# Intrinsic AC Dielectric Breakdown Strength of Polyimide Films at the Extreme: New Breakthrough Insights on Thickness Dependence

Sombel Diaham, Paul Lambkin, Lawrence O'Sullivan, Baoxing Chen

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Sombel Diaham, Paul Lambkin, Lawrence O'Sullivan, Baoxing Chen. Intrinsic AC Dielectric Breakdown Strength of Polyimide Films at the Extreme: New Breakthrough Insights on Thickness Dependence. Advanced Materials Interfaces, 2024, 11 (5), pp.2300822. 10.1002/admi.202300822. hal-04777964

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# Intrinsic AC Dielectric Breakdown Strength of Polyimide Films at the Extreme: New Breakthrough Insights on Thickness Dependence

Sombel Diaham,* Paul Lambkin, Lawrence O'Sullivan, and Baoxing Chen

To date, the AC dielectric breakdown strength of polyimide (PI) films, as for most polymers, is understood to follow a thickness dependency with a measured power law exponent, $n \approx 0.5$. However, this work experimentally demonstrates that the AC dielectric strength of PI films is quasi-thickness independent. Evidence is presented showing that the thickness dependency described in the literature can be explained by an extrinsic failure mode, driven by partial discharges occurring at the dielectric-oil-electrode triple point. Triple points can be avoided by electrode encapsulation, which subsequently recovers a purely intrinsic failure mode for PI films over a large thickness range. Consequently, the AC dielectric strength of thick PI films is intrinsic and quasi-thickness independent, at least for film thickness up to 60 µm. For the first time, a “theoretical” AC breakdown field for PI films is reported as $\approx 520 V_{rms} \mu m^{-1}$. Finally, the highest experimental breakdown field values are obtained here with 505 $V_{rms} \mu m^{-1}$ and 705 $V \mu m^{-1}$ under AC and DC fields, respectively.

## 1. Introduction

The electrical breakdown strength of insulating polymers has been a focus of study for decades[1,2] driven by a need to optimize electrical power systems and electronic devices for performance and long-term reliability. This pressure continues to grow

S. Diaham
LAPLACE
Université de Toulouse
UPS
CNRS
Toulouse France, 31062
E-mail: sombel.diaham@laplace.univ-tlse.fr

S. Diaham, P. Lambkin, L. O'Sullivan
Analog Devices International
Limerick, Ireland V94 RT99
B. Chen
Analog Devices Inc.
Wilmington MA, USA, 01887

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/admi.202300822

© 2023 The Authors. Advanced Materials Interfaces published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/admi.202300822

with the deployment of higher operating voltages in smaller volumes leading to severe requirements for the insulating materials in use.[3] Consequently, for solid dielectrics, a deeper understanding of the breakdown field strength ($E_{BD}$), failure mechanisms and the dependence on thickness (d), is increasingly important as materials are used closer to their intrinsic physical limits.

Many experimental and modeling studies on the thickness dependence of the dielectric breakdown strength ($E_{BD}(d)$) have been reported for many polymers with at least four different expressions identified.[4–6] A major state-of-the-art review, reported by Zhao and Liu[6] concluded that: i) there is no unique relationship between $E_{BD}$ and thickness, ii) the underlying mechanism responsible for a thickness dependence

is not well understood and iii) the valid range of thickness for some $E_{BD}$ expressions remains unclear. That said, the dependence on thickness can be divided into two regimes where: i) $E_{BD}$ is independent of thickness (i.e., $E_{BD}(d) = const$), in which case the breakdown is classified as intrinsic, otherwise; ii) the breakdown is extrinsic[5–7] with additional factors giving thickness an influence. A transition thickness ($d_t$) can then be defined that separates these functional dependencies. For polymers, the transition $d_t$, which ultimately depends on the set-up, has been determined,[5] albeit imprecisely, between 10 and 100 µm. The intrinsic breakdown ($d < d_t$) represents the maximum breakdown strength of the dielectric material. In the case of an extrinsic breakdown ($d > d_t$), a decreasing tendency of $E_{BD}$ with increasing thickness is mostly reported in the literature. Usually, an inverse power law describes the thickness dependence of the extrinsic breakdown field strength[4]:

$$E_{BD}(d) = kd^{-n} \quad (1)$$

where d is the thickness of the dielectric material, n is the power exponent, and k is a constant associated with the material under test.

