Effects of Frequency and Temperature on Electric Field Mitigation Method via Protruding Substrate Combined with Applying Nonlinear FDC Layer in Wide Bandgap Power Modules

Our previous studies showed that geometrical techniques including (1) metal layer offset, (2) stacked substrate design and (3) protruding substrate, either individually or combined, cannot solve high electric field issues in high voltage high-density wide bandgap (WBG) power modules. Then, for the first time, we showed that a combination of the aforementioned geometrical methods and the application of a nonlinear field-dependent conductivity (FDC) layer could address the issue. Simulations were done under a 50 Hz sinusoidal AC voltage per IEC 61287-1. However, in practice, the insulation materials of the envisaged WBG power modules will be under square wave voltage pulses with a frequency of up to a few tens of kHz and temperatures up to a few hundred degrees. The relative permittivity and electrical conductivity of aluminum nitride (AlN) ceramic, silicone gel, and nonlinear FDC materials that were assumed to be constant in our previous studies, may be frequencyand temperature-dependent, and their dependency should be considered in the model. This is the case for other papers dealing with electric field calculation within power electronics modules, where the permittivity and AC electrical conductivity of the encapsulant and ceramic substrate materials are assumed at room temperature and for a 50 or 60 Hz AC sinusoidal voltage. Thus, the big question that remains unanswered is whether or not electric field simulations are valid for high temperature and high-frequency conditions. In this paper, this technical gap is addressed where a frequencyand temperature-dependent finite element method (FEM) model of the insulation system envisaged for a 6.5 kV high-density WBG power module will be developed in COMSOL Multiphysics, where a protruding substrate combined with the application of a nonlinear FDC layer is considered to address the high field issue. By using this model, the influence of frequency and temperature on the effectiveness of the proposed electric field reduction method is studied.


Introduction
Due to the trend toward replacing heavy mechanical, pneumatic, and hydraulic actuators and systems with electrical alternatives with lower weight, higher efficiency, and fewer operational and maintenance costs, a higher electrical demand is needed. The increases in electrical power demand require higher voltages or higher currents. Owing to the weight and voltage drop, an increase in the current is not preferred, and thus higher voltages are being considered. Another trend, especially in the aerospace and defense industries, is reducing the size and weight of equipment. For example, the annual growth in global air traffic passenger demand is expected to be 4.7% until 2028 [1], with temperature-dependency of the relative permittivity and electrical conductivity of three mentioned materials (AlN, silicone gel, and nonlinear FDC material) are used to study the influence of frequency and temperature on the electric field reduction method proposed in [26][27][28][29][30][31][32].

Silicone Gel
There are rare experimental data about the thermal and frequency dependence of ε r and σ ac of silicone gel reported in the literature. Figures 1 and 2 show the frequency dependence of ε r and σ ac , respectively, of silicone gel at several temperatures between 20 and 160 • C, reproduced from [43] and used in this paper for simulations. The commercial silicone gel was used for experiments. Plate-to-plate electrodes with a gap distance of 1 mm, assuring a uniform electric field within the sample, were used. The electrodes were immersed in silicone gel under a vacuum for about 1 h to remove trapped gas bubbles just before the polymerization.
Energies 2020, 13, x FOR PEER REVIEW 3 of 11 frequency-and temperature-dependency of the relative permittivity and electrical conductivity of three mentioned materials (AlN, silicone gel, and nonlinear FDC material) are used to study the influence of frequency and temperature on the electric field reduction method proposed in [26][27][28][29][30][31][32].

Silicone Gel
There are rare experimental data about the thermal and frequency dependence of and of silicone gel reported in the literature. Figures 1 and 2 show the frequency dependence of and , respectively, of silicone gel at several temperatures between 20 and 160 °C, reproduced from [43] and used in this paper for simulations. The commercial silicone gel was used for experiments. Plateto-plate electrodes with a gap distance of 1 mm, assuring a uniform electric field within the sample, were used. The electrodes were immersed in silicone gel under a vacuum for about 1 h to remove trapped gas bubbles just before the polymerization.    frequency-and temperature-dependency of the relative permittivity and electrical conductivity of three mentioned materials (AlN, silicone gel, and nonlinear FDC material) are used to study the influence of frequency and temperature on the electric field reduction method proposed in [26][27][28][29][30][31][32].

