborg University
Citation for published version (APA):
Wu, R., Wang, H., Ma, K., Ghimire, P., Iannuzzo, F., & Blaabjerg, F. (2014). A Temperature-Dependent Thermal
Model of IGBT Modules Suitable for Circuit-Level Simulations. In Proceedings of the 2014 IEEE Energy
Conversion Congress and Exposition (ECCE) (pp. 2901-2908). IEEE Press.
https://doi.org/10.1109/ECCE.2014.6953793
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A Temperature-dependent Thermal Model of IGBT
Modules Suitable for Circuit-level Simulations
Rui Wu, Student Member, Huai Wang, Member, IEEE, Ke Ma, Member, IEEE, Pramod Ghimire, Student Member,
Francesco Iannuzzo, Senior Member, and Frede Blaabjerg, Fellow, IEEE
Centre of Reliable Power Electronics (CORPE), Department of Energy Technology
Aalborg University, Pontoppidanstraede 101, 9220
Aalborg, Denmark
rwu@et.aau.dk, hwa@et.aau.dk, kema@et.aau.dk, pgh@et.aau.dk, fia@et.aau.dk, fbl@et.aau.dk.
Abstract— A basic challenge in the IGBT transient simulation
study is to obtain realistic junction temperature, which
demands not only accurate electrical simulation but also
precise thermal impedance. This paper proposed a novel
thermal impedance model considering of local temperature
effects through Finite Element Method (FEM) simulation. The
proposed method is applied to a case study of 1700 V/1000 A
IGBT module. Furthermore, a testing setup the studied IGBT
open module and an ultra-fast infrared (IR) camera has been
constructed to validate the proposed model.
I. INTRODUCTION
When design modern power electronic systems, it is
critical to improve whole system performance meanwhile
fulfilling the robustness and reliability requirements [1]. One
of the critical robustness requirements for IGBT converters
design is how to monitor power semiconductor’s junction
temperature precisely and then control it at adequate level.
This is because junction temperature is a key parameter for
predicting and preventing IGBT’s failure. For instance, a
critical high junction temperature is usually connected with
the phenomena of current constriction, thermal runaway,
which are responsible for failures of IGBT modules during
heavy loads and short-circuits. High junction temperature is
also connected to various initial failure-triggering factors for
final destruction (e.g. dynamic voltage breakdown, gate
driver failure) [2].
In long-term real-time operation, it is prevail to use
saturation voltage V
ce,sat
to estimate virtual junction
temperature. However, it is still a challenge to measure
transient junction temperature during short-circuits or
overloads, which may cause IGBT overstress failure [3].
Meanwhile, simulation techniques have provided immense
possibilities in researching and optimized designing of
thermal management and junction temperature control in
power electronic systems [4]. A precise thermal impedance
model is essentially required to accurately estimate the
junction temperature of IGBT modules to prevent potential
failures with high confidence levels in circuit design.
The Cauer and Foster thermal impedance models have
been widely used in power electronic circuit simulations.
The former model is correlated to the physical property and
packaging structure of IGBT modules and the latter is an
equivalent one fitted from measured or simulated results [5].
These models are simple, time efficient, and can be easily
integrated in various circuit simulators (e.g. PLECS, Spice,
Saber) [6]-[8]. However, there is still a deficiency for current
Cauer and Foster models. The present models are applying
temperature-invariant parameters, which are not realistic due
to most material’s physical properties are temperature
dependent. This shortage becomes more fatal especially in
case of wide temperature range (from room temperature to
hundreds of degree) in IGBT transient operations (µs or ms -
level), typical situation during short-circuits and overloads.
It has been proved that temperature influences strongly to
the physical parameters of the semiconductor components in
prior-art research. The correlation of thermal resistance and
ambient temperature has been studied in [9]-[12] for the
semiconductor devices. However, the studies on thermal
resistance of low power devices (e.g. LED [9], transistors
[10]) may not be applicable to high power IGBTs due to the
dramatic difference in material and geometry. IGBT thermal
resistance dependence on power loss is studied and proved
by experiments in [11], whereas it is difficult to apply the
results in circuit simulations due to a lack of quantitative
conclusion. A case study of dynamic thermal behavior is
implemented with IGBT modules with sintered nano-silver,
which evidences that the Finite-Element Method (FEM) is
suitable for accurate transient thermal impedance study [12].
On the foundation of the above study, this paper proposes
a novel thermal model for IGBT junction temperature
simulation. It is based on FEM thermal simulations with the
consideration of temperature-dependent physical parameters.
Then an updated Cauer thermal model with varying thermal
parameters is obtained, which can be applied to IGBT
circuit-level simulations.
TABLE I. CORRESPONDENCE BETWEEN ELECTRICAL AND
THERMAL PARAMETERS
Electrical Parameters
Thermal Parameters
Voltage, U (V)
Temperature difference, ΔT (K)
Current, I (A)
Heat flow, P (W)
Resistance, R (V/A)
Thermal resistance, R
th
(K/W)
Capacitance, C (As/V)
Thermal capacitance, C
th
(Ws/K)
P(t)
Zth
T
Rth1 Rth2 Rth,n
Cth1 Cth2 Cth,n
Fig. 1. Cauer thermal model.
