A Thermal Model for Insulated Gate Bipolar Transistor Module Zhaohui Luo, Hyungkeun Ahn, and Mahmoud A

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902 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 4, JULY 2004 A Thermal Model for Insulated Gate Bipolar Transistor Module Zhaohui Luo, Hyungkeun Ahn, and Mahmoud A. El Nokali, Senior Member, IEEE

Abstract—A thermal resistor–capacitor ( ) model is intro- the thermal network can be extracted from the thermal dy- duced for the power insulated gate bipolar transistor (IGBT) namic curve [7]. modules used in a three-phase inverter. The parameters of the The manufacturer of IGBT module provides the transient model are extracted from the experimental data for the transient thermal impedance curve of junction to case to the users. In thermal impedance from-junction-to-case j and case-to-ambient . The accuracy of the model is verified by comparing a real application environment, the IGBT module is mounted its predictions with those resulting from the three–dimensional on a heatsink in order to keep the device temperature in the finite element method simulation. The parameter extraction safe operation area. Natural air, forced air or water-cooling [8] algorithm is easy to adapt to other types of power modules in an are typical methods of cooling used. The thermal behavior of a industrial application environment. system is therefore determined by the thermal impedance of the Index Terms—Finite element method (FEM), insulated gate IGBT from junction to case, the thermal impedance of the inter- bipolar transistor (IGBT), thermal resistor–capacitor ( ) face (thermal grease, etc.) between the IGBT and the heatsink network, transient thermal impedance. in addition to the heatsink thermal behavior. If we assume the system to be linear and use a one-dimensional formulation, I. INTRODUCTION we can extend the thermal network from junction-to-case OMMERCIALLY available since 1988, the insulated gate to a network from junction-to-ambient. However, since the C bipolar transistors (IGBTs) are widely used in today’s junction temperature is not easy to measure in an actual power conversion systems for high switching frequency and system, the user is unable to produce the thermal impedance medium power ranges [1]. The IGBT combines the advantages curve from junction to ambient directly from experiment. An of high current density associated with bipolar operation alternative approach would collect thermal measurement data with fast switching and low drive power of metal oxide for the module case which is accessible and easy to obtain semiconductor (MOS) gated devices. Additional advantages and combine it with the thermal impedance data to extract include low steady-state losses, very low switching losses, the network parameters for the whole system. With this high short-circuit capability, and the easiness of connecting thermal network, we can predict the junction temperature the devices in parallel. As the power density and switching of the IGBT in a real time application. This method is verified frequency increase, thermal analysis of power electronics by the 3-D FEM simulation results. system becomes imperative. The analysis provides valuable information on the semiconductor rating, long-term reliability, II. TRANSIENT THERMAL IMPEDANCE FROM and efficient heatsink design. JUNCTION-TO-CASE Thermal resistor–capacitor ( ) networks are widely used The term IGBT module used in this work refers to what the for thermal analysis because they are easy to integrate into ex- manufacturer labels as single module. The module used in this isting circuit simulators, like SPICE or SABER making them paper has a rating of 1200 A/1700 V. The module contains capable of simulating both the electrical and thermal character- IGBTs and freewheeling diodes and is used as a power switch istics of systems. The thermal model is flexible and can be in various applications. This is different from an inverter that used to describe one-dimensional (1-D) [2], two-dimensional would normally be built using six of these modules. (2-D) [3], or three-dimensional (3-D) [4] problems. The model Usually the manufacturer of power semiconductor devices can be built through the discretization of the thermal conduction will provide the user with the transient thermal impedance equation by using either finite difference [2] or finite element curve. Fig. 1 depicts the transient thermal impedance data for method (FEM)[5]. The two approaches are analyzed and their both diodes and IGBTs inside the module. In this work, we accuracies are compared in [6]. Alternatively, the elements of 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 Manuscript received October 18, 2003; revised February 7, 2004. Recom- extract the network model for the IGBT chips. The same mended by Associate Editor M. C. Shaw. Z. Luo and M. A. El Nokali are with the Department of Electrical En- concept applies to the extraction of the thermal network gineering, University of Pittsburgh, Pittsburgh, PA 15261 USA (e-mail: model for the diode chips when only the diodes are powered. [email protected]). In order to understand the definition, derivation, assumption H. Ahn is with the Department of Electrical Engineering, Konkuk University, Seoul, Korea. and application of the curve, the measurement process is Digital Object Identifier 10.1109/TPEL.2004.830089 introduced.

Fig. 2. Thermal g network from junction to case.

