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

The collective properties of self-assembled nanoparticles with long-range order bear immense potential for customized electronic materials by design. However, to mitigate the shortcoming of the finite-size distribution of nanoparticles and thus, the inherent energetic disorder within assemblies, atomically precise nanoclusters are the most promising building blocks. We report an easy and broadly applicable method for the controlled self-assembly of atomically precise Au32(nBu3P)12Cl8 nanoclusters into micro-crystals. This enables the determination of emergent optoelectronic properties which resulted from long-range order in such assemblies. Compared to the same nanoclusters in glassy, polycrystalline ensembles, we find a 100-fold increase in the electric conductivity and charge carrier mobility as well as additional optical transitions. We show that these effects are due to a vanishing energetic disorder and a drastically reduced activation energy to charge transport in the highly ordered assemblies. This first correlation of structure and electronic properties by comparing glassy and crystalline self-assembled superstructures of atomically precise gold nanoclusters paves the way towards functional materials with novel collective optoelectronic properties.


Micro-crystal sample for GISAXS measurements
shows an optical micrograph of the micro-crystal sample used for GISAXS. The majority of micro-crystals is oriented flat on the surface. Minor agglomerates cause distortions of the resulting GISAXS pattern, as described in the main text.

Dispersity of the micro-crystals
To determine the dispersity of the micro-crystals, scanning electron micrographs were used to measure the axis lengths of the micro-crystals (ImageJ software). The dispersity Đ is calculated according the IUPAC definition using the following equation Optical spectrum of Au32( n Bu3P)12Cl8 nanoclusters Figure S3 shows an optical absorbance spectrum of Au32-NCs dissolved in hexane. Several distinct molecular-like transitions are observed, together with a HOMO-LUMO transition at 1.55 eV. Figure S3: Optical spectrum of Au32-NCs. Absorbance spectra of Au32-NCs dispersed in hexane. Absorbance is energy corrected using the expression I(E) = I(λ) × λ 2 . The peak at 1.55 eV (800 nm) is attributed to the HOMO-LUMO transition. This spectrum corresponds to the spectrum shown in Figure 3a with larger energy range.

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Optical spectra of individual Au32-NC micro-crystals Figure S4 shows the absorbance spectra of several individual Au32-NC micro-crystals, all exhibiting the enhanced peak at around 1.55 eV (800 nm).

Electrode layout for electronic measurements of individual micro-crystals
Optical micrographs of typical electrode devices (Si/SiOx substrate) are given in Figure S5.

Evaluating the effective width of a micro-crystal within a channel
The effective width of a micro-crystal on a channel is described best by the mean of W along the channel. Figure S6 shows a SEM micrograph of a micro-crystal covering two channels. The measured conductance G of the channels is different, due to differences in effective width. For every channel, different widths are present (caused by the parallelogram shape). The calculated conductivities σ of the two channels should be the same, since the same micro-crystal is probed.
Normalizing the measured conductance G with the channel geometry L/W gives essentially the same value (as thickness h is the same). This geometry normalized conductance values, using the mean width, are identical with 39.5 pS and 39.9 pS for the micro-crystals in the two different channels, respectively. Thus, using the mean width along the electric field is the most appropriate dimension. Using the mean value of W to calculate the conductivity σ yields the same value for geometry normalized conductance for both channels bridged by the same micro-crystal. Scale bar: 5 µm.
8 Figure S7 shows representative I-V curves of a self-assembled Au32-NC micro-crystal with conductivity σcrystal = 2.4 × 10 -4 S/m and a spin-coated Au32-NC thin film with σfilm = 4.4 × 10 -6 S/m.   Figure S9 displays the thickness characterization of spin-coated Au32-NC thin films by profilometry (Bruker, Dektak XT). The samples were prepared with a scratch ( Figure S9a) to identify the absolute film thickness by scanning across (Figure S9b). Several height profiles were taken per sample to calculate the mean value and standard deviation of the film thickness.

Thickness characterization of Au32-NC thin films
Measuring the thickness on several positions of the samples and calculating the mean value ± standard deviation yields values of 30 ± 2 nm and 47 ± 4 nm (relative deviations of 6.7-8.5%).  Figure S10a and S10c display typical plots of temperature-dependent conductivity of an Au32-NC micro-crystal and a spin-coated thin film, respectively. Figure S10b and S10d show the corresponding Arrhenius plot, where ln(σ) is plotted as a function of T -1 . Fitting the linear curve yields the activation energy EA.

