An Aging-Degree Evaluation Method for IGBT Bond Wire with Online Multivariate Monitoring

Abstract

The aging fracture of bonding wire is one of the main reasons for failure of insulated gate bipolar transistor (IGBT). This paper proposes an online monitoring method for IGBT bonding wire aging that does not interfere with the normal operation of the IGBT module. A quantitative analysis of aging degree was first performed, and the results of multivariate and univariate monitoring were compared. Based on the relationship between the monitoring parameters and the aging of the IGBT bonding wire, gradual damage of the IGBT bond wire was implemented to simulate aging failure and obtain the aging data. Moreover, the change of junction temperature was considered to regulate monitoring parameters. Then, the aging degree was evaluated by an artificial neural network (ANN) algorithm. The experimental results showed the effectiveness of the proposed method.

1. Introduction

In modern industrial systems, power semiconductor devices have become increasingly indispensable. They are widely used in electric locomotive traction, aerospace, industrial automation, transportation, new energy generation, and so on. Power switching devices as the core components of electronic devices are becoming increasingly important [1,2,3]. Among them, insulated gate bipolar transistors (IGBTs) are the most widely used power switching devices in the industrial field. As one of the most inefficient devices in power converters [4,5], IGBT failure is mainly caused by the breakage and shedding of bond wires due to aging [6]. In order to improve the reliability of power converters, it is necessary to monitor the state of the IGBT module and study the aging process.

The health management and condition monitoring methods for IGBTs have been widely studied and discussed. The mainstream research can be divided into two categories. The first category is IGBT life assessment technologies. Here, life analysis models, such as the Coffin–Manson model [7], the Norris–Landzberg model [8], and the Bayerer model [9], have been proposed. In addition, physical models of finite element simulation analysis based on different physical properties of materials have also been proposed to more accurately analyze the change in stress [10]. The second category is the IGBT condition monitoring technologies. Gate voltage oscillations are monitored to analyze the relationship between bond wire degradation and high frequency response. The k-nearest neighbor algorithm based on the cycle aging of power is explored to evaluate its health status through power characteristics such as V_ce(on) [11]. Moreover, training data is used to evaluate the weight factor of each feature according to the statistical feature weighting method. The accuracy of the optimized classification is analyzed to estimate the remaining life [12]. In addition, the rupture of the bond wire can be clearly monitored by eddy current pulse thermal imaging, which requires the application of additional measuring equipment on the IGBT module and may affect the normal operation of the IGBT module [13]. The saturation conduction voltage drop V_ce-sat [14,15,16] and the bond wire equivalent resistance R_J [17] are also often used for the detection of bond wire shedding as well as monitoring of the IGBT turn-off time as a symptom of the latch-up effect [18]. These techniques cannot quantitatively analyze the loss rate of the IGBT bond wire and may affect the normal operation of the IGBT in the application.

In view of the above discussion, an online monitoring and evaluation method based on multivariable IGBT bond wire aging is proposed in this paper. An IGBT aging test bench and monitoring system was built to realize online evaluation of the aging state of IGBT bond wire. First, the failure mechanism of IGBT was analyzed theoretically. Then, the relationship between IGBT’s conduction voltage drop V_ce, Miller platform voltage V_ge, Miller platform duration t_ge, and bond line aging was evaluated. Through the gradual destruction of the IGBT bond wire, the aging failure of the IGBT bond wire was simulated. Meanwhile, V_ce, V_ge, and t_ge at different degrees of aging were obtained. Then, the relationship between junction temperature and the three parameters was established through experiments. Junction temperature correction was performed after standardizing the three parameters at different temperatures. Finally, an artificial neural network (ANN) algorithm was used to evaluate and monitor the current aging degree of IGBT bond wires.

2. Characteristics Analysis of IGBT Aging Mechanism

2.1. IGBT Failure Mechanism

The key parameter to assess the degree of system performance degradation is reliability, and the life cycle of a power device is determined by the module failure mechanism. Therefore, the power device failure mechanism is the basis of state evaluation [3].

A fully packaged IGBT module is a multilayer structure with different materials packaged together, as shown in Figure 1.

Figure 1. Diagram of insulated gate bipolar transistor (IGBT) cross-sectional structure.

