Developing a Simplified Analytical Thermal Model of Multi-chip Power Module

MR-12220; No of Pages 14 Microelectronics Reliability xxx (2016) xxx–xxx

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Developing a Simplified Analytical Thermal Model of Multi-chip Power Module Sihem Bouguezzi ⁎, Moez Ayadi, Moez Ghariani University of Sfax - Tunisia, Laboratory of Electronics and Information Technology (LETI), Electric Vehicle and Power Electronics Research Group (VEEP), B.P. 1173, 3038 Sfax, Tunisia

a r t i c l e

i n f o

Article history: Received 25 February 2016 Received in revised form 29 September 2016 Accepted 30 September 2016 Available online xxxx Keywords: Thermal modeling Multichip power module Thermal impedance measurements Analytical method Thermal influence

a b s t r a c t The study of the thermal behavior of power modules has become a necessity regarding the known rapid development in modern power electronics, and the prediction of temperature variation has generally been performed using transient thermal equivalent circuits. In this paper we have developed a simplified analytical thermal model of a power hybrid module. This analytical method is used to evaluate the thermal parameters of a device. The model takes into account the thermal mutual influence between the different module chips based on the analytical method. The thermal interaction between components is dependent on the boundary condition, the dissipated power value in the different components and the number of operating chips constituting the module. This effect is modelled as a source energy and a thermal resistance simply computed tanks to reasonably low measurement applied on the module. The derived thermal models offer an excellent trade-off between accuracy, efficiency and CPU-cost. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction During an operating cycle of a power module in an inverter or a chopper, all the chips soldered to the module dissipate heat and undergo thermal interdictions. The prediction and analysis of the behavior during the thermal cycles of operation of these systems are important to implement appropriate solutions that ensure their best efficiency irrespective of the severity of the environment. The analytical methods can be defined as the kind of methods concerned with the derivation of the exact solution. When this solution can be described by exactly evaluable expressions, then we talk about a closed form solution. Also, because the devices have to be mounted on some kind of support or substrate to be usable, the complete system can be formed by many layers of different materials, and the module may contain different chips influencing each other [1], [2], [3], [4]. In the literature, several factors influence the thermal impedance value or curve, such as the influence of the substrate thickness calculated by means of numerical calculations, as demonstrated by B. Vermeersch, G. De Mey in [5,6]. J. Ortiz-Rodriguez and al in [7] have used finite difference methods (FDMs) to solve the heat conduction equation in three dimensions. Numerical simulations and experiences represent the first and the main issue for evaluating the thermal impedance curve, but the

⁎ Corresponding author. E-mail addresses: [email protected] (S. Bouguezzi), [email protected] (M. Ayadi), [email protected] (M. Ghariani).

analytical aspect is still the most difficult method due to its structure complexity, hence the need for a powerful calculation. Here, analytical models are of fundamental and principle importance. This paper presents a simplified method based on an analytical study that can evaluate the temperature in different components of the module, with a multilayer structure, where each one operates alone, and by considering the thermal interaction between the different devices. The proposed method is based on reasonably low measurement effort that permits an optimal thermal model of the entire power module. It is useful in multi-physics simulations in the purpose of calculation of losses in individual semiconductors with respect of junction temperature modifications, mutual influence and power equilibrium. This optimized model enables a better design a better performance and a lower simulation cost. In section two of the paper, a detailed description of the studied module is presented, and the thermal behavior of the IGBT is obtained by a 3D numerical modeling that will be used as a validation mean of the multi-chip structure. On the other hand, we develop a simplified analytical method which starts from the step response and finds out the values of the different thermal resistances and capacitances. This is for a simplified RC thermal model that can be implemented in a simulator, in an attempt to extract the parameters characterizing a particular package. In the third section, we study each component operating alone using our RC thermal model and then the results are compared with those given by the numerical simulation and by the experimental results. In the fourth section, we study the thermal influence between the different components of the module to estimate the thermal influences

http://dx.doi.org/10.1016/j.microrel.2016.09.022 0026-2714/© 2016 Elsevier Ltd. All rights reserved.

Please cite this article as: S. Bouguezzi, et al., Developing a Simplified Analytical Thermal Model of Multi-chip Power Module, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.09.022

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between devices, which depend on several factors. The numerical simulations and experimental investigations are performed in order to validate the proposed analytical model. 2. Thermal behavior of an IGBT module In this section the thermal behavior of the IGBT module under the static conditions is discussed by using the numerical simulations. The thermal interference and solder size effects are also investigated.