P(t)
Zth
T
Rth1
Cth1
Rth2
Cth2
Rth3
Cth3
Rth,n
Cth,n
Fig. 2. Structure of Foster thermal model.
Furthermore, to verify the proposed thermal impedance
model, a test setup with the 1700 V/1000 A IGBT open
module has been constructed, and a +/- 1% accuracy
temperature map corroborating model predictions has been
obtained by an advanced infrared (IR) camera.
This paper is organized as follows: Section II describes
the detailed principles of thermal impedance analysis,
including traditional thermal modeling methods, FEM
analysis theory, as well as temperature effects. Section III
illustrates the procedures of the proposed approach and how
to apply it in circuit-level simulations. Section IV applies the
proposal method to study the transient thermal impedance
under different ambient temperature with a 1700 V IGBT
module case study, which demonstrates the validity of the
method. Section V evidences experimental validation of the
model proposed in Section IV with an advanced infrared
camera. Section VI offers concluding remarks.
II. PRINCIPLES OF THERMAL IMPEDANCE THEORY
A. Thermal Impedance Theory
The basic principle of the thermal impedance network is
to initially transform the thermal parameters into the
corresponding electrical parameters, as shown in Table I.
Afterwards the corresponding equivalent network can be
solved by applying advanced electrical network simulation
tools (e.g. PSpice, Saber, PLECS). Finally, the results are
transformed back into the thermal parameters. Similarly to
the electrical time constant, the product of resistance and
capacity τ=R∙C, the corresponding thermal time constant is
defined as τ
th
=R
th
∙C
th
.
Thermal resistance between two positions is defined,
similarly to Ohm’s law, as the temperature difference
divided by the heat flow:
P
T
R
th
(1)
1) Cauer Model.
Cauer thermal impedance model is correlated to the
physical property. Its equivalent circuit for modeling heat
conduction properties is as shown in Fig. 1.
Cauer thermal model is based on object’s geometry and
properties. As with the electrical parameters, the thermal
resistance and capacitance are related to the thermal
conductivity and pressure specific heat capacity,
respectively. Thermal resistance R
th
and thermal capacitance
C
th
can be calculated respectively, through:
A
d
k
R
th
1
(2)
AdcC
pth
(3)
Where d is the material thickness, A is the cross-sectional
area, k is the thermal conductivity, ρ is the density, and c
p
is
the pressure specific heat capacity.
For IGBT module, the individual RC elements can be
assigned to the individual layers, for example chip, chip
solder, substrate, substrate solder and baseplate. Therefore,
each layer’s temperature can be gained by Cauer model.
2) Foster Model.
Another thermal model is Foster model, which describes
the thermal behavior as “black box”.
The individual RC elements represent the terms of a
partial fractional division of the thermal transfer function of
the system, whereby the order of the individual terms is
arbitrary. The partial fractional representation directly shows
the uniqueness of this network which is given by the fact that
it has a mathematically simple, closed-form specifiable step
response:
n
m
m
C
m
R
t
mth
eRZ
1
)1(
(4)
In this way, it can determine the values of the equivalent
elements based on calculation of temperature curves for
simple power dissipation profiles. It is the reason of the wide
application and popularity of this equivalent network. There
is no relationship between the physical nodes and the internal
structure of this network.
The Foster model can be extracted according to IEC
standard 60747-9 6.3.13 [13]. Thus, it is commonly used by
the manufacturers, and can be found in datasheets.
TABLE II. IGBT MODULE MATERIAL PROPERTIES AT 25 ºC
[14].
Material
Aluminum
Silicon
Solder
Copper
Thermal
Conductivity
(W/m-K)
237
148
57
401
Heat Capacity
(J/Kg-K)
897
705
220
385
Density (kg/m
3
)
2700
2329
7500
8960
TABLE III. MATERIALS THERMAL PROPERTIES AT DIFFERENT
TEMPERATURE [14].
Temperature
25 ºC
75 ºC
125 ºC
225 ºC
325 ºC
Si
Thermal
Conductivity
(W/m-K)
148
119
98.9
76.2
61.9
Heat
Capacity
(J/Kg-K)
705
757.7
788.3
830.7
859.9
Al
Thermal
Conductivity
(W/m-K)
237
240
240
236
231
Heat
Capacity
(J/Kg-K)
897
930.6
955.5
994.8
1034
Cu
Thermal
Conductivity
(W/m-K)
401
396
393
386
379
Heat
Capacity
(J/Kg-K)
385
392.6
398.6
407.7
416.7
3) FEM Model.
The other common thermal analysis model is FEM
model. The geometric data of the package is entered into the
FEM model to calculate the thermal impedance. In this way,
the time-consuming measurements in the upper two models
can be avoided.
The basic principle is to apply FEM to solve the
diffusion-convection-reaction problem. Defined by Fourier’s
law, the heat flux in a given direction is from the thermal
conductivity and the temperature gradient [14]:
),( trTkq
iii
(5)
In Eq. (5),
i
q
is the absorption/production coefficient,
i
k
is thermal conductivity, T is temperature,
r
is the
location, t is time.
