PD measurements, failure analysis, and control in high‐power IGBT modules

Increased voltage blocking capability and the development of packaging technology for IGBTs can enhance the local electric field that may become large enough to increase partial discharges (PDs) within the module. The study presents a survey on (i) simulation the electric field within an IGBT module; (ii) current standards for evaluation of the insulation systems of IGBTs; (iii) PD detection and localisation methods as well as other diagnostic and quality control test methods about IGBTs; and (iv) various methods for PD control in an IGBT module. The survey shows remarkable technical gaps in all four areas. More sophisticated numerical and theoretical techniques are needed to model complicated geometries, e.g. extremely sharp edges of the copper metallisation and protrusions in the substrate, and composite non-linear field grading materials. There is no model to take into account defects in the gel and on the ceramic substrate. IEC 61287-1 cannot sufficiently assess the behaviour of PDs on IGBT module under the actual operating conditions exposing fast rise pulse-width modulation-like voltages. There is no agreement on the exact origin and location of PDs in the module with relying on measured phase-resolved PD patterns. PD control methods using non-linear grading materials are not mature enough.


Introduction
The rapid growth of renewable energy, the continuing trend toward higher electrification and grid-level power flow controls calls for a dynamic and increasingly important role for power electronics [1]. However, for evolution in power electronics, the evolution of power semiconductor devices is needed where simultaneous operation at high-power and high-switching frequency is the primary challenge. The advent and development of silicon (Si)based-insulated gate bipolar transistors (IGBTs) with a broad range of voltage from 300 V to 6.5 kV, and current handling capability larger than power metal-oxide-semiconductor field-effect transistors have been a response to the mentioned challenge. Moreover, due to the low expenditure required for activating and wiring IGBT modules compared with gate-turn-off thyristors (GTOs) as well as their excellent electrical properties, GTOs used for very high-power applications will soon be ousted by IGBT modules as well. High-power IGBT modules are used as switches in static converters for applications such as generating a sinusoidal current by pulse-width modulation (PWM).
Regarding the outstanding properties, commercial availability of starting material, and maturity of the technological processes, Si carbide (SiC) and gallium nitride (GaN) with a relatively large bandgaps of 3.3 and 3.4 eV, respectively, are the more promising semiconductor materials known as wide-bandgap (WBG) semiconductors. WBG semiconductors including WBG-based IGBTs which are expected to have better efficiency, highertemperature tolerance, and higher-voltage blocking capability than their Si counterparts having a bandgap of 1.1 eV are changing the landscape of power electronics industry. Moreover, a new class of semiconductor materials so-called ultra WBG (UWBG) semiconductors with bandgaps higher than that of GaN including diamond (C), gallium oxide, and aluminium nitride (AlN) currently investigated will be generation-after-next power electronics [2]. WBG-and UWBG-based devices including WBG-and UWBGbased IGBTs can achieve higher switching frequencies, higher temperatures, higher-voltage hold-off, and lower-energy loss due to short switching transitions.
Insulated IGBT modules are now available in industry standard package dimensions with maximum blocking voltage up to 6.5 kV and currents reaching more than 2000 A [3][4][5][6]. About 6.5 kV is the maximum DC voltage which can reach between collector and emitter with gate terminal shorted to the emitter. However, withstanding higher voltages beyond 6.5 kV especially for WBG devices is expected in the future. Increased blocking voltage of IGBTs can cause the local electric field inside that where it may become large enough to induce partial discharges (PDs) in the silicone gel. The silicone gel is used to insulate conductor parts in the module and encapsulate the module. High PD damages the insulating silicone gel and leads to electrical insulation failure and reduces the reliability of the IGBT module. Moreover, highfrequency PD pulses can lead to disturbance of the power electronics and cause severe failures in high-power applications. Therefore, the PD issue calls for the demands of PD control for packaging of power electronics modules. This topic is reviewed in this paper.

