Structural, optical and electrical properties of Si-rich and N-rich PECVD silicon nitride films

Abstract

Silicon nitride (SiN_x) thin films play a crucial role in the semiconductor industry due to their controllable properties, which make them suitable for various applications. In this study, SiN_x films, with varying composition ratios (x=[N]/[Si]), were fabricated under different conditions using plasma-enhanced chemical vapor deposition (PECVD). The composition significantly affects the structural, optical and electrical properties of the films. We investigate the characteristics that depend on the stoichiometric composition of amorphous hydrogenated SiN_x films (ranging from N-rich to Si-rich) through techniques such as X-ray photoelectron spectroscopy (XPS), electron microprobe microscopy (EMP), ellipsometry, Fourier transform infrared spectroscopy (FTIR), secondary ion mass spectroscopy (SIMS), and high-voltage broadband dielectric spectroscopy (HVBDS). Key parameters, including refractive index, bonding structure, permittivity, loss factor and AC conductivity are analyzed and discussed in relation to the x=[N]/[Si] ratio. The presence of hydrogen in PECVD SiN_x is also examined with Si-H and N-H bonds varying based on the x ratio. These variations influence the film electrical conduction properties with low-frequency HVBDS accurately identifying the structural transitions between N-rich and Si-rich compositions. These results show the key role of the Si-N bonding and hydrogenation (mainly through Si-H bonding) in controlling nonlinear conduction of SiN_x films.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-14296-2.

Introduction

Silicon nitride (SiN_x) thin films are technologically important due to their exceptional optical, mechanical and thermal properties, making them suitable for a wide range of industrial applications^1–5. For example, they are used as antireflective coatings and surface passivation layers in solar cells⁶. Additionally, they serve as diffusion barriers in circuit technology, waveguide layers for photonic devices⁷, charge storage films for nonvolatile memory devices⁸, and gate dielectrics in thin-film transistors^9–11. They are used to lower leakage current thereby improving galvanic isolation of isolated-gate drivers for electric vehicles¹².

Chemical vapor deposition (CVD), particularly plasma-enhanced CVD (PECVD), is a widely used technique for depositing silicon nitride dielectrics in the semiconductor industry^13–15. The composition of SiN_x is determined by controlling the value x that corresponds to the [N]/[Si] ratio. It can be adjusted by varying the deposition parameters in the PECVD process, such as the gas ratio (silane vs. ammonia), pressure, temperature or the RF power, all of which influence the SiN_x structural, optical, and electrical properties^16–18. Many studies have focused on the structural and optical properties^19,20. However, the relationship between the physico-chemical, optical and electrical properties of PECVD SiN_x films, particularly for high voltage electrical isolation applications, is not well understood. To optimize these films for isolation applications, it is important to understand how the composition determines, not only the bonding structure and refractive index of the films, but also the dielectric and electrical conduction properties. Of particular interest is the threshold electric field, E_th, beyond which the conductivity becomes nonlinear.

In this paper, the bonding structure, refractive index and the electrical characteristics of PECVD SiN_x films have been measured as a function of composition. This is achieved by adjusting the x=[N]/[Si] ratio from N-rich to Si-rich and directly measuring the physico-chemical properties of blanket layers of SiN_x deposited on Si wafers. Dielectric and electrical measurements were performed using metal-insulator-metal (MIM) capacitor test structures probed at wafer-level using high-voltage broadband dielectric spectroscopy. The observed nonlinear behaviour can then be leveraged in the design of future electronic devices used in higher voltage applications.

Results and discussion

• A.Composition and Structure.

Blanket films of 1 μm thick amorphous SiN_x, deposited on Si substrates (see Figure 1), were characterized by different physico-chemical characterization techniques to determine their compositional and structural properties. Figure 2 shows two representative XPS spectra of a SiN_1.5 film, the first was obtained without etching and the second, after 1500s of etching. The spectra show high amplitude Si 2p and Si 2s peaks at 101.9 eV and 149.5 eV, respectively. In addition, the N 1s peak is located at 397.7 eV. These peaks, which are also present after the etching, show the dominance of Si and N components in the SiN_x film. Following Ar ion etching, the O 1s peak at 532.4 eV and the C 1s peak at 284.5 eV show a reduction related to surface pollution confined to the top-most 10 nm of the films. Deeper in the bulk, the structural oxygen that is present at the film surface completely disappears. Additional depth profiling measurements are presented in Supplementary Information SA (Figures A1 and A2).

Fig. 1.

