Simultaneous optical power insensitivity and non-volatile wavelength trimming using 2D In_4/3P₂Se₆ integration in silicon photonics

Abstract

In integrated photonic circuits, microring resonators are essential building blocks but are susceptible to phase errors due to fabrication imperfections and optical power fluctuations. Conventional active phase tuning methods are power-intensive and challenging to integrate into densely packed photonic chips. This study proposes a solution by integrating a thin 2D layer of In₄/₃P₂Se₆ (InPSe) onto silicon microring resonators (Si-MRR). This approach mitigates sensitivity to laser power and achieves non-volatile wavelength trimming. Under bias voltage, the device exhibits electro-optic behavior, offering a non-volatile phase trimming rate of −2.62 pm/V to −4.62 pm/V, corresponding to InPSe thicknesses of 45 nm to 120 nm. Low optical losses of 0.0091 to 0.0361 dB/μm were also measured, corresponding to thicknesses of 30 nm to 120 nm. The devices demonstrate stable in-situ resonance wavelength stabilization and bidirectional trimming, ensuring cyclic stability for non-volatile phase control. This advancement enhances the performance of silicon photonics across diverse applications, facilitating high-capacity, high-power operation in compact designs.

Introduction

Silicon photonics (SiPh) stands at the forefront of technological advancement, transforming data transmission by seamlessly integrating high-speed, energy-efficient optical communication into the silicon platform. Silicon has an intrinsic bandgap of 1.12 eV (1100 nm) and is transparent to photons with energies below the bandgap. However, significant optical power can induce nonlinearities in the guiding medium. Specifically, the high-power density of a propagating mode within the 1550 nm wavelength may lead to two-photon absorption (TPA)¹ (coefficient β_TPA = 5 × 10^{−1 2} m/W), and contribute to free carrier absorption (FCA)², resulting in a reduction of its refractive index. These carriers primarily relax to the ground state through interband or intraband transitions, generating thermal phonons. The heating effect arising from thermal phonons results in a positive change in the refractive index, causing a redshift in the spectral response^3,4. These optical nonlinearities have been observed to occur at relatively low optical power levels as low as 0.3 mW¹.

To address non-linear effects in Si-based micro-ring resonator Si-(Si-MRR) devices, two approaches have been explored: passive and active types. Passive athermal devices are constructed through a careful design of the geometric structure or by overlaying a material with a negative thermo-optic coefficient onto Si-MRR. For instance, B. Guha et al. utilized a ring-assisted Mach Zehnder interferometer (MZI) to counteract thermal effects, where the spectrum blueshifts with temperature, counteracting the redshift of a conventional MRR⁵. Nevertheless, these devices necessitate meticulous designs and fabrication processes, requiring strict tolerance and resulting in large footprints. Another passive approach involves depositing a polymer with a negative thermo-optic coefficient as a cladding layer, counteracting changes induced by the positive thermo-optic coefficient of silicon⁶. For example, Lee et al. have extended the application of compensating polymer claddings to Si-MRR and have exhibited significant thermo-optic compensation, resulting in a temperature-dependent wavelength shift of 2 pm/K⁷. The drawback of the polymer cladding approach is the lack of compatibility with CMOS (Complementary Metal-Oxide-Semiconductor) platform, sensitivity to humidity, and challenging control of its optical properties⁵. To overcome these limitations, polymer cladding is replaced with TiO₂, a CMOS-compatible material with a negative thermo-optic coefficient^8,9. Although passive methods can eliminate or minimize thermal-induced variations in Si-MRR, alone they are not suitable for tuning or trimming the resonance wavelength to a desired position.

In contrast, active wavelength compensation offers dynamic tuning and compensation for thermal-induced variations in Si-MRRs. The most common method is to introduce integrated heaters onto the silicon photonic devices to actively monitor and control the optical phase using feedback control circuits^10,11. However, this approach can lead to significant power overhead (~mW/phase shifter), and the produced phase shift that is volatile in nature⁵. For programmable photonics, having non-volatile phase trimmers with zero or minimal power to maintain switched states is highly desirable. Although permanent phase trimming can be realized using complex methods^12,13,14, nevertheless, they are costly, time-consuming, and real-time monitoring of the process is difficult.

Achieving simultaneous insensitivity to coupled optical power and non-volatile wavelength trimming is therefore crucial, especially when considering high-power applications. The aforementioned passive and active devices cannot fulfill simultaneous power-insensitive and non-volatile wavelength trimming alone. In this context, S. Grillanda et al. experimentally demonstrate power insensitive and trimming functions by combining the polymer-coated silicon waveguides with photosensitive As₂S₃ chalcogenide glass¹⁵. However, this method is not CMOS-compatible and relies on an external light source excitation to modulate the refractive index of the As₂S₃. In another report, a Ge implant was used to create an index trimmable section in the ring resonator and an on-chip heater to apply a precise and localized thermal annealing to tune and set its resonance to a desired wavelength¹⁶. This method is CMOS compatible but dissipates electric power to drive the heaters. Therefore, achieving a dual performance remains an ongoing challenge.