Structures of a metallised ceramic substrate of an IGBT module
PWM voltage source variable frequency drives (VFDs) are the most widely used motor controllers, and IGBT is the most used power semiconductor in these drives. Fig. 1 shows a type of structure for a metallised ceramic substrate of an IGBT module, where the substrate is soldered to a base plate and IGBTs or diodes are soldered onto the metallisation. IGBTs or diodes are mounted on a metallised ceramic substrate to evacuate the heat generated by them toward heat dissipating system. Thus, substrates are chosen based on their electrical insulation properties under high voltage, thermal properties (resistance to high temperatures and good thermal conductivity), and mechanical properties (dilatation coefficients as close as possible with the other materials). The substrate materials frequently used are AlN and alumina (Al 2 O 3 ). In this regard, AlN is preferred to Al 2 O 3 for its outstanding thermal and mechanical properties. AlN ceramic has a thermal conductivity of typically 180 W/mK, whereas for Al 2 O 3 ceramic is 27 W/mK. Measurements in [7] showed that the thermal resistance of the AlN substrates assembled with IGBTs has values less than that of Al 2 O 3 substrates by a factor >3. Attaching the copper metallisation to the ceramic substrate can be done by direct bonded copper (DBC) or active metal brazing (AMB). Fig. 1 shows AMB method. No braze layers are needed for DBC as shown in Fig. 2. The substrates are then soldered onto copper or AlSiC base plate, which acts as the mechanical support and ensures good thermal diffusivity as the base is coupled to the cooler. The ceramic substrate of the module provides electrical insulation between the heat sink and the high voltages on the substrate's topside. The whole module is encapsulated by a soft dielectric such as silicone gel to prevent electrical discharges in air from occurring, to protect semiconductors, substrates, and connections against humidity, dirt, and vibration. Silicone gel also prevents thermal induced movements of bond wires attached to the semiconductor. The final encapsulation is achieved using a polymer housing.
Owing to the high electric fields in particular at the edges of the copper metallisation, PDs can be initiated from these regions. The worst situation is protrusions with extremely sharp edges of some braze below the metallisation in AMB as shown in Fig. 3. The various methods to reduce high electric fields along two critical edges have been investigated. These methods are evaluated in depth in Section 6.
3 Simulation of maximum electric field magnitudes inside an IGBT Experiments show that PD does not occur all along the sharp edges. This is because a combination of material defects and the high electric field magnitude leads to PD. To the best of my knowledge in simulations of the electrical field distribution inside IGBT module/substrate reported in the literature, materials' defects have not been modelled and simulated so far. However, identifying the critical spots with the maximum electric field magnitude due to only sharp edges can be useful to develop strategies to reduce the electric field magnitude peaks due to the effect of one contributing factor. Electrostatic electrical field simulations for determining the electrical field distribution inside a power module were carried out in [8][9][10][11][12][13][14][15][16][17].
Note that the maximum electric field magnitude at perfectly sharp edges is infinite leading to mesh-dependent maximum electric field magnitude values. As the grid cell size decreases, the electric field magnitude peak increases and mathematically there is no convergence point. Although assuming a rounded edge converges to a finite maximum electric field magnitude with increasing resolution of the mesh grid, the value depends on the assumed edge radius. The smaller assumed edge radius, the higher amount of maximum electric field magnitude. To address this issue, four lines of measurement including two starting at the upper metal edge (ML1 and ML2) and two starting at the lower metal edge (ML3 and ML4) as shown in Fig. 4 are considered in [8,10]. Fig. 4 is the studied section shown in Fig. 2.
The electric field magnitudes along the measuring lines were calculated in [8,10] for different mesh grid sizes for relative permittivity values of 8.9 and 2.7 for AlN and silicone gel, respectively, and the voltages of 10 kV and 0 for the upper and lower metal layers, respectively, and for a 1 mm ceramic layer and 300 μm thickness for upper and lower copper metallisations. It was shown that when the distance to the edge becomes larger than 20 μm, the differences between the electric field magnitude profiles are <1%. To be on the safe side, a distance of 50 μm to the edge along ML1-ML4 is selected as measuring points for the electric field magnitude shown as red circles in Fig. 4. A rounded edge was considered in [9,[11][12][13][14][15][16][17] for calculating electric field magnitudes.
