Life Prediction Model for Press-Pack IGBT Module Based on Thermal Resistance Degradation

Abstract

The contact interfaces of a press-pack insulated-gate bipolar transistor (PP-IGBT) module under fluctuating thermal stress will undergo minor friction and mutual sliding during service, which results in damage to the contact surface and a decline in the thermal performance of the contact interface. Therefore, the temperature inside the module will continue to increase, leading to eventual failure. In this work, a life prediction method based on thermal resistance degradation within a PP-IGBT module is established. The junction temperature can be determined via power loss and a resistance-capacitance (RC) thermal network model, and a life prediction model of the PP-IGBT module is developed based on thermal resistance degradation. The method considers the service quality under power cycling conditions and the influence of the self-accelerating effect of damage accumulation at the contact interface of the PP-IGBT module on fatigue life. The experimental results verify that the proposed PP-IGBT module life prediction method can effectively predict service life under power cycling conditions.

1. Introduction

Press-pack insulated-gate bipolar transistor (PP-IGBT) modules, characterized by their high power density and dual-sided cooling, are frequently employed in the power grid field [1,2]. The operational life of PP-IGBT modules is crucial for ensuring the safety of the entire equipment. During service, the power loss of the PP-IGBT module will fluctuate repeatedly with changes in operating conditions, causing the junction temperature to fluctuate as well. The different material layers in the module will undergo different degrees of thermal expansion with increasing temperature. Due to the dissimilar coefficients of thermal expansion (CTEs) among the various materials, the adjacent material layers at the contact interface will undergo minor friction and sliding, causing damage to the contact interface, leading to changes in its thermal behavior and ultimately causing permanent failure [3].

Accurately assessing the service life of PP-IGBT modules not only avoids system failure and reduces system maintenance costs but also helps to improve the design of PP-IGBT modules and increase their service reliability. The following steps are currently used for predicting the lifespan of common bond-wired IGBT modules: First, the power loss is computed in accordance with the operating conditions specific to the IGBT module. Then, the junction temperature is determined through the calculation of power loss. Next, the stress or strain at the critical location of the IGBT module, i.e., the bonded wires, are calculated using the junction temperature. Ultimately, the service life is calculated using life prediction models of the IGBT module, including the strain-based life model, the stress-based life model, and the energy-based life model [4,5]. However, for PP-IGBT modules, the main failure mode is no longer the cracking of bonded wires; therefore, the above life prediction methods are no longer applicable, and it is important to establish a life prediction model for the failure characteristics of PP-IGBT modules.

Fretting wear is the primary cause of failure in a PP-IGBT module. Deng et al. [6] analyzed the fretting damage in a PP-IGBT module using the finite element (FE) method, and the service life was evaluated by combining the Coffin–Mason model and the Basquin model. Ran et al. [7] obtained the fretting damage of each contact surface of a PP-IGBT module via FE simulation. Then, based on Basquin’s law and considering fretting wear, a life prediction model of PP-IGBT modules was established and was subsequently verified via power cycling experiments.

This paper presents an approach to predicting PP-IGBT module service life, based on power cycling experiments. The thermal resistance values after each power cycle are obtained through thermal resistance tests. Considering thermal resistance degradation as the key parameter, the prediction of the PP-IGBT module service life is achieved by combining power loss calculation, an RC thermal network model, and the thermal resistance degradation model.

2. Life Prediction Method Based on PP-IGBT Module Thermal Resistance

Figure 1 presents the proposed method for predicting the life of PP-IGBT modules, which involves the following aspects:

(1)

Calculating the power loss: Power loss is assessed by applying the established power loss model under the specified test conditions.

(2)

Calculating the junction temperature: The junction temperature is derived by constructing an RC thermal network model and assessing the power loss obtained in the first step.

(3)

Calculate the thermal resistance degradation: Using the thermal resistance degradation model and the junction temperature, the degradation of thermal contact resistance is quantified.