Table 1 Dimension and thermal properties of materials of IGBT module. Q

wi (mm)

ki (W/mK)

ρCi (J/Kcm3)

Silicon Solder 1 Copper Isolation Copper Solder 2 Base plate Grease

0.4 0.053 0.35 0.636 0.35 0.103 3 0.1

140 35 360 100 360 35 280 1

1.7 1.3 3.5 2.3 3.5 1.3 3.6 2.1

2.1. Structure of the studied power module Our study is made on the Semikron module SKM 75GB 123D (75 A/1200 V) [5–11] presented in Fig. 1a. Each component is made up of a silicon chip. The studied module is an inverter leg with two IGBTs and two DIODEs. Fig. 1b shows the schematic structure of the IGBT module, which consists of seven principle materials. This module has been developed in 75 A and 1.2 kV ratings and was targeted specifically at the traction drives application. The physical system is the laying over of seven principal materials qualified by their thickness (wi), thermal conductivity (ki) and thermal capacity (ρCi). Table 1 presents the characteristics of the materials in the different layers of the module, as exposed in Fig. 1b. These values are given by the manufacturer and/or in the literature [12–18]. The essential input value characterizing the thermal behavior in the component that characterizes its cooling system is the transient thermal

impedance ZthJC(t) between the junction and the case. It can be given by the following formula [19–21]:

Z thJC ðt Þ

¼

T j ðt Þ

−T c ðt Þ P

ð1Þ

where Tj(t) is the hot spot temperature (junction temperature), Tc is the bottom temperature of the base plate (case temperature), and P is the average dissipated power. 2.2. Numerical modeling of IGBT module As a suitable 3D numerical simulation tool, the COSMOS/M program [22] is exploited for calculating the temperature fields and the thermal influence between the different components. This software is supported on calculations with the finite element method. A restricted region of

Fig. 1. Schematic of an IGBT module 1200 V–75 A (SEMIPAK module SKM75GB123D) a) General view, (b) Cross-section view.

Please cite this article as: S. Bouguezzi, et al., Developing a Simplified Analytical Thermal Model of Multi-chip Power Module, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.09.022

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3

Y

Front view a-a’

Chip

Z

X

Substrate Base plate

X 44 14

0

22

31

36

42

48 46

mm 54

59

68

76

91

0 2

Left view b-b’

Copper

Base plate

b 10 11

IGBT

IGBT DIODE

a

18 19

Base plate

DIODE

b'

a'

Copper

29 31

Copper Isolation

Active region

Silicon

mm

Isolation Solder Base plate (Copper)

Fig. 2. Restricted region of IGBT module for COSMOS/M modeling.

the IGBT module, 91 mm × 31 mm × 4842 mm, is modelled as shown in Fig. 2. The upper area of the device is distributed into 91 × 31 cells allowing the discretisation of the (0.9 × 0.9) cm2 active area of the IGBT chip into 81 (9 × 9) elementary cells and the (0.6 × 0.6) cm2 active area of the diode chip into 36 (6 × 6) elementary cells. In the case of the studied devices (vertical structure), the power is expected to be dissipated at the upper surface of the chip. In the perpendicular axis on this surface, the discretisation step is variable; it is low in the most active parts of the module and bigger in the lower layer (case). The whole thickness of the module is divided into 60 elements. The final structured mesh has about 51,800 elements and 57,300 nodes. Two boundary conditions are adapted to solve the heat conduction equation of the COSMOS/M. First, the power dissipation is applied in an active region of the silicon devices. The heat associated with the IGBTs and diodes assumes to be generated in uniform over the 70% area of devices [23,24], shown in Fig. 2. This area is referred to the active region. A summary of the boundary condition, which is used in numerical modeling, as follows:

where K0 is Silicon thermal conductivity at 300 K (= 1.548 Wcm−1 K−1) and T is the absolute temperature (K), [25]. Fig. 3 displays the numerically solved temperature distribution by using COSMOS/M. Regarding the IGBT module components, heat flows from the operating hot semiconductor devices to the base plate. The flow path is decided by the specific thermal conductivity and quantity of transferred heat. The hottest spot temperature of 342 K is observed in and around the center of the IGBTs with 110 W applied power dissipation (the case temperature is fixed at 306 K for each simulation). The simulation results show that the thermal resistance of the IGBT is equal to Rth = 0.32 °C/W. This value is in good agreement with the value deduced from the manufacturer data sheet (0.3 °C/W) [26]. Similarly, for a power loss in the diode is equal to 50 W these results show that the thermal resistance of the diode is equal to Rth = 0.62 °C/W. This value

342K 306K

- Uniform heat power is applied in the active region of the IGBTs or diodes. - The module is fixed on a radiator (Fig. 1b). - Adiabatic conditions are imposed on all other boundaries. - Thermal conductivity in silicon is assumed to be non-linear and 4=3

equal to KðTÞ ¼ K 0 ð300 T Þ

,

332K

306K

Fig. 3. Simulation of thermal distribution of IGBT module (Front view a–a′).

Please cite this article as: S. Bouguezzi, et al., Developing a Simplified Analytical Thermal Model of Multi-chip Power Module, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.09.022

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2L 2l

X w

In this section, we present the analytical approach used for the thermal resistance calculation of the assembled chips as a function of their size and according to the module construction and structure. The closed form calculation of the thermal resistance has been usually accomplished through a Variable Angle Model also (VAM) [27,28]. For the geometry shown in Fig. 4, which consists of square elements of dimensions 2 L ∗ 2 l on a square substrate of size 2 L ∗ 2 L, where the sidewalls and top of the substrate are supposed to be adiabatic, the VAM gives a relationship for the thermal resistance: ZW Rth ¼

Z

dRth ¼ 0

1 k

ZW

dz 2

0

4ðl þ z tanα Þ

¼

1 w 4kl l þ w tanα

ð2Þ

Fig. 4. Model definition and dimensions for square geometry.