TABLE II PARAMETERS OF THE RC NETWORK OF FIG.2

In order to derive the parameters of the thermal network, (3) needs to be expressed in the following form: Fig. 1. Experimental transient thermal impedance from junction to case of an IGBT module (1200 A/1700 V). (4)

TABLE I EXPONENTIAL TERMS EXTRACTED FROM THE TRANSIENT THERMAL IMPEDANCE CURVE IN FIG.1FOR IGBT CHIP This can be achieved by using a continuous-fraction expan- sion (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 rings in the thermal network. By using the method outlined above, the model describing the thermal behavior of a power module mounted on By using a thermal control system [10], the temperature of an ideal heatsink is derived. Fig. 2 shows the resulting the power module case, , is set at a fixed value (such as the thermal network for an IGBT module from junction to case. ambient temperature). A single square power pulse with ampli- Table II lists the value of the RC parameters. It is instructive tude is applied to the module until the junction temperature to note that only ideal or nearly ideal heatsink can keep the reaches its steady state. The module junction temperature case temperature constant while applying power through the is measured at different instances by way of thermal imaging module. or by using temperature-sensitive thermometers. The transient thermal impedance is defined at time as III. TRANSIENT THERMAL IMPEDANCE FROM CASE-TO-AMBIENT

(1) 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 From a network perspective, the transient thermal impedance above. When the IGBT module is mounted on a nonideal curve is equivalent to a step response with zero-initial conditions heatsink which is more realistic to expect, then knowing the and therefore it fully describes the system under consideration. transient thermal impedance from junction to ambient can The experimental transient thermal impedance is then fitted into lead to the derivation of the network parameters that describe a series that consists of a finite number of exponential terms the thermal behavior of the module. However, as mentioned before, the thermal impedance curve from junction to ambient (2) 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 where , , and are specified by the manufacturer. For the application such as a three-phase inverter. Fig. 3 shows the curve in Fig. 1, the values of these parameters are listed in system schematics of a three-phase inverter using single IGBT Table I [9]. modules as power switches. Eight single IGBT modules are The transfer function (input impedance) of the thermal mounted on the heatsink which is made of aluminum. In this network is found by applying Laplace transform to (2) application, six modules are used to drive an ac motor and other two modules are for the braking process. The thermal (3) 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 g 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 g network including heatsink.

(6) TABLE III PARAMETERS OF THE g NETWORK OF FIG.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 using the experimental data collected by the user. From (2), we junction to case can be represented by a four-ring network know that can be expressed as the sum of four expo- as shown in Fig. 2. The heatsink connected to the IGBT module nential terms. Similarly we can curve-fit the experimental data can be represented by a second network. The two networks as the sum of two exponential terms. The resulting are connected at the node called “case” as shown in Fig. 4. To will therefore be expressed in a series containing six exponen- find the elements of the new six-ring network, assume that tial terms. Fig. 5 shows the transient thermal impedance we apply a constant power to the junction. The junction tem- curve for the module and the curve-fitting parameters. Fig. 6 perature above the ambient is and is given by shows the network for the whole system in which the parameters are extracted from the experimental data from Fig. 1 (7) and Fig. 5. The RC parameters are listed in Table III. We need The transient thermal impedance from junction to ambient is to locate the node that represents the case in the network defined as 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 (8) s to the left of it is approximately equal to the steady state value of the thermal resistance from junction-to-case. The latter Combining (7) and (8) yields 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 (9) case immediately after as shown in Fig. 6. It is instructive to note that the change in the position of the case node between The first term in the righthand-side of (9) is the thermal Figs. 4 and 6 can be attributed to two reasons: First, the model impedance from junction to case obtained from the manufac- is not a physical one otherwise the position of the case node turer, and the second term can be calculated from (6) 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 ap- pearing in Fig. 4. The position of the case in Fig. 6 does not Fig. 8. Transient thermal impedance from case to ambient of IGBT chips with diodes unpowered. (solid line: simulation results by ANSYS, dash line: therefore correspond to a physical node but rather is the result experimental data). 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.