(4)

Obtain the degradation curve of thermal resistance: A new junction temperature is calculated following the alteration in thermal resistance. The decrease in thermal resistance is then ascertained and, by repeated calculations, a curve depicting the thermal resistance degradation is generated.

(5)

Life prediction: By combining the thermal resistance degradation curve obtained in the previous step with the failure criterion, the number of power cycles during module failure is obtained, that is, the life prediction result of the PP-IGBT module.

2.1. Power Loss Model

There are two factors that account for power loss. The first is the threshold voltage drop and on-resistance in the gate conduction state, which cause the module’s conduction loss; the second is the current–voltage asynchrony during the switching process, which causes switching loss [8,9]. In this work, a direct current (DC) power cycling experiment is used; thus, there is no switching loss, and only the conduction loss caused by the threshold voltage and internal resistance is considered here.

For IGBT chips, in a switching cycle, the average conduction loss P_con is as follows:

$$P_{\mathrm{con}}=V_{\mathrm{ce}}(t)I_{\mathrm{c}}\delta$$

(1)

where V_ce represents the collector–emitter voltage at both ends; I_c represents the current flowing into the collector; and δ is the duty cycle.

According to the characteristic curve, V_ce(t) can be rewritten as follows:

$$V_{\mathrm{ce}}\left(t\right)=V_{\mathrm{ce}0}+I_{\mathrm{c}}{r}_{\mathrm{ce}}$$

(2)

where V_ce0 represents the collector–emitter voltage when the input current is zero, and r_ce is the collector–emitter on-resistance.

By substituting Formula (2) into Formula (1), we obtain the following formula:

$$P_{\mathrm{con}}=I_{\mathrm{c}}{V}_{\mathrm{ce}0}\delta +I_{\mathrm{c}}^2{r}_{\mathrm{ce}}\delta$$

(3)

All the parameters of the above equation can be determined from the output characteristic curve obtained through the experiment.

2.2. RC Thermal Network Model

Under service conditions, heat generated by the IGBT chip is transferred mainly in the form of heat conduction inside the module. There are two heat dissipation paths in the PP-IGBT module, located on the collector side and the emitter side, respectively, as shown in Figure 2. On the collector side, the IGBT chip releases heat, which is absorbed by the collector heat sink. On the emitter side, the heat flows in a similar manner, beginning at the IGBT chip and moving towards the emitter heat sink. The positions marked in red in Figure 2 are the contact interfaces between the material layers, which are, from top to bottom, the contact interfaces between collector Cu and collector Mo, IGBT chip and emitter Mo, emitter Mo and Ag, as well as Ag and emitter Cu.

In this work, the Cauer model is applied to describe the heat transfer characteristics of the PP-IGBT module, which can mirror the actual physical structure and is able to obtain the temperatures of each layer in the PP-IGBT module. Figure 3 shows the established Cauer model. The model consists of five cells on the collector side, matching the four material layers—the collector Cu plate, the collector Mo plate, the solder layer, and the collector-side IGBT chip—as well as one contact interface, namely collector Cu/collector Mo. On the emitter side, the model includes seven cells, which correspond to the four material layers—the emitter-side IGBT chip and Al metallization layer, the emitter Mo plate, the Ag shim plate, and the emitter Cu plate—along with three contact surfaces, specifically the Al metallization/emitter Mo, the emitter Mo/Ag shim plate, and the Ag shim plate/emitter Cu plate.

The Cauer model is constructed using MATLAB R2018b/Simulink.

2.3. Thermal Resistance Degradation Model

In this work, the impact of temperature is considered. The Arrhenius equation can be used to describe the thermal resistance degradation rate, k_R, using the average junction temperature, T_j,avg [10], which can be expressed as follows:

$$k_{\mathrm{R}}={\displaystyle \frac{\mathrm{d}{R}_{\mathrm{th},\mathrm{jc}}}{\mathrm{d}t}}=A\exp \left(-{\displaystyle \frac{E_{\mathrm{a}}}{K_{\mathrm{B}}{T}_{\mathrm{j},\mathrm{ave}}}}\right)$$

(4)

where A, E_a, and K_B, respectively, are the Arrhenius constant, the activation energy, as well as the Boltzmann constant.