For the thermal capacitance we find [29]: C th ¼ VρC

2l

ð3Þ

with: X

α1

1

k1

2

V: volume of the geometry for calculation Rth and Cth. ρ: is the medium density, used to convert volume to mass. C: the heat capacity (per unit mass) as the relevant characteristic of the medium filling that volume.

k2 α2

Z

Fig. 5. Bending of flow lines when crossing a boundary between two media.

is in good agreement with the value deduced from the manufacturer data sheet (0.6 °C/W) [26]. The obtained results show the accuracy of the proposed technique to estimate the channel temperature in the IGBT.

2.3. Analytical approach to determine thermal parameters of the RC component model Nowadays, numerical techniques such as the finite element method, the finite difference method and the boundary element method, have become very popular for performing accurate and detailed thermal analysis of the heat transfer in the IGBT modules. However, the use of detailed numerical models is often limited to the thermal analysis of the system level packages. Even with the most advanced computer however, the package module and the heat sink in the locomotive systems is not yet feasible. Equivalent electrical circuits such as thermal network models are often used because of their easy implementation in the circuit simulation. The thermal network model is described as an equivalent electrical circuit that contains the lumped resistance and capacitances representing the physical dimensions.

When we add to the model the capability of dealing with multilayer structures, we have an approach that makes possible the spreading angle change according to boundary conditions and system dimensions. Accordingly, there will be a continuity in temperature and heat flux across the surface of separation of the two media, Fig. 5. The surface conditions of the two media can be written as follows: ð∂T Þ ¼ ð∂T Þ and k1 ð ∂T Þ1 ¼ k2 ð∂T Þ ∂x 1 ∂x 2 ∂z 2 ∂z

(4)

which gives after some manipulations: tan α 1 ð∂T=∂xÞ1 =ð∂T=∂zÞ1 k1 ¼ ¼ tan α 2 ð∂T=∂xÞ2 =ð∂T=∂zÞ2 k2

ð5Þ

If we make its thickness finite and introduce a second medium as a boundary for the first, then the spreading angle will depend on the ratio of the thermal conductivities according to equation 5. If we define: φi ¼ ki =kiþ1

ð6Þ

As the thermal- conductivity ratio of the layer i to that of the layer i + 1 in a multilayer substrate, the spreading angle of the layer i will depend only on φi. Using some other assumptions and other mathematical

Fig. 6. Equivalent circuit adopted for analytical simulation (RCAM).

Please cite this article as: S. Bouguezzi, et al., Developing a Simplified Analytical Thermal Model of Multi-chip Power Module, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.09.022

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5

450

Table 2 Numerical RC values for diode and IGBT. IGBT

Layer

Rth (K/W)

Cth (K/W)

Rth (K/W)

Cth (K/W)

Silicon Solder 1 Copper Isolation Copper Solder 2 Base plate

0.2633 0.198 0.0511 0.0482 0.0273 0.0087 0.0082

0.0241 0.0035 0.109 0.2109 0.235 0.0494 1.786

0.0956 0.563 0.0067 0.1043 0.0026 0.006 0.0063

0.0204 0.0022 0.1984 0.1599 0.4612 0.0523 1.9148

Saturation Current Isat (mA)

400

DIODE

350 300 250 200 150 100 50 0 302,14

equations, the calculation of the spreading angle is effected by using this formula:   l ð tan α Þi ¼ ð F S Þi 1− i Li

ð7Þ

317,11

324,7

332,8

349,6

363

378

Temperature (K) Fig. 8. Experimental evolution of calibration curve corresponding to IGBT saturation current (Isat). (VGS = 6 V).

with ð F S Þi ¼

wi þ ρi =ð1 þ ρi Þ:li wi þ 1=ð1 þ ρi Þ:li

ð8Þ

The new values of thermal resistance and capacitance under these conditions are: 1 wi Rth ¼  4ki li li þ wi ð tanα Þi

ð9Þ

C th ¼ V i ρC i

ð10Þ

with: Zw 2 V ¼ 4 ðli þ z tan α i Þ dz h0 i 2 ¼ 4 li w þ ð2li tan α i Þw2 =2 þ tan α i 2 w3 =3

ð11Þ

Up to now, all what is done to obtain the transient thermal response of our system is to calculate the value of the (lumped) elements of its equivalent circuit in the thermal-electrical analogy, i.e., the thermal resistance and capacitance for the different layers that make it up. At this point, it is convenient to make a digression on the RC network topology. The equivalent circuit is shown in Fig. 6. The RC values,

Overheating

calculated with the adopted analytical approach, are provided in Table 2, for the diode and the IGBT. 2.4. Thermal behavior of each component operating alone In order to study the thermal behavior of each module component, operating alone, a simple simulation in MATLAB Simulink [30] is provided to observe the transient evolutions of the thermal impedance. The obtained results are compared with those given by the numerical simulation and by the experimental results. 2.4.1. Measure of the transient junction temperature of power module The experimental estimation of the junction temperature of the IGBT module is based on measuring of the thermo-sensitive parameter. For example: - Measure Vth which implies a fine control of the voltage VGS in order to ensure a low current density inside the device during the cooling phase. - Measure the saturation current for a high gate-to-source voltage value. The results are not unique since they depend on circuit parameters, and the temperature calibration of the saturation current may not be performed without power losses that participate to the device self-heating. - Measure the saturation current during a cooling phase of the component, but for a low voltage VGS (slightly larger than Vth at room temperature).