Each material increases in volume to a certain extent after being heated, also known as thermal expansion. The coefficient characterizing this property is called the coefficient of thermal expansion. Each layer is composed of a different material, and the coefficient of thermal expansion is also different. The difference in thermal expansion coefficient of the aluminum bonding wire and the solder layer is large. In actual work, the on-state loss and switching loss of the IGBT cause the junction temperature of the device to rise. The material of each layer expands, and the device cools to shrink the materials of each layer. Different thermal expansion coefficients lead to different degrees of expansion of different materials during temperature cycling. Therefore, different materials are subjected to different compressive or tensile stresses, so the thermomechanical stress inside the IGBT is generated by the power cycle. These thermal stresses cause repeated impacts on the material joints of the various layers within the IGBT module, especially the bonding of the bond wires to the chip and the solder layer. In the end, the joints, such as the solder layer, the bonding wires, and the terminal pads, are directly damaged, causing fatigue of the solder layer, cracking, crack growth, and even delamination of the layers, voids, and bonding wires, causing the module to fail [19].

2.2. Influence of Aging of IGBT Bond Wire on Turn-On Voltage

The IGBT module used in this study was Infineon FF225R17ME4. This module is similar to most existing IGBT structures. A diagram of the opened IGBT module is shown below in Figure 2.

Figure 2. The opened IGBT module.

The IGBT module comprises a whole IGBT bridge arm and two IGBT submodules. Each submodule has three modules in which one IGBT chip and one diode chip are connected in antiparallel, and each IGBT chip has four bond wires. A direct cutting IGBT bond wire can be used to simulate the aging of IGBT bond wire and ensure an effective simulation of IGBT bond wire failure [20].

The equivalent circuit diagram of IGBT is shown in Figure 3, where L_j and R_j are the equivalent inductance and resistance of the bonding wire, respectively; L_g and R_g are the gate parasitic inductance and parasitic resistance, respectively; C_ge is the gate-emitter parasitic capacitance; and C_gc is the gate-collective parasitic capacitance, where C_gc = C_gdj + C_oxd.

Figure 3. Equivalent circuit diagram of IGBT.

When the IGBT is fully turned on, the mathematical expression of the turn-on voltage drop V_ce is as follows:

$$V_{\mathrm{ce}}=V_{\mathrm{pn}}+V_{\mathrm{drift}}+I_{\mathrm{e}}{R}_{\mathrm{j}}$$

(1)

The V_pn (pn junction voltage drop of the IGBT) and the V_drift (conduction voltage drop of the drift region) remain substantially unchanged when the IGBT is fully turned on, and the bond line equivalent resistance R_j gradually becomes larger as the bonding wire ages and breaks. The IGBT turn-on voltage drop rises, with the emitter current I_e not changing.

2.3. Influence of Aging of IGBT Bond Wires on Miller Plateau Voltage and Its Duration

Due to the existence of gate parasitic capacitance, the gate voltage of the IGBT is determined by the charge and gate capacitance, which is given by

$$U=\frac{Q}{C}$$

(2)

When the IGBT is turned on, the change in gate voltage is not linear but rather a multistage process. The changing process of gate voltage U_ge during the turn-on process is shown in Figure 4.

Figure 4. The gate voltage U_ge changing process.

At point A, U_ge rises when the gate capacitance C_ge is charged, and U_ge rises exponentially, affected by the gate capacitance C_ge. At point B, U_ge reaches the flatband voltage U_fb, and part of the C_ge capacitor, called metal–oxide–semiconductor (MOS) capacitor, no longer affects charging, which is equivalent to the reduction of C_ge at this time; the slope of U_ge rises faster than the AB segment. Up to point C, the gate voltage exceeds the threshold voltage U_ge(to), at which point the IGBT begins to conduct. In the CD segment, the charging process of the gate is affected by C_gc. During this time, the IGBT starts to conduct, the collector–emitter voltage U_ce decreases continuously, the current I_gc discharges to the gate through C_gc, and the discharge current needs the driving current I_drive to compensate. At this point, a constant voltage appears at the gate, and this voltage is called the Miller platform voltage. In the DE segment, the drive current charges the gate to point E, and the IGBT is fully turned on to saturation; the turn-on voltage is the saturation voltage U_ce-sat. Figure 5 shows the gate voltage and the collector–emitter current and the collector–emitter voltage when the IGBT is actually turned on. We can see that the actual voltage change and conduction process are in good agreement with our analysis, which also confirms the correctness of our analysis process.