To study the benefit from applying non-linear field grading materials to relieve high electric field regions especially at protrusions, finite element simulations were used in [9] as shown in Fig. 5. As shown in Fig. 5, the sharp edges at the edges of the copper metallisation and protrusions are rounded with a radius of 30 and 5 µm, respectively, to reach convergence points for the maximum electric field magnitudes as explained above. The coating layer as shown in Fig. 5 is a 30 µm thick and 2 mm long layer considered in finite element method (FEM) model that is discussed more in Section 6.3.

Present standards for evaluation of the insulation system of power electronics modules
The current standard commonly used for IGBT working at 1.5 kV or more is IEC 61287-1 [18]. The applied voltage is an AC root mean square voltage (50 or 60 Hz) equal to 1.5U m / 2 or higher, where U m is the maximum blocking voltage of the module. For a 6.5 kV IGBT, it is 1.5 × 6.5/ 2 ≃ 6.9 kV. The voltage is ramped up to 1.5U m / 2 in 10 s, and is maintained for t 1 = 1 min as shown in Fig. 6. During this time t 1 , some PDs may be observed. After t 1 ,   the voltage is decreased to 1.1U m / 2 in 10 s. For a 6.5 kV IGBT, it is 1.1 × 6.5/ 2 ≃ 5.1 kV. The voltage 1.1U m / 2 is applied for t 2 = 30 s. During the last 5 s of t 2 , the level of PD is measured. A typical value to pass the test for a component and a subassembly is 10 and 50 pC, respectively.
However, IGBT modules are subjected to PWM stress type and the studies in [19][20][21] show that PD behaviour under 50 or 60 Hz AC sinusoidal voltage is different from fast rise bipolar highfrequency square wave voltages. Thus, it calls a need for new standards to consider an actual test voltage for power electronic modules.
In IEC 61287-1, the main terminals of a power electronics module including collector, emitter, and gate are connected, and PDs are measured when an alternating voltage is applied between the interconnected terminal and the metal base plate. The drawback is that it tests only the insulation of the substrate and other insulation systems, e.g. those associated with the encapsulation of the components are not tested. In [22][23][24], a new testing method for detection PD problems in a power electronic module was proposed that leads to detect PD for voltages lower than the one necessary to trig them during IEC 61287-1 test. The test voltage is an AC voltage superimposed on a DC one that is directly applied to the component turned off using a negative gate polarisation. The inverse DC offset of magnitude greater than the AC peak value used as the test voltage avoids diode conduction. Although neither the test proposed in [22][23][24] nor IEC 61287-1 test can represent thoroughly the stresses endured by the power modules in inverters, the testing method proposed in [22][23][24] can provide useful information on PDs during normal operation by stressing all the components involved in the packaging.

PD measurements
Research done on PD localisation inside an IGBT can be divided into electrical and optical PD measurements. For electrical PD measurement, measured phase-resolved PD (PRPD) patterns were analysed in [10, 11, 13-16, 19-23, 25-27] to identify the type and location of PD. In a PRPD pattern, the apparent charge of PD events is synchronised with the AC test voltage. It was observed in [13,14] that the PD of a metallised ceramic in an isolating liquid occurs at the maximum voltages at 90° and 270° and the amount of PD does not rise sharply with increasing voltage. However, for the same metallised ceramic embedded in silicone gel, PD was found at a phase between zero and maximum voltage between 0-90° and 180-270° and as the number and magnitudes of the PDs strongly increases with rising voltage, it was argued that the origin of this discharge phenomenon is due to discharges at the interface between the silicone gel and the substrate and not due to locally restricted cavities in silicone gel. Thus, it was emphasised in [13,14] on the need for the silicone gel to adhere well to the substrate as well as the improved etching process. In [27], silicone gel was used as an insulating material between two spherical electrodes with a radius of 5 mm separated by 3 mm. By an injection syringe, a spherical void of a diameter 1 mm was implemented in the middle of two spherical electrodes. A PD-induced breakdown at a voltage (11 kV) of only 1.5 kV above inception voltage (9.5 kV) and far below the breakdown strength of the material (15 kV/mm) was observed. Its apparent charge-ageing time curve is similar to that for epoxy resin with a high apparent charge of about 200 pC at the beginning of the ageing period that decreases to about 0 pC after a few hours and remains there for several days, and then it increases slightly to about 10 pC leading to the breakdown. Thus, it was concluded in [27] that voids inside the silicone gel significantly accelerate the ageing of the materials even at a normal operating electric stress. It was also found that an extremely nonuniform electric field resulted by a needle-sphere electrode with no artificial void inside the material can also lead to rapid ageing at a normal operating electric stress. In this case, it is thought in [27] that the electrical treeing in front of the needle tip produces gasfilled voids inside the silicone and these weak points besides conductive channels of trees lead to shortening the lifetime of the insulation.