For most polymers (but also for inorganic dielectrics), n ranges from 0 to 1, depending on voltage waveform conditions (DC, AC, or impulse), even though many publications highlight an average around $n \approx 0.5$.[6] The scatter in the reported n, makes correlation
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Reported electrical breakdown strength of polyimide as a function of thickness in a single-layer configuration under AC (rms) and DC fields. Temperature, surrounding environment conditions and publication sources are detailed in the legend.</figcaption></figure>

to specific failure mechanisms problematic. Focusing on the AC, $E_{BD}$ dependence with $d$ for various polymers, it is observed that the power exponent varies between 0.24 and 0.51.[6] and thus the AC failure mode extrinsic. This is supported by Mason[8] who reported that polypropylene (PP) breakdown is usually assisted by

surface discharges coming from the transformer oil surrounding the sample under test. Likewise, Helgee and Bjellheim[9] and Bjellheim and Helgee[10] reached the same conclusion for polyimide (PI) films by showing that partial discharges (PDs) in the surrounding oil preceded breakdown for the thickest samples and that the oil permittivity had a significant influence.

For any electrical or electronic application that involves high voltage, it is important to know the transition thickness $d_t$ determining intrinsic and extrinsic breakdown mechanisms. This is critical for system or device insulation dimensioning. Unfortunately, existing theory, such as the avalanche, thermal, or electromechanical breakdown models, do not describe the thickness-dependence that is experimentally observed.[5] As such, only a meticulous experimental approach can resolve $d_t$, assuming that the thickness step variation is small enough, a condition rarely met in practice. Finally, a key question arises as to how to adapt the insulation design such that the intrinsic breakdown mode is extended to higher thicknesses (i.e., how to increase $d_t$)?

This work first outlines a fundamental understanding of the physical origins of both intrinsic and extrinsic breakdown and to determine where $d_t$ occurs for polyimide films used in this study. It also demonstrates how the intrinsic breakdown can be extended to larger thicknesses simultaneously yielding the highest AC electrical breakdown strength for PI films reported to date.

<figure><img src="image_3.png" /><figcaption>**Figure 2.** a) The electric field distribution in a PI single-layer configuration with an oil environment. The field scale is normalized to the uniform field. b) The electric field distribution in a fully PI encapsulated configuration without triple point. c,d) Schematics of the physical origins of PD initiated breakdown at the PI–oil interface and intrinsic breakdown in a fully PI encapsulated configuration.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Figure 3.** A comparison of the maximum *E*-field enhancement factor between a PI single-layer configuration in oil and a fully PI encapsulated configuration without triple point. Here the electrode is formed in 4 µm thick gold with a representative 0.5 µm radius of curvature at the metal corners.</figcaption></figure>

## 2. State-of-the-Art of Polyimide Breakdown Field versus Thickness and Fringe Field Modeling

Polyimide is an industrially important polymer used as insulating material in various applications such as electrical mo-

tor windings, aeronautics and aerospace, power electronics and microelectronics.[11] For instance, it can be found as a coating film or tape for power device passivation,[12] wafer-level packaging[13] isolation barrier for digital isolators,[14] or in transmission cables.[15] Over the last decades, the dielectric breakdown strength of PI films, mostly reported on Kapton tapes or on spin-coated films, have been widely investigated under AC,[9,10,16–22] DC[16,17,23–26] or impulse[18] voltages. From this extensive literature, the thickness-dependent dielectric breakdown has been extracted and presented in **Figure 1**.

These data were collected from tests performed either at room temperature (RT, in oil or air) or at 77 K, under liquid nitrogen (LN₂) conditions. Additionally, most of these studies involved similar electrode configurations employing rounded edges (even if dimensions may have slightly varied) in order to mitigate the fringing field at the triple junction with the surrounding medium (see inset in Figure 1). From this analysis, two clear groups of data emerge with two different thickness dependencies. Under DC fields, the highest values of *E*<sub>BD</sub> and a weak thickness dependence (i.e., *n* < 0.3) are observed, whereas the AC breakdown regime exhibits lower *E*<sub>BD</sub> values (in rms) and a stronger thickness dependence. Thus, independent of the test laboratory, measurements under AC fields yielded *n* ≈ 0.5 thereby making the breakdown of the PI film, in a single-layer configuration, extrinsic in nature.

