Hybrid Si₃N₄–Si–Si₃N₄ Waveguide Structures

• Hybrid Si₃N₄–Si–Si₃N₄ waveguides are integrated photonic structures that merge CMOS-compatible Si₃N₄ with high-index Si to enhance mode control and design flexibility.
• They employ both vertical layering and lateral hybridization to achieve polarization-selective confinement, efficient coupling, and adiabatic light transfer with low propagation loss.
• Implementations such as CTAP devices and transformation-optics mode converters demonstrate high transfer fidelity and efficient fiber–chip interfacing in compact photonic integrated circuits.

Hybrid silicon nitride–silicon–silicon nitride (Si₃N₄–Si–Si₃N₄) waveguide structures are advanced integrated photonic components that leverage the distinct optical properties of each constituent material to achieve superior mode control, coupling efficiency, and design flexibility compared to monolithic waveguides. These hybrid structures merge the moderate refractive index, CMOS compatibility, and low propagation loss of stoichiometric Si₃N₄ with the high refractive index and compactness of crystalline or amorphous silicon (Si or a-Si), enabling new device architectures for photonic integrated circuits (PICs). Several seminal designs—employing both vertical layering and lateral hybridization—demonstrate enhanced performance for light routing, mode transformation, polarization control, and adiabatic optical transfer mechanisms.

1. Fundamental Cross-Sectional Geometries

Two main geometric paradigms have been established for hybrid Si₃N₄–Si–Si₃N₄ waveguides: vertically layered and laterally hybridized structures.

• Vertically layered (“sandwiched”) geometry: An a-Si layer (n ≈ 3.54 at λ = 1.55 µm) of thickness t₂ is symmetrically embedded between two Si₃N₄ slabs (n ≈ 1.89, t₁, t₃), forming a tripartite core typically surrounded by SiO₂ cladding below and air or SiO₂ above. Layer thicknesses are nominally t₁ = t₃ = 200 nm, t₂ = 100 nm, with total core height H = 500 nm (Dash et al., 2023).
• Laterally hybridized geometry for CTAP: Two Si₃N₄ waveguides (w = 0.55 µm, h = 1.0 µm) are placed laterally, separated by a narrow gap (d ≈ 0.32 µm), with a much thinner Si waveguide (w_Si = 0.1 µm, h = 1.0 µm) embedded between them along the centerline. All cores are fully buried in SiO₂ (Borovkova et al., 10 Dec 2025).

This duality of vertical and lateral hybridization enables both polarization-selective mode confinement and optimized inter-channel coupling for adiabatic light transfer.

2. Optical Mode Properties and Polarization Engineering

The layered index profile in hybrid Si₃N₄–Si–Si₃N₄ structures enables independent control over the effective indices, field confinement, and polarization birefringence of fundamental modes.

• Polarization-dependent confinement: For vertical stacks, the high index contrast between a-Si and Si₃N₄ causes the TE₀ mode to localize strongly within the a-Si region (confinement factor Γ{a-Si} ≈ 0.685), while the TM₀ mode is largely confined to the Si₃N₄ layers (Γ{Si₃N₄} ≈ 0.718 at f = t₂/H = 20%, W = 700 nm).
• Birefringence control: Varying the a-Si fraction f tunes the TE–TM effective-index splitting (Δn) from near-zero up to ≳0.3, providing a direct route to polarization-selective devices or phase-matched conditions for active elements (Dash et al., 2023).
• Mode propagation constants (CTAP): The lateral hybrid CTAP structure’s high-confinement Si₃N₄ guides yield n_eff ≈1.5647 and β ≈6.34×10⁶ m⁻¹ at λ = 1.55 µm, with the central Si guide acting as a transient state in the adiabatic process (Borovkova et al., 10 Dec 2025).

3. Light Routing and Adiabatic Transfer: Hybrid CTAP Structures

The hybrid Si₃N₄–Si–Si₃N₄ CTAP (Coherent Tunneling by Adiabatic Passage) waveguide employs three coupled channels—|1⟩ (input, Si₃N₄), |2⟩ (central, Si), |3⟩ (output, Si₃N₄)—to enable robust, loss-minimized optical transfer via adiabatic evolution of the system’s dark state.

The effective Hamiltonian governing the process is:

$$H(z) = \sum_{j=1}^3 \beta_j|j⟩⟨j| + \Bigl[\kappa_{12}(z)|1⟩⟨2| + \kappa_{23}(z)|2⟩⟨3| + \text{h.c.}\Bigr]$$

Here, the coupling coefficients κ{12}(z), κ{23}(z) are spatially modulated through the waveguide layout (curvature R = 2.5 mm, offset Δx = 16 µm) to ensure the counter-intuitive sequence required for adiabatic transfer. The central Si guide’s high index largely suppresses optical population in |2⟩ (≲1%), minimizing losses associated with absorption or scattering in this intermediate channel (Borovkova et al., 10 Dec 2025).

High-fidelity transfer (>99%) is achieved over compact device lengths (∼110 µm), with substantial robustness against dimensional variations: ±10 nm in core width yields output fluctuations <10%, and ±0.5 mm in bend radius causes output drops <4%.

