Geometry-Optimized Silicon Nanorods

• Geometry-optimized silicon nanorods are precisely engineered semiconductor structures that enhance optical and surface properties by tailoring rod dimensions and array configurations.
• Advanced optimization methods including inverse design, evolutionary algorithms, and FDTD simulations enable control over resonant enhancements, phase shifts, and directional radiation.
• State-of-the-art fabrication techniques such as RSML, e-beam lithography, and cryogenic RIE facilitate scalable production with high aspect ratios for photonic, sensing, and superhydrophobic applications.

Geometry-optimized silicon nanorods are nanostructures in which the spatial configuration, shape, and aspect ratio of silicon rods or related building blocks are precisely engineered to optimize specific optical, photonic, or physicochemical functionalities. Optimization is typically defined with respect to application-driven metrics such as emission enhancement, directional radiation, wavefront shaping, antireflectivity, or superhydrophobicity. Recent methodologies leverage inverse design, global optimization algorithms, and advanced lithographic fabrication, enabling robust control over individual rod dimensions, position, and array topology over wafer-scale surfaces. This entry surveys the state-of-the-art in geometry-optimized silicon nanorods, detailing design strategies, physical mechanisms, fabrication routes, exemplary performance metrics, and principal applications.

1. Design Strategies and Parameterization

Fundamental to all geometry-optimized silicon nanorods is a rigorous definition of their constituent dimensional parameters—typically length, width, and height for rods; diameter and pitch for arrays; and additional angles or tapering for cones. In single-objective and multi-objective optimization studies, multiple geometric models are considered:

• Resonant nano-rod configuration: Exemplified by arrays of five silicon rods ($L=300\,\mathrm{nm}$, $W=50\,\mathrm{nm}$, $H=100\,\mathrm{nm}$) whose lateral positions $(x_i, y_i)$ and binary orientations (0°/90°) are adjusted to manipulate local field enhancement and directionality, yielding a 15-dimensional parameter space (Hernandez et al., 2023).
• Meta-optical unit cells: Metalenses based on nanorods use individual silicon rods (height $h_\mathrm{rod}=1.1\ \mu\mathrm{m}$, radius $r=30$—110 nm) per cell, modulating phase and reflectance by radius and height sweeps (Ahmed et al., 2 Dec 2025).
• Array-shape modulations: RSML-developed rods/pillars (diameter $d$, height $h$, pitch $p$) are engineered for high aspect ratios ($AR = h/d$ typically 10–20), with tunable base (re-entrant) or top (tapered) profiles for advanced wetting or optical functions (Michalska et al., 2021).

Reflective or transmissive targets, as well as modal resonance selection, place additional constraints on rod geometry with respect to wavelength-scale material and environmental parameters, such as silicon’s complex permittivity, the substrate refractive index, and exclusion volumes for host emitters.

2. Optimization Algorithms and Simulation Frameworks

Systematic geometry optimization of silicon nanorods employs global search algorithms coupled to full-wave or modal simulation solvers. Notably:

• Evolutionary Optimization: Differential Evolution (DE) governs population-based optimization in the configuration space of rod positions and orientations. Each candidate geometry is evaluated for emission enhancement and directionality using frequency-domain Green’s Dyadic Method implemented via pyGDM (Hernandez et al., 2023). Convergence is reached after several hundred to several thousand generations depending on the degree of freedom, with trade-offs between solution quality and runtime resources.
• Parametric FDTD Sweeps: In metalens design, the interaction of NIR light with the nanorod is simulated using Lumerical FDTD with finely meshed regions (down to $\Delta x = 2$ nm), producing discrete lookup tables of phase shift $\varphi(r, h_\mathrm{rod})$ and reflectance $R(r, h_\mathrm{rod})$ for interpolation-based design (Ahmed et al., 2 Dec 2025).

Fitness functions depend on application: Purcell-factor enhancement ($F = \Gamma/\Gamma_0$), directionality ratio ($R_\mathrm{dir} = I_\mathrm{dir}/I_\mathrm{rest}$), and phase-quantization error ($<5^{\circ}$ in metalens mapping) are typical. For arrays, reflectivity, contact angle, and hysteresis serve as metrics (Michalska et al., 2021).

3. Physical Mechanisms and Optical Phenomena

The functional properties of geometry-optimized silicon nanorods arise from tailored electromagnetic resonances and interference effects:

• Mie Resonant Enhancement: Central rods in optimized nano-antenna assemblies function as high-Q Mie-type electric dipole resonators near target wavelengths (e.g., $\lambda_0=637$ nm for quantum emitters), locally enhancing the photonic density of states and hence the emission rate (Purcell effect) (Hernandez et al., 2023).
• Directional Interference: Arrays of director rods at half-wavelength intervals ($\sim \lambda_{\mathrm{eff}}/2$) constructively steer emission into targeted directions, manifesting Yagi–Uda or Bragg-mirror-like behavior.
• Whispering Gallery Modes: In inversely tapered nanocones, leaky whispering gallery modes (WGMs) with high Q ($Q\sim1300$) and small mode volume ($V_m\sim0.01$–$0.05\ \mu\mathrm{m}^3$) originate from the variable local circumference and result in Purcell factors $\sim200$, supporting strong photoluminescence over multiple peaks (Schmitt et al., 2015).
• Phase Control for Metalenses: Systematic variation of nanorod diameter allows arbitrary assignment of phase delay $0\to 2\pi$ at each metasurface cell, while maintaining high reflectance ($R>0.8$), enabling focusing and wavefront shaping at the subwavelength scale (Ahmed et al., 2 Dec 2025).