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Electrical test structures for the breakdown experiments of PI films as a function of thickness: a) A single-layer PI structure for wafer-level testing, b) a double-layer, encapsulated PI structure for wafer-level testing and c) a double-layer PI structure with molding compound for package-level testing.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Figure 5.** a) Experimental setup for AC breakdown voltage testing at wafer-level with simultaneously current-voltage pre-breakdown waveforms observation and failure location recording. b) Experimental setup for AC ramp and AC withstand breakdown voltage testing at package unit level.</figcaption></figure>
<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 6.** AC voltage and PD current versus time measured at wafer-level on a double-layer PI structure in oil for three different thicknesses: a) 5.1 µm thick b) 12.5 µm thick and c) 23 µm thick PI films. The current spikes correspond to extrinsic PD occurrences. d) Zoom-in of some of the PD current spikes for the 12.5 µm thick and 23 µm thick PI films.</figcaption></figure>

To understand why the failure mode in AC is extrinsic, the electric field distribution for a single-layer PI film, surrounded by insulating oil, has been calculated by electrostatic modeling using finite elements method (FEM) (see Figure 2a). In this owned developed FEM modeling example, the E-field scale is normalized to the uniform electric field giving a field enhancement factor ($\eta = \frac{E_{\text{fringe}}}{E_{\text{uniform}}}$). The triple point (i.e., the junction between electrode-PI-oil) appears as the location of a significant increase in electric field governed partly by the permittivity ratio between the surrounding oil medium ($\epsilon_{\text{oil}} \approx 2$) and the PI film ($\epsilon_{\text{PI}} \approx 3.2$). The maximum E-field value is located within the insulating oil. When the fringe field exceeds the discharge inception field of the insulating oil, discharge activity can occur at the PI film surface leading to premature failure and lowering the estimate of the dielectric strength. Consequently, when the dielectric strength is measured disregarding fringe field magnitude, the experimental breakdown field values $E_{\text{BD}}$ can correspond to an extrinsic failure type, with a clear dependence on thickness ($n \approx 0.5$), and with poor correlation to the theoretical or actual dielectric strength of the material. This extrinsic failure is very sensitive to PDs and is driven by electrical discharges initiated at the triple point and

their ability to advance along the PI/oil interface before drilling through the PI film at some weakness towards the grounded electrode (see Figure 2c).

To avoid the triple-point, a PI overlayer must replace the oil at the edge of the electrode. This is illustrated in Figure 2b. In this configuration, the permittivity is now uniform around the electrode edge such that the fringing field is now largely determined by the electrode curvature. It shows a significant fringe field mitigation and any potential PD creepage would be delayed to higher voltages or even completely eliminated. Such a design, assuming void-free conformal coating, should yield higher breakdown voltages and a more accurate estimate of the intrinsic dielectric strength (see Figure 2d). This has, indeed, been recently reported by Li et al. and by Andersson et al. in crosslinked polyethylene (XLPE) and low-density polyethylene (LDPE), respectively, for other applications.[27,28]

To illustrate the reduced fringing due to encapsulation, Figure 3 shows the variation in the E-field enhancement factor $\eta$ calculated at an electroplated Au electrode edge (5 µm thick and 0.5 µm radius of curvature) as a function of the PI insulating film thickness in the case where the encapsulation is either an insulating oil or a subsequent PI capping overlayer. The
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

**Figure 7.** AC peak electric field and pre-breakdown AC current versus time-before-breakdown applied to a double-layer PI stack (5.1 µm thick film) tested at wafer-level in oil: a) waveforms up to failure showing the intrinsic pre-breakdown nonlinear current and b) a zoom-in of the last periods prior to failure. Here, the current exhibits peaks in-phase with the voltage related to a strong dissipative component near breakdown (intrinsic feature of the failure). The inset shows the current density replotted versus the peak electric field.

<figure><img src="image_13.png" /></figure>

**Figure 8.** AC breakdown voltage and PDIV versus PI film thickness for a double-layer PI structure tested at wafer-level in oil. The ratio PDIV/V<sub>BR</sub> is also reported. The vertical dashed line shows the transition thickness d<sub>t</sub>, separating an intrinsic PD-free breakdown (V<sub>BR</sub> < PDIV) from an extrinsic PD-driven breakdown mode (V<sub>BR</sub> > PDIV).

<figure><img src="image_14.png" /></figure>

**Figure 9.** Weibull probability of failure for different PI film thicknesses versus AC breakdown field for a double-layer PI structure tested at wafer-level in oil. The solid lines correspond to the best linear fits of the experimental data. The dashed lines show the 90% confidence intervals.

