Bulk and interface second harmonic generation in the Si₃N₄ thin films deposited via ion beam sputtering

The integration of multiple photonic devices together on a substrate according to the concept of integrated photonics has attracted a considerable attention during the last years [1, 2]. The Si-based photonic materials, including Si₃N₄, stand out due to their promising applications in photonics and optoelectronics [1, 3, 4]. Besides its use in the nano- and microelectronics industry [5, 6], Si₃N₄ has a wide range of applications, like light-emitting materials, waveguide structures, photonic crystal nanocavities, plasmonic structures, and optical modulators [4–6]. Therefore, exploring its complete optical properties, linear and nonlinear optical features, is of utmost importance [1–4].

A number of works have reported on exploring the nonlinear optical properties of Si₃N₄, where the origin of an efficient second harmonic generation (SHG) was one of the major topics [5, 6]. SHG is a nonlinear optical process, where the photons of frequency (ω) interact with a nonlinear material and generate new photons with a doubled frequency (2ω) [2, 4, 7–10]. The second-order nonlinear process via the electric dipole contribution is allowed only in materials with the broken inversion symmetry. For bulk centrosymmetric materials, the SHG occurs only at the material surface or interface or due to the multipole interaction [2, 4, 11–18]. Since amorphous Si₃N₄ poses the inversion symmetry, the efficient SHG has been highly debated in the literature. Several reports have documented the second-order optical properties of the Si₃N₄ thin films prepared by plasma-enhanced chemical vapor deposition method [7, 8, 19, 20], as well as by the low-pressure chemical vapor deposited and sputtered microresonators and waveguides [21, 22]. The reports brought controversial conclusions ascribing the SHG generation to the Si₃N₄ volume [7, 23], as well as the silicon nitride–crystalline silicon (c–Si) interface [21].

In this article, we report on the SHG in Si₃N₄ films deposited by using dual ion beam sputtering (IBS). Unlike in the previous reports, where the SHG in the thin films of Si₃N₄ was measured in the transmission regime, here we use a setup capable to record the angle-dependent SHG signal in the reflective mode. This allowed us to carry out SHG characterization of Si₃N₄ thin films deposited on a c-Si wafer. In such a case, the SHG signal is expected to contain both bulk and interface contributions. By using the polarization-resolved angle-dependent SHG signal for three different thicknesses of the Si₃N₄ films, we discuss the relative contribution of the surface, interface, and bulk dipole SHG responses of thin-film systems. The SHG in the thick sample (3890 nm) can be well reproduced by the bulk SHG model with the second-order nonlinear tensor values, which are in agreement with the previously reported ones. Nevertheless, we observe the significant contribution of the Si–Si₃N₄ interface SHG for the 600 nm thick film, pointing out its importance for the thin Si₃N₄ structures. Our results provide a connecting link between the reports on the bulk-like SHG in the Si₃N₄ thin films and interface-like SHG commonly observed in the microstructures.

We deposited Si₃N₄ thin films by the dual IBS apparatus described elsewhere [25, 26]. The primary Ar⁺ ion source sputtered Si atoms on a substrate (c-Si with <100> orientation and BK-7) from a Si target, while the assistant ion source aimed nitrogen ions on the sample to form Si₃N₄. The beam voltage and beam current of the primary ion source was set to 600 V and 108 mA, respectively. The assistant ion source parameters were set to 120 V for discharge voltage and 0.6 A for discharge current. Other parameters of the assistant ion source are representing gas flow. The flow of nitrogen was set to 49 sccm.

Both transmittance (T) and reflectance (R) spectra were measured within wavelengths 380 and 980 nm by EssenOptics Photon RT spectrometer. The measurements were carried out for the incident angles 4°, 8°, 20°, 30°, 40°, 50°, 60°, and 70°, where the angle of 4° was used only for the measurement of transmittance. The spectra were measured for both p- and s-polarizations. The ellipsometric measurements were carried out via Sentech SE850 with microspots. We measured the visible range of wavelengths between 280 nm and 850 nm under the incident angle of 70°.