In [10], a linear function as PD Inception Voltage (PDIV) (kV) = 20.4−0.35E(kV/mm) was obtained, where E is the arithmetic mean of MaxA and MaxB. MaxA is the maximum electric field calculated at MP1 and MP4. MaxB is the maximum electric field at MP2 and MP3. MP1-MP4 are the points shown in Fig. 4 and described in Section 3. PDIV in the mentioned function is the PD inception voltage measured for three different thicknesses of the Indeed, a correlation of electric field magnitude simulations with PRPD measurements as the above function was obtained in [10]. However, it should be noted that PRPD measurements in [10] are for the dielectric liquid instead of the silicone gel.
In [15,16], an optical PD localisation setup benefitting from compact charge-coupled device camera modules was used to record the small light intensities emitted by electroluminescence effects as well as the light caused by PD. It should be noted that before PD inception, insulating polymers subjected to high electrical fields usually display electroluminescence as a result of the radiative relaxation of excited molecular states within the gel excited by high electrical field [16]. The measurement of electroluminescence allows the critical regions of high electric fields to be identified in the translucent silicone gel insulation even before electrical ageing begins. Increasing the voltage, PD starts at distinct locations. Bright shining spots in the image show the higher possibility for PD inception. Optical localisation of PD of AlN and Al 2 O 3 substrates embedded in silicone gel or liquids was also reported in [12,19,20,25,26,28]. In [26,28], the results concerning both electrical and optical detection of PD's occurring in the silicone gel were presented. That work showed that optical measurements could be used to study PD's in transparent gels, with any voltage shape and with very high sensitivity (<1 pC).
It was shown in [29,30] that besides PRPD measurements, time-dependent dielectric response measurements such as insulation resistance and polarisation index, and frequency-dependent dielectric response measurements such as loss factor and frequency response analysis (FRA) can also be used as diagnostic and quality control test methods to discriminate the dielectric condition between new and aged IGBT samples and reveal the influence of moisture on dielectric condition of IGBT modules. Humidity as a result of the condensation caused by the difference in the interior and exterior temperatures may impact on the dielectric integrity of IGBT modules. For five identical samples of IGBT modules rated 3.3 kV and 1200 A, it was found in [29] that the presence of moisture reduces the insulation resistance of samples from a range of 1-3 TΩ under a dry condition to a range of 0.23-0.78 TΩ under M85-85 condition. M85-85 is denoted as placing the samples in a climate chamber for at least a week at 85°C temperature and 85% humidity. The polarisation index defined as the ratio of insulation resistance measured at 10 and 1 min., proportional-integral (PI) = R10min/R1min, of samples also reduces considerably from 2.6-3.5 under a dry condition to 1.5-2 under M85-85 condition. Moreover, the presence of moisture can introduce a significant increase in the loss factor of IGBT samples throughout the test frequency span of 100 µHz-100 kHz in particular at a very low frequency. FRA also shows that the presence of moisture can cause a remarkable left shift of the resonant peak. The tests carried out on 6.3 kV, 600 A IGBT samples show that PIs measured at 60 and 15 s (PI = R60/R15) of aged samples are higher ranging 3.0-3.5 than new samples ranging 2.0-2.5. Also, the insulation resistance of aged samples is higher ranging 1 (at 10 s)-3(at 600 s) TΩ than new samples ranging 1 (at 10 s)-8(at 600 s) TΩ. Moreover, the insulation resistance of new samples reaches a steady state beyond 150 s while the aged samples did not reach steady state after 600 s. However, further investigation is needed to determine permissible levels for the mentioned dielectric and diagnostic test methods for IGBT and other high-voltage high-density power electronic modules.