Recently, the integration of two-dimensional (2D) materials onto the SiPh platform has emerged as a promising alternative enabling technology. It is endowed with a compelling array of inherent attributes, including high-speed operation, compact form factors, cost-effective manufacturing, low power consumption, and seamless compatibility with mainstream semiconductor production lines. Several recent studies have reported the integration of 2D materials onto Si photonic platforms for phase-shifting applications^{17,18,19,20,21}. These studies have utilized thermo-optic²², all-optical^23,24, and capacitive-controlled carrier concentration mechanisms²⁴. Nonetheless, thermo-optic and all-optical-based 2D integrated phase shifters tune the resonant wavelength by redshifting it, which, as a result, is not helpful for compensating redshift in the Si ring resonator due to high input optical power. On the other hand, this lack of electro-optic properties in 2D materials has led to the use of complex fabrication involving three-terminal capacitive device structures to achieve resonance wavelength trimming.

In this study, we demonstrate simultaneous power-insensitive and non-volatile phase trimmer functions based on heterogeneous integration of a two-terminal InPSe device on-silicon platform. The dual performance is enabled by leveraging InPSe’s electro-optic effect. The phase trimmer exhibits a switching energy as low as 60 pJ, which is over an order of magnitude reduction compared to state-of-the-art technologies. Additionally, a phase trimming rate of −24 pm/min has been achieved. This innovative approach opens avenues for enhanced performance and broader adoption in diverse fields.

Results

Material characterization

The In_4/3P₂Se₆ (InPSe) compound is part of the MPX₃ family. The metal thio- and selenophosphates (MPX₃: M = Ni, Zn, Fe, Sn, Co, In, etc., and X = S or Se) constitute a type of layered metal phosphorus trichalcogenide. The framework of MPX₃ comprises anionic [P₂X₆]₄ units created by bonding between a dumbbell-like P dimer and six X atoms. Divalent metal (MII) ions are dispersed in a honeycomb pattern around [P₂X₆]₄. Due to the weak interaction between anions and cations, a wide range of metal elements can be incorporated into the structure. Furthermore, MPX₃ materials exhibit diverse physical and chemical characteristics due to the distinct properties of multiple metal cations.

Only one R3-type +3 valence single cation M_4/3³⁺□_2/3[P₂Se₆]^4– type compound is reported to exist for the selenide sub-class of the greater MPX₃ family, known as In_4/3P₂Se₆. Here □_2/3 represents the cation vacancies. The In_4/3P₂Se₆ is a layered semiconductor that contains indium vacancies and is described as In_1.33□_0.67P₂Se₆²⁵. which can be seen as being stacked by a quintuple (Se–P–In–P–Se) layer bonded by van der Waals forces. Figure 1a shows a side-view schematic representation of the In_4/3P₂Se₆ crystal. In certain instances within older literature, the crystal is depicted as In_2/3(PSe₃) and In₄(P₂Se₆)₃^25,26. To verify its stoichiometry, an Energy-Dispersive X-ray Spectroscopy (EDS) spectrum was obtained from a bulk crystal, as shown in Fig. 1b. Identifiable peaks for the elements In, P, and Se is evident, and the estimated atomic ratio of In/P/Se in the samples is determined to be approximately 1:1.5:4.5. This ratio closely aligns with the formula In_4/3P₂Se₆.

Fig. 1: Schematic and structural characteristics of InPSe.

a Schematic representation of the InPSe in the side view. b EDS spectrum was obtained from the bulk crystals. The table in the inset indicates a stoichiometry ratio of the crystal flakes. c A high-resolution TEM (HRTEM) image of the flake and the scale bar is 5 nm. The inset shows the SAED patterns obtained from the HRTEM image and the scale bar is 51/nm. d PL and Raman spectra of the flake. The insets show the optical image of the exfoliated flake and its corresponding PL mapping at 674 nm and the scale bar is 5 µm.

A typical High-Resolution TEM (HRTEM) image obtained from exfoliated InPSe flakes is shown in Fig. 1c. The flakes were exfoliated from bulk crystals using the mechanical exfoliation method and transferred to a Transmission Electron Microscope (TEM) copper (Cu) grid. Additionally, Selected Area Electron Diffractometry (SAED) depicted in the inset of Fig. 1c reveals well-defined spots, indicating high-quality single-crystalline features and a hexagonal structure. The slightly darker spots in the inner circle result from weaker diffraction peak intensity.

The optical and structural properties of the InPSe flakes were further examined through photoluminescence (PL) and Raman spectroscopy using 532 nm laser wavelength excitation. Micro-PL spectra (Fig. 1d) collected from the flake display characteristic PL peaks located at ≈674 nm, aligning with the reported band-to-band transition of InPSe^27,28. An optical image of the flake is provided in the left inset of Fig. 1d. To gain more insights into the PL uniformity, μ-PL mapping scanned images were obtained from a selected area of the flake. They are highlighted with a red box in Fig. 1d left inset. The observed spatial variations in the PL intensity of InPSe could be attributed to thickness variation, as clearly evident from the optical image color contrast. Furthermore, the bottom inset of Fig. 1d shows characteristic resonance peaks obtained at 152.4 (E_g), 166 (E_g), 218 (A_g), and 256 cm^-1, which align well with reported studies^27,28.