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

**Figure 10.** a) AC breakdown field and PDIF and b) shape parameter versus the film thickness for a double-layer PI structure tested at wafer-level in oil. The vertical dashed line shows the transition thickness d<sub>t</sub>.
<figure><img src="image_17.png" /><figcaption>**Figure 11.** Comparison of the AC breakdown field versus the film thickness for a double-layer PI structure, a single-layer PI structure tested at wafer-level in oil, and a Kapton HN tape tested in a rod-plane electrodes configuration in oil. The vertical dashed line shows the transition thickness $d_t$.</figcaption></figure>

enhancement factor $\eta$ increases monotonically with the PI insulating film thickness. This emphasizes that field fringing is more significant for thicker films. Second, the FEM modeling reveals that a fully encapsulated test structure with a capping PI, mitigates the enhancement factor $\eta$ and should, in principle, extend the intrinsic breakdown region to a higher thickness range. This paper presents the results from an experimental verification both at material and device level.

# 3. Experimental Section

To test the encapsulation hypothesis, new high voltage devices using a polyimide film as the encapsulating and insulating barrier layer between two gold metal plates were fabricated. They were used to measure the PI intrinsic electrical breakdown strength and the transition thickness, $d_t$, separating the intrinsic and extrinsic failure modes.

## 3.1. Materials and Sample Preparation

The polyimide films used in this investigation were prepared from a liquid polyamic acid solution (PAA) dissolved in an N-methyl-2-pyrrolidone (NMP) polar solvent. This was the precursor of a final poly(4,4'-oxydiphenylene pyromellitimide) (PMDA-ODA) having completed the thermal imidization reaction at high curing temperature.

Samples were prepared in an industrial production line, inside a high-class clean room facility. The PAA solution was spin-cast onto Si wafers (8"-diameter) preprocessed with a PECVD oxide layer and electroplated with a blanket TiW/Au bilayer to create the bottom electrode. The spin-coating speed was adjusted to give a final, post cure PI film thickness within the range from 5 µm to 60 µm using a multilayer coating process, as previously reported.[29] The deposited film stack was subsequently metalized with another TiW/Au bilayer. Test structures were lithography patterned to obtain circular PI capacitors (Figure 4a). To remove the triple points at the top metal edges, some of the test

structures were also encapsulated with a 15 µm thick PI overlayer thereby forming a PI capping layer as illustrated in Figure 4b. Finally, for the purpose of breakdown testing at application level (i.e., at package unit level), some of the test chips, after wafer dicing, were packaged using an industrial SOIC epoxy-base molding compound. Electrical contact was achieved with Au bonding wires on metal pads as shown in Figure 4c. Further details concerning the fabrication process can be found elsewhere.[14,30]

## 3.2. Breakdown Measurements

Four different techniques were used for the electrical breakdown characterization in this study: i) AC ramp breakdown at wafer-level, ii) DC ramp breakdown at wafer-level, iii) AC ramp breakdown testing at package-level, and iv) AC withstand breakdown testing at package-level. Before any electrical test, each sample was dried in an air oven at 150 °C for 1 week and on reaching room temperature (23 °C), immediately immersed in fluorinert oil and tested. A population of 25 failed samples for each test structure was used for an accurate Weibull statistical analysis.

At wafer-level, breakdown testing was carried out using a high voltage probe station configured to observe real-time voltage and current waveforms and the ability to record the failure location with a CCD camera (Figure 5a). For AC breakdown voltage ($V_{BR}$) measurements, the test structures were biased by applying the high voltage on top electrode whilst the bottom metal layer was grounded using contact needles controlled with micropositioners. The testing was carried out by amplifying a low amplitude, 50 Hz, AC sinewave voltage coming from a waveform generator using an HV amplifier (gain: ×3000, slew rate: >500 V µs⁻¹, bandwidth: >10 kHz, distortion: <2%). The amplifier output voltage, $V_m(t)$, was applied to the sample and detected on an oscilloscope after attenuation via a HV probe (1/1000). The total current, $i(t)$, flowing across the sample was collected on the oscilloscope through a clamp-on hall effect current sensor (10 µA accuracy). The HV voltage ramp rate was varied from 0.5 to 1 kVp s⁻¹ in compliance with the test duration specified in the international ASTM D149-20 standard. Preliminary experiments, however, showed minor dependence on this parameter. For DC breakdown voltage testing, the amplifier was replaced by a high voltage modular power supply (6 kV DC) directly connected to the sample. Here, the voltage ramp was raised at 200 V s⁻¹.