In [19,20], PDs in liquid embedded power electronics under three different waveforms as sinusoidal (50 Hz) voltage, a slow rise bipolar square voltage with a rise time of 400 μs, and a fast unipolar positive and negative rise square voltage with a rise time of 100 ns were investigated. Both electrical and optical techniques were used to study PD behaviour of IGBT insulation. Since AlN is electroluminescent and has a porous nature leading to produce light at voltages below PDIV as found in [25], a printed circuit board which is non-electroluminescent was used in [19,20] for optical PD studies in the pressure test cell shown in Fig. 7.
Converters are often located in cubicles under atmospheric pressure, and the most widely used material for encapsulation of power electronic circuits is silicone gel. However, for VFD fed motors used in the subsea factory for oil and gas production at depths more than 3000 m, the development of pressure tolerant power electronics is envisaged where an incompressible insulating material is needed for power electronic modules. Thus, liquid embedded power electronics are investigating as shown in Fig. 7, where the cell was filled with mineral oil. A pressurisation system capable of producing pressure up to 100 bar was used in [19,20], where Fig. 8 shows its pressure vessel.
Regarding a good correlation found in [19,20] between the measured electrical and optical PDs, optical PDs can also be considered for the characterisation of PD phenomena. Another significant result obtained in [19,20] is that the fast rise square voltage has the lowest PDIV while the sinusoidal voltage has the highest one as shown in Fig. 9.
Moreover, it was reported in [19,20] that the number and magnitude of PDs decrease when the pressure of the liquid in the test cell increases as shown in Fig. 10. In other words, pressure can collapse the propagation of the streamers, and that is the great merit of liquid embedded power electronics used for the subsea application.

Geometrical electric field control
Assuming the measuring points introduced in Section 3 for the electric field magnitude values, the influence of following geometrical options are examined in [8] on reducing the electric field magnitude values: i. The thickness of the metallisation layer. ii. The thickness of the substrate. iii. The shape of the edge. iv. Metal/conductive layer offset. Among four parameters above, the thicknesses of the substrate and metal/conductive layer offset have a strong influence on the electric field magnitude. By varying the thickness of the ceramic, the electric field strength does not follow the equation of a plate capacitor: a doubling of the thickness (1 to 2 mm) reduces the electric field strength in MP1/2 only by about 30% and not by 50% [8]. However, an increased substrate thickness decreases cooling efficiency of the semiconductors, and this technique may not meet the miniaturisation needs of power electronics as well.
Defining an offset of the two metallisation layers as r off = r u − r l for r u and r l shown in Fig. 4, Fig. 11 shows the electric field magnitude values at the four measuring points for different values of r off in the range from −2 to 2 mm for a 1 mm ceramic layer. It can be seen that with decreasing offset the electric field magnitude at the upper edge at ML1 is reduced while the electric field magnitude at the lower edge at ML4 increases. The electric field magnitude values meet at an offset of about −0.9 mm. Fig. 12 depicts the offset for which the lowest-peak electric field magnitude for both ML1 and ML4 is reached for different substrate thicknesses.

Linear resistive electric field control
Applying functional materials on the highly stressed region can reduce the electric field. Two types of stress relieving composite dielectrics are as follows: (i) the conductivity of the material varies with the electric field [field-dependent conductivity (FDC)] and (ii) the permittivity of the material changes with the electric field [field-dependent permittivity (FDP)]. We evaluate the FDC type in this section and Section 6.3, and the FDP type in Section 6.4.