Figure 5. Comparison chart of U_ge, I_ce, and V_ce.

Thus, the Miller platform voltage V_m and the Miller platform duration t_m are determined by the gate equivalent capacitance C_ge and the feedback capacitance C_ce (also called Miller capacitance). The effect of aging of the IGBT bond wire on the gate equivalent capacitance C_ge and the feedback capacitance C_ce were analyzed. A concrete diagram of the internal structure of the gate equivalent capacitor C_ge and the feedback capacitor C_ce of the IGBT is shown in Figure 6.

Figure 6. IGBT internal equivalent capacitance diagram.

The gate equivalent capacitance C_ge is usually composed of two parts. One part overlaps the gate polysilicon from the source N₊ region, including C_oxs and C_s, and another part overlaps the top surface of the gate polysilicon and the P well region, including C_oxc and C_c. The specific mathematical expression of the gate equivalent capacitance is as follows:

$$C_{\mathrm{ge}}=\frac{C_{\mathrm{oxs}}{C}_{\mathrm{s}}}{C_{\mathrm{oxs}}+C_{\mathrm{s}}}+\frac{C_{\mathrm{oxc}}{C}_{\mathrm{c}}}{C_{\mathrm{oxc}}+C_{\mathrm{c}}}$$

(3)

with

$$C_{\mathrm{oxs}}={\epsilon }_{\mathrm{o}}{\epsilon }_{\mathrm{ox}}\frac{A_{\mathrm{ges}}}{t_{\mathrm{oxge}}}$$

(4)

$$\begin{array}{l}{C}_{\mathrm{oxc}}={\epsilon }_{\mathrm{o}}{\epsilon }_{\mathrm{ox}}\frac{A_{\mathrm{gec}}}{t_{\mathrm{oxge}}}\end{array}$$

(5)

where A_ges and A_gec represent the area of the gate polysilicon overlapping the source N+ region and the P-well region, respectively; t_oxge is the thickness of the oxide between them; and ${\epsilon }_{\mathrm{o}}$ and ${\epsilon }_{\mathrm{ox}}$ are the dielectric constant and conductivity of the oxide, respectively. In the IGBT chip, the breakage caused by the aging of the bond wire leads to the decreasing of A_ges and A_gec, and this causes a decrease in C_oxs and C_oxc, even leading to a decrease in C_ge.

The gate-collector capacitance, that is, the Miller capacitance C_ce, is composed of a gate oxide capacitor C_oxd and a depletion layer capacitor C_dep in series. The specific mathematical expression is as follows:

$$C_{\mathrm{gc}}=\frac{C_{\mathrm{oxd}}{C}_{\mathrm{dep}}}{C_{\mathrm{oxd}}+C_{\mathrm{dep}}}$$

(6)

with

$$C_{\mathrm{oxd}}=C_{\mathrm{ox}}{A}_{\mathrm{ai}}$$

(7)

$$C_{\mathrm{dep}}=\frac{{\epsilon }_{\mathrm{si}}{A}_{\mathrm{ai}}}{W}$$

(8)

where C_ox is the oxide capacitance per unit area; A_ai is the area between the cells in the die; and W is the length of the oxide depletion region. As analyzed previously, the breakage caused by the bonding wire aging causes the A_ai and W to decrease, which causes the gate oxide capacitance C_oxd to decrease and the depletion layer capacitance C_dep to change, thereby causing the Miller capacitance C_ce to change.

Based on the above analysis, we can find that the gate equivalent capacitance C_ge and the Miller capacitance C_ce change with the IGBT bond wire aging and breakage, therefore affecting the Miller platform voltage V_m and the Miller platform duration t_m.

3. Accelerated Aging Experiment of IGBT Bonding Wire

3.1. Design Aging Experiment and Parameter Acquisition

An IGBT aging test bench and monitoring system were built. The schematic diagram is shown in Figure 7. The main circuit consisted of a programmable DC power supply, a resistive load, and an IGBT. The drive circuit was composed of a function generator, an IGBT driver board, and a patch cord. The IGBT driver board could only drive the IGBT by setting the driving frequency in the function generator. The monitoring system consisted of a probe, a voltage sensor, a current sensor, a high-precision oscilloscope, and a host computer. The parameters used are shown in Table 1.