At package level, AC withstand breakdown voltage testing was performed at 50 Hz using an industrial tester with a bias capability of up to 30 kV<sub>rms</sub> (Figure 5b). The voltage was increased in steps of 1 kV<sub>rms</sub> for 1 s until the device failed. The high voltage was applied to the PI film through lead frames, themselves contacted to the top and bottom metals through gold bond wires. Tests involved immersing the packaged units in a fluorinert liquid to prevent external surface discharges. For comparison, AC ramp breakdown testing was performed by using a HV AC amplifier (up to 100 kV<sub>rms</sub>) at 50 Hz on other packaged units. The voltage was raised in this case with a ramp of 1 kV<sub>rms</sub> s⁻¹ until the unit fails.

# 4. Results and Discussion

Critical to the analysis here was establishing if partial discharges participated during the breakdown test. This enables the
<figure><img src="image_18.png" /><figcaption>**Figure 12.** Typical failure location analysis of the double-layer PI structures for different film thicknesses after the AC breakdown voltage testing at wafer-level in oil. The percentiles indicate the samples that have failed intrinsically (direct vertical BD path underneath the electrode) or extrinsically (indirect vertical BD path after a first lateral creepage along the capping PI/oil interface).</figcaption></figure>

classification of the breakdown event as of intrinsic (i.e., PD-free) or extrinsic (i.e., PD-driven) origin. As such, the pre-breakdown current waveforms during the AC breakdown tests were studied in detail to establish the transition thickness $d_t$.

### 4.1. Partial Discharge Inception Voltage (PDIV)

**Figure 6** presents the applied AC voltage and the PD current versus time of a double-layer PI structure for two different thicknesses of 5.1 and 12.5 µm measured at wafer-level in oil. In the case of the 5.1 µm PI film (Figure 6a), the measured current does not exhibit any anomalies in the tested sequence confirming that no PD occurred before the breakdown. In contrast, for the 12.5 µm and thicker PI films (Figure 6b,c), at the inception voltage, discharges start to occur generating the characteristic signature of fast current spikes during the voltage rise (positive or negative polarity), as also reported elsewhere in other oil.[31] The current spikes are indicative of discharge activity during the breakdown test signifying when the breakdown field is influenced by extrinsic PD degradation processes ($V_{BR} > PDIV$). The observation of the first current spike during the tests was used to determine the PDIV.

### 4.2. Nonlinear Intrinsic Prebreakdown AC Current

For the thinner PI films, which are fully free of PDs before the breakdown ($V_{BR} < PDIV$), a specific response is recognizable prior the failure. In this case, the AC current, above a certain threshold electric field ($E_{th}$), shows a nonlinearity. This manifests as an in-phase resistive component with respect to the applied

AC field whose amplitude increases over the subsequent periods (see **Figure 7**). This phenomenon was recently reported[32] in PI films measured using a novel HV broadband dielectric spectroscopy technique. The nonlinear conduction corresponds to a Poole-Frenkel AC polarization due to charge de-trapping processes from donor centers that are released with the help of the frequency. Here, the sensitivity of current sensor is lower compared to that of the current detection in HV broadband dielectric spectroscopy. The nonlinear threshold field is therefore only observed from $600 V_p \mu m^{-1}$ (or $425 V_{rms} \mu m^{-1}$), as shown in the $J-E$ hysteresis loops in the inset of Figure 7a. This can be compared to previously reported value for the on-set of non-linearity occurring at a threshold field $\approx 100 V_{rms} \mu m^{-1}$.[32]

The AC current nonlinearity, in the form of periodic current peaks, contrasts with that of the non-periodic PD current spikes observed for the thicker PI films (Figure 6b,c). It highlights the genuine intrinsic, degradation process within the PI films prior their electrical breakdown. Indeed, up to the ultimate period at the breakdown (Figure 7b), the nonlinear current peak continuously increases and is likely the feature of a thermal runaway in the PI bulk that brings the material to fail intrinsically without any PD occurrence (as $V_{BR} < PDIV$).

### 4.3. Relationship between AC Breakdown Voltage and PDIV

To accurately identify the transition thickness, $d_t$, delineating a thickness-independent from a thickness-dependent breakdown regime, AC breakdown experiments, with AC current waveform analysis, were performed to correlate the breakdown voltage with PDIV occurrence. **Figure 8** shows the AC breakdown voltage and PDIV of the double-layer PI structures versus the film thickness
<figure><img src="image_19.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>(c)</figcaption></figure>

**Figure 13.** Main failure location scenarios of the AC breakdown at wafer-level in oil for the double-layer PI structures for different $V_{BR}$ conditions with respect to PDIV and in relation with the different film thicknesses: a) $V_{BR} < \text{PDIV}$ or $d < d_t$, b) $V_{BR} \sim \text{PDIV}$ or $d \sim d_t$, c) $V_{BR} > \text{PDIV}$ or $d > d_t$.

tested at wafer-level in oil. The plot also presents the PDIV/$V_{BR}$ ratio when the partial discharges has started with respect to the failure.

