902 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 4, JULY 2004
Abstract— A thermal resistor–capacitor ( ) model is introduced for the power insulated gate bipolar transistor (IGBT) modules used in a three-phase inverter. The parameters of the model are extracted from the experimental data for the transient thermal impedance from-junction-to-case bient ca
. The accuracy of the jc and case-to-ammodel is verified by comparing its predictions with those resulting from the three–dimensional finite element method simulation. The parameter extraction algorithm is easy to adapt to other types of power modules in an industrial application environment.
Index Terms— Finite element method (FEM), insulated gate bipolar transistor (IGBT), thermal resistor–capacitor ( ) network, transient thermal impedance.
I. I NTRODUCTION
C OMMERCIALLY available since 1988, the insulated gate bipolar transistors (IGBTs) are widely used in today’s power conversion systems for high switching frequency and
medium power ranges [1]. The IGBT combines the advantages
of high current density associated with bipolar operation with fast switching and low drive power of metal oxide semiconductor (MOS) gated devices. Additional advantages include low steady-state losses, very low switching losses, high short-circuit capability, and the easiness of connecting the devices in parallel. As the power density and switching frequency increase, thermal analysis of power electronics system becomes imperative. The analysis provides valuable information on the semiconductor rating, long-term reliability, and efficient heatsink design.
Thermal resistor–capacitor ( ) networks are widely used for thermal analysis because they are easy to integrate into existing circuit simulators, like SPICE or SABER making them capable of simulating both the electrical and thermal characteristics of systems. The thermal model is flexible and can be
used to describe one-dimensional (1-D) [2], two-dimensional
(2-D) [3], or three-dimensional (3-D) [4] problems. The model
can be built through the discretization of the thermal conduction
equation by using either finite difference [2] or finite element method (FEM)[5]. The two approaches are analyzed and their accuracies are compared in [6]. Alternatively, the elements of
Manuscript received October 18, 2003; revised February 7, 2004. Recommended by Associate Editor M. C. Shaw.
Z. Luo and M. A. El Nokali are with the Department of Electrical Engineering, University of Pittsburgh, Pittsburgh, PA 15261 USA (e-mail: elnokali@ee.pitt.edu).
H. Ahn is with the Department of Electrical Engineering, Konkuk University,
Seoul, Korea.
Digital Object Identifier 10.1109/TPEL.2004.830089
the thermal
namic curve [7].
network can be extracted from the thermal dy-
The manufacturer of IGBT module provides the transient thermal impedance curve of junction to case to the users. In a real application environment, the IGBT module is mounted on a heatsink in order to keep the device temperature in the
safe operation area. Natural air, forced air or water-cooling [8]
are typical methods of cooling used. The thermal behavior of a system is therefore determined by the thermal impedance of the
IGBT from junction to case, the thermal impedance of the interface (thermal grease, etc.) between the IGBT and the heatsink in addition to the heatsink thermal behavior. If we assume the system to be linear and use a one-dimensional formulation, we can extend the thermal network from junction-to-case to a network from junction-to-ambient. However, since the junction temperature is not easy to measure in an actual system, the user is unable to produce the thermal impedance curve from junction to ambient directly from experiment. An alternative approach would collect thermal measurement data for the module case which is accessible and easy to obtain and combine it with the thermal impedance data the to extract network parameters for the whole system. With this thermal network, we can predict the junction temperature of the IGBT in a real time application. This method is verified by the 3-D FEM simulation results.
II. T RANSIENT T HERMAL I MPEDANCE F ROM
J UNCTION -T O -C ASE
The term IGBT module used in this work refers to what the manufacturer labels as single module. The module used in this paper has a rating of 1200 A/1700 V. The module contains
IGBTs and freewheeling diodes and is used as a power switch in various applications. This is different from an inverter that would normally be built using six of these modules.
Usually the manufacturer of power semiconductor devices will provide the user with the transient thermal impedance curve. Fig. 1 depicts the transient thermal impedance data for both diodes and IGBTs inside the module. In this work, we have not considered the thermal coupling between the diodes and the IGBTs. In other words, only the IGBTs were powered to obtain the thermal impedance data that were then used to extract the network model for the IGBT chips. The same concept applies to the extraction of the thermal network model for the diode chips when only the diodes are powered.