Equations used for the investigation of electronic properties
The field-effect mobilities µ of individual micro-crystals or polycrystalline thin films are calculated using the gradual channel approximation, given in Equation S2. The charge carrier concentration n is calculated using Equation S3.  Figure S11 shows the distribution of the field-effect hole mobility µ(h + ) of individual microcrystals. Figure S11: Distribution of the field-effect hole mobility µ(h + ) of 21 individual micro-crystals.

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A schematic drawing of the devices is given in Figure S12. The micro-crystals are deposited onto the electrodes with a thickness of ~10 nm. Accordingly, there is a gap between the microcrystals and the dielectric of 0-10 nm. This is what we refer to as non-ideal channel geometry.
In contrast, the spin-coated films form a relatively conformal layer within the channel, which leads to much better contact. Nonetheless, there is still an appreciable transconductance in the micro-crystals, which -after renormalization for the different channel geometry -is ~30 higher for the micro-crystals compared to the spincoated films. This further indicates the more efficient charge transport in highly ordered micro-crystals. Details about the current normalization considering the different channel geometries: • thin film: Ifilm(-40 VG, 5 VSD) = 5.5 × 10 -8 A • micro-crystal: Icrystal(-40 VG, 5 VSD) = 9.0 × 10 -9 A Normalized to geometry: • thin film:

Evaluation of the contact resistance of Au32-NC devices
To measure the contact resistance RC of the Au32-NC devices, we apply the Y-function method (YFM), which is a common technique for the evaluation of MOSFETs and OFETs. 1-3 Figure S13 illustrates the YFM technique to estimate the RC of a FET device (exemplarily shown for an Au32-NC thin film channel). and fitting Y as a function of VG in the linear regime yields the slope s1 ( Figure S13c). Next, the function 1 √ versus VG is determined and linearly fitted to calculate the slope s2 (Figure 13d).
Hence, the Y-function method verifies the applicability of simple 2-point-probe measurements, as the effect of RC is negligible. 1-3

Calculation of the Coulomb charging energy EC
The estimation of the Coulomb charging energy is performed as described below.
The Coulomb charging energy EC is given in Equation S6 .
Here, e is the elementary charge and CΣ the total capacitance of the particle to its surrounding.
The interparticle capacitance can be estimated using Equation S7. 4,5 Here, ε0 is the vacuum permittivity, εr the dielectric constant of the surrounding medium (~2.0-2.5 for alkanes and phosphine), r is the NC radius (~0.45 nm) and 2d the interparticle distance.
Knowing that individual micro-crystals are oriented face-on to the surface, the in-plane Au core-core distance corresponds to the axis a and b with ~1.9 nm. As the core size is 0.9 nm the interparticle distance is 2d ≈ 1.0 nm. As each NC in the array has eight nearest neighbours, the total capacitance can be calculated to CΣ = 8 C. Accordingly, an estimation of charging energy yields EC ≈ 276 meV.

Details on self-assembly process of Au32-NC micro-crystals
Different parameters have been investigated to tune the morphology and amount of the microcrystals. Using a larger quantity of particle solution leads to a higher amount of micro-crystals on the substrate ( Figure S14)

Mechanism of micro-crystal self-assembly
To investigate the place and process of the formation of the micro-crystals, a self-built interference reflection microscope was used. A Framos Lt 225 camera with 16 nm/px resolution was used along with a Nikon TIRF objective with oil immersion and a numerical aperture of NA = 1.52. The sample was illuminated by a Rebel High Power LED with a wavelength of 460 nm. A Teflon tube was sealed onto a glass cover slide, filled with acetone and placed onto the microscope. The microscope was focused just above the glass slide into the subphase. An Au32-NC solution (0.5 mM, octane) was added onto the subphase to start the process of selfassembly. After the duration of 15 min, the sudden appearance of micro-crystals was observed.
From this, we deduce that the process of crystallization does not take place at the substrate but at the liquid-air interface. From there, the micro-crystals start to sink down through the subphase as soon as they reach a critical mass. After reaching the glass slide/substrate, the micro-crystals are able to move laterally within the subphase along the bottom. Upon removal of the subphase, the micro-crystals are deposited onto the substrate.