In FDC stress relieving control or also called resistive field control, a conductive layer is applied at the metallisation edge. The field distribution is modified by flowing the conduction current through the layer. Materials used for resistive field control can be a linear or non-linear. The conductivity of linear resistive field control materials is not field dependent. Therefore, the conductivity of the layer made of linear materials must be carefully selected. If the conductivity is too low, it does not affect. For too high conductivity, the layer either behaves as a prolongation of the metallisation, and the high field problem is merely transferred to the end of the layer for the case of a non-bridging layer or leads to massive leakage current for the case of a layer bridging high voltage and ground potential.
In [35], a 300 nm high-impedance layer made of semiconducting amorphous Si, a-Si:H, was applied by plasmaenhanced chemical vapour deposition process to the edge of the substrate connecting the top copper metallisation with the bottom one as shown in Fig. 13. To homogenise the electric field, the magnitude of the conduction current should be higher than the capacitive current. To achieve that, the electrical conductivity of the layer was adjusted to 10 5 Ω cm [35]. The same value of the electric conductivity of the layer was obtained in [11,12] through electrostatic electric field simulations.
To study the influence of a-Si:H coating on the PD behaviour, two modules with and without a-Si:H coating were built under   manufacturing conditions in [35]. As shown in Fig. 14, while the PD increases sharply at low voltages of 3-4 kV without an a-Si:H coating, it does not exceed 10 pC up to a voltage of 10 kV with an a-Si:H coating layer satisfying the PD requirements based on IEC 61287-1. However, it should be noted that the linear resistive field control depends on the frequency and its advantage reduces with increasing frequency.

Non-linear resistive electric field control
The intrinsic semi-conductive nature of the particles and their connectivity lead to non-linear behaviour of non-linear resistive electric field control composites. In this regard, the particle-toparticle contact is possible if the filler concentration is above a prescribed limit. The electrical field magnitude must also be high enough to allow conduction through the semi-conductive particles and barriers between particles. In this section, we first focus on how to deal with the non-linearity relation of these composites when calculating electric field distribution. For quasi-static fields which is the case for all high-voltage field calculations for insulation systems, there are slowly timevarying field quantities, but their coupling is so weak that ∇ × E = − ∂B/∂t = 0. To solve Maxwell equations in the quasistatic formulation in the domain Ω shown in Fig. 15, assume an arbitrary number of dielectrics D i i = 1, …, N D , conductors C i i = 1, …, N C and non-linear resistive stress grading materials S i i = 1, …, N S are present.
In the quasi-static model of Maxwell equations, the electric field E is represented by a scalar potential function V From the Ampere-Maxwell equation, we have where J is the conduction current density and D is the electric displacement. The electric displacement D in linear isotropic materials is related to the electric field as The current density J and the electric field can be related to nonlinear materials S i i = 1, …, N S by where σ E is an FDC. Substituting (1), (3), and (4) into (2) gives (5) for all points in the non-linear regions S i To solve the problem numerically, (5) can be discretised by applying the backward Euler method where t is the time and Δt is a suitable small time interval. Equation (6) can be rewritten as A Galerkin method was developed in [36,37] to solve (7). As another method, the non-linear equation (4) was directly implemented in the FEM tool [9]. A basic understanding of the behaviour of field grading materials with strongly field-dependent conductivities has been provided in [38]. A survey of such nonlinear grading materials with a focus on ZnO microvaristors can be found in [39]. In [9], ZnO microvaristors were examined to reduce local enhancement at protrusions of some braze below the metallisation in the AMB in an IGBT. For a non-linear material, losses are not permanent. They occur when the electrical field magnitude passes a threshold known as switching field, where the material switches to a conductive behaviour. However, losses are permanent for linear resistive field grading materials. Assume the geometry shown in Fig. 5 without a coating layer. The maximum electric field was calculated 2.6 MV/cm that is around three times higher than the reported field magnitude of silicone gel [40] and the module would likely fail the PD test.