In addition, ΔT_j is the difference between the highest and the lowest junction temperatures in a cycle, which plays a crucial role in determining the life of the PP IGBT module; the impact of ΔT_j on the degradation rate of Rth_,jc also needs to be considered, which can be accounted for by decreasing the energy barrier to be overcome by the degradation reaction, that is, the larger the ΔT_j, the smaller the activation energy required for Rth_,jc to degrade, as expressed in the following equation:

$$E_{\mathrm{a}}=E_{\mathrm{a}0}-X\Delta T_{\mathrm{j}}$$

(5)

where E_a0 and X are the coefficients to be determined.

Substituting (5) into (4) yields (6), as follows:

$$k_{\mathrm{R}}=A\exp \left(-{\displaystyle \frac{E_{\mathrm{a}0}-X\Delta T_{\mathrm{j}}}{K_{\mathrm{B}}{T}_{\mathrm{j},\mathrm{ave}}}}\right)$$

(6)

where A, E_a0, and X are the coefficients to be determined based on the experimentally measured Rth_,jc degradation curve.

2.4. Life Prediction

By combining the Cauer model and power loss model, the junction temperature curve is calculated; the ΔT_j and T_j,avg in one cycle after the junction temperature stabilizes are as follows:

$$\Delta T_{\mathrm{j}}=T_{\mathrm{j},\max }-T_{\mathrm{j},\min }$$

(7)

$$T_{\mathrm{j},\mathrm{avg}}={\displaystyle \frac{T_{\mathrm{jmax}}+T_{\mathrm{jmin}}}{2}}$$

(8)

where T_j,max represents the highest junction temperature achieved the moment the power is turned off, and T_j,min denotes the lowest junction temperature reached the moment the power is turned on.

Taking ΔT_j and T_j,avg as input parameters, the current Rth_,jc is calculated from the thermal resistance degradation model, i.e., Equation (6), and the previous total thermal resistance degradation, ΔR_th,jc, is obtained via accumulation. The updated ΔR_th,jc is fed back into the Cauer model to calculate the new T_j. As Rth_,jc increases, T_j increases, which in turn contributes to the degradation of Rth_,jc. The above steps are repeated until ΔR_th,jc satisfies the failure criterion, that is, the thermal resistance increases by 10% [11], the loop ends, and the PP-IGBT module failure life N_f is obtained.

3. Power Cycle Experiment

3.1. PP-IGBT Under Test

The sample used in the DC power cycling experiment is a single-chip PP-IGBT module rated at 3300 V/50 A, which consists of a collector Cu plate, a collector Mo plate, a solder layer, an IGBT chip, an emitter Mo plate, an Ag shim, and an emitter Cu plate. The collector Mo plate is connected to the IGBT chip via the solder layer. The emitter Mo plate and Ag gasket are secured to the emitter Cu plate by a plastic frame, and the gate pin is led out on the side. The outer part is sealed with a ceramic shell, and the shell is insulated with nitrogen. In addition, the surface of the emitter side of the IGBT chip is coated with an Al-metallized layer.

3.2. Power Cycling Test Equipment

The power cycle test equipment, as presented in Figure 4, mainly consists of the power supply system, water cooling, drive protection system, and data acquisition system. A special fixture holds the device under test (DUT) in place, which provides stable and continuous rated pressure for the DUT, and the pressure on the chip is approximately 1200 N/cm² [12]. Moreover, the fixture provides a heat sink for the DUT to be tested on both sides. The main circuit provides the load current for the DUT, the driver circuit supplies a 15 V voltage to the gate of the DUT to keep it on, and the test circuit provides the PP-IGBT module with the testing current required for testing. The water cooling system provides cooling for both sides of the DUT to reduce the temperature. The data acquisition system collects the V_ce data.