Top view (a) and cross-section (b) SEM image of a blanket SiN_1.36 layer deposited on Si wafer.

Fig. 2.

XPS survey of a SiN_1.5 layer before and after 1500s of Ar etching.

Table 1 shows the x=[N]/[Si] ratio values obtained along with the atomic percentages of Si and N atoms contained in the different SiN_x films, as measured by FEG-EPMA. The obtained x values, ranging from 0.86 to 1.50, vary according to the deposition conditions from samples 1 to 10, where the silicon concentration increases and the nitrogen content decreases. The resultant composition was changed with the first three samples being N-rich (x > 1.33). The remaining samples (x < 1.33) are regarded as Si-rich. The SiN_1.36 film (sample 3) is the closest to an ideal stoichiometry of Si₃N₄ where x = 1.33.

Table 1.

List of the investigated SiN_x films with their atomic percentages of N and si, the [N]/[Si] ratio, and the film thickness determined through FEG-EPMA and ellipsometry, respectively.

Sample#	Thickness [µm]	[N] Atomic%	[Si] Atomic%	x=[N]/[Si]	Type
1	1.06	59.721	39.715	1.50	N-rich
2	1.10	59.209	40.217	1.47
3	1.12	57.336	42.134	1.36
4	1.11	53.346	46.099	1.15	Si-rich
5	1.09	51.21	48.276	1.06
6	1.06	49.558	49.888	0.99
7	1.03	48.945	50.495	0.96
8	1.01	48.545	50.907	0.95
9	0.97	47.572	51.873	0.91
10	0.95	46.18	53.262	0.86

• B.Refractive index and thickness.

Figure 3 shows the RI and the thickness distributions across the SiN_0.95 film deposited on a 200 mm wafer. The color gradients represent the refractive index and thickness, indicated by the scale bars. Overall, one can observe the low RI and thickness variation across the wafer showing excellent deposition control and film quality. All the RI and thickness maps are provided in the Supplementary Information SB (Figure B1). The average SiN_x films thicknesses are reported in Table 1 and show a very low decrease with the reduction in the x=[N]/[Si] ratio which may result from subtle changes in growth kinetics associated with the different deposition temperatures where at higher temperatures, the reaction rate and surface mobility are altered, leading to reduced film growth rates and thus thinner films^21,22. However, the thickness remains consistent across the entire 200 mm wafer, averaging 1 μm ± 0.05 μm.

Fig. 3.

Variation of the refractive index (a) and the thickness (b) of the SiN_0.95 layer measured by ellipsometry across the entire 200 mm wafer. The x-y wafer dimensions are in millimeters.

Figure 4 shows the average RI of the SiN_x films, as determined by ellipsometry, for each value of x=[N]/[Si]. Thus, the RI reaches its highest value (n = 2.20) at the highest Si content (x = 0.85), where the high-RI element, i.e. the Si, dominates. As the Si content decreases, the RI decreases, reaching its lowest value (n = 1.87) for the SiN_1.5 film. This decrease indicates a significant changing in the element composition of the SiN_x film as the composition ratio x=[N]/[Si] is modified.

Fig. 4.

Refractive index variation of the SiN_x films versus the x=[N]/[Si] ratio.

• C.Bonding structure.

FTIR measurement is one of the key tools for the characterization of the covalent bonding configuration. FTIR measurements were performed on the SiN_x films which have different Si and N proportions, as shown in Figure 5. The variation in the absorption spectra is shown as a function of the ratio x=[N]/[Si] where each spectrum has been normalized to the layer thickness for an accurate comparison. For the Si-N symmetric stretching, Si-N asymmetric stretching, N-H wagging, Si-H stretching, and N-H stretching modes, the energies are, respectively, at 470 cm^− 1, 850 cm^− 1, 1180 cm^− 1, 2160 cm^− 1, and 3350 cm^− 123. The SiN_x films undergo a hydrogenation that produces Si-H and N-H bonds, according to the FTIR spectra. The results indicate that as the ratio x=[N]/[Si] changes, there is a clear variation in the absorption peaks corresponding to Si-H and N-H bonds.

Fig. 5.

Variation of the FTIR absorbance spectra of the SiN_x films as function of the ratio x=[N]/[Si].

In order to study the behavior of hydrogen-related absorption peaks in the SiNₓ films, the peak area of each corresponding FTIR band (Si–H stretching, N–H stretching, and N–H wagging) was calculated and plotted as a function of the atomic ratio x = [N]/[Si], as shown in Fig. 6.

