Parameter Study of 500 nm Thick Slot-Type Photonic Crystal Cavities for Cavity Optomechanical Sensing

Abstract

In recent years, research on light-matter interactions in silicon-based micro/nano cavity optomechanical systems demonstrates high-resolution sensing capabilities (e.g., sub-fm-level displacement sensitivity). Conventional 2D photonic crystal (PhC) cavity optomechanical sensors face inherent limitations: thin silicon layers (200–300 nm) restrict both the mass block (critical for thermal noise suppression) and optical Q-factor. Enlarging the detection mass in such thin layers exacerbates in-plane height nonuniformity, severely limiting high-precision sensing. This study proposes a 500 nm thick silicon-based 2D slot-type PhC cavity design for advanced sensing applications, fabricated on a silicon-on-insulator (SOI) substrate with optimized air slot structures. Systematic parameter optimization via finite element simulations defines structural parameters for the 1550 nm band, followed by 6 × 6 × 6 combinatorial experiments on lattice constant, air hole radius, and line-defect waveguide width. Experimental results demonstrate a loaded Q-factor of 57,000 at 510 nm lattice constant, 175 nm air hole radius, and 883 nm line-defect waveguide width (measured sidewall angle: 88.4°). The thickened silicon layer delivers dual advantages: enhanced mass block for thermal noise reduction and high Q-factor for optomechanical coupling efficiency, alongside improved ridge waveguide compatibility. This work advances the practical development of CMOS-compatible micro-opto-electromechanical systems (MOEMS).

1. Introduction

Cavity optomechanical systems [1] represent a novel class of MOEMS [2,3] that simultaneously host optical cavity modes and mechanical oscillation modes at micro/nano scales, with their defining feature being the strong coupling interaction between these two modes. Leveraging this light–matter interaction, researchers have achieved unique physical phenomena such as quantum ground-state cooling of mechanical resonators and quantum entanglement in multimode cavity optomechanical systems [4,5], which hold significant scientific value in both classical and quantum physics [6]. Advances in nanofabrication have propelled all-dielectric optical nanoresonators [7,8] to the forefront of research due to their low-loss characteristics, high field localization capabilities, and efficient electromagnetic wave manipulation. Under specific laser power excitation, these devices exhibit parametric optomechanical oscillations, multimode resonant interactions, and nonlinear dynamic behaviors such as chaos, frequency synchronization, and optomechanical frequency combs [9,10,11,12], offering new pathways for time–frequency standards and precision measurement technologies.

In recent years, mesoscale cavity optomechanical systems based on all-dielectric resonators have demonstrated exceptional performance in high-precision measurements of force [13,14], mass [15,16], acceleration [17,18], angular rate [19,20], and magnetic fields [21,22]. However, reported 2D photonic crystal-based optomechanical inertial sensors typically adopt silicon layer thicknesses of 220–250 nm [23,24,25] to ensure air hole sidewall angles close to 90° after electron beam lithography (EBL). As sensor performance requirements escalate, enlarging the detection mass block in such thin-layer structures introduces critical challenges: expanding the detection area without increasing silicon thickness exacerbates in-plane height nonuniformity (e.g., pronounced center sagging versus minimal deformation near support beams). This structural flaw not only degrades device robustness in dynamic environments but also limits their applicability in high-precision sensing.

To address these limitations, this study proposes a 500 nm thick silicon-based 2D slot-type PhC cavity [26,27] for optomechanical displacement detection, enhancing sensing performance through optical parameter optimization and nonlinear dynamics investigation. The design incorporates a line-defect waveguide loaded with an air slot, enabling strong Drude plasma coupling induced by two-photon absorption (TPA) on an SOI substrate. Finite element simulations identify viable parameter combinations (lattice constant, air hole radius, width of the line-defect waveguide) for the 1550 nm band, followed by 6 × 6 × 6 parameter scanning experiments. Experimental results demonstrate that silicon thickness under 500 nm and 88.4° etching angle, a lattice constant of 510 nm, air hole radius of 175 nm, and width of 883 nm yield an optical loaded Q-factor of 57,000, with distinct parametric optomechanical oscillations observed in the cavity’s mechanical modes. The thickened silicon layer strategy concurrently improves compatibility with ridge waveguide integration and increases the mass block within the same footprint, providing a new approach for CMOS-compatible cavity optomechanical sensor development.