In order to understand the definition, derivation, assumption and application of the curve, the measurement process is introduced.
0885-8993/04$20.00 © 2004 IEEE

LUO et al.
: THERMAL MODEL FOR INSULATED GATE BIPOLAR TRANSISTOR MODULE 903
Fig. 2.
Thermal
RC network from junction to case.
TABLE II
P ARAMETERS OF THE RC N ETWORK OF F IG . 2
Fig. 1.
Experimental transient thermal impedance from junction to case of an
IGBT module (1200 A/1700 V).
In order to derive the parameters of the thermal
(3) needs to be expressed in the following form: network,
(4)
TABLE I
E XPONENTIAL T ERMS E XTRACTED F ROM THE T RANSIENT T HERMAL
I MPEDANCE C URVE IN F IG . 1 FOR IGBT C HIP
By using a thermal control system [10], the temperature of
the power module case, , is set at a fixed value (such as the ambient temperature). A single square power pulse with amplitude is applied to the module until the junction temperature reaches its steady state. The module junction temperature is measured at different instances by way of thermal imaging or by using temperature-sensitive thermometers.
The transient thermal impedance is defined at time as
This can be achieved by using a continuous-fraction expansion (denominator divided by numerator continuously). Four or five exponential terms are enough to curve-fit with enough accuracy for the intended application. The number of exponential terms determines the number of thermal network.
rings in the
By using the method outlined above, the model describing the thermal behavior of a power module mounted on an ideal heatsink is derived. Fig. 2 shows the resulting thermal network for an IGBT module from junction to case.
Table II lists the value of the RC parameters. It is instructive to note that only ideal or nearly ideal heatsink can keep the case temperature constant while applying power through the module.
From a network perspective, the transient thermal impedance curve is equivalent to a step response with zero-initial conditions and therefore it fully describes the system under consideration.
The experimental transient thermal impedance is then fitted into a series that consists of a finite number of exponential terms where , , and are specified by the manufacturer. For the curve in Fig. 1, the values of these parameters are listed in
Table I [9].
The transfer function (input impedance) of the thermal network is found by applying Laplace transform to (2)
(1)
(2)
(3)
III. T RANSIENT T HERMAL I MPEDANCE F ROM
C ASE -T O -A MBIENT
When an IGBT module is mounted on an ideal heatsink, the thermal network parameters can be extracted from the transient thermal impedance from junction to case as outlined above. When the IGBT module is mounted on a nonideal heatsink which is more realistic to expect, then knowing the transient thermal impedance from junction to ambient can lead to the derivation of the network parameters that describe the thermal behavior of the module. However, as mentioned before, the thermal impedance curve from junction to ambient cannot be obtained directly from experiment since the junction temperature of the device is not easy to measure. The case temperature of the module however can be measured in real application such as a three-phase inverter. Fig. 3 shows the system schematics of a three-phase inverter using single IGBT modules as power switches. Eight single IGBT modules are mounted on the heatsink which is made of aluminum. In this application, six modules are used to drive an ac motor and other two modules are for the braking process. The thermal impedance data is measured by turning ON six IGBT modules and connecting them in series. Given that the current through

904 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 4, JULY 2004
Fig. 3.
Schematics of IGBT modules used in a three-phase inverter.
Fig. 4.
Thermal
RC network with extension to include heatsink.
Fig. 5.
Experimental transient thermal impedance from case to ambient of
IGBT chips with diodes unpowered.
the circuit is , and assuming that the voltage drop across each module is , then the power losses in one module is given by
(5)
After being subjected to this constant power losses for a duration , the increase in the case temperature above the ambient temperature is measured as . The thermal impedance at time is then equal to
Fig. 6.
Thermal
RC network including heatsink.
(6)
TABLE III
P ARAMETERS OF THE
RC
N ETWORK OF F IG . 6
The case temperature is measured every 1 second until it reaches its steady state. Based on the experimental data collected, we can extend the thermal network that appears in
Fig. 2 to include the heatsink, the interface between the device and the heatsink, and the cooling method used in a real system.