Device fabrication

A schematic diagram of the Si-MRR/InPSe device is shown in Fig. 2a. The resonator geometry is optimized using finite difference time domain (FDTD) simulation. The radius of the micro-ring, the gap between it and the bus waveguide, the index of refraction of 2D flake, and the thickness of the silicon waveguide are key parameters that determine the resonance wavelength. These designs are based on silicon-on-insulator (SOI) wafers with a 220 nm top silicon layer and a 2 µm buried oxide layer. The MRR cavity has a waveguide width (d) of 460 nm and a radius of 50 μm. A bus waveguide with a gap spacing of 100 nm couples light to the micro-resonator, which is collected via a through port at the output.

Fig. 2: Si-MRR/InPSe device characterization.

a A schematic representation of the Si-MRR integrated InPSe phase trimmer. b SEM images of fabricated Si-MRR/InPSe device. The corresponding optical image is shown in the inset. The scale bars are 10 μm. c AFM height profile of the Si-MRR/InPSe device, displaying the blue and white cross-section lines representing the bare Si-MRR and the Si-MRR with the InPSe layer, respectively. The scale bar is 10 µm. d The extracted thickness of the Si-MRR and Si-MRR/InPSe revealed a difference of 30 nm between them.

A lensed fiber is used to butt-couple light between the fiber and the silicon chip. Additionally, two metal pads of Ti/Au (10 nm/120 nm) were symmetrically placed on the sides of the resonator as electrodes to test its static performance. The multilayer InPSe on top of the Si-MRR was transferred using a deterministic dry transfer process^29,30,31. This approach allows for free cross-contamination while causing no damage to the architecture of the target device. The InPSe flake is strongly adhered to the surface of the micro-ring waveguide as a result of the van der Waals (vdW) interaction forces and the absence of dangling bonds on the flake’s surface. The two electrodes on both sides of the waveguide are in contact with the two ends of the InPSe flake.

The scanning electron microscopy (SEM) and optical microscope images of the device are shown in Fig. 2b and inset, respectively. The surface texture and thickness profile of the transferred InPSe are measured using an atomic force microscope (AFM) as shown in Fig. 2c, d, respectively. As depicted, the flake is properly aligned and conformably adheres to the photonic waveguide structure beneath it, resulting in efficient light/InPSe coupling. The thickness of the 2D flake is measured as ~30 nm where the observed variations in the thickness profile of the AFM are due to the non-planar structure of the metal pads and ring resonator structure. It is worth noting that the metal pads are deposited 100 nm below the waveguide top surface, which induces a strain on the transferred flake. In this study, several devices were tested for flake thickness in the range between ~30–120 nm (see Supplementary Note 1 and Fig. 1).

Electrical and optical characterization

The transferred flake’s structural integrity is first verified through low-power PL intensity mapping images at 674 nm. It corresponds to the band-to-band emission of the InPSe flake that is performed on the integrated device (see inset in Fig. 3a). Results show the crystal maintains its original properties. However, a distinct difference in PL emission intensity is noted, with stronger intensity on the ring resonator surface and weaker intensity away. This difference is attributed to the non-planar flake surface due to height variations between metal pads and the ring resonator.

Fig. 3: Optical properties and guided light/InPSe interaction.

a Optical parameters (n and k) of the InPSe extracted from ellipsometry. The inset shows the PL mapping of the flake on Si-MRR. The scale bar is 4 µm. b Guided light-multilayer InPSe interaction: Electric-field profiles (|E|²) of TE mode of bare Si waveguide (top panel) and 30 nm InPSe on Si (bottom panel) at 1550 nm. c The transmission spectra of the MRR without (black) and with (red) the InPSe flake for the TE mode. d Electrical characteristics of the Si-MRR/InPSe device (30 nm) under dark and 532 nm light excitation. The inset shows the dark current of the Si-MRR/InPSe device.

Next, to assess the impact of the flake’s refractive index (RI) on the light confinement factor within the resonator, its optical index parameters are characterized. Accurion high-resolution ellipsometry, coupled with EP4-Model software, was employed to measure the real (n) and complex (k) optical parameters of the InPSe flake (30 nm). The obtained results are depicted in Fig. 3a. Notably, the experimental demonstration of the optical parameters of InPSe crystals has not yet been demonstrated. At a wavelength of 1550 nm, the extracted in-plane values are n = 2.943 and k = 0.021. Following that, the influence of the InPSe refractive index on Si-MRR optical guided modes is analyzed. The FDTD simulated quasi-transverse electric (TE) polarizations, both with and without InPSe flakes, are depicted in Fig. 3b for a flake thickness of 30 nm at 1550 nm wavelength. The performed simulation results indicate an effective TE polarization confinement within Si-MRR and InPSe (see Supplementary Fig. 2), while the TM (Transverse Magnetic) polarization (not shown) exhibits lower guidance and higher transmission losses. Considering that TE polarization exhibits stronger non-linearities in the Si-MRR with increased laser power, all experiments were conducted for these polarization-guiding conditions.