Silicone Gel
There are rare experimental data about the thermal and frequency dependence of and of silicone gel reported in the literature. Figures 1 and 2 show the frequency dependence of and , respectively, of silicone gel at several temperatures between 20 and 160 °C, reproduced from [43] and used in this paper for simulations. The commercial silicone gel was used for experiments. Plateto-plate electrodes with a gap distance of 1 mm, assuring a uniform electric field within the sample, were used. The electrodes were immersed in silicone gel under a vacuum for about 1 h to remove trapped gas bubbles just before the polymerization.     Figure 1, ε r for the base case and Cases 1-4 are 2.72, 2.29, 2.29, 2.05, and 2.05, respectively. As seen from Figure 1, ε r is frequency-independent for the 50-1000 Hz range, but it decreases with temperature. From Figure 2, σ ac for the base case and Cases 1-4 are 1.1 × 10 −14 , 3.9 × 10 −13 , 3.9 × 10 −13 , 8.8 × 10 −11 , and 7.4 × 10 −11 S/m, respectively. For 110 • C, σ ac was measured up to 100 Hz (3.9 × 10 −13 S/m) in [43] as shown in Figure 2. We assume that σ ac for 450 and 1000 Hz is also 3.9 × 10 −13 S/m. For 22 • C, σ ac was reported up to 4.5 Hz (1.1 × 10 −14 S/m) in [43] and we assume that for 50, 450 and 1000 Hz, it does not almost change and is 1.1 × 10 −14 S/m. From Figure 2, it can be seen that σ ac is almost frequency-independent, thus the assumptions above are acceptable.
Note that since ε r and σ ac in [43] are reported up to 160°C and 1 kHz, we have to do simulations up to those limits.

Nonlinear FDC material
Polymeric composites using fillers such as SiC, carbon black, or blends of different oxides, e.g., BaTiO 3 , TiO 2 , SiO 2 , Fe 3 O 4 , mica, have been used both for end corona protection of motor stator bars and cable accessories for a long time.
More recently, a new nonlinear field grading material based on ZnO microvaristors has become available and, for the first time, its feasibility for electric field reduction in power modules was studied through simulations [22]. In   Figure 1, for the base case and Cases 1-4 are 2.72, 2.29, 2.29, 2.05, and 2.05, respectively. As seen from Figure 1, is frequency-independent for the 50-1000 Hz range, but it decreases with temperature. From Figure 2, for the base case and Cases 1-4 are 1.1 × 10 −14 , 3.9 × 10 −13 , 3.9 × 10 −13 , 8.8 × 10 −11 , and 7.4 × 10 −11 S/m, respectively. For 110 °C, was measured up to 100 Hz (3.9 × 10 −13 S/m) in [43] as shown in Figure 2. We assume that for 450 and 1000 Hz is also 3.9 × 10 −13 S/m. For 22 °C, was reported up to 4.5 Hz (1.1 × 10 −14 S/m) in [43] and we assume that for 50, 450 and 1000 Hz, it does not almost change and is 1.1 × 10 −14 S/m. From Figure 2, it can be seen that is almost frequency-independent, thus the assumptions above are acceptable.
Note that since and in [43] are reported up to 160 ℃ and 1 kHz, we have to do simulations up to those limits.