By regarding the situation as a flow problem and utilizing
conservation of energy the diffusion-convection-reaction
equation can be derived:
HtrTk
t
T
c
p
),(
(6)
where ρ is the density, c
p
is the heat capacity at constant
pressure.
The first term of Eq. (6) is the transient properties of the
temperature. The first term on the right is the steady state
heat conduction. The final term is the change in stored
internal energy. Solving Eq. (6) is ideal for a finite element
approach which can be based on the ANSYS/Icepak [15] or
COMSOL [16].
With solving the Eq. (6), the temperatures of the
individual components (chip, solder, and baseplate) can be
obtained. What’s more, the temperatures can be viewed
individually or in combination.
FEM simulation provides accurate temperature
estimation, while at the expense of increased simulation
time. This is very critical to circuit level simulation.
Therefore, it could be a promising approach to extract a
simplified Cauer model for circuit-level simulation based on
FEM simulations.
B. Temperature Effects on Thermal Parameters
At present, temperature effects on thermal parameters are
not considered in thermal models usually. However,
basically all material’s properties are temperature related.
Although variation of the density in power devices
relevant working temperature range (from 25 ºC to about 200
ºC) is limited, thermal parameters are dramatically dependent
on temperature.
The common used materials for IGBT modules are
Silicon (Si), Aluminium (Al) and Copper (Cu). The thermal
conductivity, heat capacity and density information of these
typical materials used in the power module at 25 ºC is listed
in Table II.
Table III reports the detailed information for thermal
conductivity and specific heat of the materials (Si, Al, Cu)
[14], [17]-[18]. The temperature effects on the thermal
parameters of Si, Al, and Cu are plotted in Fig. 3. From
Table III and Fig. 3, it can be seen that the thermal
conductivity of silicon decreases strongly with an increasing
temperature; the exact opposite is the case with the pressure
specific heat capacity. According to the handbook, the
silicon thermal conductivity around 250 ºC is only half of the
value around 25 ºC [17]. Based on this, it is clear that the
power module thermal behavior depends directly on the local
temperature [18].
This point is very critical for overloads and short-circuits
analysis, where the chip temperature rises dramatically
(several hundreds of ºC), even if for limited time duration (in
the range of several milliseconds). Therefore, this nonlinear
temperature behavior should also been included in the FEM
model to improve the simulation accuracy.
P(t)
Cth(chip)
Tjunction
Rth(chip) Rth(solder) Rth(ceramic) Rth(baseplate)
Cth(solder) Cth(ceramic) Cth(baseplate)
Fig. 4. The proposal updated Cauer thermal model with temperature-
dependent thermal parameters.
Al Layer
Chip Si
Solder SnAg
DCB Cu
DCB Al2O3
DCB Cu
Solder SnAg
Baseplate Cu
Fig. 5. Schematic cross-section of the multilayer in a typical IGBT power
module.
Fig. 6. Geometry of the 1700 V/1000 A IGBT power module with six
sections in parallel.
(a)
(b)
Fig. 3. Temperature effects on material’s thermal properties (a). Thermal
conductivity, (b). Specific heat capacity of Si, Al, Cu.
III. PROPOSED NOVEL THERMAL IMPEDANCE MODEL
Based on the analysis in Section II, an updated Cauer
model based on FEM model with temperature effects is
promising for the circuit-level thermal simulations. With
temperature-dependent thermal parameters, it can obtain a
more accurate junction temperature.
At first, a detailed model should be constructed in FEM
software, which should include the geometry and material
information. The information in Table II and III, is also
included, as illustrated in last section.
Second step is to perform transient thermal impedance
simulations at different ambient temperature and power loss
levels. After that, lumped thermal impedance network would
be extracted from the FEM results. Finally, the obtained
thermal impedance values will be integrated into the updated
Cauer model.
In the updated Cauer thermal network, Z
th
(chip) is related
to local temperature (e.g. power loss P
loss
(t) and ambient
temperature T
a
), as shown in Fig. 4. The function parameters
are obtained by aforementioned FEM simulations. The
detailed procedures are illustrated in the case study in section
IV.
IV. A STUDY CASE OF THE PROPOSED MODEL
A. Information of the Studied IGBT Module
In order to well illustrate the proposal thermal model, a
case study of a 1700 V/1000 A commercial IGBT module is
given below.
The main specifications of the IGBT module are shown
in Table IV. The maximum operation temperature is 150 ºC.
The module’s internal structure is as follows: the chips
are soldered on a standard DCB layer, which consists of a
ceramic layer (Al
2
O
3
) and two Cu layers. DCB is further
soldered to a Cu baseplate, and the detailed cross section is
as shown in Fig. 5.
The internal structure of the power module is shown in
Fig. 6. There are six identical sections connected in parallel
inside the IGBT module. Each section has two IGBT chips
and two freewheeling diode chips, which are configured as a
half-bridge. Ten Al bond-wires connect each IGBT chip
emitter and the freewheeling diode chip anode.
