Spatially-Controlled Planar Czochralski Growth

• Spatially-controlled planar Czochralski growth is a guided crystallization technique that spatially seeds and directs a single crystalline front in low-loss Sb₂S₃ phase-change materials.
• The method employs engineered reservoir-channel architectures and precise isothermal annealing to yield uniform optical and electrical properties in lithographically-defined, planar geometries.
• This approach mitigates stochastic nucleation and grain boundary scattering, enabling multilevel, non-volatile, programmable photonic circuits with enhanced device uniformity.

Spatially-controlled planar Czochralski growth is a guided crystallization technique enabling quasi-monocrystalline extension of low-loss chalcogenide @@@@1@@@@ (PCMs), particularly Sb₂S₃, within lithographically defined, planar-confined geometries. Unlike conventional PCM crystallization methods, which are governed by stochastic, simultaneous nucleation and grain merger, this method spatially seeds and subsequently directionally propagates a single or filtered crystalline front into previously amorphous PCM films. The approach addresses inhomogeneous crystal grain structures and ensures uniform optical and electrical properties—essential for reconfigurable nanophotonic devices—which are otherwise limited by uncontrolled polycrystallinity and grain boundary scattering. The spatially-controlled planar Czochralski method incorporates engineered reservoir-channel architectures, thermal annealing strategies, and in situ monitoring, culminating in scalable, robust, non-volatile device functionalities for photonic integration (Bentata et al., 23 Apr 2025).

1. Experimental Platform, Apparatus, and Fabrication Architecture

The experimental realization comprises two primary device classes: Mach–Zehnder interferometer (MZI) test structures and programmable metasurfaces. For MZI experiments, 600 nm-thick, 600 nm-wide silicon nitride (Si₃N₄) waveguides, fabricated using deep-UV lithography and reactive ion etching in a commercial foundry, provide the photonic platform. Metasurface devices are based on 150 nm-thick amorphous Sb₂S₃ films on glass, further capped with a 15 nm silicon nitride layer to mitigate chemical degradation during subsequent annealing.

Sb₂S₃ PCM films (50 nm for MZI, 150 nm for metasurfaces) are deposited via electron-beam evaporation at ~0.7 Å/s and <5 × 10⁻⁶ mbar base pressure. Pattern definition employs photolithography and lift-off for MZI structures, and electron-beam lithography followed by inductively-coupled plasma (ICP) RIE for metasurfaces. The patterned chips incorporate a reservoir (≈100 µm × 100 µm) directly linked to guidance channels of tunable width (2–50 µm), as well as functional PCM domains. A protective overlayer of SiO₂ (50 nm, for MZI) or Si₃N₄ (15 nm, for metasurfaces) is deposited as a chemical and mechanical barrier during high-temperature annealing steps.

Thermal treatment is implemented using a programmable hotplate with ±1 °C stability, enabling isothermal annealing at 250–260 °C with durations scaled for desired crystal growth distance. In-situ visualization utilizes bright-field and cross-polarized optics to track the crystal front progression via optical contrast (yellow-to-magenta color transformation), and transmission/reflection spectroscopy quantifies the photonic response.

2. Seeding, Channel Guidance, and Crystallization Protocol

Crystallization architecture exploits a large-area reservoir to guarantee at least one stochastic nucleation event; this approach eliminates the randomness inherent to nucleation in narrow channels. Channels of widths between 2 µm (single-grain filtering) and 50 µm (polycrystalline, high-speed growth) are lithographically defined, with the probability of spontaneous nucleation suppressed for $w < 10$ µm. Isothermal annealing near the Sb₂S₃ crystallization threshold ($\sim$250–260 °C) induces nucleation within the reservoir after a short incubation period, at which point the emergent crystal acts as a seed.

The ensuing crystalline front subsequently invades the adjacent channel with near-constant velocity—analogous to a Czochralski "pull" process but restricted to a two-dimensional lateral geometry. Channel confinement ensures a single advancing front; the sidewalls suppress off-axis nucleation, providing directional and orientation filtering. This deterministic guidance yields either polycrystalline or quasi-monocrystalline output, depending on channel width.

3. Crystallization Kinetics and Phenomenological Models

Although the original study does not furnish a full continuum kinetic model, phenomenological relations are extracted. The isothermal front velocity is described as

$v(T) \simeq v_0\,\exp\left[-E_a/(k_B T)\right],$

where $v(T)$ is the front velocity, $E_a$ the activation energy, and $T$ the anneal temperature. The front position evolves as

$x(t) = v(T) t$

with experimental values at $250\,^\circ$C giving $v \approx 16.5\,\mu$m/min ($\sim 275$ nm/s). The classical Johnson–Mehl–Avrami–Kolmogorov (JMAK) law applies in the reservoir:

$X(t) = 1 - \exp[-K(T)\,t^n],$

denoting the crystalline volume fraction $X$ over time $t$ for a given nucleation and growth rate $K(T)$ and Avrami exponent $n$.