To evaluate the impact of the InPSe integration with Si-MRR, optical transmission spectrum measurements were performed on both the bare and loaded Si-MRR configurations. The measurements were carried out for the TE polarization in the wavelength range of 1520 nm to 1560 nm. In Fig. 3c, the TE transmission spectra before and after the integration of a 30 nm InPSe flake with a ~20 µm interaction length are illustrated. The Si-MRR’s initial resonance dip loss (RDL) is approximately 15 dB, with a free spectral range (FSR) of 1.89 nm. Following the integration of the InPSe flake, the RDL of Si-MRR/InPSe is increased by ~2 dB, while the measured FSR increases to 1.91 nm with a resonance shift toward a longer wavelength. By applying a Lorentzian fit to the measured transmission spectra shown in Fig. 3c (see Supplementary Fig. 3), we determined that the full width at half-maximum (FWHM) of the resonant spectra for bare Si-MRR and Si-MRR/InPSe were 0.1803 nm and 0.1937 nm (30 nm), respectively (see Supplementary Fig. 4). Calculating the loaded Q-factor (Q_loaded = λ₀/FWHM) from these FWHM values yields 21.2 × 10³ for Si-MRR and 9.03 × 10³ for Si-MRR/InPSe (30 nm). The observed decrease in the Q factor of Si-MRR/InPSe can be attributed to the propagation loss (α) induced by InPSe, encompassing bending loss, scattering loss, and material absorption loss. The propagation α for both the bare Si-MRR and Si-MRR/InPSe structures can be determined through the intrinsic quality factor (Q_int) of the MRR. Q_int and α are calculated using the following equations^32,33,34:

$${Q}_{\mathrm{int}}=\frac{{2Q}_{\text{loaded}}}{1+\sqrt{{T}_{0}}}$$

(1)

$${\alpha }_{\text{ring}}=\frac{2\pi {n}_{\text{g}}}{{Q}_{\mathrm{int}}{\lambda }_{0}}=\frac{{\lambda }_{0}}{{Q}_{\mathrm{int}}\cdot {FSR}\cdot {R}_{\text{ring}}}$$

(2)

$${\alpha }_{{InPSe}}=\frac{{\alpha }_{{Si}/{InPSe}}-{\alpha }_{{s}_{i}}\left(1-{n}_{\text{f}}\right)}{2\varPi {n}_{\text{f}}{R}_{{ring}}}$$

(3)

Where n_g is the group index, FSR is the free spectral range, R_ring is the radius of the ring resonator, and T₀ is the fraction of transmitted optical power measured by the photodetector at the resonant wavelength λ₀. Using Eqs. (1) and (2), the calculated propagation losses in Si-MRR (α_Si) and Si-MRR/InPSe (α_Si/InPSe) are 4.48 dB/cm and 10.03 dB/cm respectively. The optical loss attributed to InPSe is determined using Eq. (3) (the losses are in dB), where ${n}_{\text{f}}$ corresponds to the InPSe fractional coverage length on a ring resonator (${n}_{\text{f}}$ = 1/15.7). The calculated propagation losses (${\alpha }_{{InPSe}}$) due to 30 nm InPSe amount to 0.0091 dB/μm. However, ${\alpha }_{{InPSe}}$ increases with increasing InPSe thickness (see Table 1). However, remarkably, the achieved losses are lower than those reported for on-chip integrated 2D devices. For instance, Si-chip integrated graphene exhibits losses of ~0.04 dB/µm to 0.33 dB/µm for C-band wavelength propagation³⁴.

Table 1 A comparison of the thickness-dependent figure of merits of the Si-MRR/InPSe device under passive and active operation configuration

Following the passive device characterization, the devices underwent electrical testing (I–V) to validate electrical contact between the metal pads and the transferred flake (30 nm). Measurements were conducted in a bias voltage range of −20 V to +20 V, see Fig. 3d. The recorded dark current (I_dark) of the device fell within the pico ampere range (~10 pA), indicating the dielectric nature of the flake under dark conditions. Subsequently, the device was tested under vertical illumination using a 532 nm laser. The illumination I-V indicates a photosensitive characteristic, with the current (I_ill) jumping to 27 × 10⁻⁶ A. This transition from the “off” state to the “on” state resulted in a light current on/off ratio (I_ill/I_dark) of about 10⁶. The observed Schottky behavior of the device is attributed to the asymmetric contact area of the flake with the metal pads and interface states, leading to a slightly different barrier for the symmetric electrodes. Importantly, the dark current of InPSe remains similar irrespective of the InPSe flake’s thickness. Supplementary Fig. 5 depicts the dark current for a 120 nm thick InPSe device.

Passive phase compensation: optical power insensitivity

The objective of this study is to validate the power-insensitive and phase-trimming capabilities of the hybrid waveguide structure. In this experiment, a continuous wave (CW) laser source with TE-polarization at a wavelength center of 1550 nm was employed, and the laser power was gradually adjusted from 4.85 mW (6.86 dBm) to 39.90 mW (16.02 dBm). It is important to mention that, due to 12 dB/facet insertion losses to the silicon chip, the actual power delivered to the resonator is 0.30 mW (−5.14 dBm) and 2.52 mW (4.02 dBm), respectively. Initially, we investigated the resonance wavelength shift of the unloaded Si-MRR to input laser power. In the case of the bare Si-MRR, the optical mode is efficiently confined owing to the refractive index contrast between silicon and air. The absence of cladding results in a broader spatial distribution of the mode within the core and higher optical intensity confinement. This increased intensity elevates the likelihood of experiencing nonlinear effects.

In Fig. 4a, the resonance wavelength of the bare Si-MRR is shown as the laser power is gradually increased. A noticeable redshift in the resonance peak position is observed. This shift is depicted in Fig. 4b. The plot reveals a significant linear optical power dependence of approximately 31.7 pm/mW. Here, a maximum resonance wavelength shift of ~70 pm is observed as the power varies from 0.30 mW to 2.52 mW.