At the lowest film thicknesses, the breakdown is reached without any PD and the failure remains purely intrinsic. The results clearly show a transition thickness, $d_t \approx 12$ µm. However, at $d \sim d_t$, the PDIV is close to the breakdown voltage, around 92%. Thus, the 12.5 µm thick PI films are weakly affected by the discharge activity and the breakdown voltage remains proportional to the thickness. For thicknesses $d > d_t$, the PDIV occurs prior to BD with values corresponding to 87% and 77% of the breakdown voltage for the 15 and 23 µm thick films, respectively. For these, discharges around the electrode edges and within the insulating oil, was readily observed during the AC breakdown tests. Similar results have reported by Mason in polyethylene and polypropylene.[8] They showed that the electric strength of the oil needed to exceed that of the film, to avoid local stress concentration and heating in the film thereby reducing electric strength. This corresponds to the experimental observation for the PI films studied here. For thicknesses $d > d_t$, the failure is driven by the discharge activity at the oil/PI/electrode triple point which is the source of the inflection in the breakdown voltage curve as a function of the film thickness.

### 4.4. AC Breakdown Field: Thickness Limit of the Intrinsic Failure Mode

The Weibull plots for the double-layer PI test structures tested in oil versus are shown in **Figure 9**. They demonstrate a high dielectric strength ($\approx 500 V_{rms} \mu m^{-1}$) of the PI films when the thickness range favors an intrinsic failure mode ($d < d_t$). The results in this region are also highly reproducible. This is inferred from the high shape parameter, $\beta$, namely, the slope of the Weibulls. However, when $d > d_t$, the extrinsic failure mode lowers the mean BD field and broadens the distribution lowering the $\beta$ value.

In **Figure 10**, the variation in the BD field and its associated $\beta$ parameter have been plotted as function of the PI film thickness. Two slopes in the AC breakdown field versus thickness can be identified. Below $d_t$, in the PD-free region, the dielectric strength has weak thickness dependence. Above $d_t$, in the PD-driven region of the oil, the AC breakdown field collapses, corresponding to an extrinsic failure.

The thickness-dependence of the shape parameter $\beta$ is given in **Figure 10b**. It also emphasizes the transition between the intrinsic to the extrinsic failure mode of the PI films in oil. Whereas the intrinsic region is characterized by extremely high values of $\beta$ (>250), rarely observed for dielectric films, in the extrinsic failure region, the value collapses to around $\approx 12$. This is more in line with values reported in the literature.[33–35] Hence, the inflection in the $\beta$ curve also reveals a failure mode change with thickness. Consequently, our results indicate that, at least for PI films, previous AC dielectric strength data showing both a power law thickness dependence ($n \approx 0.5$) and a low shape parameter value, $\beta < 30$, is likely a result of an extrinsic breakdown mechanism.
<figure><img src="image_22.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>(c)</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>(d)</figcaption></figure>

**Figure 14.** Application of the embedded-electrodes design to high voltage integrated IC units with extended intrinsic breakdown voltage. a) Device under test during AC withstand breakdown. b) Microscope cross-section of the stack and its related FEM electrostatic modeling in high voltage. c) FIB-SEM image of the breakdown channel in cross-section occurring at the top electrode outer edge of the test chip. d) Representation model of the intrinsic breakdown concept extension for $V_{BR} > PDIV$.

**4.5. Extrinsic Breakdown Mode: Effect of Triple Point**

To confirm the extrinsic feature of the breakdown for the thicker films when tested in oil, different test-chip designs have been investigated. **Figure 11** presents a comparison of the AC breakdown field versus PI film thickness for the different test structures tested in oil: i) the double-layer structure, ii) the single-layer structure, and iii) a single stand-alone Kapton HN tape in rod-plane electrodes configuration for comparison.