Fig. 6.

Variation of the peak area of the different hydrogen chemical bonds and the cumulative H-bonds as function of the ratio x=[N]/[Si].

It is evident that the Si-H bond intensity in the Si-rich films (with x ranging from 0.86 to 1.15) is much greater than in the N-rich films (with x in the range from 1.36 to 1.5). This trend is explained by the higher concentration of Si atoms available to form Si–H bonds in Si-rich compositions. Conversely, the intensity of N–H bonds (both wagging and stretching modes) increases with x, resulting in a higher total H-related bond content in N-rich films. This is explained by the fact that SiN_x films with lower x values have higher amounts of Si atoms within the layer. More Si-H bonds are created in the films when the extra Si atoms link with H atoms (i.e., when x decreases). The cumulative peak area for all types of hydrogen bonds is also plotted in Fig. 6 and it shows an increasing trend as the ratio x=[N]/[Si] increases. This indicates a higher hydrogen incorporation in the N-rich SiN_x films compared to the Si-rich films.

To confirm the hydrogenation, a detailed SIMS study has been carried out to quantify the hydrogen content profile throughout the SiN_x films. As an example, Fig. 7 shows the hydrogen elementary atomic concentration in the SiN_1.06 film as a function of the film’s depth (with the thickness starting from the top surface). Regardless of the x values, all the SiN_x films contain a significant quantity of hydrogen atoms, confirming the FTIR results. Moreover, the hydrogen concentration stays relatively constant throughout the sample’s depth. In Si-rich films, the majority of the hydrogen atoms are bonded to Si atoms with a minimal formation of N-H bonds. On the contrary, in the N-rich films, as the x ratio increases, the hydrogen is progressively distributed between Si-H and N-H bonds. At the largest x ratios, the number of N-H bonds rises and surpasses the number of Si-H bonds. The [H] concentration, plotted as a function of x=[N]/[Si] as shown in the inset in Fig. 7, presents a monotonically decrease as the Si content increases (low x values), indicating that fewer hydrogen atoms are bonded. This trend is consistent with the total hydrogen bonds plotted in Fig. 6.

Fig. 7.

A SIMS depth profile of the H-atom concentration in the SiN_1.06 film. The top line indicates the nominal material type (i.e., Au, SiN_x or Si wafer). The inset plot summarizes the average [H] concentration at a depth of 500 nm plotted as a function of x for the different SiN_x films.

• D.Dielectric Properties.

Ten distinct metal-insulator-metal (MIM) capacitor test structures (see Fig. 8) were fabricated using the SiNx insulator materials under study. These underwent high-field electrical AC testing. In order to correlate the relationship between the structural changes in the SiN_x with their dielectric properties, the permittivity of each film has been evaluated. Figure 9 (a) presents the frequency dependence of the real part of the complex permittivity for the different SiN_x films with various x ratios. Dielectric spectroscopy was used to test a range of MIM capacitor structures in a frequency range between 1 Hz and 1 kHz at a low voltage of 1 V.

Fig. 8.

(a) Schematic illustration of the cross-section of a MIM capacitor wafer-level test structure. On the left, a digital microscope image shows the top view of the MIM structure capped with a polyimide final encapsulation layer. (b) SEM image of cross-sectional view of MIM structure prepared by Focused Ion Beam FIB.

Fig. 9.

(a) Permittivity versus frequency for the different SiN_x films. (b) Correlation between the permittivity and x=[N]/[Si] ratio at different frequencies.

Across all compositions, the permittivity demonstrates a stable behavior. It is worth noting that the frequency-dependent decrease is more prominent for the Si-rich films which highlights higher polarizability of the Si-rich SiN_x network containing more Si-H bonds.

To emphasize the compositional effects, the permittivity of SiN_x films is replotted versus the x ratio for different frequencies, as shown in Fig. 9 (b). The sample exhibiting the highest permittivity (ε’~7.2) corresponds to SiN_0.86 which is the film with the highest Si content. Permittivity decreases with increasing x with values of ε’ ranging from ~ 7.2 down to ~ 6.3, in agreement with recent findings in the literature^{24]– [25}. The permittivity value reaches a minimum ε’~6.25 when x gets closer to stoichiometry for the SiN_1.36 films. Finally, the N-rich films show a minor increase to ε’~6.35, although the permittivity is still low. There is, therefore a strong dependence of the dielectric constant on the ratio x=[N]/[Si]. Si-N and N-H bonds have relatively high dipole moments, while Si-H bonds have relatively low dipole moments²⁶. Therefore, permittivity measurement can be used to assess the degree of nitridation.