Fig. 4: Passive bare Si-MRR optical properties.

a Transmission spectra of the Si-MRR under various propagating laser powers for the TE polarization. b Measured resonance shift of Si-MRR at versus powers.

Next, we studied the effect of laser power on a loaded Si-MRR/InPSe device was investigated. The measured transmission spectrum analysis on the Si-MRR/InPSe device with a 30 nm thickness under varying laser powers, incrementally increasing from 0.30 mW to 2.25 mW, as illustrated in Supplementary Fig. 6a. Figure 5a presents a comparison of the resonance shift between the Si-MRR/InPSe and bare Si-MRR under low and high-power conditions. Notably, we observed a significantly lower dependence on laser power in the Si-MRR/InPSe configuration. There was a total shift of approximately 3 pm between 0.30 mW and 2.52 mW for the Si-MRR/InPSe device, whereas the bare Si-MRR exhibited a shift of approximately 70 pm. This stark difference underscores the passive device compensation capability of the InPSe-loaded structure.

Fig. 5: Passive compensation of Si-MRR/InPSe devices.

a Comparison of the transmission spectra of Si-MRR and Si-MRR/InPSe measured for a flake thickness of 30 nm at both low power (0.30 mW) and high power (2.52 mW). b Corresponding spectra were measured for flake thicknesses of 45 nm, 60 nm, and 90 nm. c Corresponding spectra for 120 nm thick flake. d The measured resonance shifts of Si-MRR/InPSe devices vary with different flake thicknesses at various powers. The inset illustrates the measured resonance shift between low (0.35 mW) and high power (2.55 mW) versus the thickness of the InPSe flake.

The observed power-insensitive behavior of Si-MRR/InPSe devices can be attributed, at least in part, to mode dispersion into InPSe. This dispersion is a consequence of the refractive index contrast (~0.6) between Si and InPSe, leading to a reduction in effective confinement within Si. Consequently, it diminishes the power buildup inside the silicon core, maintaining a power-insensitive operation. Importantly, the extension ratios of Si-MRR with InPSe at both low and high-power levels closely resemble those of Si-MRR with air cladding. This similarity suggests that the integration of a 30 nm InPSe on Si-MRR is almost transparent to telecom C-band propagation.

In our subsequent analysis, we investigated the influence of InPSe flake thickness on the compensation of the resonance wavelength shift. We examined various thicknesses—45 nm, 60 nm, 90 nm, and 120 nm—at different powers ranging from 0.30 mW to 2.52 mW, as depicted in Supplementary Fig. 6b–e. Figure 5b, c illustrate the corresponding resonance shifts for low- and high-laser power operations for the 45 nm, 60 nm, and 90 nm thick InPSe flake. All devices exhibited partial compensation, while the corresponding propagation losses increased from 103 dB/cm to 134.2 dB/cm (see Table 1). Figure 5c presents a comparison of the resonance shift between the Si-MRR/InPSe (120 nm) and bare Si-MRR under low- and high-optical power conditions. Notably, we observed that the device exhibits a high optical loss of 361.1 dB/cm along with reduced compensation capability under passive device operations. The extracted power-induced resonance shift of all measured devices for different thicknesses at various laser powers is depicted in Fig. 5d. Notably, it shows a pronounced dependence on flake thickness, resulting in shifts of 3 pm (30 nm), 19.31 pm (45 nm), 22.1 pm (60 nm), 28.2 pm (90 nm), and 44.75 pm (120 nm) between the low and high power. This is shown in the inset of Fig. 5d.

The thickness of the integrated InPSe layer plays a crucial role in shaping the mode profile distribution and thereby governing the nonlinear effects within the Si/MRR structure. The thickness-dependent mode profile distribution simulations were presented in Supplementary Fig. 2. As the thickness of the InPSe layer increases, there is a reduction in mode confinement inside the Si-MRR, while the confinement within the InPSe layer becomes more pronounced. This can result in increased nonlinearities within the InPSe flake. For example, G. Liu et al., recently reported second harmonic generation in InPSe³⁵. This observation implies that high optical powers induce nonlinearities in InPSe that can lead to its own redshift in the resonance wavelength. Furthermore, the InPSe flakes exhibit an in-plane anisotropy (see Supplementary Note 2 and Fig. 7). This anisotropy influences the light-matter interaction when integrated into the Si ring resonator. Those insights underscore the intricate interplay between InPSe flake thickness, transferred flake orientation, and optical power insensitive performance.

Active electro-optic phase trimming

While the passive Si-MRR/InPSe device exhibits a lower resonance shift compared to the bare Si-MRR, minimizing or eliminating the deviation between the resonance peaks at low and high-power levels is still required. Additionally, passive compensation lacks the precision to accurately adjust the resonance wavelength, emphasizing the need for active electro-optic fine-tuning.