Nonlinear FDC material
Polymeric composites using fillers such as SiC, carbon black, or blends of different oxides, e.g., BaTiO3, TiO2, SiO2, Fe3O4, mica, have been used both for end corona protection of motor stator bars and cable accessories for a long time.
More recently, a new nonlinear field grading material based on ZnO microvaristors has become available and, for the first time, its feasibility for electric field reduction in power modules was studied through simulations [22]. In    In this paper, the ZnO microvaristor-silicone compound shown in Figure 3 is considered as nonlinear FDC material for simulations. The measurement data shown in Figure 3 can be fitted by where (a,b) for 22 and 90 • C are (4.83×10 −12 , 8.552×10 −6 ), and (3.092 × 10 −11 , 5.272 × 10 −6 ), respectively. The data for 90 • C in Figure 3 are used for the case studies considered in this paper for 110 and 160 • C, since as seen in Figure 3 and argued in [45], conductivity of the ZnO microvaristor-silicone compound is rather temperature-independent. It is also reported that ε r only weakly depends on a frequency above 50 Hz and it is 11.47, 11.18, and 11.11 for 50, 450 and 1000 Hz, respectively [45]. The frequency-dependency of resistivity and temperature-dependency of ε r for microvaristor-silicone compounds are not reported in [45] and we could also not find such data in other literature. Thus, the conductivity and ε r of the microvaristor-silicone compound considered for simulations are assumed to be frequency-independent and temperature-independent, respectively. Thus, for Cases 1-4, (a, b) from (1) is 3.092 × 10 −11 , 5.272 × 10 −6 . ε r for the base case and Cases 1-4 is 11.47, 11.18, 11.11, 11.18, and 11.11, respectively. Figure 4 shows the schematic cross-section of a metalized AlN substrate that is the established insulation technology for current power module packaging. However, weak points including sharp edges of the metallizations, protrusions formed by active metal brazing of the copper layers, and triple points where silicone gel, AlN, and copper layers meet, can induce enhanced local electric stress.

Modeling and Simulation Results
Energies 2020, 13, x FOR PEER REVIEW 5 of 11 In this paper, the ZnO microvaristor-silicone compound shown in Figure 3 is considered as nonlinear FDC material for simulations. The measurement data shown in Figure 3 can be fitted by where ( , ) for 22 and 90 °C are (4.83×10 −12 , 8.552×10 −6 ), and (3.092 × 10 −11 , 5.272 × 10 −6 ), respectively. The data for 90 °C in Figure 3 are used for the case studies considered in this paper for 110 and 160 °C, since as seen in Figure 3 and argued in [45], conductivity of the ZnO microvaristor-silicone compound is rather temperature-independent. It is also reported that only weakly depends on a frequency above 50 Hz and it is 11.47, 11.18, and 11.11 for 50, 450 and 1000 Hz, respectively [45]. The frequency-dependency of resistivity and temperature-dependency of for microvaristor-silicone compounds are not reported in [45] and we could also not find such data in other literature. Thus, the conductivity and of the microvaristor-silicone compound considered for simulations are assumed to be frequency-independent and temperature-independent, respectively. Thus, for Cases 1-4, ( , ) from (1) is 3.092 × 10 −11 , 5.272 × 10 −6 .
for the base case and Cases 1-4 is 11.47, 11.18, 11.11, 11.18, and 11.11, respectively.  The advantage of the protruding substrate introduced in [18] and shown in Figure 5 is that the sharp edges of the metallization layers have been rounded, and also that the triple point has been moved to a region with less electric stress by soldering the copper metallization on a ceramic substrate with the specific height and width of the protrusion. The advantage of the protruding substrate introduced in [18] and shown in Figure 5 is that the sharp edges of the metallization layers have been rounded, and also that the triple point has been moved to a region with less electric stress by soldering the copper metallization on a ceramic substrate with the specific height and width of the protrusion. Despite the noticeable electric field reduction within the ceramic substrate through the protruding substrate, a negligible improvement in the electric field distribution within the silicone gel is yielded. To address the enhanced local electric stress within the silicone gel, a nonlinear FDC layer as shown in Figure 6 is applied to high-stressed regions, including the high voltage metallization edges and the rims of the ceramic substrate close to the high voltage zone. Nonlinear FDC materials influence the electric field distribution in the module by increasing the leakage current within the module when the electric stress exceeds a threshold value. To study the influence of temperature and frequency on the electric field distribution of a 6.5 kV power module benefitting from a protruding substrate combined with the application of a nonbridging nonlinear FDC layer, the geometry shown in Figure 6 is modeled in COMSOL Multiphysics.