Another important analysis is the correlation between the real part of the permittivity ε^’and the square of the refractive index n². The measured permittivity ε^’ reflects the total polarization of the material, including contributions from electronic, ionic, and dipolar mechanisms. In contrast, the refractive index n, measured in the optical frequency range by ellipsometry, primarily reflects the electronic polarization, as slower mechanisms cannot respond to such high-frequency fields.

Correlating ε^’ and n² provides insight into whether the structural features that influence the optical response also govern the dielectric behavior. This approach is supported by classical models such as the Clausius–Mossotti relations, which link the dielectric constant, refractive index, and polarizability of a material²⁷. If a consistent trend is observed between ε ^’and n², it suggests that polarizability is dominated by common structural factors such as bonding configuration and composition, across different frequency regimes.

Figure 10 shows the dependence of the permittivity ε^’ on the squared RI (n²) (at high frequency of 6 kHz) collected throughout the different SiN_x films. The graph shows a highly correlated relationship, as might be expected. This indicates that variations in bonding environments, notably in Si–H and N–H bond densities, affect both the optical and dielectric responses in a structurally consistent manner.

Fig. 10.

Dependence of the permittivity ε^’ (at 6 kHz) on the squared refractive index n² for all the SiN_x films.

• E.Nonlinear conduction at high electric field.

The influence of composition on the electrical conduction is shown in Fig. 11, which shows the variation of the AC conductivity with the applied electric field for different values of x. A similar behavior is observed across all the SiN_x samples with varying x ratios: i.e., a linear response up to a threshold field E_th. The N-rich SiN_x films exhibit the largest linear conduction regions (i.e., field-independent), with a threshold field reaching up to E_th~530 V_rms/µm for the SiN_1.5 film. In this case, the applied electric field extends beyond 800 V_rms/µm to reach the nonlinear regime. In contrast, the Si-rich SiN_x films show the smallest linear regions with a threshold field of only E_th~100 V_rms/µm for the SiN_0.86 film. Si-rich films show an earlier and sharper transition, the conductivity increases nonlinearly at lower fields and more suddenly whereas N-rich films need higher electric fields to start showing nonlinear behavior, and the transition is more gradual, not as steep or sudden.

Fig. 11.

AC conductivity of the SiN_x films as a function of the applied electric field at 50 Hz for the different x values.

Figure 12 shows the correlation between the threshold electric field E_th, extracted from Fig. 11, and the x=[N]/[Si] ratio. This reveals the increase in the threshold field with x which eventually stabilizes at a constant value in N-rich regions. The extraction of the threshold electric field is provided in the Supplementary Information SC (Figure C1). The nonlinear behavior in amorphous silicon nitride is likely to be associated with variations in the density of localized states, which may arise from structural irregularities, silicon dangling bonds, or impurities such as hydrogen and oxygen. These localized states significantly influence the material’s conductivity²⁸.

Fig. 12.

Correlation between the threshold electric field E_th in the SiN_x films and the x=[N]/[Si] ratio at 50 Hz.

In order to understand charge transport mechanisms low frequency AC conductivity analysis is crucial²⁹. It highlights the role of the bonding configuration in the charge transport mechanisms as it allows the observation of physical events over long time intervals. The behavior of slow transportation of the charge carriers is more apparent at these low frequencies in the impedance response, indicating their interactions with the microstructure of the material.

To support this, Fig. 13 shows the AC conductivity of a representative N-rich film (x = 1.5) as a function of frequency f. A clear plateau is observed between 0.1 Hz and approximately 1 Hz, where the conductivity remains nearly constant. This frequency-independent region indicates that the conduction mechanism in this range is dominated by long-range, drift-like charge transport, resembling DC conduction. In this regime, the response is not influenced by capacitive effects or localized polarization phenomena such as dipolar or interfacial relaxation, which typically manifest at higher frequencies.

Fig. 13.

Frequency dependence of AC conductivity for a representative SiNₓ film (x = 1.5).

Therefore, analyzing conductivity at such low frequencies allows us to isolate and probe the intrinsic transport behavior of the SiNₓ films. It also ensures that the observed trends reflect actual conduction pathways rather than short-range dielectric or polarization responses.