DC power cycling experiments are carried out on the PP-IGBT module; a total of four sets of power cycling experiments are performed. When the main circuit is activated, the DUT is applied with a load current I_c = 50 A, and the water cooling tank supplies 45 °C cooling water to the heat sink. Moreover, a test current of I_test = 100 mA is applied to measure the V_ce, and the T_j is obtained via the temperature-sensitive electrical parameters (TSEPs) method [13].

Table 1. Power cycling test conditions.

No.	Ic (A)	δ	t (s)	N (Cycles)	Tw (°C)
Module-A	-	-	-	0	-
Module-B	50	0.5	4	100 k	45
Module-C	50	0.5	4	250 k	45
Module-D	50	0.5	4	400 k	45

I_c is the current input to the collector; δ is the duty cycle; t is the cycle time; N is the quantity of test cycles; and T_w is the cooling temperature.

shows the test conditions, where the cycle period is set at 4 s, with t_on = 2 s and t_off = 2 s. Meanwhile, the temperature of the cooling water is maintained at 45 °C. Power cycles of 0, 100,000, 250,000, and 400,000 were carried out for four PP-IGBT modules in the experiment.

3.3. Thermal Resistance Test

3.3.1. K Curve Measurement

Set the temperature to 20 °C and heat the DUT. When the DUT reaches the set target value, apply a driving voltage to the gate to turn on the module and, at the same time, pass a test current set at 100 mA to record the V_ce at the current temperature, and then adjust the temperature to 50 °C, 80 °C, and 110 °C in order. Repeat the above-mentioned steps, record the V_ce at temperatures of 20 °C, 50 °C, 80 °C, and 110 °C, respectively, and then fit the data linearly to obtain the expression T_j = f(V_ce). The results are shown in Figure 5. The DUT was supplied with a test current (100 mA) during the off-time of the main circuit. The V_ce of the DUT was recorded to obtain the K curve, and T_j was calculated. The T_j,max and ΔT_j of the DUT in the initial state were 62.14 °C and 8.56 °C, respectively.

3.3.2. Transient Thermal Impedance Curve Acquisition

In order to obtain the thermal resistance and heat capacity parameters of the material layers in the Cauer model, the transient thermal impedance curves of four PP-IGBT modules were measured using the T3Ster test equipment. The experiment commenced with adiabatic heating on the collector side and the activation of the heat sink on the emitter side. Then, the testing current was passed into the main circuit to ensure that the DUT reached thermal equilibrium. The current was then turned off to begin the water cooling process. The V_ce of the module under test during the cooling process was measured within 1 μs after switching the equipment off. The junction temperature T_j(t) was obtained via the TSEPs method in the cooling phase. Zth_,cooling(t) is the transient thermal impedance that can be determined from T_j and the heating power P during the junction temperature reduction process, as expressed in the following equation:

$$Z_{\mathrm{th},\mathrm{cooling}}\left(t\right)={\displaystyle \frac{T_{\mathrm{j}}\left(t\right)-T_{\mathrm{j}}\left(t=0\right)}{P}}$$

(9)

The transient thermal impedance curves of DUTs on the emitter side are shown in Figure 6.

The emitter side was heated adiabatically and, subsequently, the heat sink on the collector side was activated and tested. This process enabled the acquisition of transient thermal impedance curves of the DUTs on the collector side.

3.3.3. Structural Function Curves

The thermal impedance transient response curve is processed through a series of mathematical processes to obtain an accurate spectrum of time constants, which are then discretized to form the Foster model [14], which is then transformed into the Cauer model [14]. Finally, the cumulative structure function is obtained by summing the thermal resistance and thermal capacity of each layer of the Cauer model. When the slope of the cumulative structure function curve changes, the heat flow into another substance is indicated; by analyzing the changes in the slope, the cumulative curve can be divided to extract the thermal resistance. Differentiating the cumulative structure function yields the differential structure function. The inflection points at the peaks and troughs of the differential structure function curve serve as the boundaries between the adjacent material layers, or between the adjacent material layers and the contact interface.