2. Experimental System and Device Fabrication

The chip-scale cavity optomechanical oscillator is fabricated using silicon-on-insulator (SOI) technology and operates in the 1480–1620 nm wavelength band. As shown in Figure 1a, the experimental system consists of a tunable narrow-linewidth laser (Santec TSL-510). The amplified laser is adjusted to transverse electric (TE) polarization using a fiber polarization controller (FPC). The polarized light is then coupled to the cavity via a high-transmission tapered fiber in a vacuum environment. The coupled signal passes through a variable optical attenuator (VOA) and splits into two detection paths. The first path connects to a low-speed photodetector (Thorlabs PDB440C, 15 MHz) and an electronic spectrum analyzer (Keysight N9010B) for frequency domain analysis. The second path routes signals to a high-speed photodetector (Thorlabs PDB465C, 200 MHz) and a data acquisition card (NI USB-6212, 400 kS/s) for real-time time domain measurements.

Figure 1b shows the scanning electron microscopy (SEM) image of the fabricated cavity, featuring a periodic air hole array in the silicon slab. The SOI substrate has a standard three-layer structure: a 500 nm top silicon layer, a 1–3 μm buried oxide layer, and a 700 μm silicon handle layer. The cavity comprises two PhC plates (16.0 μm × 5.5 μm × 500 nm). To mechanically decouple the fixed block and sensing mass, a 100 nm wide air slot segments the line-defect waveguide. Rectangular openings on both sides release mechanical degrees of freedom in the central region. As shown in the inset of Figure 1b, symmetry-breaking displacement perturbations (red: 5 nm, green: 10 nm, purple: 15 nm) are introduced at the cavity center, compressing the modal volume into the perturbed region to enhance field localization.

The photonic bandgap is governed by lattice constant (a) and air hole radius (r). Initial simulations with a = 500 nm and r = 187.5 nm reveal a bandgap of 135.13–213.6 THz (1403.1–2217.9 nm). Since the operational band (187.3–199.8 THz, 1500–1600 nm) fully resides within this range, the design meets theoretical requirements. SEM characterization in Figure 1c confirms air hole sidewall angles of 88.3°–88.5° after EBL, with ±10 nm line-defect width variations caused by EBL alignment errors and anisotropic etching. To mitigate fabrication tolerances, we adopt a hierarchical parameter expansion strategy: All parameters are sampled at 6 equally spaced intervals within their ranges. For each lattice constant (a = 480–530 nm), a 6 × 6 parameter matrix is constructed. The vertical axis varies air hole radius proportionally (0.284a–0.382a), while the horizontal axis scans line-defect waveguide width (√3a–1.5√3a), forming a dual-parameter co-optimization framework.

3. Experimental Results

3.1. Optical Q-Factor Enhancement

This study determines the structural parameter ranges for the target wavelength band through finite element simulations, systematically investigating the synergistic effects of lattice constant, air hole radius, and line-defect waveguide width (w) using a hierarchical parameter expansion method. For six distinct lattice constants, each group constructs a 6 × 6 parameter matrix (fixed a, scanned r and w variations), and their optical mode responses are illustrated in Figure 2.

As shown in Figure 2a, when a = 510 nm, variations in the line-defect waveguide width induce an optical mode wavelength shift of approximately 1 nm. Comprehensive analysis in Figure 2b–f reveals that w-induced wavelength shifts generally in the range from 0 to 5 nm. The Q-value exhibits high sensitivity to waveguide width. When w > 1.1√3a, the increased width weakens the photonic bandgap confinement, causing optical field leakage into non-resonant regions and triggering sharp Q-value degradation [27]. To avoid invalid data interference, Figure 2 exclusively retains parameter sets with w ≤ 1.1√3a. According to the power threshold formula for optomechanical oscillation (OMO)

$$P_{\mathrm{th}\_\mathrm{OM}}\propto 1/\left(g_0^2{Q}_{\mathrm{m}}{Q}_{\mathrm{o}}^3\right)$$

(1)

where g₀ is the vacuum optomechanical coupling rate [27], and Q_m/Q_o denote mechanical/optical quality factors. When pump power exceeds this threshold, OMO is excited. Thus, w must be constrained within √3a–1.1√3a in practical applications.

Figure 2a also demonstrates that the increasing air hole radius shifts optical modes toward shorter wavelengths (1500 nm). Limited by the laser scanning range (1480–1630 nm), some parameter combinations could not be characterized. Figure 2b–f collectively show that air hole radius gradients induce wavelength shifts up to 40 nm. Fabrication imperfections (e.g., air hole ellipticity and radius deviations) further exacerbate experimental mode shifts.

Finally, cross-comparison of six lattice constant groups identifies an optimal Q-value region at a = 510 nm. Multi-power optical scans for cavities with this parameter yield the transmission curves in Figure 3a: the optical fundamental mode resides at 1580 nm, with higher-order modes near 1584 nm. Figure 3b presents Lorentzian fitting of low-power cold-cavity transmission spectra, where the inset’s fundamental mode electric field distribution exhibits strong localization. Experimental results confirm that at a = 510 nm, r = 175 nm, and w = 883 nm (500 nm silicon thickness, 88.4° sidewall angle), the loaded optical quality factor reaches Q_L = 57,000, representing a 2–3× improvement over conventional 220–250 nm thin-layer structures (Q_L = 20,000 [28], Q_L = 27,000 [10]).

