Structural order enhances charge carrier transport in self-assembled Au-nanoclusters

Self-assembled molecules and particles offer opportunities for microelectronic applications including LEDs, FETs, and sensors. While three-dimensional assemblies with long-range order can be made from gold nanoparticles, conventional nanoparticles have finite-size distributions that introduce energetic disorder in ensembles. Atomically precise inorganic molecular clusters (superatoms) provide well-defined structures, larger dielectric constants than organics, and strong quantum confinement, making them promising building blocks. Prior work on Au nanocluster ensembles reported conductivity in polycrystalline assemblies and formation of highly ordered microcrystals, but quantifying the influence of perfect order on electronic properties has remained challenging. This study addresses that gap by forming idiomorphic microcrystals of Au32((t)Bu3P)12Cl8 with high phase purity and preferred growth direction, and comparing their optoelectronic properties to disordered, polycrystalline ensembles. The microcrystals are semiconducting, exhibit p-type hopping transport limited by Coulomb charging, and show negligible energetic disorder, whereas disordered assemblies show reduced conductivity and higher activation energy due to disorder.

• Self-assembled thin films from inorganic nanoparticles, organic π-systems, and conjugated polymers are widely used, with prior work demonstrating 3D assemblies with long-range order using gold nanoparticles. However, size dispersion leads to energetic disorder in such ensembles.
• Atomically precise molecular clusters (superatoms) have been explored as building blocks for solid-state materials, enabling control by design, larger dielectric constants, and quantum confinement effects.
• Previous Au nanocluster (NC) studies: conductivity measurements on polycrystalline assemblies and reports of highly ordered microcrystal formation. Yet attempts to quantify how perfect order affects electronic properties were unsuccessful.
• Interest exists in exploiting properties of perfectly ordered NC microcrystals (e.g., superconductivity in metalloid Ga84R20Cl4 clusters). The present work directly compares ordered microcrystals vs. polycrystalline films of the same atomically precise Au32 clusters to quantify the role of long-range order in transport and optics.

Synthesis of Au32(nBu3P)12Cl8 nanoclusters: 1 mmol nBu3PAuCl dissolved in 20 ml ethanol; add 38 mg NaBH4 suspension in ethanol; stir 1 h; remove solvent under reduced pressure; extract residue with CH2Cl2 and layer with diethyl ether (3x). After 1 week, a gold mirror forms; dark supernatant filtered and concentrated; crystals obtained by storing at −30 °C for a few days.

Self-assembly of microcrystals (liquid–air interface method): Add 200 µl of 0.5 mM Au32-NC solution in octane to an acetonitrile subphase in a Teflon chamber. Microcrystals form at the phase boundary during solvent evaporation, then sink through the subphase and adhere to a pre-placed substrate (e.g., Si/SiO2 or glass). After 45 min, insert a glass slide to separate residual floating membrane from the bottom substrate. Remove subphase and dry at ambient conditions.

Microcrystal device fabrication: Pattern Au electrodes on Si/SiO2 (200 nm SiO2) by standard photolithography (negative tone resist). Thermally evaporate Ti (~2.5 nm) adhesion layer and Au (8–10 nm). Perform ultrasonic-assisted lift-off. Create electrode gaps (channel length L) of 1.5–2.5 µm. Deposit microcrystals via the self-assembly method and identify channels bridged by a single microcrystal via microscopy.

Thin-film fabrication: Use OFET substrates with interdigitated electrodes for devices; Si/SiO2 wafers for GISAXS; glass slides for absorbance. Deposit 100 µl of 0.5 mM Au32-NC solution (hexane or heptane), allow 2 min, then spin-coat at 760 rpm or 2000 rpm for 30 s. Prepare films at ambient conditions. Measure thickness by profilometry (30 ± 2 nm to 47 ± 4 nm for electronic devices).

GISAXS: Xeuss 2.0 (Xenocs), Cu Kα, λ = 1.5418 Å (8.04 keV), beam ~500 × 500 µm2, Pilatus 300K detector at 365 mm, incidence angle 0.2°. Acquisition: 60 min (microcrystal ensemble), 30 min (thin film). Index peaks to triclinic unit cell (a ≈ 1.90 nm, b ≈ 1.94 nm, c ≈ 3.48 nm; α ≈ 72°, β ≈ 86°, γ ≈ 59°) using GIXSGUI (MATLAB). Compare to macroscopic single-crystal parameters (a ≈ 1.91 nm, b ≈ 1.93 nm, c ≈ 3.32 nm; α ≈ 73.2°, β ≈ 86.7°, γ ≈ 63.4°).