Osc

CurrentMesurement (Isat)

(Saturation current measurement)

R RG IGBT DUT

10s

E

+15V +6V

Power dissipation

Fig. 7. Experimental electric circuit proposed for the IGBT thermo-sensitive parameter calibration. (E = 18 V and R = 2,2 Ω,VGS = 6 V).

3μs

Phase of saturation current measurement

Fig. 9. Electriccircuit used for IGBT saturation current measurement during cooling phases (E = 18 V; R = 2,2 Ω and VGS = 6 V).

Please cite this article as: S. Bouguezzi, et al., Developing a Simplified Analytical Thermal Model of Multi-chip Power Module, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.09.022

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placed in a hole in the heat sink at the interface with the module base plate. Thus, with the operating of Fig. 8 and Fig. 10 and by using Eq. (1) we can deduce the experimental thermal impedance evolution Zth-IGBT. On the other hand, the experimental estimation of the junction temperature of the diode is also based on the measurement of the thermosensitive parameter [32]. The most conventional and most used method is that of measuring the drop voltage (Vj) in the on-state during the heating phase of the device.

Saturation Current Isat(mA)

130 110 90 70 50 30 10 0

200

400

600

800

1000

Time (s) Fig. 10. Experimental response of the IGBT saturation current during the heating phase (VGS = 6 V).

The literature [31] shows that the last method is the simplest and most precise. In the following we use this technique for the estimation of the maximum junction temperature in the IGBT module. An essential characteristic to estimate the hottest temperature in the IGBT is in the calibration curve, which involves taking the saturation current for different temperatures in the component. The module is heated from the outside by an electric oven. The ambient temperature is measured by a thermocouple that is fixed inside the oven. Fig. 7 shows the measurement setup for the thermo-sensitive parameter Isat, and Fig. 8 illustrates the experimental temperature calibration curve. We put forward a simple technique based on the measurement of the saturation current during the cooling phase, to measure the thermal impedance of the IGBT. To measure the transient junction temperature of the IGBT, a power dissipation echelon is applied to the component where the control-signal gate source is fixed at VGS = 6 V. The used electrical circuit is shown in Fig. 9. Every 10 s, a pulse of a very short duration (a few microseconds) of equal magnitude of 6 V is applied to the IGBT gate. During this pulse the saturation current in the IGBT and the case temperature are recorded. The variation of the internal averaged temperature on the top surface of the component is neglected for a few microseconds. The saturation current response because of the power dissipation of 30 W in the IGBT is shown in Fig. 10. To measure the case, a thermo-resistance is

2.4.2. Validation of the model Matlab Simulink is used to implement our RC network adopted with the values found by VAM. The dissipated power in the IGBT is equal to 30 W (the device is operating alone in the module). Fig. 11 shows the evolution of the thermal impedance Zth-IGBT, between the junction and the case, obtained by the analytical method using the RC values of the IGBT (and DIODE) presented in Table 2 and the equivalent circuit adopted for analytical simulation (RCAM). In Fig. 12 we have presented the diode thermal impedance Zth-Diode by using the same approach. A good agreement is shown between these two results. This evolution is in concordance with the thermal impedance evolution given by the manufacturer data sheet and the experimental results. This proves that the simulated structure of the studied module is rightly modelled in the COSMOS/M simulator, and the results acquired from these numerical simulations can be evaluated as a reference in our study. By comparing the transient thermal impedance evolutions obtained with the experiments and those deduced from the module data sheet, we can conclude that the transient thermal impedance value in the steady state phase and the thermal response time in the first case are higher than those obtained by the data sheet. Therefore, the transient thermal impedance between the junction and the case of the IGBT in the multi-chip structure depends mainly on boundary conditions at the module case. This is due to the importance of the 3D thermal phenomenon in the module structure. Thermal investigations in module structure, using the manufacturer data sheet and the thermal characteristics, are not correct. Among applications that may give us more details on the behavior of the IGBT and diode in some particular cases, we choose to study the thermal behavior of the two modules following the application of

Fig. 11. IGBT transient thermal impedance evolutions obtained by experiments, by 3D numerical simulations and by analytical model (RCAM) (dissipated power in IGBT = 30 W).

Please cite this article as: S. Bouguezzi, et al., Developing a Simplified Analytical Thermal Model of Multi-chip Power Module, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.09.022

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7

Fig. 12. DIODE transient thermal impedance evolutions obtained by experiments, by 3D numerical simulations and by analytical model (RCAM) (Dissipated power in the DIODE = 10 W).

200

Fig. 13. IGBT Junction temperature evolutions obtained by experiments, 3D numerical simulation and analytical method for power pulse equal to 26 W.

Fig. 14. Diode case temperature evolutions obtained by experiments, by 3D numerical simulation and analytical method for power pulse equal to 10 W.