As shown in Figure 7, the structure function curves for the emitter side of four the PP-IGBT modules demonstrate that the thermal resistance of the material layers are nearly identical. In contrast, the thermal contact resistance at multiple contact interfaces grows substantially with the rising number of power cycles, which in turn results in a higher total thermal resistance [15].

4. Life Prediction of the PP-IGBT Module

4.1. Power Loss Calculation

Figure 8 shows the output characteristic curve at room temperature obtained from the electrical characteristic test. Fitting the linear segment of the curve in the figure, the intersection point with the horizontal coordinate is the threshold voltage drop V_ce0 of 1.786 V, and the collector–emitter resistance r_ce0 of 2.16 × 10⁻² Ω is obtained by the reciprocal of the slope of the line segment. Substituting the obtained parameters into (3) yields the following:

$$P_{\mathrm{con}}=1.786I_{\mathrm{c}}+0.0216I_{\mathrm{c}}^2$$

(10)

Through the above-mentioned formula, power loss can be calculated.

4.2. Determination of the Junction Temperature Resulting from Power Loss

The thermal contact resistance R_th,contact and average thermal capacitance C for each contact interface of the four tested PP-IGBT modules are derived by analyzing the structure function curves, as presented in

Table 2. Parameters of thermal contact resistance and thermal capacity at contact interfaces.

Contact Interface	${\mathit{R}}_{\mathbf{t}\mathbf{h}\mathbf{,}\mathbf{contact}}^{\mathbf{0}}$ (K/W)	${\mathit{R}}_{\mathbf{t}\mathbf{h}\mathbf{,}\mathbf{contact}}^{\mathbf{100}}$ (K/W)	${\mathit{R}}_{\mathbf{t}\mathbf{h}\mathbf{,}\mathbf{contact}}^{\mathbf{250}}$ (K/W)	${\mathit{R}}_{\mathbf{t}\mathbf{h}\mathbf{,}\mathbf{contact}}^{\mathbf{400}}$ (K/W)	C (W·s/K)
Al/emitter Mo	0.02395	0.02353	0.02818	0.03288	0.1815
emitter Mo/Ag	0.09436	0.08641	0.09660	0.1136	1.025
Ag/emitter Cu	0.04554	0.05061	0.05131	0.06519	12.59
Mean value	0.054617	0.053517	0.058697	0.070557	4.598833
Standard Deviation	0.036072	0.031541	0.034803	0.040627	6.933393

. Additionally,

Table 3. Parameters of thermal resistance and thermal capacity for material layers.

Material Layer	Rth (K/W)	Cth (W·s/K)
Collector Cu	0.01984	48.03
Collector Mo	0.01487	0.2378
solder	0.02222	0.1636
IGBT chip (C)	0.01661	0.1316
IGBT chip (E)	0.02015	0.1556
Emitter Mo	0.01588	0.2987
Ag	0.02494	1.895
Emitter Cu	0.02337	47.41
Mean value	0.01974	12.29
Standard Deviation	0.00345	20.46

lists the thermal resistance Rth and thermal capacitance Cth of the material layers, which are obtained through the same structure function division process. By substituting the parameters into the Cauer model established in Section 2.2 and inputting the power losses, the resulting change in junction temperature can be effectively calculated.

4.3. Determination of the Emitter Thermal Resistance Degradation Rate in PP-IGBT Modules

With three contact surfaces on the emitter side, the fluctuations in thermal contact resistance play a more critical role in influencing the module’s overall thermal resistance. As a result, the thermal resistance degradation model focuses on the changes in the thermal resistance of the emitter side.