Figure 7. Process diagram of monitoring and analysis.

Table 1. Main circuit parameter.

Udc	R	IGBT Switching Frequency	Driving Voltage
100 V	50 Ω	500 Hz	15 V

The aging failure in the IGBT operation by gradual damage to the IGBT bond wire (cutting the IGBT bond wire one by one) was simulated. Then, the electrical parameters under the online operation, which included the conduction voltage drop V_ce, Miller platform voltage V_m, Miller platform duration t_m, and temperature T, were separately recorded in different IGBT aging conditions. The physical diagram is shown in Figure 8.

Figure 8. Physical diagram of the test system.

Nearly 90% of the simulation data for several IGBTs was used to establish the neural network relationship, while the rest was applied for verification of the method. As the actual waveform had voltage fluctuations, the actual voltage value and the average conduction voltage drop V_ce and the Miller platform voltage V_m in one cycle was collected into the computer so as to get more reliable experimental data.

Figure 9 shows the effect of breakage of the bond wire, with each broken bond line indicating a 25% increase in bond aging. It can be seen the Miller plateau voltage gradually reduced, and the Miller platform duration also gradually reduced. This is because the bond wire breakage affected the change of the IGBT gate equivalent capacitance. The course changed as the process was affected. The specific structure of an IGBT is complicated, and it is difficult to quantitatively analyze the influence of bonding wire aging on Miller platform voltage value and Miller platform duration. Therefore, in this study, the neural network model was used for subsequent data processing to deal with this relationship.

Figure 9. U_ge, I_ce, and V_ce waveforms with different IGBT bond line losses: (a) bond wire without loss; (b) bond wire after one break; (c) bond wire after two breaks; (d) bond wire after three breaks; (e) comparison of U_ge with different IGBT bond line losses.

The average value of V_m in one cycle was taken as the actual value of the IGBT Miller platform voltage in the current state, thereby effectively reducing the measurement error. The IGBT turn-on voltage, the true value of the Miller platform voltage, and the Miller platform duration in the different states are shown in Table 2. It can also be seen from the table that the true value of the Miller platform voltage is the same as our analysis.

Table 2. Actual value of V_m, V_ce, and t_m at different IGBT bond wire losses.

Number of Bond Wire Breaks n	0	1	2	3
Bond wire loss rate Rl	0	25%	50%	75%
Vm/V	10.5191	10.4233	10.3277	10.2074
tm/ns	520	490	480	470
Vce/V	2.094117	2.165013	2.256523	2.29834

The above treatment was similarly performed on the turn-on voltage drop V_ce. Figure 10 shows the change in V_ce with the bond wire, while Figure 11 gives a comparison of V_ce in different states. The actual value of V_ce in one cycle was averaged as the true value of the IGBT turn-on voltage in the current state. It can also be seen from Table 2 that the true value of the turn-on voltage is the same as our analysis.

Figure 10. Waveform of V_ce at different IGBT bond wire losses: (a) bond wire without loss; (b) bond wire after one break; (c) bond wire after two breaks; (d) bond wire after three breaks.

Figure 11. Comparison of V_ce in different states.

3.2. Junction Temperature Conversion Experiment

As the IGBT operates under different working conditions, the internal junction temperature of the IGBT is different, and the change of the temperature causes the internal resistance of the IGBT to change. Therefore, the on-voltage drop V_ce, the Miller platform voltage V_m, and the Miller platform duration t_m of the IGBT vary depending on the junction temperature, which affects predictions. In order to avoid this effect, the IGBT was placed in an incubator to establish the relationship between the junction temperature of the IGBT at different temperatures and the on-state voltage drop V_ce, the Miller platform voltage V_m, and the Miller platform duration t_m. When the data was processed, the V_ce, V_m, and t_m at the current temperature were corrected, and the data obtained at different temperatures were equivalent to the data monitored at the same temperature, thus avoiding the influence of the junction temperature fluctuation on the experimental results.