In the case of the single layer PI configurations (including that of Kapton tape), the AC breakdown field exhibits a thickness dependency over the entire measured range. This trend is strongly related to the triple point where discharges at the PI/oil interface occurs prior to breakdown. On the contrary, for the double-layer PI structure, a transition thickness is observed after which the AC breakdown field decreases converging to that of the single layer

PI configuration. Although there is no triple point in this configuration, this degradation is still explained by the progressive occurrence of electrical discharges at the upper PI/oil interface that make the final breakdown of extrinsic origin as well. The insulating oil used during the tests, even owning good dielectric properties (i.e., ≈20 kV mm⁻¹ and ≈10¹⁵ Ω cm), remains still a weak dielectric environment to maintain the intrinsic breakdown strength at large PI thicknesses.

**4.6. Failure Analysis**

To further confirm the transition from intrinsic to extrinsic breakdown, some representative failure analysis has been performed. **Figure 12** shows optical microscope top-view images of the typical failures for the double-layer PI structures for
<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /><figcaption>**Figure 15.** Validation of the intrinsic breakdown field's thickness range ex- tension at large PI film thicknesses: a) AC breakdown field and AC with- stand breakdown of fully embedded test chip in IC packaged units in oil, b) comparison of the AC breakdown field with the state-of-the-art and c) intrinsic DC breakdown field compared with the state-of-the-art.</figcaption></figure>

different film thicknesses after AC breakdown voltage testing in oil.

For $d \lesssim d_i$, both the 5.1 µm and 12.5 µm thick PI test struc- tures have a breakdown channel located within the top electrode. Moreover, the outer edge of the electrode is free of any prebreak- down discharge degradation. In this thickness range, 100% of the tested samples showed similar failure under the electrode without involving the edge thereby confirming the genuine in- trinsic failure mode of PI. For thickness $d \sim d_i$, for which PDIV becomes significant, PD erosion is visible at the outer edge of the top electrode with 20% of the tested samples failing in this re- gion. Finally, for, $d > d_i$, the 23 µm thick PI test structures show a clear lateral degradation before a vertical drilling through the PI stack. This discharge creepage is also related to a first punct- ure through the upper PI layer before to go laterally at the PI/oil interface.

The main AC breakdown paths are schematically shown in Figure 13 for the double-layer PI structures in oil and for the dif- ferent breakdown voltage conditions with respect to PDIV and film thickness. In the two situations where $V_{BR} <$ PDIV or $V_{BR} \sim$ PDIV (see Figure 13a,b), the failure is directly vertical, intrinsic and occurs under the electrode where the E-field is uniform and there is no major impact of electrode edge effect. On the other hand, when $V_{BR} >$ PDIV, the accumulation of mobile surface charge carriers at the upper PI/oil interface enhances the electric field until the discharge inception is reached and surface elec- trical treeing develops laterally. At some points, away from the electrode outer edge, the treeing becomes vertical and reaches the ground electrode. This extrinsic process gives breakdown a thickness-dependency.

## 4.7. Intrinsic Breakdown of PI Films in High Voltage ICs

The next generation of HV ICs will need to operate at higher voltages continuously and reliably and to guarantee more strin- gent safety requirements in terms of electrical insulation. To val- idate that the double-layer PI test structures can fail intrinsically at larger film thicknesses, test chips were assembled in a Small Outline Integrated Circuit (SOIC) package. Here the structure re- ceives an additional epoxy-based encapsulation provided by the molding compound.

**Figure 14a** shows a packaged double-layer PI structure IC con- nected to the breakdown voltage setup. **Figure 14b** shows a cross- section microscope view of the internal stack and its associated E- field modelling around the Au top electrode. This stack removes the insulating oil in the vicinity of the upper PI layer which is now replaced by the SOIC molding compound. As a consequence, this fully encapsulated design, with no liquid/solid interface close to the HV gold electrode, protects the PI film against an extrinsic premature electrical degradation. The failure path is restricted to the PI insulating layer and exhibits a pure, vertical, intrinsic breakdown occurring at the outer edge of the electrode where the fringe E-field is at a maximum. It does not involve any lateral
Design routes to extend intrinsic breakdown strength at high polyimide thickness

<figure><img src="image_29.png" /><figcaption>Figure 16. Overview of the routes to extend the intrinsic AC dielectric breakdown strength in polyimide at high film thicknesses based on fully embedded electrodes for higher electrical insulation safety in transportation electrification and renewable energy. Comparison with the state-of-the-art of AC breakdown field.</figcaption></figure>

pre-breakdown degradation, as shown by the FIB-SEM cross-section of the breakdown channel in Figure 14c,d.