We employed an amplified Yb:YAG femtosecond laser system Pharos (Light Conversion) at 1028 nm with a pulse length of 225 fs, which was operated at the repetition rate of 10 kHz. From the output pulse energy of 100 μJ, we targeted 2 μJ into the SHG experiment. In our SHG set-up (scheme 1), the laser beam intensity was set by a λ/2 waveplate combined with a polarizing cube. The desired polarization of the fundamental radiation was controlled by the second λ/2 waveplate. The laser beam passed through a color filter that suppressed any radiation at the SHG wavelength generated by the laser or optical components in the beam. Then the laser beam with a diameter of 3.7 mm was focused by a lens (f = 500 mm) on the sample mounted on the motorized rotation stage. The SHG photons were collimated by a lens with a selected polarization and coupled by an off-axis parabolic mirror into a multiple-mode fiber. The used thin-film polarizer selectively transmits the SHG photons, while the IR (fundamental) beam stays unaffected. Owing to the fiber, the collected radiation is highly depolarized and outcoupled in a fixed detection set-up. It is worth noting that the present set-up can serve both for the measurement of SHG in both reflectance and transmittance mode. By using a fused silica prism and dichroic mirror, we split the IR beam and the SHG beam, and we detect them by using a large-area photodiode (Thorlabs, DET100A/M) and a photomultiplier module (Hamamatsu H9306-03) with a built-in amplifier, respectively. The SHG detection is shielded from the IR (fundamental) beam detection by using a pinhole and a set of filters, which efficiently block both the fundamental and the third harmonic radiation. The SHG signal was pre-filtered by a low-pass frequency filter, and the SHG intensity was extracted by using lock-in Anfatec 250 combined with an optical chopper. The simultaneously detected reflected IR signal was used to verify the quality of the light collection for the used range of incident angles by its comparison to the expected sample reflectance (figure S1 (available online at stacks.iop.org/JOPT/23/024003/mmedia), supporting materials).

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We deposited three samples of Si₃N₄ thin films on c-Si and BK-7 substrates with highly different layer thickness. Firstly, we characterized the Si₃N₄ layers with respect to their linear optical response, i.e. refractive index, and subsequently used this information to evaluate the SHG properties. We characterized the refractive index of the Si₃N₄ layer and the layer thicknesses by globally fitting their linear optical response (transmittance, reflectance, and ellipsometry). We applied the commonly used transfer-matrix approach, where the refractive index dispersion was approximated by using the Tauc–Lorentz model [25, 26]. This model is commonly used for wide-bandgap dielectric materials. We fitted the layer thickness and parameters of two oscillators, where one oscillator dominated and the second one accounted for a minor correction (1% of the amplitude). The fitting procedure is described in detail in our previous work [25, 26].

Figure 1 (left panels) provides a comparison between the experimentally measured transmittance and reflectance data (blue curves) and calculated curves (red lines) for s- and p- polarizations for the incident angle of 60 degrees. This angle is close to the Brewster angle, and therefore the optical response highly depends on the refractive index. A good agreement is also present for the ellipsometric data (top right graphs). The used Tauc–Lorentz model allowed us to achieve a very good agreement over the broad range of wavelengths 380–980 nm. The fit was carried out for all three deposited homogeneous layers, where the fitted refractive index (figure 1, bottom right graph) agreed with the precision of ±0.015 and the resulting thicknesses were 600 nm, 1510 nm, and 3890 nm, respectively. Owing to the smooth refractive index wavelength dependence, the values at the wavelength of 1028 nm were extrapolated from the fitted model. This data was further used to fit the experimentally observed SHG signal.

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Even though a centrosymmetric material does not generate SH in its bulk by the electric dipole contribution, the thin film is a special case. The symmetry is broken in the direction perpendicular to the surface, which is commonly denoted as the z-axis, and the resulting C_∞v symmetry yields three non-zero ${\chi ^{\left( 2 \right)}}$components, which are denoted as ${\chi _{xxz}}$, ${\chi _{zxx}}$, and ${\chi _{zzz}}$, respectively [2, 7, 23]. Morevoer, the deposition process of the thin film can cause local inhomogeneities and strains, which can effectively break the local symmetry of the material.

Two approaches have been reported in the literature: the first approach focuses on the signal generated at the interfaces between the thin layer and adjacent materials, i.e. substrate and superstrate [2]. This approach considers the SHG in two thin polarization sheets located at the thin film interfaces and we will denote it as an 'interface SHG'. The second approach is based on the use of a Green's function to extract the SHG signal by the integration of the infinitely thin sheets along the direction of the thin film thickness [7, 23]. This contribution still has the dipole origin, and we will call it 'bulk SHG'. Finally, there is a contribution due to the electrical multipole interaction, which will be discussed as well.

To characterize the thin films, we acquired SHG signals for a range of incident angles (35–65 degrees) and varying orientations of light polarization. We verified the second-order nonlinear origin by measuring the SHG signal intensity as a function of the fundamental laser intensity, which followed the quadratic dependence (figure S2, supporting materials).