4. Fabrication Techniques and Geometry Control

Fabrication routes are highly determinative of achievable geometry and final device quality:

• Regenerative Secondary Mask Lithography (RSML): Polymer micelle (PS-b-P2VP) self-assembly and repeated CHF₃/Ar/H₂ and O₂ plasma cycles enable glass (SiO₂) hard mask creation with tunable height and diameter, transferred into silicon via high-selectivity Cl₂ ICP etching. This method achieves well-controlled aspect ratios (up to 20), pitches down to 50 nm, and base diameters as low as 20 nm across full 6" wafers (Michalska et al., 2021).
• E-beam Lithography and Reactive Ion Etching: For single or sparse arrays—nanoantenna applications—standard EBL with sub-20 nm alignment and plasma etching achieves rods or blocks with lateral placement and orientation control (Hernandez et al., 2023).
• Colloidal Lithography and Cryogenic RIE: Used for inverted nanocone (SiNC) formation supporting WGMs, with passivation steps to ensure low-loss interfaces (Schmitt et al., 2015).
• Layered Nanorod Metalens Stacks: Deposition of silicon on SiO₂ and metallic reflectors, followed by FIB or EBL patterning, defines vertical rods of prescribed height and lateral dimension for phase-controlled metalens applications (Ahmed et al., 2 Dec 2025).

Architecture versatility is realized through control of lateral scaling (modulation factor $\alpha=d_m/d_0$), stack height, and process gas chemistry.

5. Performance Metrics and Benchmarks

Geometry-optimized silicon nanorods demonstrate exceptional metrics in both single-emitter and array-based systems:

Property	Achieved Value/Range	System Reference
Purcell enhancement (F)	Up to ~200 (SiNC), F~5 (nano-rods)	(Schmitt et al., 2015, Hernandez et al., 2023)
Directionality ratio	$R_{\mathrm{dir}} > 8$	(Hernandez et al., 2023)
Reflectance (visible)	$<5\%$ (all $\lambda=400$–$1000$ nm, AR > 7)	(Michalska et al., 2021)
Adv. contact angle	$158^\circ$ (superhydrophobic, AR > 7)	(Michalska et al., 2021)
NA (metalens/SiNC WGMs)	NA~0.15 (metalens); NA~0.22 (SiNC vertical out)	(Ahmed et al., 2 Dec 2025, Schmitt et al., 2015)
Focusing FWHMs	$3.1\times2.7~\mu$m (metalens)	(Ahmed et al., 2 Dec 2025)
PL Enhancement (SiNC)	$200\times$ (integral); $670\times$ (peak mode)	(Schmitt et al., 2015)

Key sensitivities include placement tolerance (robust to tens of nanometers), bandwidth (FWHM~30 nm for nano-antenna resonance), and phase quantization error ($<5^{\circ}$).

6. Practical Applications and Design Guidelines

Optimized geometries enable diverse applications:

• Quantum Emitter Antennas: Enhanced and directed emission via optimized nano-rod assemblies with mirror symmetry layouts provide robust, lithographically defined placements for deterministically coupled diamond centers or emitters (Hernandez et al., 2023).
• Reflective Metalenses: Single-layer, subwavelength arrays of Si nanorods on SiO₂/Au deliver $0$–$2\pi$ phase coverage and high focusing efficiency, suitable for NIR imaging, optical communication, and sensor platforms (Ahmed et al., 2 Dec 2025).
• Superhydrophobic, Antireflective Coatings: Wafer-scale arrays of high-AR silicon nanorods, with tunable pitch and base diameter, yield uniform low reflectivity and water contact angles approaching 158°, targeting photovoltaics and antifouling surfaces (Michalska et al., 2021).
• Enhanced Photoluminescence: Si nanocones fabricated for leaky WGM resonance maximize light extraction and emission rates, suited for silicon photonics and NIR emitters (Schmitt et al., 2015).

Design “recipes” specify BCP block molecular weights, spin parameters, etch cycles, and mask modulations for application-driven pillar geometry, with empirical correlations between $AR$, $d$, $p$, reflectance, and hydrophobicity (Michalska et al., 2021).

7. Future Directions and Robustness

Current research demonstrates significant robustness to geometric disorder: both Purcell enhancement and directionality in quantum emitter antennas vary by $<10\%$ for $\pm40$ nm displacement, with potential for further functional gain at smaller emitter–antenna distances (Hernandez et al., 2023). Spectral band control and modal engineering in nanocone arrays remain open to further optimization, promising tailored multi-functional surfaces. The scalable, high-throughput fabrication via RSML extends utility to larger substrates and cost-sensitive applications. A plausible implication is that as simulation-accelerated iterative design workflows increase in fidelity and integration with fabrication constraints, geometry-optimized silicon nanorods will play a central role in next-generation nanophotonic and surface-engineered devices.

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References

• (Hernandez et al., 2023) Directional silicon nano-antennas for quantum emitter control designed by evolutionary optimization
• (Ahmed et al., 2 Dec 2025) Reflective Metalenses for Near-Infrared Wavelengths Based on Silicon Nanorods
• (Michalska et al., 2021) A route to engineered high aspect-ratio silicon nanostructures through regenerative secondary mask lithography
• (Schmitt et al., 2015) Observation of strongly enhanced photoluminescence from inverted cone-shaped silicon nanostuctures