To understand the meaning of the experimental data resulting from the use of (6), let us recall that the IGBT device from its junction to case can be represented by a four-ring network as shown in Fig. 2. The heatsink connected to the IGBT module can be represented by a second network. The two networks are connected at the node called “case” as shown in Fig. 4. To find the elements of the new six-ring network, assume that we apply a constant power to the junction. The junction temperature above the ambient is
The transient thermal impedance from junction to ambient is defined as
Combining (7) and (8) yields and is given by
(7)
(8)
(9)
The first term in the righthand-side of (9) is the thermal impedance from junction to case obtained from the manufacturer, and the second term can be calculated from (6) using the experimental data collected by the user. From (2), we know that can be expressed as the sum of four exponential terms. Similarly we can curve-fit the experimental data as the sum of two exponential terms. The resulting will therefore be expressed in a series containing six exponential terms. Fig. 5 shows the transient thermal impedance curve for the module and the curve-fitting shows the parameters. Fig. 6 network for the whole system in which the parameters are extracted from the experimental data from Fig. 1 and Fig. 5. The RC parameters are listed in Table III. We need to locate the node that represents the case in the network in order to find the case temperature. A simple way to achieve this objective is to locate the node at the point where the sum of s to the left of it is approximately equal to the steady state value of the thermal resistance from junction-to-case. The latter is equal to 0.013 C/W as shown in Table II. Since the sum of
, , and is equal to 0.012 C/W, it is safe to locate the case immediately after as shown in Fig. 6. It is instructive to note that the change in the position of the case node between
Figs. 4 and 6 can be attributed to two reasons: First, the model is not a physical one otherwise the position of the case node would be fixed since it would correspond to a real structure of

LUO et al.
: THERMAL MODEL FOR INSULATED GATE BIPOLAR TRANSISTOR MODULE 905
Fig. 7.
Simplified structure of the system for 3-D modeling.
the system. Second, the network describing the heat sink is not known a priori otherwise we would have cascaded it with the network from junction to case with the case node located as in Fig. 4. The movement of the “case node” can be explained by the loading effect that occurs when experimental data are used to derive the thermal network extension appearing in Fig. 4. The position of the case in Fig. 6 does not therefore correspond to a physical node but rather is the result of satisfying the thermal properties of the structure namely that it corresponds to the point where the sum of to the left is approximately equal to the steady state value of the thermal resistance from junction to case.
Fig. 8.
Transient thermal impedance from case to ambient of IGBT chips with diodes unpowered. (solid line: simulation results by ANSYS, dash line: experimental data).
IV. T HREE -D IMENSIONAL FEM S IMULATION
In order to verify the validity of the approach that extends the thermal network from junction-to-case to junction-to-ambient, 3-D simulation using the commercial software package
ANSYS [11] is used to predict the thermal behavior of an IGBT
module mounted on a heatsink. The module is part of a package shown in Fig. 3 and used as a three-phase inverter to drive an ac motor. As described before, six IGBT modules are used to drive the motor and the other two modules are for the braking process. The modules are mounted on a heatsink which is made of aluminum. The heat sink has plate fins on the bottom of the base plate in order to increase the contact area between the heat sink and the cooling air from the fan. So besides conduction, forced convection plays an important role in thermal analysis.
Taking into account the limit on the maximum number of nodes that can be used in the FEM software and the CPU and storage requirements, one needs to simplify the system before building the model. Because of the symmetry of the structure, only half of the system is included. Furthermore, although the modules are not located symmetrically on the half plane of the base of the heatsink and while the loading conditions are not the same
(one IGBT is for braking while the other three are for acceleration), the analysis is simplified by assuming that the middle lines between the IGBT modules are insulated. So only 1/8 of the structure is modeled as shown in Fig. 7. The structure inside the IGBT module is presented in detail on this figure: many
IGBT chips and diode chips are soldered to the ceramic substrate, and the base plate provided the mechanical support for the whole power module. The simplified model will not include the details of the heatsink fins which act as effective heat transfer coefficients on the base plate of the heatsink. Furthermore, the conduction within the heatsink fins will be equalized as the extension of the base plate of the heatsink. As a result, the heatsink
Fig. 9.