Bulk SHG, which was reported as a dominating source of SHG in Si₃N₄ thin films, is known to be prominent for the thick samples measured under a high incident angle [24]. Therefore, we extracted the second-order susceptibility tensor components of the Si₃N₄ bulk SHG from the measurement of the sample with 3890 nm layer thickness at 55 degree incidence angle. In the case of polarization measurements, the SHG field for p- and s-polarized light outside the thin film can be expressed as [23]:

$$\begin{equation}E_{{\text{SHG}}}^{\,\text{p}} = {f^{\,\,\text{p}}}{({e^{\text{p}}})^2} + {g^{\text{p}}}{({e^{\text{s}}})^2},\end{equation} \tag{ 1a }$$

$$\begin{equation}E_{{\text{SHG}}}^{\,\text{s}} = {h^{\text{s}}}{e^{\text{p}}}{e^{\text{s}}},\phantom{00000000.}\end{equation} \tag{ 1b }$$

where e^p (e^s) is the amplitude of the polarization component of the fundamental field parallel (perpendicular) to the plane of incidence, and f^p, g^p, and h^s are the auxiliary expansion coefficients indicating the polarization signatures of the SHG response [23, 24]. To describe the nonlinear response correctly, we had to take into account multiple reflections since the beam spot is greater than the thickness of the thin films [15, 23]. Hence, the expansion coefficients can be expressed as functions of the SHG tensor components as:

$$\begin{equation}\left[ {\begin{array}{*{20}{c}} {{f\,^{\text{p}}}} \\ {{g^{\text{p}}}} \\ {{h^{\text{s}}}} \end{array}} \right] = {\text{M}}\left[ {\begin{array}{*{20}{c}} {{{{\chi }}_{xxz}}} \\ {{{{\chi }}_{zxx}}} \\ {{{{\chi }}_{zzz}}} \end{array}} \right],\end{equation} \tag{ 2 }$$

where the matrix M depends on the experimental geometry of polarization and the linear optical material parameters of the nonlinear film and the substrate, which were determined in the previous section. We adopted the approach used by Koskinen et al [15, 23]. The polarization-dependent SHG signal for a range of λ/2-waveplate angles is depicted in figure 2 for two SHG polarizations with corresponding fitted curves. Note that the λ/2-waveplate rotation by an angle α corresponds to the polarization angle rotated by 2α.

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Analogously to the previous reports, the s-polarized SHG intensity is low as compared to p-polarized one. The results from all four measurements were simultaneously fitted for f^p, g^p, and h^s values, which were recalculated into relative bulk tensor components χ_zzz , χ_xxz , χ_zxx , and listed in (table S1, supporting materials) leading to their relative values 0.03, 0.03, and 1.0, respectively. It is evident from the tensor components that the most prominent contribution is coming from the χ_zzz , which is well corroborated with the previous reports [7, 23].

In order to estimate the absolute values of the tensor components of Si₃N₄, we have performed a calibration against the Y-cut quartz crystal, which has the dominant tensor component of χ_xxx = 0.80 pm V⁻¹ [7, 13, 23]. We have followed Ning et al to calibrate the Si₃N₄ tensor components using the transmission mode SHG photon collection of the Y-cut quartz crystal [7]. The sample thickness was precisely measured (precision <300 nm) by using Mitutoyo LEGEX 774 and consequently confirmed by angle-dependent SHG signal from the reference sample. The estimated absolute values for the independent tensor components (χ_zzz, χ_xxz , and χ_zxx ) of the bulk were found to be 2.6, 0.08, and 0.08, respectively (table S1, supporting materials). It is worthwhile to mention here that the estimated absolute value of the χ_zzz tensor component is very similar to the previously reported literature values for the Si₃N₄ thin films, where Koskinen et al reported the calibrated value of χ_zzz tensor components ranging from 0.8 to 5.1 pm V⁻¹ for SiN_x thin films with a varying content of Si [23]. In another work, Kauranen and co-workers also reported the calibrated of χ_zzz tensor components of 2.47 pm V⁻¹ for the Si₃N₄ thin film [7, 23].