The change in the IGBT turn-on voltage drop V_ce in the same state at different temperatures was measured, as shown in Figure 12. It can be seen that there was a significant change in the conduction voltage drop V_ce at different temperatures. In addition, it is obvious that, as the temperature rose, the IGBT turn-on voltage drop V_ce gradually increased. However, because there was a certain voltage fluctuation when the IGBT was turned on, preliminary processing was performed on the V_ce before fitting the relationship between the conduction voltage drop V_ce and the IGBT junction temperature. The actual data was then collected into the computer. The V_ce of the on-period was averaged as the actual value of the IGBT turn-on voltage drop at the current temperature. The results are shown in Table 3.

Figure 12. Comparison of V_ce at different temperatures.

Table 3. Actual value of V_ce at different temperatures.

T (°C)	Vce (V)
20	2.078
30	2.1369
40	2.3595
50	2.4195
60	2.4085
70	2.5261
80	2.5132
90	2.6008

It can be clearly seen that, as the temperature rose, the IGBT conduction voltage drop also increased. We made a function fit of the junction temperature and the tube pressure drop. Figure 13 is a fitted graph, and the fitting results were as follows:

$$V_{\mathrm{ce}}=0.0072T+1.9855$$

(9)

Figure 13. A function fitting diagram of V_ce and T.

Because IGBTs have different conduction voltages V_ce at the same temperature, the fitting data wad made usable for different IGBT monitoring by standardizing V_ce at 20 °C at different temperatures. The relationship between the conduction voltage drop and the temperature after the standardization at different temperatures was obtained. Table 4 is the data of the conduction voltage drop V_ce after the standardization, and Figure 14 is the fitting map after the standardization. The fitting results were obtained as follows:

$$V_{\mathrm{ce}}{}^{*}=0.0035T+0.9555$$

(10)

Table 4. Comparison of V_ce at different temperatures.

T (°C)	Vce*
20	1
30	1.0605
40	1.0955
50	1.1155
60	1.1655
70	1.2005
80	1.2355

Figure 14. A function fitting diagram of V_ce* and T.

Table 4 shows the correspondence between V_ce* and T at a partial temperature. Meanwhile, the change of gate voltage U_ge at different temperatures is illustrated in Figure 15. It is obvious that U_ge was basically unchanged with the IGBT junction temperature, which means that U_ge was basically unaffected by the change in IGBT junction temperature. The literature [20,21] also shows that the Miller platform voltage is not affected by the IGBT junction temperature. Considering the fact that V_m is not affected by the IGBT temperature, taking the average value of V_m at different temperatures as the actual value of V_m, as shown in Table 5, it is clear that U_ge has no relationship with junction temperature.

Figure 15. Comparison of U_ge at different temperatures.

Table 5. Table of actual values of V_m as a function of temperature.

T (°C)	Vm (V)
30	11.08953
40	11.08679
50	11.1175
60	11.07855
70	11.07898
80	11.0616

4. The Method of Monitoring IGBT Bond Wire Aging

4.1. Artificial Neural Networks

With the increasing speed of the CPU, more and more neural network structures are used to solve the mapping relationship between parameters. In this study, through theoretical analysis and experimental conclusions, it was found that there is a relationship between the saturation conduction voltage drop V_ce of the IGBT, the Miller platform voltage V_m, the Miller platform time t_m, and the bond line equivalent resistance R_j. As mentioned above, the breakage of the bonding wire affects the change of the equivalent capacitance of the IGBT gate, which causes the conduction process to be affected and changed. This law of variation is nonlinear, and it is difficult to quantitatively analyze the influence of bond line aging on Miller platform voltage value and Miller platform duration. It is meaningful to use the ANN structure to establish the corresponding relationship. Therefore, there is a need to fully analyze the specific relationship between the gate voltage U_ge and the degree of bond line loss when IGBT is turned on.

As shown in Figure 16, by substituting the test result data after the junction temperature correction and the standardization experiment, the saturation conduction voltage drop V_ce of the IGBT, the Miller platform voltage V_m, and the Miller platform time t_m were set as the input layer. The bond wire loss rate R_loss was set to the output layer, and the ANN correspondence was established by setting a reasonable activation function f(x) in the neural network toolbox. After establishing the neural network structure, the current IGBT bond wire loss rate could be calculated by inputting the result obtained from online monitoring of the IGBT.

Figure 16. Structural diagram of artificial neural network (ANN).