Owing to the excellent intrinsic properties such as thermal stability (weight losses <1% at 500°C), relatively low losses especially at higher temperatures (tan δ < 10 −2 ) and thermomechanical matching with components, polyimide (PI) was investigated as SiC power device passivation layer at high operating temperatures [41][42][43]. In [43], the dielectric breakdown field of PI films for 25-400°C under DC ramps for a range of area from 0.0707 to 19.635 mm 2 and thickness from 1.4 to 6.7 μm was studied. It was observed that breakdown field value of PI shows a decrease in increasing area, thickness, and temperature, but always remains above 2 MV/cm. At the room temperature (25°C) and for an electrode area of 1 mm 2 , breakdown field value of PI was reported 5 MV/cm in [43] while that for the same temperature and electrode area for silicone gel was around 0.8 MV/cm [40]. The mentioned breakdown field values are under the uniform field. The 0.8 MV/cm value obtained with spheres electrodes under 50 Hz AC, DC, and 50 Hz unipolar positive impulse [40]. However, under divergent field caused by needle-plane geometry, the breakdown field value decreases with increasing the tip radius of the needle. In other words, the smaller electrode area, the higher breakdown field value for silicone gel. Moreover, the experimental results obtained in [40] propose different pre-breakdown mechanisms in silicone gel and insulating liquids such as silicone oil and admit the need for further research. It should be noted that the protrusions make divergent fields. However, comparing with the breakdown field values for the uniform field, it can be seen that PI has higher breakdown strength than silicone gel. Therefore, coating the metallisation edges with PI may be one possible way to mitigate the problem of field enhancement at protrusions or other defects. The results from a simulation with a 30 µm thick PI coating (ε r = 3.5) are summarised in Table 1 [9]. This table presents the results for a high permittivity (ε r = 40) layer of polymer/ceramic composites [44] as well. The relative permittivity of the polymers without ceramic loading is ranged from 2.8 to 4.6. Loading a ferroelectric ceramic particle, e.g. lead magnesium niobate-lead titanate into a polymer, e.g. polyacrylic acid, a polymer/ceramic composite with a high relative permittivity of 40 produced [44] whose relative permittivity is in a good agreement with the theoretical equation by Jayasundere and Smith given by [45] ε eff = ε p v p + ε c v c 3ε p / ε c + 2ε p 1 + 3v c ε c − ε p / ε c + 2ε p v p + v c 3ε p / ε c + 2ε p 1 + 3v c ε c − ε p / ε c + 2ε p (8) where ε eff , ε p , ε c , v p , and v c are the relative permittivity of the composite, polymer, ceramic, the volume fraction of the polymer, and volume fraction of the ceramic, respectively. Although the mentioned polymer/ceramic composite can reduce the maximum electric field, the electric field in the gel reaches higher values than with PI coating.
The non-linear resistive coating layer can efficiently solve this problem. The dependency of the resistivity on the electric field of the model material used in [9] is shown in Fig. 16. Another significant result reported in [9] is that the highest value of the electric field in the non-linear layer does not occur at peak voltage that is due to the space charge formation in the non-linear materials generating an internal field [35].

FDP stress relieving control
Using a high-permittivity layer moves high field values toward the low-permittivity gel and especially the weak interface between the layer and the gel encapsulation. Thus, refractive electric field control method as a coating layer does not work. The problem was solved in [17] through the inclusion of a ferroelectric filler, barium titanate, in the base silicone gel to form an FDP stress relieving dielectric material. The ferroelectric filler particles enhance polarisation mechanisms leading to reduce high electrical stresses. However, this advantage has two limits. First, the mentioned stress relieving merit disappears above a specific temperature known as the Curie point. For pure barium titanate, it is ∼130°C [46]. However, the Curie point in a filled gel increases and is above the maximum junction temperature of IGBT devices of 150°C in the transistor and 125°C in the diodes [17]. Second, the advantage is only realisable under AC fields.