Optical measurements: Solutions measured with Cary 5000 UV–vis–NIR. Thin films on glass with PerkinElmer Lambda 950. Individual microcrystals: inverted microscope (Nikon Eclipse Ti-S) with white-light illumination (100 W halogen), x60 objective (NA 0.7), spectrograph (Andor Shamrock SR-303i) and iDus CCD. Apply energy Jacobian correction. Photoluminescence: home-built confocal microscope; CW diode laser at 488 nm; photon-counting module (SPCM-AQR-14) for imaging; spectra with Acton SpectraPro 2300; background-subtracted.

SEM: HITACHI SU 8030 at 30 kV; estimate thickness by tilting samples by 85°.

Electrical measurements: Vacuum probe station (Lake Shore CRX-6.5 K), overnight vacuum (<1e-5 mbar), W-tips to contact Au electrodes; Keithley 2636B. Back electrode as gate. Two-point conductivity: voltage sweeps ±1 V; linear fit to I–V for conductance G; conductivity σ = (G × L)/(W × h). Dimensions (L, W, h) from SEM (microcrystals) or profilometry (thin films). FET (bottom-gate, bottom-contact): measure ISD at VSD while sweeping VG; calculate field-effect mobilities using gradual channel approximation. Temperature-dependent σ: devices cooled to 8 K and measured from 170–340 K with Lake Shore 336 controller; at least two measurements per temperature; verify reversibility on cooling. Analyze Arrhenius behavior σ = σ0 exp(−EA/kBT) by linear fit of ln σ vs 1/T to extract activation energy EA.

Structural/morphological characterization: Quantify microcrystal geometry (long axis A, short axis B, angle at sharp edge, thickness h) by SEM. Analyze size distributions and aspect ratio A/B; relate to triclinic unit cell geometry.

• Self-assembly yields µm-sized idiomorphic Au32((t)Bu3P)12Cl8 microcrystals with parallelogram shape, flat surfaces, and sharp edges. Typical lateral dimensions: A = 17.4 ± 4.2 µm and B = 10.6 ± 2.5 µm (aspect ratio A/B ≈ 1.64), thickness 50–600 nm; angle ≈ 63°, matching the γ-angle of the unit cell, indicating idiomorphic growth. Lateral size dispersion ~24%.
• GISAXS of microcrystal ensembles shows sharp diffraction peaks consistent with triclinic unit cell (a ≈ 1.90 nm, b ≈ 1.94 nm, c ≈ 3.48 nm; α ≈ 72°, β ≈ 86°, γ ≈ 59°), in excellent agreement with macroscopic single-crystal data (a ≈ 1.91 nm, b ≈ 1.93 nm, c ≈ 3.32 nm; α ≈ 73.2°, β ≈ 86.7°, γ ≈ 63.4°). Dominant peak at qz ≈ 0.37 Å−1 (d ≈ 1.7 nm) indicates c-axis aligned along surface normal; most microcrystals lay flat with a and b parallel to substrate. Spin-coated thin films exhibit ring-like, smeared peaks, indicating polycrystallinity and high angular disorder.
• Optical absorption: Dispersed Au32-NCs show molecular-like transitions with a prominent peak at 2.58 eV (481 nm); HOMO–LUMO transition at 1.55 eV (800 nm). In microcrystals, the 1.55 eV peak is strongly enhanced; absorption onset red-shifted by ~100 meV; the 2.57 eV peak red-shifted by ~10 meV and broadened; similar but weaker effects in thin films, indicating increased electronic coupling in ordered assemblies.
• Photoluminescence: Individual microcrystals exhibit a broad emission around 670 nm (1.85 eV) upon 488 nm excitation; no emission observed in solution.
• Electrical conductivity: Individual microcrystals show mean σ = 1.56 × 10−4 S/m (SD ± 0.90 × 10−4 S/m; N = 54). Polycrystalline thin films show σ ≈ 1 × 10−6 S/m (N = 19). Thus, microcrystals have ~100× higher conductivity.
• Temperature-dependent transport: Arrhenius behavior with activation energies EA = 227 ± 17 meV (microcrystals) vs EA = 366 ± 62 meV (polycrystalline films), indicating reduced activation energy in ordered microcrystals.
• FET behavior: p-type conduction in both systems. Thin films (L = 2.5 µm, W = 1 cm, h = 30 ± 2 nm) show ON/OFF ~4000, hole mobility µ(h+) ~ 10−6–10−5 cm2 V−1 s−1; ambipolar behavior appears at VG > 40 V. Individual microcrystals (W ~5–10 µm) show mean µ(h+) = 0.8 × 10−4 ± 0.58 × 10−4 cm2 V−1 s−1 with maxima up to 2 × 10−4 cm2 V−1 s−1.
• Charge carrier concentration in microcrystals estimated as n(h+) ≈ 2 × 10^17 cm−3, corresponding to ~1 free charge per 1000 Au32-NCs (NC concentration ~1.9 × 10^20 cm−3).
• Estimated Coulomb charging energy EC ≈ 276 meV. In microcrystals, EA ≈ EC, implying negligible energetic disorder; in polycrystalline films, EA > EC suggests significant energetic disorder due to structural/orientational defects.