In this study, we leverage the electro-optic properties of InPSe to actively adjust the resonance wavelength of the Si-MRR. Recent studies have highlighted the non-centrosymmetric characteristics and second harmonic generation in InPSe crystals³⁶. In addition, exfoliated InPSe flakes tested using piezoelectric force microscopy (PFM) measurements reveal the presence of ferroelectric characteristics (See Supplementary Note 3 and Fig. 8). Furthermore, under bias voltages, InPSe exhibits ionic conductivity, similar to CuInP₂S₆ and CuCrP₂S₆ ferroionic materials^37,38. The refractive index of such materials is influenced by their electronic and ionic structure³⁹. In a material with high ionic conductivity, the movement of ions can lead to changes in the local electric field, affecting its polarization and, consequently, its refractive index³⁹. Such attributes typically signify their potential to exhibit electro-optic effects. Therefore, an applied bias voltage can induce a change in the refractive index in a simple two-terminal InPSe device, it can expand its trimming range and, hence, the controllability of the resonance wavelength.

Thickness-dependent active phase trimming

To illustrate the thickness-dependent active phase trimming, we selected devices with thicknesses of 30 nm, 45 nm, 60 nm, 90 nm, and 120 nm, each with a coverage length of 20 µm. Figure 6a–c demonstrates the electro-optic tuning behavior of the 30 nm, 90 nm, and 120 nm InPSe flake transmission spectra at various bias voltages. As the applied bias increases, the resonance wavelengths experience a blue shift attributed to the change in the flake’s refractive index. Figure 6d depicts the measured resonance shift versus applied voltage, demonstrating a tuning efficiency or resonance wavelength tunability (α_λ = $\Delta$λ/$\Delta$V) in the range of 2.628–4.62 pm/V as the thickness of the InPSe flake increases from 45 nm to 120 nm. Interestingly, the 30 nm InPSe flake did not exhibit any electro-optic-induced shift until −10 V, which could be attributed to the fact that the refractive index change with voltage depends on the confinement factor inside the flake (Δn/ΔV = Γ_InPSe)⁴⁰. The performed simulations (see Supplementary Fig. 2) revealed that the mode confinement is less pronounced in the 30 nm thickness.

Fig. 6: Active electro-optical testing of hybrid Si-MRR/InPSe.

a–c Spectral response of the hybrid Si-MRR/InPSe with a thickness of 30 nm, 90 nm, and 120 nm respectively, for TE mode with a coverage length of ~20 µm for different DC voltages. d illustrates the measured thickness-dependent resonance shift plotted against the applied voltage, along with their corresponding linear fitting.

Furthermore, the devices with thicknesses ranging from 45 nm to 120 nm did not exhibit any blue shift until a voltage equal to −4 V was applied, suggesting that lower voltages may fall below the coercive field. The coercive field represents the energy barrier that must be surpassed to switch the orientation of dipoles within the ferroelectric material. Additionally, the current-off state (high resistance) switches to the current-on state (low resistance) at a threshold voltage of ~−4 V due to the activated In³⁺ ions migration. When the flakes experience an external electric field exceeding the coercive field and/or low-resistance state, the dipoles progressively align with the applied field until saturation.

From the measurement of the resonance peak shift (Δλ), the refractive index change (Δn) and phase shift change (φ) of the device can be obtained using Eqs. (4) and (5) below⁴¹:

$$\Delta n\left(V\right)=\frac{\lambda }{L}\left[\frac{\Delta \lambda \left(V\right)}{\text{FSR}}\right]$$

(4)

$$\phi =\Delta nL\,.\,\frac{2\pi }{\lambda }$$

(5)

$${V}_{\pi }.L=\frac{{\lambda }_{\text{FSR}}.\,L.{\rm{\Delta }}V}{2\Delta {\rm{\lambda }}}$$

(6)

Here, λ, Δλ, FSR, and L stand for the resonance wavelength (at 0 V), resonance wavelength shift, free spectral range (see Table 1), and the InPSe flake length (20 μm), respectively.

Therefore, the observed wavelength trimming ranges between 23.9 pm to 44.5 pm when −10 V is applied, corresponding to a refractive index change (Δn) of 9.8 × 10⁻⁴ to 1.8 × 10⁻³ RIU (see Supplementary Fig. 9) and a phase shift change (φ) of 0.07948 to 0.14642 rad. The factor V_π·L, defining the voltage needed to be applied on the phase shifter of length L to achieve a π phase shift, measures the modulation efficiency and footprint of the device. This half-wave-voltage length product is calculated from Eq. (6) as 0.72–0.41 V cm when the thickness varies from 45 nm to 120 nm. Table 1 summarizes the thickness-dependent figure of merits of the Si-MRR/InPSe device under passive and active operation configuration. In the following sections, to demonstrate in-situ trimming, bidirectional trimming, and non-volatile function and stability, we selected the Si-MRR/InPSe device with a thickness of 90 nm. This choice was made due to its low propagation loss and better resonance wavelength tunability.

In-situ phase trimming and bi-directional trimming

Figure 7a illustrates the transmission spectra acquired under passive conditions at both low (0.30 mW) and high power (2.52 mW) optical coupling for a 90 nm flake. The high-power spectrum demonstrates a discernible redshift of 29.85 pm from the low-power resonance peak. To compensate for this redshift, the device was operated in the active configuration. Initially, the device was tested under 0 V at high power operation, and the resonance peak position was found to be similar in both passive and active configurations. Subsequently, after applying −10 V, the transmission spectrum underwent a blue shift (−29.85 pm), precisely matching the resonance wavelength observed under low-power conditions.