Please cite this article as: S. Bouguezzi, et al., Developing a Simplified Analytical Thermal Model of Multi-chip Power Module, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.09.022

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Fig. 15. Temperature distributions in power module obtained by numerical simulation in 3D when IGBT is operating alone.

power pulses during a limited period of time utilizing the developed thermal analytical model. Thus, we apply on the IGBT a power pulse of 26 W during 750 s, and a pulse of 10 W on the diode during 1180 s. Based on the work described previously, the IGBT junction temperature evolution and the diode case temperature evolution are illustrated in Fig. 13 and Fig. 14. In these figures, the heating phase seems to be in an acceptable agreement between experiments and analytical results, which proves that our model is available and the analytical approach can be very useful. The figures show also an error during the cooling phase.

Voltage measurement Osc

3. Simplified thermal modeling of multi-chip structure Classical thermal analysis based on the thermal impedance provided by the manufacturer data sheet independent of cooling system characteristics and dissipated power magnitude is incorrect. Components under the dissipated power in the multi-chip structures cause heating of its neighborhood. An experimental simple technique is proposed to estimate the thermal influences caused by the different chips in the hybrid structure. This method is based on the measure of the IGBT and DIODE thermo-sensitive parameters. Experimental characteristics that provide the variation of the device's thermal mutual as a function of the case boundary conditions and dissipated power magnitude are

Power module

Component 1

R4 (2) Osc R3 Voltage measurement

R2

V3 (4)

IN2

(3)

V2

IN1 (1)

V4

Osc Current measurement

thermal influences

Driving signal (for IGBT)

R1 V1

Driving signal (for IGBT) Component 2

Osc

Current measurement

thermal influences

Fig. 16. Experimental circuit proposed to measure the thermal influences between the components of the hybrid structure layout.

Please cite this article as: S. Bouguezzi, et al., Developing a Simplified Analytical Thermal Model of Multi-chip Power Module, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.09.022

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determined. The proposed techniques can be used to develop a simplified, preferment and low cost thermal model of different multi-chip structures based on a 1D thermal model.

9

PIGBT1 IGBT1

diode1

IGBT2

diode2

3.1. Thermal interactions in hybrid structures In this section, we are supposed to study the thermal influence between the different components of the module. We perform thermal 3D finite element simulations to inspect the thermal influences between the different components of the same module. Fig. 15 shows the temperature distributions of the module got by 3D numerical simulations. It can be seen that the thermal influences between components exist when two adjacent devices operate together. This thermal interaction depends mainly on [33,34]: -

These influences are between (Fig. 16): - Components in circuit's top and right bottom - Components in circuit's left and right side The suggested technique will permit the adjustment of the devices average junction temperature value, which have been obtained by simply using the transient thermal impedance. In practice, the users of the module structure should use the thermal impedance devices obtained by experimental measurements. These characteristics mainly depend on the dissipated power magnitude and the base-plate boundary conditions. Further experiments are required to predict the thermal influences values between the different devices. This technique is based on the measurement of the thermo-sensitive parameter. The component undergoing the power dissipation causes the heating of its neighborhood. Hence, it is question of measuring of the parameter thermo-sensible of the other components undergoing this influence. Indeed the principle method as shown in Fig. 16 consists of the following: - When the switch IN1 is in position (1), the component 2 is traversed by an important current (heating phase) and component 1 is turned

IGBT2)

in (K)

100

110 W

90

(2)

80

RIGBT1-diode2 RIGBT1-IGBT2 Fig. 18. Different lateral thermal resistance of influence between IGBT1 and other components of the structure.

The dissipated power value in the different components The silicon chip disposition The boundary condition at the heat-sink The number of operating components

Thermal influence (ΔT IGBT1 on

RIGBT1-diode1

off (IN2 is of course is off). The case temperature in the steady-state is measured by a thermocouple. - When the switch IN1 commutes to position (2), and the thermosensitive parameter of component 1 is measured according to 0the circuit (V2, R2, component 1) conditions. If component 1 is the IGBT or DIODE, a saturation current parameter measurement and drop voltage measurement are performed, respectively. - To measure the thermal influences between the lateral components of the hybrid structure When the switch IN2 is in position (3), IGBT dissipates power (heating phase) and DIODE is turned off (IN1 is of course is off). The switch IN2 commutes to position (4) and the thermo-sensitive parameter of DIODE is measured in a steady-state condition. The same principle will be applied to measure the thermal influences between the lateral components of the hybrid structure. So from the evolution of the calibration curve, as shown in Fig. 8, we can obtain the thermal influence of the IGBT (or DIODE) on IGBT. For example, Fig. 17 shows the thermal influence evolution of the IGBT1 on IGBT2 according to the power dissipated in both component and boundary conditions at the base-plate of the module [35]. These results are obtained by 3D numerical simulations and experiments. We have noticed: - A good arrangement between these results; - That just below the component under test, and the ambient air (IGBT1 in the case), the equivalent resistance of the heat sink (Rhea-IGBT1) represents the thermal resistance between the baseplate; - That even for a low dissipated power magnitude, the magnitude of the thermal influence between the nearby devices in the module structure is not negligible.