To gain insight into the origin of the second-order optical response of thin-film systems, we have carried out angle-dependent SHG studies. Owing to the fact that we use the unusual reflectance mode of the SHG optical set-up, we can track the SHG in the thin film on the opaque c-Si substrate and we can avoid the SHG signal from the substrate. We verified that the substrate itself did not generate any signal (data not shown). The experimental values of SHG intensities in Si₃N₄ thin films of three different thicknesses in the reflective geometry are shown in figure 3 (symbols; green = 600 nm, brown = 1610 nm, and blue = 3890 nm, respectively). These values were compared to the bulk-SHG contribution calculated via equations (1) and (2), where we employed the ${\chi ^{\left( 2 \right)}}\,$values for the bulk extracted in the previous section (see dashed black lines). We observed a reasonable agreement between the theory and experiment, including the scaling factor between the curves. However, we observed clear discrepancies in the curve shapes in the case of thin-film samples.

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Therefore, we also included into our analysis the interface-SHG model described by Gielis et al, where we took into account both the superstrate-layer (surface) and substrate-layer (interface) contributions [2]. We fitted the experimental data by a combination of bulk and interface SHG, where the bulk ${\chi ^{\left( 2 \right)}}\,$values were fixed, while the interface and surface contribution to SHG were left as a fitting parameter. By carrying out a set of optimization with random starting parameters, we attained a set of fitting parameters, where the statistics between the best matching fit served to determine the precision of the values. The fitted values of the SHG susceptibility tensor components of the Si₃N₄ are presented in table 1. The resulting curves (solid lines in figure 3) significantly decreased a deviation from the measured SHG signal, especially for the thinner layers, where the contribution from the surface SHG is expected to be more pronounced. In accordance with the expectations, the fit revealed a significant contribution of the Si₃N₄–Si interface, while the Si₃N₄-air contribution was subtle. It is worth noting that the signal for the 600 nm sample is relatively low due to the necessity to adjust the incident power well below the damage threshold of the material. Nevertheless, the angular dependence of SHG intensity of 600 nm sample could not be reproduced for low incident angles by any form of the bulk SHG contribution and the interface SHG contribution was dominating the signal.

The observed significant Si₃N₄–Si interface contribution is in the agreement with the results of the M. Kauranen group [23], who studied the Si₃N₄-silica thin film samples and were able to describe the SHG layer response based on the bulk model only, since the Si₃N₄–Si interface is not present.

We observed that the consideration of the surface and interface SHG contributions enhanced the agreement between measured data and the predictions of the theoretical model. However, a combination of the number of fitting parameters with the remaining discrepancies between the model and data lead to high relative errors of the ${\chi ^{\left( 2 \right)}}$ tensor components. The remaining difference between the theoretical values and experimental data can be partly subscribed to the minor inhomogeneity in the SHG signal depending on the beam position on the sample, which inevitably slightly drifted during the measurement. By measuring on multiple spots of each sample, we verified that the variation of curves does not exceed the noise level and the shape of the curve is consistent. Nevertheless, this variation was pronounced the most on the 600 nm sample. We ascribe it to the fact that while the bulk of the thin film produced by IBS was highly uniform, the uniformity of the layer-substrate interface was more prone to vary and caused the fluctuation.

It is also worth noting that we did not take into account the complete SHG signal originating from the multipole interactions and dipole magnetic interaction, denoted in the literature by the coefficients, γ, and, δ [15]. Even though the β coefficient vanishes for the isotropic materials and γ is indistinguishable from the interface SHG, and it is therefore included, the δ coefficient was not taken into account.

In summary, we report on linear and nonlinear optical properties of Si₃N₄ thin films deposited via the dual IBS method. The reflective indices, transmittance, and thickness of the films have been evaluated by global analysis of ellipsometric, transmittance, and reflectance data. The deposited Si₃N₄ thin films exhibit significant second-order nonlinear optical behavior, which we studied by means of the unconventional reflectance mode of the SHG optical set-up. This allowed us to study the response of samples deposited on a c-Si substrate. We observe that the dominating origin of the SHG for the thick layer (3980 nm) consists in the dipole bulk contribution, where the absolute value is similar to the previously reported values. However, for the thin layer (600 nm) the Si₃N₄–Si interface contribution was comparable to the bulk origin. Our work provides the first quantification of SHG on IBS-deposited thin films. Moreover, we provide a link between the contradictory results proposing the SHG in Si₃N₄ to occur either in the material volume or its interface.

The authors gratefully acknowledge the financial support from The Czech Academy of Sciences (ERC-CZ/AV-B, Project Random-phase Ultrafast Spectroscopy; reg. no ERC100431901), the Ministry of Education, Youth and Sports ('Partnership for Excellence in Superprecise Optics,' Reg. No. CZ.02.1.01/0.0/0.0/16_026/0008390), and the Czech Science Foundation (GACR 19-22000S).

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