Thermal gradients across film thickness are negligible under hot-plate conditions, yielding in-plane isothermal growth. The channel interfaces stabilize the crystal-melt boundary, ensuring front planarity and precluding lateral nucleation events.

4. Parameter Sensitivity and Optimization Regimes

Critical process parameters are precisely manipulated for optimized device performance. For MZI devices, annealing at $250\,^\circ$C yields short incubation and stable propagation at $v \approx 16.5$ µm/min. For single-crystal metasurface fabrication, $T = 260\,^\circ$C affords reproductible seeding in $100$ µm-wide reservoirs and robust channel propagation even at channel widths as low as $2\,\mu$m. Wider channels ($w \sim 50\,\mu$m) facilitate rapid polycrystalline front migration, while narrow channels ($w \sim 2\,\mu$m) act as orientation filters to attain quasi-monocrystalline films.

Reservoir dimensions of $10$–$100\,\mu$m per side are sufficient for high-probability ($>$1) nucleation under standard conditions. Film thickness selection (50 nm for MZI, 150 nm for metasurfaces) negotiates between optical mode confinement and achievable crystallization rates. Anneal durations are used as a spatial control dial, tuning the physical extent of the crystalline phase for multilevel programmability.

5. Characterization of Structural and Optical Uniformity

Structural assessment employs polarized optical microscopy: polycrystalline regions in the reservoir manifest as a multihue mosaic, while crystallized channels exhibit spatially uniform coloration under cross-polarizers, indicative of single-orientation (quasi-monocrystalline) morphology. Micro-Raman spectroscopy reveals invariant spectral signatures (Ag modes at $\sim$191 cm⁻¹, 283 cm⁻¹, 301 cm⁻¹) within the guided channel, and strong intensity fluctuations in the reservoir.

The refractive index of Sb₂S₃ is measured as $n_\mathrm{amorph}(1.55\,\mu$m$) \approx 2.37$ and $n_\mathrm{cryst} \approx 2.54$; extinction coefficients $k < 10^{-4}$ validate ultra-low-loss performance in both phases. For MZI devices, effective index modulation ranges from $n_\mathrm{eff}^{\mathrm{amorph}} = 1.608$ to $n_\mathrm{eff}^{\mathrm{cryst}} = 1.625$ ($\Delta n_\mathrm{eff} \approx 0.017$), enabling continuous and non-volatile phase tuning. Ten distinct, stable transmission states with wavelength shifts of $5\,\mathrm{nm}$ and amplitude modulations up to $15\,\mathrm{dB}$ at $1550\,\mathrm{nm}$ are achieved by precise halting of the crystalline front.

Reflectivity band diagrams of the metasurface reveal bound state in the continuum (BIC) resonances at normal incidence. Amorphous-to-crystalline phase transition induces a sharp $100\,\mathrm{nm}$ red-shift in the BIC peak for quasi-monocrystalline regions—five times larger than the $20\,\mathrm{nm}$ shift measured in polycrystalline analogs.

6. Demonstrative Device Implementations

Two prototype devices are realized. The first is a multilevel, non-volatile MZI phase shifter, wherein a $50\,\mathrm{nm}$-thick Sb₂S₃ channel over one interferometer arm prevails. The extent of the crystalline region, programmable through anneal time, controls the accumulated phase via

$$\Delta \varphi = (2\pi/\lambda)\,\Delta n_\mathrm{eff}\,L_\mathrm{cryst}.$$

Ten stably distinct output states are demonstrated, retaining their programmed values indefinitely without power.

The second is a programmable metasurface, featuring a periodic array of rectangular holes ($w=200$ nm, $L=600$ nm, $P=900$ nm) milled into a $150$ nm Sb₂S₃ film with a 2 µm-wide guidance channel to achieve quasi-monocrystalline extension from the nucleation reservoir. The reflectivity spectrum reveals a spectrally sharp and large tunable BIC resonance, supporting programmable, non-volatile operation with high reproducibility.

7. Implications for Integrated Photonics and Future Prospects

Spatially-controlled planar Czochralski growth transforms random PCM grain formation into a deterministic seed-and-guide protocol. This achieves sub-micron spatial positioning of the crystalline front, device-to-device uniformity of crystal orientation, negligible additive optical loss, and continuously programmable, driftless non-volatile phase control. The method overcomes key limitations of conventional PCM integration, namely stochasticity in in-plane grain growth and elevated absorption, and enables scalable, power-free, multi-level programmable photonic circuits including phase-programmable meshes, reconfigurable filterbanks, and photonic switching fabrics.

Anticipated future advancements may integrate addressable, on-chip micro-heaters for local, electrically actuated planar Czochralski growth—potentially coupled with melt-quenching cycles to restore amorphous states—culminating in rewritable, non-volatile FPGA-style photonic chips (Bentata et al., 23 Apr 2025).