Fig. 7: In-situ phase trimming and bi-directional trimming.

a In-situ phase trimming by applying bias voltage. b Bias voltage-dependent bi-directional phase trimming. c, d Schematic representation of the In³⁺ ion migration under positive and negative bias voltages.

Furthermore, we investigated the effects of both positive and negative voltages. Figure 7b demonstrates the impact of positive and negative bias on the resonance peak shift. Initially, the transmission spectrum of the MRR/InPSe was measured at 0 V, and then measurements were taken at +4 V and +10 V bias. The transmission spectra obtained at +4 V and +10 V exhibited a blue shift from the resonance peak measured at 0 V. As illustrated in Fig. 7c, this shift occurred because, under positive bias, In³⁺ ions migrated away from the positive voltage terminal.

Subsequently, transmission spectra were measured under −10 V and − 4V negative bias. These spectra showed a redshift from the resonance peak observed at +10 V, indicating the device’s ability to shift the resonance peak position bidirectionally. Under negative bias, the In³⁺ ions moved towards the negative terminal, as depicted in Fig. 7d. It’s noteworthy that ion migration under negative bias occurs in the opposite direction to that induced by positive bias. These results suggest that the direction of ion migration governs the refractive index of the InPSe. Finally, the transmission spectrum of the MRR/InPSe was measured at 0 V. Remarkably, the resonance wavelength remained at its newly trimmed position even after releasing the voltage (set to 0 V), and it remained stable even after 90 min. This observation underscores the non-volatile nature of wavelength trimming. The impact of the holding time period will be discussed in the next section.

The electric power required for performing phase trimming is a key aspect that characterizes the performance of the phase tuning and trimming mechanism. Therefore, as illustrated previously in Fig. 3d, a low dark current in the range of 10 pA was measured which corresponds to a remarkably low tuning power of only 60 pW. This tuning power is extremely low compared to BaTiO₃ and silicon thermo-optic tuning elements, which typically exhibit tunning power values exceeding 100 nW and ~1 mW, respectively^42,43. Notably, the resonance linewidth and extinction ratios remained unaffected when bias was applied across the device, indicating that the active migration of In³⁺ ions did not impact the imaginary part of the refractive index.

Non-volatile stability

To evaluate the repeatability of the non-volatile property of the devices, we conducted a series of tests utilizing set/read/hold-repeat functions. Initially, the voltage was set to −6 V for 5 min, and subsequently, the resonance peak position was read. Following this, the voltage was removed (set to 0 V), and a 15-minute hold period was allowed before verifying whether the resonance peak position remained consistent with the previously recorded position. This stability test was performed continuously for 420 min, as depicted in Fig. 8a. The results indicate that the resonance peak positions during the read and hold functions remained consistent throughout the entire 7-hour test duration.

Fig. 8: Non-volatile memory and stability test.

a A continuous test lasting 420 min using the set/read/hold function. The inset illustrates the schematic of the set/read/hold cycle function. b, c display the transmission spectra obtained during the read and hold functions, respectively, spanning from 5 min to 420 min. d The stability of the Si-MRR/InPSe device was evaluated over a continuous testing operation lasting 6 days. The device exhibited a non-volatile nature throughout the entire duration of the six-day test.

Figure 8b, c further illustrates the resonance peak positions obtained during the read and hold phases over the continuous 420-minute operation. To assess stability, the device was continuously tested over six days, as shown in Fig. 8d. During these six days of measurements, several tests were conducted by applying both positive and negative bias voltages and allowing the devices to rest at 0 V for several hours between measurements. Notably, the resonance peak of Si-MRR/InPSe is consistently blue-shifted to approximately 0.9 nm on day 6 and exhibited a non-volatile nature throughout the six days of operation. Additionally, the peak variation between each read signal was measured, as shown in Supplementary Fig. 10, and the device exhibited a consistent peak shift of 18.68 ± 1.39 pm (for each set/read /hold cycle).

Effect of polling time on phase trimming

While the effect of voltage polling on the electrical characteristics of other multiferroic 2D materials that are close in structure, such as CuInP₂S₆ and CuCrP₂S₆, is well-documented, there is a noticeable gap in the literature regarding studies on the polling time of InPSe. Our investigations aimed to fill this gap by evaluating the influence of voltage polling time on the refractive index variation of InPSe. Thus, we examined the resonator wavelength response under a fixed polling time bias. As depicted in Fig. 9a, c, resonance spectra were consistently recorded at −6 V and −10 V during each step of the polling period. The flake thickness is 90 nm and has a length of ~20 µm. Results are recorded at one-minute intervals over a maximum duration of fifteen minutes. Across all scans, a consistent and uniform blue shift in resonance wavelengths was observed. Notably, the resonance linewidth and extinction ratios remained unaffected when bias was applied across the device.

Fig. 9: Effect of polling time on phase trimming.

a Transmission spectrum of Si-MRR/InPSe device at different polling times at a fixed DC voltage of −6 V. b A linear blue shift at a rate of 4.85 pm/min (~0.66 GHz/min), resulted in a total shift of 66.3 nm (~8 GHZ/min) during the 15-minute polling time. c Transmission spectrum of Si-MRR/InPSe device at different polling times at a fixed DC bias of −10 V. d A linear blueshift at a rate of 24 pm/min (~2.9 GHz/min), resulting in a total shift of 0.35 nm (~42 GHz/min) during the 15-minute polling time.