The aggregate thermal resistance Rth_,jc on the emitter side is demonstrated in Figure 9, which shows that the Rth_,jc has not yet begun to degrade before the 100 k power cycles. After the 250 k power cycles, the Rth_,jc increased significantly by 6.26%, which did not reach the failure threshold. When the DUT had undergone the 400 k power cycles, the emitter thermal resistance increased by 20.6%, and the failure threshold of a 10% change in thermal resistance was exceeded [16].

The degradation rate can be calculated as follows:

$$k_{\mathrm{r}}=2.776\times {10}^{-8}\exp \left(0.8504{\displaystyle \frac{\Delta T_{\mathrm{j}}}{T_{\mathrm{j},\mathrm{ave}}}}-{\displaystyle \frac{0.485}{T_{\mathrm{j},\mathrm{ave}}}}\right)$$

(11)

With the thermal resistance degradation data from the emitter side of the DUT, the Rth_,jc degradation rate k_R(t_i) at any moment t_i can be calculated via the following equation:

$$k_{\mathrm{R}}\left(t_i\right)={\displaystyle \frac{\mathrm{d}{R}_{\mathrm{th},\mathrm{jc}}}{\mathrm{d}t}}={\displaystyle \frac{R_{\mathrm{th},\mathrm{jc}(i+1)}-R_{\mathrm{th},\mathrm{jc}(i)}}{t_{i+1}-t_i}}$$

(12)

Equation (6) was fitted to the thermal resistance degradation data to obtain the thermal resistance degradation model parameters, and these parameters are presented in

Table 4. Parameters of thermal resistance degradation model.

A	X/KB	−Ea0/KB
2.776 × 10−8	0.8504	−0.485

.

4.4. PP-IGBT Module Life Prediction Result

Using the proposed PP-IGBT module life prediction method, the variations in Rth_,jc of the DUT under the experimental conditions are calculated over time and verified by the experimental results, which are shown in Figure 10. The life results obtained in the experiments are between 250 k cycles and 400 k cycles, and according to the analysis in this paper, the PP-IGBT module’s life is estimated to be around 320 k cycles, which is within the range obtained by the experiment results. Before 250 k cycles, the calculated results of Rth_,jc degradation are close to the experimental results. After 250 k cycles, the calculated results of Rth_,jc increase but are slightly lower than the experimental results. In addition, the error increases gradually with increasing ageing time. At 400 k cycles, the experimentally obtained Rth_,jc results are already much larger than the model predictions.

There may be two reasons for the increasing error after 250 k cycles. On the one hand, the power loss in the life prediction model does not change with the increase in number of cycles, and as the contact interface damage grows, the on-resistance rises, subsequently boosting the power loss, which leads to inaccuracies in the life prediction results. On the other hand, changes in thermal resistance on the collector side are not considered.

5. Conclusions

According to the thermal resistance test results of the PP-IGBT modules, the thermal resistance degradation model is established. In addition, combined with the power loss model and the Cauer model, a PP-IGBT module life prediction method based on thermal resistance degradation is proposed.

The thermal resistance degradation of the emitter is indicated by the amount of thermal contact resistance degradation, the life is predicted based on the amount of thermal resistance degradation, and the accelerating effect of the cumulative changes in contact surface morphology on life is also accounted for. By comparing the results of four sets of power cycling experiments with different cycle numbers, the proposed life prediction method proposed in this paper indicates a lifespan of about 320,000 cycles, which is more aligned with the results of the power cycling experiments between 250,000 cycles and 400,000 cycles. The life prediction method established in this paper relies on computational simulation and small-batch experiments to predict the life of PP-IGBT modules, which is faster and more effective than the actual power cycling tests to evaluate the PP IGBT modules. However, the data of 0, 100,000, 250,000, and 400,000 power cycle tests are limited; to improve the precision of predicting the PP IGBT module’s life, further power cycle tests at around 100,000 cycles are required to determine the thermal resistance change at the onset of PP-IGBT module degradation. In addition, the power cycle test results of about 320,000 cycles also need to be obtained to further confirm the precision of the life prediction model established in this work.