90 W

(1)

70

1.15

50 40

60 W

(2) (1)

30 20

1.05

RIGBT1-IGBT2 RIGBT1-diode2

1

(1)

0.95

(2) (1)

0.9

(1) : 3D numerical simulation (2) : Experiment

10

RIGBT1-diode1

1.1 Rik (K/W)

(2) (1)

60

(2) (1)

0.85

0

(2)

0.8

0.2

0.4

0.6

0.8

1

1.2

Rhea-IGBT1 (K/W) Fig. 17. Thermal influence evolutions caused by IGBT1 on IGBT2 in function of dissipated power and boundary conditions.

0

10

20

30

40

50

60

70

PIGBT1 (W) Fig. 19. Variations of coupling resistance in function of power dissipated obtained by: (1) 3D simulation, (2) Experiment (Rhea-IGBT1 = 1 K/W).

Please cite this article as: S. Bouguezzi, et al., Developing a Simplified Analytical Thermal Model of Multi-chip Power Module, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.09.022

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We proposed then the superposition technique which is useful for effective thermal resistance characterization of thermal models on multi-chip modules, hybrid devices, or devices with multiple heat sources [36,37]. This method requires only one test for each independent heat source present. During each test, junction temperatures for all devices must be measured. The experimental results are used to deduce the global thermal mutual in the different module devices by using the superposition technique. In fact, the good agreement between 3D numerical simulations and the experimental results demonstrate that the simulated structure of the studied module is accurately modelled in the COSMOS/M simulator. Therefore, the results got from these numerical simulations can be considered as a reference in the present study. The thermal influence evaluation is experimentally possible in the steady state condition, between two components in a multi-chip structure. Applying the superposition method, using experimental results and performing 3D numerical simulations of the studied structure provides results that show that we can represent the thermal influences between the different components by simple mathematical equations depending on the power dissipation and the boundary conditions. In our case, the linearization from these evolutions, we can deduce that: The thermal influence of IGBT1 on IGBT2 is equal to: ΔTIGBT1 on IGBT2 = 0,9 × PIGBT1 × Rhea-IGBT1 − 0,14 × PIGBT1. The equivalent resistance (component operating alone) is given by temperature the following formula: Rhea−IGBT ¼ Case Temperature−ambiante : Power dissipation in component

Pdiode1

3.2. Developed thermal model In this part, a simplified 1D thermal model, to estimate the junction temperature of the IGBT and the diode in the case where the devices operate simultaneously, (chopper or inverter) is developed. We note that the developed model takes into account the thermal influences between the different chips of the structure. Fig. 18 highlights the different lateral thermal resistance of influence between IGBT1 and the other components of the structure. It seems clear that the thermal influences between devices are modelled by the presence of those lateral resistances and each device has three thermal resistances of influence in the inverter condition, called coupling resistance. Fig. 19 shows the variation of the coupling resistance in function of the dissipated power. We notice a good concordance between the two results, obtained by 3D simulation and by experiment. Taking into account the boundary conditions affect the change in the thermal resistance side, a study of mutual thermal phenomena in multi-chip structures cannot be made without the consideration of these two parameters: dissipated power and boundary conditions. The coupling resistance is given by the following formula: Rik ¼ Thermal influence Power dissipation in component

The proposed model is the 1D simplified network shown in Fig. 20 (RCAMD). Each component of the layer is represented by an RC pair already calculated by the adopted analytical method. The heat sink is represented by a thermal model represented by three RC pairs, for example. Taking into account for the thermal influences between the different components of the module, the notion of power of influence was

PIGBT2

RIGBT1-diode1

Pdiode2

RIGBT1-IGBT2

RIGBT1-diode2

Silicon

Solder 1 Copper

Isolation Copper

Heat sink + Grasse

Solder 2 Base plate

PIGBT1

Junction temperature Case temperature

Base plate

Heat sink

Fig. 20. Proposed thermal model of power module (RCAMD), IGBT1 for example.

Please cite this article as: S. Bouguezzi, et al., Developing a Simplified Analytical Thermal Model of Multi-chip Power Module, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.09.022

S. Bouguezzi et al. / Microelectronics Reliability xxx (2016) xxx–xxx

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Junction temperature in (K) 3D simulation Analytical method

460 440

Without thermal influence

With thermal influence 420 400

(a)

With thermal influence (2)

(1)

380 360

(1) Without thermal influence

340

(2)

320 300 0.1

0.2

0.3

0.4

0.5

0.6

0.7

Req-heat sink (K/W) Junction temperature in (K) 440

3D simulation Analytical method

With thermal influence (1)

(1)

420

400

Without thermal influence

(b)

380

With thermal influence 360

(2)

340

Without thermal influence (2)

320 0.08

0.18

0.28

0.38

0.48

0.58

0.68

Req-heat sink (K/W) Fig. 21. Evolution of maximal junction temperature, in IGBT1 in function of boundary conditions at power module case. (a): The power module operates in a chopper condition; (b): The power module operates in an inverter condition. (1): PIGBT = 110 W and PDIODE = 60 W; (2): PIGBT = 60 W and PDIODE = 35 W.

were modelled by the injection of three power sources (Pdiode1, PIGBT2 and Pdiode2) in serial with three coupling resistances, RIGBT1-diode1, RIGBT1-IGBT2 and RIGBT1-diode2, respectively.

introduced. In the case of inverter operation, all the components of the module are operating simultaneously, each component undergoes the thermal influence of the other three components. These influences PIGBT2 189W

Times in (ms) 5

10

20

30

35

PDIODE1 113W

Times in (ms) 5

10

20

30

35

Fig. 22. Pulse train power dissipated in IGBT1 and DIODE1 in chopper operation.