Transient thermal impedance from junction to ambient of IGBT chips with diodes unpowered. (solid line: simulation results by ANSYS, dash line: prediction by
RC network).
base plate will have the same boundary condition as with fins.
The nonlinearility of the thermal conductivity of silicon is considered as function of temperature in ANSYS.
The simulated dynamic thermal impedance from case to ambient is shown in Fig. 8 together with the experimental data. The figure reveals a very good match between the two sets of results which confirms the correctness of the 3-D model and justifies our reliance on it to test the results of extending the network to cover the case to ambient portion of the IGBT module.
The transient thermal impedance from junction to ambient resulting from the network is shown in Fig. 9 together with the 3-D simulation results. The difference in the thermal resistance between the simulation and the verifies the correctness of model is 6.3%. This network model extracted from the experimental data of and temperature of the IGBT module.
in predicting the junction

906 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 4, JULY 2004
The data are then used to obtain the thermal impedance and to extract an circuit that would represent the thermal coupling effect of the diodes on IGBT. The input to the circuit is the power losses in the diode chips. This new circuit yields an
IGBT case and junction temperatures that are to be added to the respective temperatures obtained from the analysis in the
paper [13].
In conclusion, we have developed a thermal model for a power IGBT module and introduced an extraction method that relies on transient thermal impedance from-junction-to-case and transient thermal impedance from-case-to-ambient to determine its parameters. The accuracy of the approach is verified by comparing its predictions with the results of 3-D
FEM simulation. The extraction algorithm is easy to adapt to other types of power modules in an industrial application environment.
Fig. 10.
Transient thermal impedance
Z of IGBT chips at different power levels with diodes unpowered.
V. C ONCLUSION
It is worth mentioning that the thermal conductivity of silicon is a function of temperature, and because the convection is a nonlinear process, the system described is nonlinear. The transient thermal impedance is therefore a function of power.
Fig. 10 compares the numerically obtained transient thermal impedance of IGBT at two different power levels. In steady state, the difference between the thermal resistances is within 11%. We can therefore conclude that the assumption of a system being linear is quite reasonable in this application.
This work also supports the use of the network to model the thermal behavior of the power module in a real application system.
As mentioned before, only the thermal model for the
IGBT chips inside the module is derived for simplicity. The method can be extended to derive a thermal network for the diode chips inside the module in order to predict the junction temperature variation of the diode chips. As for the issue of thermal coupling we know that some IGBTs and diode chips share the same substrate and that all the substrates sit on the same base plate of the module. So when the diode chips are powered, the substrate and the base plate will be heated up and this will increase the junction temperature of the IGBT chips inside the module. This means that thermal coupling exists between IGBTs and diodes.
Since the heat transfer is dominated by conduction then
the superposition principle [12] applies namely that when
the system has multiple independent heat sources operating simultaneously, the temperature fields and heat fluxes will be the linear add-up solution of each heat source when it operates alone. To find the effect of powering the diodes on the IGBT chips, a set of experimental data is obtained for the case when the IGBTs are turned OFF while the diodes are turned ON.
R EFERENCES
[1] B. J. Baliga, M. S. Adler, R. P. Love, P. V. Gray, and N. D. Zommer, “The insulated gate transistor: a new three-terminal MOS-controlled bipolar power device,” IEEE Trans. Electron Devices , vol. ED-31, pp. 821–828,
June 1984.
[2] A. R. Hefner, “A dynamic electro-thermal model for the IGBT,” IEEE
Trans. Ind. Applicat.
, vol. 30, pp. 394–405, Mar./Apr. 1994.
[3] A. Ammous, K. Ammous, H. Morel, B. Allard, D. Bergogne, F. Sellami, and J. P. Chante, “Electrothermal modeling of IGBTs: application to short-circuit conditions,” IEEE Trans. Power Electron.
, vol. 15, pp.
778–790, July 2000.
[4] T. Kikunaga and T. Ohi, “Analysis and simulation technologies for highreliability design of power modules,” R & D Progress Rep., Mitsubishi,
2003.
[5] J. T. Hsu and L. Vu-Quoc, “A rational formulation of thermal circuit models for electrothermal simulation—part I: finite element method,”
IEEE Trans. Circuits Syst. I , vol. 43, pp. 721–732, Sept. 1996.