Figure 9b, d depict the resonance shift corresponding to each polling time. The observed wavelength trimming rates were −4.85 pm/min and −24 pm/min for −6 V and −10 V DC bias, respectively. The achieved trimming rates are within a similar range to those reported in trimming studies¹⁵. Notably, at higher voltage (−10 V), the shift is almost 5 times faster than at low voltage (−6 V). This underscores the dynamic nature of refractive index modulation under distinct polling conditions, providing essential insights for optimizing device performance.

Discussion

Without cladding, the increased intensity and larger mode confinement in bare Si MRR can enhance two-photon absorption (TPA) effects. TPA is dependent on the intensity of the incident light and it leads to absorption of two photons simultaneously, contributing to nonlinear losses. The integration of InPSe on Si–MRR, aims to mitigate this effect regardless of variations in input power. The thickness of the InPSe layer determines the extent to which the optical mode overlaps with it. Phase tunning in Si-MRR/InPSe is achieved through bias voltage, inducing a refractive index change. This change is attributed to potential ferroelectricity and ion migration in InPSe.

Piezoresponse Force Microscopy (PFM) measurements conducted on InPSe validate its potential ferroelectric nature. Additionally, InPSe shares similarities with recently explored ferroionic semiconductors such as CuInP₂S₆ and CuCrP₂S₆. Previous reports on these materials indicate their ferroelectricity coupled with ionic conductivity^37,38. In our measurements, the applied bias voltage can alter the orientation of electric dipoles and also induce ionic (In³⁺) migration. It is crucial to note that the spatial redistribution of In³⁺ ions within the layers may lead to dynamic electric field variations, influencing charge carrier injection and distribution, which can also influence the refractive index of the material. Therefore, the observed change in the refractive index of InPSe could be attributed to a combination of ferroelectric and ionic conduction.

The non-volatile phase trimming relies on the interaction between ferroelectric polarization and defect dipoles. For example, in ferroelectric perovskite oxide ABO₃, titanates, assumed to be predominant native defects, significantly influence material properties⁴⁴. We believe, the inherent Indium (In) vacancies in InPSe, act as native defects, allowing control of ferroelectric properties like a P-V hysteresis loop by modifying the polarization-switching process⁴⁵. Defects impact thermodynamic stability, serve as nucleation centers for polarization switching, and act as pinning sites for domain walls⁴⁶. During electrical switching, aligned defect dipoles reinforce matrix polarization due to symmetry. Upon voltage removal, the internally generated field by defect dipoles safeguards against polarization reversion. This interlocking switchable defect dipole mechanism introduces a strategy for maintaining permanent phase trimming retention.

This investigation showcases the simultaneous integration of key functionalities: optical power insensitivity, phase trimming, and non-volatile phase characteristics. Previous literature has separately reported these functions or combined negative thermo-optic materials with phase-trimming techniques. However, no study has demonstrated the simultaneous incorporation of all these functions in a single solution. In our work, we have achieved these characteristics through the utilization of both passive and active phase-trimming techniques. Passive Si-MRR/InPSe maintains stable performance even in the face of laser power fluctuations that would traditionally disrupt functionality. On the other hand, active Si-MRR/InPSe demonstrates both phase trimming and non-volatile characteristics. The non-volatile nature of the phase trimmer, which consumes minimal electrical power during switching (~60 pW) and none in a steady state, highlights its efficiency. The power-insensitive and trimmable waveguide technology provides the capability to stabilize the absolute wavelength and spectral response of photonic devices, exhibiting minimal dependence on laser power. In essence, InPSe emerges as a pioneering class of non-volatile material, where phase trimming induces refractive index modulation with low loss penalties. This finding paves the way for advanced and robust applications in photonic technology.

Methods

Materials supply

InPSe crystal flakes were procured from 2D semiconductors, accessible at https://www.6carbon.com/.

Scanning electron microscopy

The photonic chips were fixed to an SEM stub using carbon tape and visualized in high vacuum mode with a (FEI) Quanta 450 field emission scanning electron microscope operating at an electron energy of 10 kV.

Mode analysis and FDTD simulation

The eigenmode solver in MODE Solutions, a component of Lumerical’s Device Multiphysics Simulation Suite, was employed to analyze the electric field profile within the silicon. Subsequently, this electric mode profile was utilized to infer the confinement of light within the integrated InPSe flake.

Spectroscopic imaging ellipsometer

Accurion’s Imaging Ellipsometry was employed to analyze the optical properties of multilayer InPSe. This technique integrates optical microscopy with ellipsometry to provide spatially resolved measurements of layer thickness and refractive index. The EP4 model software was utilized to fit the ellipsometric parameters, namely Psi (ψ) and Delta (Δ).

Optical characterization

The light was coupled into the device structure at the edge using a lensed fiber, and optical transmission tests were conducted with a tunable laser operating in the O-optical band (Keysight 8164B Lightwave Measurement System). The output response from the devices was collected by an output lensed fiber and measured using a power meter. To calibrate the light polarization (TE), reference rings with identical geometries were fabricated on the same devices. Additionally, the output optical power intensities were calibrated before device testing using a conventional photodiode power sensor.