IV. THREE-DIMENSIONAL FEM SIMULATION 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. Fig. 9. Transient thermal impedance from junction to ambient of IGBT chips Taking into account the limit on the maximum number of nodes with diodes unpowered. (solid line: simulation results by ANSYS, dash line: prediction by g network). 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 base plate will have the same boundary condition as with fins. of the system is included. Furthermore, although the modules The nonlinearility of the thermal conductivity of silicon is con- are not located symmetrically on the half plane of the base of sidered as function of temperature in ANSYS. the heatsink and while the loading conditions are not the same The simulated dynamic thermal impedance from case to am- (one IGBT is for braking while the other three are for acceler- bient is shown in Fig. 8 together with the experimental data. The ation), the analysis is simplified by assuming that the middle figure reveals a very good match between the two sets of results lines between the IGBT modules are insulated. So only 1/8 of which confirms the correctness of the 3-D model and justifies the structure is modeled as shown in Fig. 7. The structure in- our reliance on it to test the results of extending the network side the IGBT module is presented in detail on this figure: many to cover the case to ambient portion of the IGBT module. IGBT chips and diode chips are soldered to the ceramic sub- The transient thermal impedance from junction to ambient strate, and the base plate provided the mechanical support for resulting from the network is shown in Fig. 9 together the whole power module. The simplified model will not include with the 3-D simulation results. The difference in the thermal re- the details of the heatsink fins which act as effective heat transfer sistance between the simulation and the model is 6.3%. This coefficients on the base plate of the heatsink. Furthermore, the verifies the correctness of network model extracted from conduction within the heatsink fins will be equalized as the ex- the experimental data of and in predicting the junction tension of the base plate of the heatsink. As a result, the heatsink temperature of the IGBT module. 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 of IGBT chips at different power levels with diodes unpowered. REFERENCES [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. V. C ONCLUSION [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. Sel- It is worth mentioning that the thermal conductivity of sil- lami, and J. P. Chante, “Electrothermal modeling of IGBTs: application icon is a function of temperature, and because the convection to short-circuit conditions,” IEEE Trans. Power Electron., vol. 15, pp. 778–790, July 2000. is a nonlinear process, the system described is nonlinear. The [4] T. Kikunaga and T. Ohi, “Analysis and simulation technologies for high- transient thermal impedance is therefore a function of power. reliability design of power modules,” R & D Progress Rep., Mitsubishi, Fig. 10 compares the numerically obtained transient thermal 2003. [5] J. T. Hsu and L. Vu-Quoc, “A rational formulation of thermal circuit impedance of IGBT at two different power levels. In models for electrothermal simulation—part I: finite element method,” steady state, the difference between the thermal resistances is IEEE Trans. Circuits Syst. I, vol. 43, pp. 721–732, Sept. 1996. within 11%. We can therefore conclude that the assumption of [6] A. Ammous, S. Ghedira, B. Allard, H. Morel, and D. Renault, “Choosing a thermal model for electrothermal simulation of power semiconductor a system being linear is quite reasonable in this application. devices,” IEEE Trans. Power Electron., vol. 14, pp. 300–307, Mar. 1999. This work also supports the use of the network to model [7] G. L. Skibinski and W. A. Sethares, “Thermal parameter estimation the thermal behavior of the power module in a real application using recursive identification,” IEEE Trans. Power Electron., vol. 6, pp. system. 228–239, Apr. 1991. [8] C. S. Yun, P. Malberti, M. Ciappa, and W. Fichtner, “Thermal compo- As mentioned before, only the thermal model for the nent model for electrothermal analysis of IGBT module systems,” IEEE IGBT chips inside the module is derived for simplicity. The Trans. Adv. Packag., vol. 24, pp. 401–406, Aug. 2001. [9] Technical Information Documents, Eupec IGBT 1200R17KF6, 2003. method can be extended to derive a thermal network for [10] F. Blaabjerg, J. K. Pedersen, K. D. Madsen, and K. F. Rasmussen, the diode chips inside the module in order to predict the junc- “An advanced microprocessor based temperature controlled heatsink,” tion temperature variation of the diode chips. As for the issue in Proc. International Conf. Industrial Electronics, Control, and Instrumentation (IECON’93), vol. 2, 1993, pp. 785–789. of thermal coupling we know that some IGBTs and diode chips [11] ANYSYS, Inc., Trademark Name, Houston, PA, 2003. share the same substrate and that all the substrates sit on the [12] Fundamentals of thermal resistance measurement, Analysis Tech same base plate of the module. So when the diode chips are www.analysistech.com, 2003. [13] Z. Luo, Ph.D. dissertation, Univ. Pittsburgh, Pittsburgh, PA, Oct. 2002. 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 Zhaohui Luo was born in Yangling, China. She the superposition principle [12] applies namely that when received the B.S degree in optoelectronics from the system has multiple independent heat sources operating Tianjin University, Tianjin, China, in 1990 and the M.S and Ph.D degrees in electrical engineering simultaneously, the temperature fields and heat fluxes will be from the University of Pittsburgh, Pittsburgh, PA, in the linear add-up solution of each heat source when it operates 1999 and 2002, respectively. Her doctoral research centered on power semiconductor device modeling alone. To find the effect of powering the diodes on the IGBT including thermal effect. chips, a set of experimental data is obtained for the case when the IGBTs are turned OFF while the diodes are turned ON. LUO et al.: THERMAL MODEL FOR INSULATED GATE BIPOLAR TRANSISTOR MODULE 907

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