4. Transformation-Optics-Enabled Mode Converters

Efficient coupling between dissimilar waveguide platforms, notably broad Si₃N₄ and narrow SOI (Si), leverages transformation optics and metamaterial grading.

• Luneburg-lens-based index matching: A truncated, flattened Luneburg lens with quasi-conformal transformation optics implements a refractive index profile that spatially bridges n ≈ 1.98 (Si₃N₄) and n = 3.45 (Si) over R_lens = 1.0 µm. The index profile is:

$$n_{\text{lens}}(r) = n_{\text{edge}} \sqrt{\frac{1 + f^2 - (r/R_{\text{lens}})^2}{f}},\quad n_{\text{edge}} = 1.98,\ f = 1$$

• Graded photonic crystal realization: The required graded index is physically synthesized via a rectangular array of Si rods of varying radius (50–109 nm), embedded in Si₃N₄, on a grid a_x = 225 nm, a_y = 250 nm. The effective permittivity ε_eff,ij at each grid point is set via the TE effective-medium relation (Badri et al., 2020).
• Performance: Mode conversion between the 1.8 µm × 0.22 µm Si₃N₄ input and the 0.5 µm × 0.22 µm SOI output is achieved across a 1.93 µm coupler with 0.13 dB mean insertion loss (97% efficiency, return loss >20 dB) in the C-band (λ = 1530–1565 nm), with robustness to fabrication imperfections (±10 nm rod radius yields ≤0.05 dB excess loss).

5. Grating Couplers and Ring Resonator Responses in Hybrid Platforms

Hybrid Si₃N₄–Si–Si₃N₄ waveguides support efficient fiber–chip interfaces and resonant photonic elements by leveraging polarization-dependent mode confinement.

• Surface grating couplers: Surface gratings are patterned either selectively within the a-Si layer (for TE) or fully through the stack (for TM). Period Λ for phase-matched coupling at λ ≈ 1550 nm (θ ≈ 10°) is set by

$$\Lambda = \frac{\lambda}{n_\text{eff} - n_c \sin\theta}$$

Optimized designs (oxide-clad, f=20%, H=500 nm, W ≈ 700 nm) deliver η_TE = –3.27 dB (∼47% efficiency, 100 nm 3dB bandwidth) and η_TM = –8.0 dB (16%, 92 nm bandwidth) (Dash et al., 2023).

• Thermo-optic ring resonator characterization: 100 µm-diameter rings demonstrate polarization-selective excitation, with measured group indices agreeing with simulations: n_g,TE ≈ 3.38 (FSR = 2.23 nm), n_g,TM ≈ 2.18 (FSR = 3.31 nm). Resonance wavelength shifts as a function of temperature yield material thermo-optic coefficients: dn_{a-Si}/dT ≈ 2.05×10⁻⁴ K⁻¹, dn_{Si₃N₄}/dT ≈ 2.67×10⁻⁵ K⁻¹.

6. Fabrication Considerations and Design Flexibility

These hybrid structures are designed with lithographic compatibility and fabrication robustness.

• Process flows: For lateral hybrid CTAP, the central Si core width (w_Si) can be engineered without affecting adjacent Si₃N₄ guides, which is advantageous for integration of active functionalities (electro-optic, magnetic) (Borovkova et al., 10 Dec 2025). In transformation optics couplers, the Si rod GPC is patterned via e-beam lithography and plasma etching prior to Si₃N₄ deposition (Badri et al., 2020).
• Tolerances: Simulated performance remains high despite moderate parameter variations: e.g., grid coarsening from 225 nm to 290 nm in the GPC lens increases loss from 0.13 dB to ~0.86 dB. Control over a-Si fraction in sandwiched stacks enables device reconfiguration between high/non-birefringent operation (Dash et al., 2023).

Potential improvements include using higher-index hosts to further reduce device footprint, optimizing transformation optics mappings to lower reflection, implementing multistep index grading, and deploying inverse-design approaches (adjoint optimization) to drive insertion loss below 0.1 dB.

7. Comparative Assessment and Outlook

Hybrid Si₃N₄–Si–Si₃N₄ waveguide structures offer distinct advantages over single-material configurations. In CTAP devices, hybridization reduces central mode population below 1% (vs. 5–10% for all-Si₃N₄), mitigating loss in doped/absorbing guides and introducing an independent control parameter via w_Si. Overall, device lengths, spectral bandwidth, and transfer efficiencies remain comparable (>98% over ~110 µm), but central loss and device sensitivity are improved.

In layered architectures, polarization-selective confinement and tunable birefringence are exploited for high-performance fiber–chip coupling, phase control in resonators, and nonlinear applications.

A plausible implication is that hybrid Si₃N₄–Si–Si₃N₄ platforms provide a foundational element in future PICs by combining the scalability and low loss of Si₃N₄ with the strong confinement and functionality of Si, supporting advanced routing, mode conversion, and integrated actuation (Borovkova et al., 10 Dec 2025, Dash et al., 2023, Badri et al., 2020).