Modeling and Simulation Results
The accuracy of the simulation results in finite element methods (FEMs) is highly dependent on the mesh resolution considered. The higher the density of the mesh elements, the more accurate and reliable the simulation results. However, using an extremely high-resolution meshing for the whole geometry results in a need for lots of memory resources and time-consuming simulations. To address the aforementioned issue, three zones (as shown in Figure 7a) with different mesh sizes were defined. An extremely dense meshing with a maximum element size of 4 µm was used for zone 1, which incorporated all sharp edges. The maximum mesh element sizes of 10 and 400 µm were also used for zones 2 and 3, respectively.
Another parameter that affects the accuracy of the simulation results is the mesh dependency of the electric field at the regions close to the sharp edges and material boundaries. Thus, to address this issue, the electric field measurements are carried out at measuring lines L1 (in AlN substrate), L2 (in nonlinear FDC layer), and L3 (in silicone gel), as shown in Figure 7b, where the lines have a minimum distance of 15 µm from interfaces.
The simulations were carried out for a WBG power module with a blocking voltage of 6.5 kV. According to IEC 61287-1 for PD measurements, a 50/60 Hz voltage with a peak of 1.1 , where Despite the noticeable electric field reduction within the ceramic substrate through the protruding substrate, a negligible improvement in the electric field distribution within the silicone gel is yielded. To address the enhanced local electric stress within the silicone gel, a nonlinear FDC layer as shown in Figure 6 is applied to high-stressed regions, including the high voltage metallization edges and the rims of the ceramic substrate close to the high voltage zone. Nonlinear FDC materials influence the electric field distribution in the module by increasing the leakage current within the module when the electric stress exceeds a threshold value.
Despite the noticeable electric field reduction within the ceramic substrate through the protruding substrate, a negligible improvement in the electric field distribution within the silicone gel is yielded. To address the enhanced local electric stress within the silicone gel, a nonlinear FDC layer as shown in Figure 6 is applied to high-stressed regions, including the high voltage metallization edges and the rims of the ceramic substrate close to the high voltage zone. Nonlinear FDC materials influence the electric field distribution in the module by increasing the leakage current within the module when the electric stress exceeds a threshold value. To study the influence of temperature and frequency on the electric field distribution of a 6.5 kV power module benefitting from a protruding substrate combined with the application of a nonbridging nonlinear FDC layer, the geometry shown in Figure 6 is modeled in COMSOL Multiphysics.
The accuracy of the simulation results in finite element methods (FEMs) is highly dependent on the mesh resolution considered. The higher the density of the mesh elements, the more accurate and reliable the simulation results. However, using an extremely high-resolution meshing for the whole geometry results in a need for lots of memory resources and time-consuming simulations. To address the aforementioned issue, three zones (as shown in Figure 7a) with different mesh sizes were defined. An extremely dense meshing with a maximum element size of 4 µm was used for zone 1, which incorporated all sharp edges. The maximum mesh element sizes of 10 and 400 µm were also used for zones 2 and 3, respectively.
Another parameter that affects the accuracy of the simulation results is the mesh dependency of the electric field at the regions close to the sharp edges and material boundaries. Thus, to address this issue, the electric field measurements are carried out at measuring lines L1 (in AlN substrate), L2 (in nonlinear FDC layer), and L3 (in silicone gel), as shown in Figure 7b, where the lines have a minimum distance of 15 µm from interfaces.
The simulations were carried out for a WBG power module with a blocking voltage of 6.5 kV. According to IEC 61287-1 for PD measurements, a 50/60 Hz voltage with a peak of 1.1 , where To study the influence of temperature and frequency on the electric field distribution of a 6.5 kV power module benefitting from a protruding substrate combined with the application of a non-bridging nonlinear FDC layer, the geometry shown in Figure 6 is modeled in COMSOL Multiphysics.
The accuracy of the simulation results in finite element methods (FEMs) is highly dependent on the mesh resolution considered. The higher the density of the mesh elements, the more accurate and reliable the simulation results. However, using an extremely high-resolution meshing for the whole geometry results in a need for lots of memory resources and time-consuming simulations. To address the aforementioned issue, three zones (as shown in Figure 7a) with different mesh sizes were defined. An extremely dense meshing with a maximum element size of 4 µm was used for zone 1, which incorporated all sharp edges. The maximum mesh element sizes of 10 and 400 µm were also used for zones 2 and 3, respectively.
Another parameter that affects the accuracy of the simulation results is the mesh dependency of the electric field at the regions close to the sharp edges and material boundaries. Thus, to address this issue, the electric field measurements are carried out at measuring lines L1 (in AlN substrate), L2 (in nonlinear FDC layer), and L3 (in silicone gel), as shown in Figure 7b, where the lines have a minimum distance of 15 µm from interfaces. bottom metallization layer is grounded. Thus, to simulate the real PD test condition, a 50 Hz AC voltage with a maximum amplitude of 7.15 kV was applied to the HV electrode. However, for Cases 1-4, in which the frequency is higher than 50 Hz, we followed the same procedure as the standard test for PD, by only changing the frequency of the applied voltage from 50 to 450 Hz in Cases 1 and 3, and to 1 kHz in Cases 2 and 4. The electrical parameters discussed in Section 2 were used for the simulations. The maximum value of , , along L1-L3 for case studies is presented in Table 1.  As seen in Table 1, the electric field reduction method as the protruding substrate design combined with the application of a nonlinear FDC layer is almost temperature-and frequencyindependent in the 22-160 °C and 50-1000 Hz range. The simulations were carried out for a WBG power module with a blocking voltage of 6.5 kV. According to IEC 61287-1 for PD measurements, a 50/60 Hz voltage with a peak of 1.1U b , where U b is the blocking voltage of the power module, must be applied to the top metallization, while the bottom metallization layer is grounded. Thus, to simulate the real PD test condition, a 50 Hz AC voltage with a maximum amplitude of 7.15 kV was applied to the HV electrode. However, for Cases 1-4, in which the frequency is higher than 50 Hz, we followed the same procedure as the standard test for PD, by only changing the frequency of the applied voltage from 50 to 450 Hz in Cases 1 and 3, and to 1 kHz in Cases 2 and 4. The electrical parameters discussed in Section 2 were used for the simulations. The maximum value of E, E max , along L1-L3 for case studies is presented in Table 1. Table 1. E max at L1-L3 for the geometry of Figure 6 for the base case and Cases 1-4. As seen in Table 1, the electric field reduction method as the protruding substrate design combined with the application of a nonlinear FDC layer is almost temperature-and frequency-independent in the 22-160 • C and 50-1000 Hz range.