Since an unfilled silicone gel sample is capacitive, the current flowing through is purely sinusoidal without any distortions. However, for a 15% barium titanate filled sample, the current has significant harmonic distortion presenting the following non-linear relation obtained in [17] between the electric field magnitude and current density: and (9) leads to the following relation: Fig. 17 shows the maximum electric field magnitude as a function of the applied voltage for three different types of gels. They are as (i) a plain silicone gel with a permittivity of 2.7; (ii) the filled gel with a fixed permittivity of 6.4; and (iii) the filled gel with the permittivity modelled by (10). As it can be seen in Fig. 17, an enhanced fixed permittivity reduces the maximum electric field within the module by around 10% while that for a non-linear performance of the filler given by (10) is 24% at 6 kV and 29% at 12 kV. Increases of 53 and 60% were reported for 15% barium titanate filled samples produced under laboratory and factory conditions, respectively [17].
It should be noted that using a filled gel method used in [17] cannot be applied for field-dependent conductive dielectric materials, where a high filler rate is needed to guarantee a particle- to-particle contact. Since an increase in the rate of the filler increases viscosity dramatically. In this regard, the viscosity of the filled gel with 15% by volume of barium titanate increases by five times that is a significant increase. However, the filled composite was still capable of being poured into the module and flowed well through the module.

Using 'good' substrates
In [25], it was doubted about the conclusion that PDs recorded with embedded substrates occur in the gel. To determine the actual origin of PDs, the influence of changing the nature of both substrate and coating materials on PD measurements was investigated. Gel was replaced by six insulating liquids [Si oil #1(Sil20), Si oil #1(Sil350), transformer oil (Toil), synthetic capacitor liquid (Scl), synthetic transformer liquid (Stl), and ester liquid (Est)] having different PD properties, and three substrate materials (AlN, Al 2 O 3 , and glass/epoxy composite) were also tested. First, a point-plane electrode geometry under 50 Hz AC voltage at room temperature (20°C) was used for tests and PDIV for six mentioned liquids showed rather a large variation. However, a substrate test geometry similar to an IGBT including a metallised ceramic substrate shows almost no changes in PDIV for the mentioned different liquids. Moreover, though PDs appear in both polarities and provide rather symmetrical patterns with a very good stability for the IGBT test geometry, PRPD patterns for the pointplane electrode geometry varied asymmetrically. Using the gel in the mentioned experiments produces no change. Therefore, it was concluded in [25] that PDs recorded with the substrate indeed do not occur within the liquid or the gel. The only remaining possibility is that PDs originate from the porous nature of the AlN or Al 2 O 3 substrates, i.e. a hypothesis opposed to the ideas commonly accepted in such situation. The experiments carried out with another sintered porous material, and with a non-porous material (epoxy resin) confirm this hypothesis. With epoxy, no stable PD regime can be achieved.

Three-dimensional (3D) module layout
This electrical field reduction solution is based on a 3D module layout as shown in Fig. 18 and in particular to limit the voltage reinforcement due to the proximity between the copper layers deposed on the top side of the substrate. However, it should be noted that this method leads to an increase of 20% in stray inductance [11].

Conclusion
The technical gaps identified on PD measurements, failure analysis, and control in high-power IGBTs are as follows. Modelling of perfectly sharp edges when using an FEM model is a challenge and needs further research. Modelling non-linear field grading materials as a coating layer or a filler in the silicone gel in FEM-based tools is another challenge, where Galerkin method was proposed as an alternative solution to model such complex structures. PRPD patterns can be used to identify the origin and location of PDs. However, the hypotheses proposed based on the measured patterns have not reached an agreement. Further investigation is needed to determine permissible levels for timeand frequency-dependent diagnostic methods for IGBT modules. The optical technique is a promising technique to localise PDs in a power electronics module. Moreover, various PD control methods including geometrical techniques, using linear and non-linear resistive electric field controls as a coating layer or using FDP materials as a filler in the silicone gel were evaluated as well. These methods are immature and need further research.