The dependency of AC conductivity at low field for the various x values at a frequency of f = 100 mHz and for an electric field of E = 200 V_rms/µm is shown in Fig. 14. When compared to N-rich SiN_x, the Si-rich SiN_x films show higher AC conductivity due to their higher Si-H bond intensity which indicates higher denisty. The Si-rich films show an AC conductivity ranging from 10^− 9 to 10^− 6 S/m. When the ratio of [N] to [Si] increases, producing N-rich films, the AC conductivity decreases to a range of ~ 10^− 12 S/m. This indicates a notable difference between the two types of SiN_x films, that the low frequency measurements reveal. Si-rich films, with the strongest Si-H bond intensities and densities (excess silicon promotes the formation of more Si-H bonds), have the largest region of nonlinear conductivity, up to 10^− 6 S/m. High electrical stress can easily break the weak Si-H bonds which are ionized at 289 kJ/mol compared to 391 kJ/mol for the N-H bonds^{30]– [31}. As seen in Fig. 15, the broken Si-H bonds create dangling Si bonds that act as electronic defect states or traps³². The primary source of the Si dangling bonds is broken Si-H bonds as N-H bonds are stronger and more stable than Si-H bonds. By capturing and releasing charge carriers, these traps have the ability to modify the electronic characteristics of the material. Specifically, by increasing the density of localized states, they participate in increasing the electrical conductivity of the SiN_x films by low-frequency charge carrier hopping^33–36. There are more dangling bonds formed when there are more Si atoms within the structure. In comparison to Si-rich films, the N-rich films contain less Si-H bonds, which lower the AC conductivity of the film by reducing electron or hole trapping. As a result, with the assistance of H atoms, a tunable dangling bond route may be achieved by varying the [N]/[Si] ratio. This is also supported by ellipsometry, which shows an increase in the refractive index in the Si-rich films. Although the optical bandgap was not directly measured, this trend is consistent with previous studies^37–39 reporting that an increase in refractive index in amorphous SiN_x:H films generally correlates with a decrease in bandgap energy. Based on this, we propose that the bandgap may decrease as the Si concentration increases. A narrower bandgap could facilitate the thermal excitation of more electrons or holes to localized states near the conduction or valence bands, since the carrier density is proportional to exp(-Eg/2k_BT)where Eg is the bandgap energy, k_B the Boltzmann constant, and T the temperature. This mechanism may contribute to the nonlinear increase in conductivity as more carriers participate in the conduction^40,41.

Fig. 14.

AC conductivity as a function of x=[N]/[Si] ratios at 100 mHz and under 200 V_rms/µm.

Fig. 15.

Schematic illustration of the formation of Si-dangling bonds on a-SiN_x:H films after applying high electric field stress.

Conclusion

SiN_x films with varying x=[N]/[Si] ratios were deposited by adjusting the PECVD deposition parameters. The SiN_x films were first chemically characterized, followed by an electrical evaluation under electric field conditions. The RI and permittivity values obtained by ellipsometry and low-field broadband dielectric spectroscopy, respectively, are correlated. The N-rich SiN_x films show lower RI, exhibit lower permittivity values, while the Si-rich SiN_x films with higher RI show the highest permittivity. FTIR and SIMS analyses reveal the hydrogenation in all the SiN_x films, with a significant presence of Si-H and N-H bonds, which are strongly affected by the x ratio. AC conductivity measurements, combined with structural analysis, provide valuable insights into charge transfer mechanisms. The SiNₓ films with higher N content exhibit a delayed switching point from linear to nonlinear conduction behavior. Field-dependent low-frequency HVBDS measurements highlight the notable differences in the conductivity between Si-rich and N-rich SiN_x films. Structural defects in amorphous SiN_x introduce trapping levels. Si-rich SiN_x films, with the highest concentration of Si-H bonds, show the highest conductivity due to Si dangling bonds, which act as defects capable of trapping and releasing electrons or holes. In contrast, the N-rich SiN_x films, where most hydrogen bonds to N atoms, have fewer Si-H bonds and result in lower conductivity and a higher nonlinear threshold field.

Methods

Physico-chemical characterization

Blanket layers of 1 μm SiN_x were deposited by PECVD in an industrial cleanroom manufacturing facility on 300 μm thick and 200 mm diameter Si wafers using silane (SiH₄) and a mixture of ammonia (NH₃) and nitrogen (N₂) as precursor gases. To obtain variable compositions, the depositions were carried out at low substrate temperatures ranging from 100 °C to 400 °C, under a pressure of 2000 mTorr. All other deposition parameters were kept constant.