3.2. Optomechanical Oscillation and Other Nonlinear Effects

The PhC cavity, fabricated on a low-resistance SOI wafer, induces high-density Drude-type electron-hole plasma oscillations via TPA under intense optical fields. These plasma dynamics synergize with thermo-optic effects, forming competitive interactions during intracavity optical field modulation. We conduct nonlinear dynamics analysis on the optimal cavity (a = 510 nm, r = 175 nm, w = 883 nm, and Q_L = 57,000). At 11 dBm input power (Figure 4b), the transmission spectrum exhibits four nonlinear regions: The first region (1584.6–1586.3 nm) corresponds to self-induced optical modulation (SOM) [29,30], with mechanical resonance characteristics shown in Figure 4a. This modulation arises from competition between free-carrier dispersion (blue shift) and thermo-optic effects (red shift). Subsequent regions (1587.8–1588.1 nm, 1589.1–1589.5 nm, 1592–1595 nm) display unstable pulse (USP) stages, with SOM-USP coexistence observed at 1594–1595 nm.

At 12 dBm (Figure 5b), spectral complexity increases: The first region (1585–1587.9 nm) is SOM-dominant. The second region (1587.9–1590.1 nm) transitions from OMO (before 1588.9 nm) to SOM. The third region (1590.1–1591.9 nm) exhibits USP-SOM coexistence within the initial 0.1 nm detuning range, followed by a complete transition to the SOM phase. The fourth region (1592.2–1595.1 nm) ends with SOM-USP coexistence.

At 13 dBm (Figure 6b), nonlinear effects span the entire scan range: starting from 1585 nm, cavity states evolve sequentially as USP → brief OMO (1585.5 nm) → SOM → OMO (1589–1589.5 nm with f_omo/2 components) → SOM/USP → OMO (1591.5–1592.5 nm) → USP/OMO. Critical regions for sensing are annotated in Figure 6a.

We further analyzed the nonlinear behavior of a non-optimal high-Q cavity (a = 520 nm, r = 178 nm, w = 900 nm, and Q_L = 14,000) as shown in Figure 7. Experimental results demonstrate that when the input power exceeds the USP-stage threshold, further power increase triggers competition between SOM and OMO. Crucially, OMO establishes stable mechanical resonance through self-sustained photon–phonon coupling—a deterministic operational phase required for sensor signal transduction. This indicates that flexible regulation of optical modes can be achieved through cavity parameter adjustments with controlled Q-factor degradation.

4. Conclusions

This study demonstrates a critical advancement in thickness limitations of traditional 2D PhC cavity optomechanical sensors through innovative structural design and systematic parameter optimization, achieving high-Q characteristics and parametric optomechanical oscillation effects in a 500 nm thick silicon-based slot-type PhC cavity. Experimental verification demonstrates that the optimal parameter combination—lattice constant (a = 510 nm), air-hole radius (r = 175 nm), and line-defect waveguide width (w = 883 nm)—achieves a loaded Q-factor of 57,000 at an 88.4° fabrication tilt angle, representing a 2–3 times improvement over conventional thin-layer structures. Through 6 × 6 × 6 parameter scanning and hierarchical extension strategies, we quantitatively reveal the structural parameter dependence of optical mode shifts (up to 40 nm) and Q-factor degradation (sharp decline when w > 1.1√3a).

Under intense optical excitation, the cavity exhibits rich nonlinear competitive effects (SOM/OMO/USP), with dynamic evolution pathways precisely regulated by pump power and wavelength detuning. High-power spectral scans typically reveal multi-stage mode transitions (e.g., USP→OMO→SOM), providing a prototypical system for investigating nonlinear dynamics such as chaos in PhC cavities. Notably, the thickened silicon layer strategy enhances both the effective mass of the detection block and optical Q-factors while establishing compatibility with ridge waveguide heterogeneous integration. Critically, the 500 nm thickness provides essential process redundancy: standard EBL etching requires >80 nm silicon retention on ridge waveguide sidewalls to avoid over-etching that results in discontinuous silicon layers, causing permanent waveguide structural damage. Compared to 220 nm platforms, this enhanced thickness enables greater parametric optimization headroom, higher transmission efficiency limits, and improved tolerance to fabrication variations. This work delivers an engineerable solution for performance enhancement and functional expansion of mesoscopic optomechanical systems using CMOS-compatible processes.