Please cite this article as: S. Bouguezzi, et al., Developing a Simplified Analytical Thermal Model of Multi-chip Power Module, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.09.022

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S. Bouguezzi et al. / Microelectronics Reliability xxx (2016) xxx–xxx

Each couple of (PDIODE1, RIGBT1-DIODE1), (PIGBT2, RIGBT1-IGBT2) and (PDIODE2, RIGBT1-DIODE2) is the modeling of the thermal influence of other components on the IGBT1. (PDIODE1, RIGBT1-DIODE1 ) is introduced at the interface between the silicon and the copper materials because the IGBT1 and the DIODE1 ships are bounded on the same copper area. (PIGBT2 , R IGBT1-IGBT2 ) and (PDIODE2 , RIGBT1-DIODE2 ) are introduced between

solder 2 and base plate because all module components have the same base plate. 3.3. Results and discussion The thermal model is implemented in the MATLAB simulator in order to estimate the junction temperature of the IGBTs and the diodes.

2

2

1

1 Junction temperature

Junction temperature

2

Temperature in K

Temperature in K

2

1 1 Case temperature

2

1 1 2

IGBT1 operates alone

Time in second

Time in second

1

1

2

2 Junction temperature

Junction temperature

1

1 2

2

Case temperature

Temperature in K

1 Temperature in K

Case temperature

DIODE1 operate alone

2

1 2

Inverter operation (IGBT1)

Time in second

Case temperature

Inverter operation (DIODE1) Time in second

Fig. 23. Evolutions of junction temperature and module case temperature obtained by 3D numerical simulations (1) and by analytical model (2). (Average power dissipated in the IGBT = 60 W; Rhea-IGBT = 0.32 K/W;average power dissipated in DIODE = 36 W and Rhea-DIODE1 = 0.47 K/W).

Please cite this article as: S. Bouguezzi, et al., Developing a Simplified Analytical Thermal Model of Multi-chip Power Module, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.09.022

S. Bouguezzi et al. / Microelectronics Reliability xxx (2016) xxx–xxx

The purpose of this study is to validate this model in the case of inverter operation and to correct the junction temperature values estimated from the transient thermal impedance. This correction depends on mutual thermal coupling between different chips of the hybrid structure. Fig. 21 shows the evolution of the maximal junction temperature in IGBT1 as a function of the boundary conditions for different dissipated power magnitudes. These results are obtained by 3D numerical simulations and by 1D thermal model in the steady state conditions. A good agreement between the evolution's two types is observed. The equivalent resistance of the heat sink (Req-heat sink) is given by the following formula: 8 T c moy −T a > > Req−heat sink ¼ < sum of power dissipation in components with Sum of case temperatures just below the operating component > > : T cmoy ¼ Number of operating components

Ta: is the ambient temperature in K. Despite the simplicity of the 1D thermal model, it is clear that the latter provides a suitable thermal behavior in steady state conditions. The technique used to represent the thermal influence between the various components allowing a good correction of the value junction temperature. For a small value of the heat sink's thermal resistance (0.2 K/W), this correction is equal to 16 K (in the case that the power module operates in an inverter condition and PIGBT = 110 W; PDIODE = 60 W). This value can be higher (50 K) when the thermal resistance increases, and as the power module is operating under nominal conditions. In an inverter operation and using the pulse width modulation (PWM) control of the IGBT, the average powers (on a modulation period) dissipated in each module component have half-sinusoid forms (Fig. 22). In this part we have to study the transient thermal behavior of the power module in the case of these power dissipation evolutions. The frequency of the inverter output current is fixed at 50 Hz and the ambient temperature is equal to 306 K·The value of the average power dissipated in the IGBT is equal to 60 W and in the diode is equal to 36 W. The equivalent heat-sink resistance (Req-heat sink) is equal to 0.37 K/W. Fig. 23 represents the transient thermal responses at the junction and the case temperature of IGBT1 and diode1. These results are obtained by the 1D thermal model and the 3D numerical simulations. A favorable agreement between both types of evolutions is observed. Fig. 23 shows the evolutions of the junction temperature and the module case temperature in IGBT and in DIODE when each component operates alone. We notice that taking into account of the thermal mutual phenomena allow an average junction temperature correction equal to 28 K (30 K on the DIODE) and a correction equal to 23 K (28 K on the DIODE) for the case temperature. This correction values in the steady state conditions are in harmony with the results shown in Fig. 21. The numerical simulation model requires 48 h while the proposed model (RCAMD) needs only 10mn. 4. Conclusion For thermal investigations in multi-chip structures, the thermal interaction between devices has been studied. At first, thermal behavior of each module component operating alone has been dealt with. An analytical method has been developed and a simple RC-model has been adopted to evaluate the thermal resistance and the thermal capacitance and then to estimate the transient thermal impedance of the IGBT and the Diode. This analytical method was a rapid and useful way to evaluate the thermal behavior of the components. We have made available a tool for thermal analysis of single heat sources on many layer substrates, in steady state as well as in transient conditions.