Case
The model and method developed in Section 3, and the measurement data used in Section 2, can be used for power modules with various blocking voltages and other geometrical electric field reduction techniques and especially for practical designs and applications.

Conclusions
In practice, the insulation materials of envisaged WBG power modules are exposed to square wave voltage pulses with a frequency up to a few kHz and temperatures up to a few hundred degrees. Temperature and frequency are two important factors that usually affect the electrical characteristics (relative permittivity and AC electrical conductivity) of the dielectric materials and they may influence electric field distribution. The electric field simulations and calculations reported in the literature to date ignore the frequency and temperature dependency of ε r and σ ac for the insulating materials used in the power modules. Therefore, there is doubt about the validation of results for high temperatures and high frequencies. This paper addresses this technical gap through: Simulations using the model and measurement data described above, where it was found that the effectiveness of our proposed electric field reduction method as protruding substrate combined with the application of a nonlinear FDC layer is not affected.
For further research, ε r and σ ac of AlN, silicone gel, and the ZnO microvaristor-silicone compound are needed to be measured up to a few ten/hundred kHz and high temperatures of up to 250 • C, as these are the envisioned conditions for next-generation WBG power modules. Then using the measurement data, the influence of frequency and temperature up to the mentioned ranges can be studied by the method presented in this paper. Another technical gap is that all ε r and σ ac values reported in the literature for different frequencies are under an AC sinusoidal voltage; however, insulating materials within power modules are under square waveforms. We do not know whether or not results will be different under square waveforms.