4.2. Establishment of Multivariate Parameters and Bond Line Aging

Due to the small gap in the actual production of IGBTs, even if the internal equivalent electrical parameters of the same type of IGBT have small gaps, it is necessary to standardize the on-voltage drop V_ce, Miller platform voltage V_m, and Miller platform duration t_m in order to make the neural network widely usable in the monitoring of similar types of IGBTs. The standard value of the standardization was taken as the value when the bonding wire had no loss. Then, using the relationship between the conduction voltage drop and the temperature established in the study, the conduction voltage drop V_ce was corrected at the current junction temperature and uniformly converted to a value at a junction temperature of 20 °C. Four IGBT bond wires were used in the study. Using the bond wire loss rate R_loss to quantify the current IGBT bond wire loss degree, the loss rate R_loss was 0% when the bond wire was intact, 25% when the bond wire broke once, 50% when the bond wire broke twice, and 75% when the bond wire broke three times. Table 6 shows the data before the standardization, and Table 7 shows the data after the standardization. Table 8 gives a comparison of the data before and after the junction temperature conversion.

Table 6. Data before standardization.

IGBT Bond Wire Loss Rate	T	Vce (V)	Vm (V)	tm/ns
0	20 °C	1.875	10.5	510
25%	20 °C	2.1125	10.375	490
50%	20 °C	2.1375	10.25	480
75%	20 °C	2.1625	10.125	470

Table 7. Data after standardization.

IGBT Bond Wire Loss Rate	T	Vce*	Vm*	tm*
0	20 °C	1	1	1
25%	20 °C	1.1266	0.98809	0.96078
50%	20 °C	1.1412	0.97619	0.94117
75%	20 °C	1.1533	0.96428	0.92157

Table 8. Comparison of the data before and after the junction temperature conversion.

Temperature T (°C)	40	50	60	70	80
loss rate Rloss	25%	25%	25%	25%	25%
Actual value of Vce (V)	2.12752	2.17454	2.20122	2.26553	2.29866
Vce converted value (V)	1.91205	1.92938	1.88864	1.87930	1.86051

Finally, the processed training set data was input to the ANN, and iterative training was performed to establish a corresponding neural network. It can be seen from the results that the accuracy of the neural network correspondence can be verified using a training set.

4.3. Verification of Results

In order to verify the effectiveness of the proposed method after establishing the corresponding neural network, the processed verification data was input into the neural network, and the monitored value results and the actual results were output, as shown in Table 9 and Figure 17. From the results, it can be seen that the monitored value results are very close to the theoretical value results, which indicates that the proposed method in this paper is effective.

Table 9. Comparison of monitored and actual values.

Rl-a (Actual Value of Rloss)	Rl-p (Predicted Value of Rloss)	Prediction Error	Rl-a (Actual Value of Rloss)	Rl-p (Predicted Value of Rloss)	Prediction Error
25%	26.20%	1.20%	50%	58.26%	8.26%
75%	73.57%	1.43%	50%	44.91%	5.09%
25%	27.04%	2.04%	75%	73.36%	1.64%
50%	47.52%	2.48%	50%	54.72%	4.72%
75%	75.16%	0.16%	75%	74.42%	0.58%
25%	26.12%	1.12%	25%	25.87%	0.87%

Figure 17. Diagram comparing the monitored and actual values.

4.4. Comparison between Univariate Monitoring and Multivariate Monitoring

A single variable was used to evaluate the aging of IGBT bond wires, and the corresponding results were compared to that of the multivariate monitoring method.

When using the univariate V_ce to evaluate the aging degree of the IGBT bond wire, the function fitting method was directly adopted, and Figure 18 shows the corresponding result. The fitting result is as follows:

$$R_{\mathrm{loss}}=47.1734V_{\mathrm{ce}}^2-97.4118V_{\mathrm{ce}}+50.2347$$

(11)

Figure 18. Fitted function between the univariate V_ce* and R_loss.

Similarly, the fitted functions between the univariate V_m and the IGBT bond wire loss rate R_loss as well as that between t_m and R_loss were adopted, and the results are presented in Figure 19 and Figure 20, respectively. The fitting results are as follows:

$$R_{\mathrm{loss}}=-17.10514V_{\mathrm{m}}+17.1346$$

(12)

$$R_{\mathrm{loss}}=-10.79154t_{\mathrm{m}}+10.6517$$

(13)

Figure 19. Fitted function between the univariate V_m* and R_loss.