[6] A. Ammous, S. Ghedira, B. Allard, H. Morel, and D. Renault, “Choosing a thermal model for electrothermal simulation of power semiconductor devices,” IEEE Trans. Power Electron.
, vol. 14, pp. 300–307, Mar. 1999.
[7] G. L. Skibinski and W. A. Sethares, “Thermal parameter estimation using recursive identification,” IEEE Trans. Power Electron.
, vol. 6, pp.
228–239, Apr. 1991.
[8] C. S. Yun, P. Malberti, M. Ciappa, and W. Fichtner, “Thermal component model for electrothermal analysis of IGBT module systems,” IEEE
Trans. Adv. Packag.
, vol. 24, pp. 401–406, Aug. 2001.
[9] Technical Information Documents , Eupec IGBT 1200R17KF6, 2003.
[10] F. Blaabjerg, J. K. Pedersen, K. D. Madsen, and K. F. Rasmussen,
“An advanced microprocessor based temperature controlled heatsink,” in Proc. International Conf. Industrial Electronics, Control, and
Instrumentation (IECON’93) , vol. 2, 1993, pp. 785–789.
[11] ANYSYS, Inc., Trademark Name, Houston, PA, 2003.
[12] Fundamentals of thermal resistance measurement , Analysis Tech www.analysistech.com, 2003.
[13] Z. Luo, Ph.D. dissertation, Univ. Pittsburgh, Pittsburgh, PA, Oct. 2002.
Zhaohui Luo was born in Yangling, China. She received the B.S degree in optoelectronics from
Tianjin University, Tianjin, China, in 1990 and the
M.S and Ph.D degrees in electrical engineering from the University of Pittsburgh, Pittsburgh, PA, in
1999 and 2002, respectively. Her doctoral research centered on power semiconductor device modeling including thermal effect.

LUO et al.
: THERMAL MODEL FOR INSULATED GATE BIPOLAR TRANSISTOR MODULE 907
Hyungkeun Ahn was born in Kyunggi-Do, Korea, on September 26, 1959. He received the B.S.
and M.S degrees in electrical engineering from
Yonsei University, Seoul, Korea in 1983 and 1985, respectively, and the Ph.D. degree from the Electrical
Engineering Department, University of Pittsburgh,
Pittsburgh, PA, in 1993. His Ph.D. thesis dealt with the modeling and simulation of high electron mobility transistor (HEMT) and its application to inverse modeling.
From 1986 to 1990, he was with the LG Semiconductor Co., Seoul, Korea, where he worked on silicon-based device design and process integration of BJT and BiCMOS for IIL and A/D, and D/A converters.
After finishing his postdoctoral research in 1995, he joined the Department of
Electrical Engineering, Konkuk University, Seoul, where he is currently an Associate Professor and Chairman. He was in the Department of Electrical Engineering, University of Pittsburgh, as a Visiting Professor from 2002 to 2003.
His research interests include nano-scaled and high power device designs and process integrations of silicon devices (BJTs, MOSFETs, and IGBTs), solar cell application, and high frequency analysis of compound semiconductor devices, especially HEMTs, MESFETs, and HBTs, for CAD modeling.
Mahmoud A. El Nokali (M’82–SM’85) was born in Alexandria, Egypt, on December 5, 1949. He received the B.S. degree in electrical engineering from Alexandria University, in 1972, and the M.Eng.
and Ph.D. degrees in electrical engineering from
McGill University, Montreal, QC, Canada, in 1976 and 1980, respectively. His doctoral research dealt with the modeling and characterization of surface acoustic wave storage correlators.
After a year as an NSERC Postdoctoral Fellow at
McGill University, he joined the faculty of the Electrical Engineering Department, University of Pittsburgh, Pittsburgh, PA. His current research interests center on semiconductor device modeling, with special emphasis on short-channel MOSFET, high electron mobility transistor (HEMT),
HBT, and power electronics.
Dr. El Nokali received the 1986 Beitle-Veltri Teaching Award and the 1988
University of Pittsburgh Chancellor’s Distinguished Teaching Award. He is a
Member of Eta Kappa Nu and Sigma Xi.