Introducing long-range structural order in atomically precise Au32 nanocluster assemblies fundamentally enhances charge transport and alters optical properties. GISAXS and morphology indicate that microcrystals are µm-sized single crystals with triclinic unit cells matching macroscopic crystals; their flat orientation on substrates supports well-defined packing. Optical spectra reveal enhanced low-energy transitions and red-shifts consistent with increased inter-cluster coupling in ordered structures, and microcrystals exhibit solid-state luminescence near 1.85 eV, in line with related Au NCs.

Transport measurements show a ~100× conductivity increase and higher mobilities in microcrystals compared to polycrystalline films. Arrhenius analysis indicates hopping transport in the Mott regime (EC ≥ β). The measured EA ≈ EC (≈276 meV) in microcrystals implies that transport is limited by Coulomb charging with negligible energetic disorder (Δα ≈ 0). In contrast, polycrystalline films have EA substantially exceeding EC, pointing to additional energetic disorder arising from grain boundaries, cracks, and lack of orientational order. Because the clusters are atomically precise, structural disorder dominates Δα in films. Systems with large EC are particularly sensitive to such disorder, explaining the pronounced improvement upon crystallization.

These findings quantify, for the first time, the advantage of perfect long-range order in Au-NC ensembles by direct comparison of ordered microcrystals and disordered films. They highlight pathways to further enhance coupling and potentially achieve a Mott insulator–metal transition (β ≈ EC), for example by reducing intercluster spacing or introducing conjugated covalent linkers to increase transfer integrals, enabling band-like transport and novel collective optoelectronic properties.

Atomically precise Au32((n)Bu3P)12Cl8 nanoclusters can be self-assembled into idiomorphic microcrystals with high phase purity and preferred growth direction. Compared to polycrystalline thin films, these microcrystals show emergent optical features (enhanced HOMO–LUMO transition, red-shifted absorption) and greatly improved electronic properties, including ~100× higher conductivity, higher mobilities, and lower activation energy consistent with Coulomb-charging-limited hopping and negligible energetic disorder. This work establishes a direct structure–property correlation for atomically precise Au nanocluster assemblies, demonstrating that long-range order suppresses energetic disorder and enhances electronic coupling. Future research should focus on increasing the transfer integral through reduced intercluster spacing or covalent coupling with conjugated linkers to approach or surpass the Mott transition and enable band-like transport in superatomic crystals.

• FET measurements on individual microcrystals exhibit noise and low modulation due to non-ideal channel geometry and unknown quality of contact between the microcrystal and the dielectric (SiOx), potentially affecting transfer characteristics.
• Temperature-dependent conductivity measurements are limited to 170–340 K; below this range, current approaches the noise level, preventing analysis at lower temperatures.
• GISAXS patterns include ring-like features from misoriented single crystals or residual agglomerations; while most microcrystals lie flat, some orientation heterogeneity exists in ensembles.
• Activation energy and EC estimations rely on Arrhenius fits and capacitance models; uncertainties in geometry and dielectric environment may affect quantitative values, though trends are robust.