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In the case of isothermal condition on a module base plate, the thermal impedance between the junction and the case of each device, obtained by the analytical model, has been in good agreement with the thermal impedance deduced from the manufacturer data sheet, and obtained by 3D simulation. In the multi-chip structures, the components under the dissipated power cause the heating of its neighborhood. Our analytical method adopted has been used to estimate the thermal influences, caused by the different chips in the hybrid structure, to ameliorate the correction caused by the thermal interaction between the various chips. The experimental characteristics giving the variation of the device thermal mutual influence in function of the case boundary conditions and dissipated power magnitude have been performed. The device temperature estimation is generally based only on the thermal impedance characteristic of each device. This method introduces high error values on the estimated temperature in multi-chip structures. Thus, a simplified assumption concept is proposed to rectify the estimated averaged hottest temperature value in the different device modules. This technique can be generated for several chips and for any technology such as MOS and bipolar. A good accuracy has been noticed. The proposed analytical model can be used to develop a simplified thermal model of the multi-chip structures based on a 1D thermal model of each structure device. The proposed thermal model is easy to implement in any circuit simulator and fruitful for the design of power converter applications. References [1] Z. Khatir, S. Lefebvre, Boundary element analysis of thermal fatigue effects on high power IGBT modules, Microelectron. Reliab. 44 (2004) 929–938. [2] R. Hocine, S.H. Pulko, A. Boudghene Stambouli, A. Saidane, TLM method for thermal investigation of IGBT modules in PWM mode, Microelectron. Eng. 86 (2009) 2053–2062. [3] X. Perpina, A. Castellazzi, M. Piton, M. Mermet-Guyennet, J. Millan, Failure-relevant abnormal events in power inverters considering measured IGBT module temperature inhomogeneities, Microelectron. Reliab. 47 (2007) 1784–1789. [4] J.M. Ortiz-Rodriguez, M. Hernandez-Mora, T.H. Duong, S.G. Leslie, A.R. Hefner, Thermal network components models for 10 kV SiC power module packages, PESC (2008) 4770–Pages 4775. [5] B. Vermeersch, G. De Mey, Influence of substrate thickness on thermal impedance of microelectronics structures, Microelectron. Reliab. 47 (2007) 437–443. [6] B. Vermeersch, G. De Mey, Dependency of thermal spreading resistance on convective heat transfer coefficient, Microelectron. Reliab. 48 (2008) 734–738. [7] J. Reichl, J.'e.M. Ortiz-Rodr'ıguez, A. Hefner, J.-S. Lai, 3-D thermal component model for electrothermal analysis of multichip power modules with experimental validation, IEEE Trans. Power Electron. 30 (6) (2015) 3300–3308 June. [8] Thomas Stockmeier, Power semiconductor packaging-a problem or a resource? From the state of the art to future trends” SEMIKRON Elektronik GmbH, Sigmundstr. 200, D-90431 Nürnberg (Germany). [9] Uta Hecht, Uwe Scheuermann Static and Transient Thermal Resistance of Advanced Power Modules SEMIKRON Elektronik GmbH. 200, 90431 Sigmundstr, Nürnberg, Germany, pp. 3–9. [10] T. Stockmeier, W. Tursky Present and Future of Power Electronics Modules SEMIKRON Elektronik GmbH, Sigmundstr. 200, 90431 Nürnberg (Germany). [11] U. Scheuermenn, E. Herr A Novel Power Module Design and Technology for Improved Power Cycling Capability SEMIKRON Elektronik GmbH, Sigmundstr. 200, 90431 Nürnberg, Germany. [12] J.-M. Dorkel, P. Tounsi, P. Leturcq, Three-dimensional thermal modeling based on the two-port network theory for hybrid or monolithic integrated power circuits, IEEE Trans. Electron Devices 19 (4) (1996) 501–507. [13] K. Bellil, P. Tounsi, J.M. Dorkel, On-state transient electrothermal modelling of large area power components and multichip power modules, IWIPP98, Chicago, Illinois, 1998 18–20 September. [14] J.M. Dorkel, P. Vales, K. Bellil, J.M. Dorkel, P. Leturcq, La simulation électrothermique en électronique de puissance: problèmes, méthodologies et exemples, EPF96, Grenoble, 1996 16–18 Décembre. [15] P. Tounsi, J.M. Dorkel, P. Leturcq, Thermal modeling for electrothermal simulation of power devices or circuits, The European Power Electronics Association, Brighton, 1993 155–160. [16] K. Bellil, Modélisation électrothermique à l'état passant de composant de puissance integrée ou de modules hybrides multi-pucesPh.D. thèse de doctorat de LAAS de CNRS, France 511, 1999. [17] P. Tounsi, Méthodologie de la conception thermique des circuits électroniques hybrides: problème connexesPh.D. thèse de doctorat de LAAS de CNRS, France 221 (1992). [18] C. Batard, N. Ginot, J. Antonios, Lumped Dynamic Electrothermal Model of IGBT Module of Inverters, IEEE Trans. Compon. Packag. Manuf. Technol. 5 (3) (2015) 355–364 March.

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