Finally, Figure 15a presents the experimental evidence that the intrinsic breakdown of PI films can be extended to a higher thickness range when the test structure is packaged in a molding compound. First, it is confirmed through the AC ramp breakdown voltage testing of the units and secondly, through the AC withstand voltage testing. In this study, all the AC breakdown voltage tests performed (at wafer or package level) have shown that the PI thickness dependence of the intrinsic breakdown strength is given by a weak power law:

$$E_{\text{BD}}(d) \propto d^{-0.04} \qquad (2)$$

For the first time, this behavior has been observed a large thickness range between 5 to 60 µm. Moreover, an estimation of the intrinsic AC breakdown strength of PI films, extrapolated to a “zero” thickness, is obtained as $E_{\text{BD intrinsic}} \approx 520 \text{ V}_{\text{rms}} \mu\text{m}^{-1}$. This is the highest value reported under AC conditions. Nevertheless, the breakdown field of PI films still decreases, albeit slowly ($n = 0.04$), over the thickness range. This reduction, cannot be attributed to fringe field effects (see Figure 3). Alternatively, the density of defects due to the multilayer coating process may have a role.

Figure 15b,c compares the AC and DC dielectric strength obtained in this study to that reported in the literature. Whereas all the previous data show a strong thickness dependence, with $n = 0.5$ and $n = 0.3$ for AC and DC conditions respectively, this study shows, on the contrary, a significantly reduced dependency of $n = 0.04$ for both DC and AC when appropriate precautions are taken in the sample preparation. That is, by fully embedding the electrodes with solid insulating layers to eliminate any triple

points. Having met these conditions, the results presented here highlight a direct correlation between the AC and DC breakdown fields, namely:

$$E_{\text{BD DC}}(d) = \sqrt{2} \times E_{\text{BD AC}}(d) = kd^{-0.04} \qquad (3)$$

This correlation implies that the intrinsic dielectric strength of PI, under AC or DC fields, has been finally experimentally identified and unified.

## 5. Summary and Outlooks

Figure 16 summarizes the electrical insulation system design routes that have been used to demonstrate the existence of the intrinsic AC dielectric breakdown strength in PI films and to extend it in a higher thickness range. Consequently, these new insights pave the way for the design of more robust electrical insulation involving polyimide in order to build higher working voltage integrated electronics devices, like digital isolators for isolated-gate drivers. The requirement of such devices is to have higher electrical insulation safety and reliability to sustain the development of the future generation of electrical conversion systems in the fields of transportation electrification and renewable energy. In that purpose, the present results bring new directions for engineering development for improving the electrical insulating performances of these devices.

## 6. Conclusion

For decades, the AC dielectric strength of PI films was considered to follow the established thickness dependence of a power
law with $n \approx 0.5$. However, this work presents new experimental evidence showing that the AC dielectric strength of PI films is almost thickness independent with a power law of $n = 0.04$. It appears that the thickness dependence of the AC breakdown field reported in the literature is related to the presence of a triple point at the junction between the HV electrode, the PI film and the insulating liquid used during the breakdown tests. In this situation the failure is of extrinsic origin and driven by partial discharges occurring in the surrounding medium. However, by adding a second conformal PI overlayer, encapsulating the HV electrode and thereby removing the triple point, the intrinsic AC breakdown field for PI films was obtained as >500 $V_{rms} \mu m^{-1}$; the highest value ever reported. In this double-layer PI test structure, a transition thickness $d_t$ between an intrinsic to an extrinsic failure mode was identified accurately around 12 µm. The change to the extrinsic failure mode beyond $d_t$ was related to the occurrence of partial discharges arising at the oil/upper-PI interface. This alters the dielectric strength at large thicknesses due to pre-breakdown degradation. By replacing the insulating oil by embedding the double-layer PI structure into a thick molding compound, it was demonstrated that the intrinsic breakdown strength could be extended to PI films of at least up to 60 µm in thickness and following the same power law of $n = 0.04$. The electrical breakdown strength of PI films is therefore only weakly dependent on thickness.

## Acknowledgements

The authors thank the European Union and the Marie Skłodowska-Curie Action (MSCA-IF, H2020 program) for financial funding of the PRISME project (grant N° 846455). The authors also acknowledge J. O'Malley and J. Fitzgibbon for their technical contribution in the sample preparation to the present work.

## Conflict of Interest

The authors declare no conflict of interest.

## Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## Keywords

AC breakdown field, dielectric strength, electrical insulation, high voltage, intrinsic failure, partial discharges, polyimide

Received: September 29, 2023

Revised: November 27, 2023

Published online:

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