The crystallinity of the SiN_x films was examined using X-ray diffraction (XRD) using a Bruker D8 advance instrument with a Cu source (see Supplementary Information SD, Figure D1).

X-ray photoelectron spectroscopy (XPS) was used to analyze the elementary composition at the extreme surface and in-depth down to 150 nm from the surface. A K-Alpha XPS system from Thermo Scientific was used and configured with an Al source (hν 1486.6 eV) and a pass energy of 30 V for high-resolution spectra (step 0.1 eV) and 160 eV for general spectra (step 1 eV). Ar ion etching was used to create a depth profile that allowed for the measurement of atomic concentrations in the SiN_x films down to a few tens of nanometers (down to 150 nm). As XPS is intrinsically surface-sensitive and is unable to completely examine a thick layer in the 1 μm range and despite its effectiveness in evaluating the chemical environment⁴², a complementary technique was used to evaluate the elementary composition in bulk.

Using a field emission gun (Cameca SXFiveFE) and an electron microprobe X-Ray microanalysis (FEG-EPMA), a more in-depth elementary characterization was achieved. FEG-EPMA permitted measurement of the atomic percentages of Si and N in carbon-coated SiN_x films using an accelerating voltage of 7 kV, a spot size of 10 μm, and at a depth of around 500 nm from the surface (i.e., at half the film thickness).

The refractive index (RI) and film thickness d were both obtained using direct ellipsometry measurements on the blanket layers.

Fourier transform infrared (FTIR) spectroscopy (Bruker Vertex 70 spectrometer) was used in transmission mode to analyze the chemical bonds and their changes within the various SiNx films in order to assess the films’ covalent bonding structure. In addition, ATR-FTIR measurements were performed on selected samples with a representative result presented in Supplementary Information SE (Figure E1), which shows the corresponding absorbance spectra. With a spectral resolution of 4 cm^− 1, FTIR spectra were obtained in the wavenumber range from 400 to 4000 cm^− 1. A reference silicon wafer was used as the background for all the measurements, which were averaged across 25 scans at ambient temperature. The chemical structures of the SiN_x films were obtained through the examination of the peak intensities.

Following the identification of Si-H and N-H bonds, secondary ion mass spectroscopy (SIMS), with a SIMS CAMECA IMS 4FE6, was used to identify hydrogen atoms in order to confirm the hydrogenation of the SiN_x films. SIMS analyses were performed on SiN_x films covered with a thin 20 nm Au metallization. Cs + was used as the main ion source utilized to sputter the samples, and the monitoring of the negative secondary ions was performed in relation to the depth and sputtering duration. The measured surface under analysis were of 30 μm in diameter. In addition to hydrogen, depth profiling of silicon Si and nitrogen N atoms was also conducted, and the results for representative SiN_x samples are provided in Supplementary Information SF (Figure F1).

Electrical characterization

The MIM capacitor test structures were obtained by depositing bottom and top electrodes consisting of TiW/Au bilayers. TiW was employed as an adhesion layer at the interfaces between SiN_x and Au, both above and below the film, ensuring structural integrity and promoting electrode stability. The MIM capacitor structure was further optimized for high-voltage characterization by symmetrizing the work functions of the electrodes through TiW layers on both sides of the SiN_x. To minimize mechanical stress on the SiN_x layer during electrical characterization, a thick Au layer was electroplated at the top electrode to provide robust electrical contact points for needle probes. Finally, the test structures were encapsulated with a polyimide capping layer, which also functioned as a masking layer for wet etching of the SiN_x to expose the bottom electrode contact. By applying AC voltages between 1 V_rms and 750 V_rms in a frequency range from 100 mHz up to 1 kHz, high voltage broadband dielectric spectroscopy (HVBDS) tests were carried out at room temperature to determine the dielectric properties (permittivity and loss factor) and AC conductivity of each distinct MIM capacitor structure. Additional the loss factor tan(δ) measurements are presented in Figure G1 of Supplementary Information SG. Further information about this measurement has been published elsewhere^43,44.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

S.D., R.L., P.L., and B.C. were responsible for funding acquisition. C.O’D. fabricated the samples. T.A.M., J.E., C.O’D., and S.D. designed and performed the experiments. T.A.M. and S.D. analyzed the results and wrote the manuscript. P.R., J.E., P.L., R.L., and B.C. discussed the work in depth and made suggestions for this study. All authors reviewed the manuscript.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

C.O’D, P.L., R.L., and B.C. works at Analog Devices, the company that develops digital isolators which are mentioned in the paper. The other authors declare no competing interests.