Figure 20. Fitted function between the univariate t_m* and R_loss.

Implementing the function of Equations (11)–(13), the estimated value of the IGBT bond wire loss rate were calculated and accordingly compared to the actual value. A comparison between the estimated value and the actual value in terms of the IGBT bond wire loss rate is given in Table 10. Additionally, it can be observed from Table 10, Table 11 and Table 12 that the average monitoring errors were Δe1 = 17.24%, Δe₂ = 7.72%, and Δe₃ = 11.52%, respectively.

Table 10. Comparison of the estimated and actual values (using the univariate V_ce).

Rl-a (Actual Value of Rloss)	Rl-p (Predicted Value of Rloss)	Prediction Error	Rl-a (Actual Value of Rloss)	Rl-p (Predicted Value of Rloss)
25%	36.38%	11.38%	50%	47.72%
75%	63.45%	38.45%	75%	63.45%
25%	32.65%	7.65%	25%	30.56%
50%	88.13%	63.13%	50%	52.42%
75%	59.52%	34.52%	75%	63.45%
25%	38.00%	13.00%	25%	30.40%

Table 11. Comparison of monitored and actual values(using the univariate V_m).

Rl-a (Actual Value of Rloss)	Rl-p (Predicted Value of Rloss)	Prediction Error	Rl-a (Actual Value of Rloss)	Rl-p (Predicted Value of Rloss)	Prediction Error
25%	23.32%	1.68%	50%	43.68%	6.32%
75%	64.05%	10.95%	75%	64.05%	10.95%
25%	38.72%	13.72%	25%	40.43%	15.43%
50%	50.45%	0.45%	50%	47.10%	2.90%
75%	74.31%	0.69%	75%	64.05%	10.95%
25%	23.32%	1.68%	25%	41.97%	16.97%

Table 12. Comparison of monitored and actual values (using the univariate t_m).

Rl-a (Actual Value of Rloss)	Rl-p (Predicted Value of Rloss)	Prediction Error	Rl-a (Actual Value of Rloss)	Rl-p (Predicted Value of Rloss)	Prediction Error
25%	28.34%	3.34%	50%	49.51%	0.49%
75%	49.51%	25.49%	75%	70.66%	4.34%
25%	70.66%	45.66%	25%	31.58%	6.58%
50%	26.19%	23.81%	50%	59.87%	9.87%
75%	72.92%	2.08%	75%	70.66%	4.34%
25%	28.34%	3.34%	25%	33.85%	8.85%

The average error Δe was 2.47% when multivariable was used to evaluate the aging degree of IGBT bond wires, which is significantly lower than that of the univariate evaluation, indicating that multivariate monitoring was more accurate.

5. Conclusions

On the basis of analyzing the aging of IGBT bond wire in relation to on-voltage (V_ce), Miller plateau voltage (V_m), and Miller platform duration (t_m), an online monitoring method with ANN is proposed in this paper for evaluating the degradation of IGBT bond wires. Before ANN was constructed with V_ce, V_m, t_m, and IGBT bond wire loss rate, V_ce, V_m, and t_m were subjected to standardization and junction temperature correction so that the method could be suitable for online monitoring of bond wire aging for different types of IGBTs. The main conclusions of this study are as follows: (1) As the IGBT bond wire aged and broke (the bond wire loss rate increased), its turn-on voltage increased, the Miller plateau voltage decreased, and the Miller platform duration decreased. (2) The monitored value of the IGBT bond wire loss rate obtained by the proposed method was close to the actual value, and the average error was 2.47%, which indicates that the method is feasible and effective. The reliability of an electronic device can be improved by avoiding failure of the entire device due to IGBT failure. This requires pre-identification of the aging degree of IGBT bond wire. In this regard, the method presented in this paper allows replacement of the IGBT module before module failure. When using this method in future works, if the actual aging of the IGBT bond wire is obtained, the result will be more reliable and more realistic. At the same time, monitoring the aging of other locations of the IGBT module is also required. In addition, considering the turn-off voltage and current to evaluate the aging degree of IGBT bond wire is open to further research.