The Role of Junctions in Nanomaterial Networks

Abstract

Printed nanomaterial networks promise scalable routes to revolutionary flexible, transparent and high-performance electronic systems, yet device characteristics are routinely throttled by inter-particle junctions. Conventional electrical characterisations, such as sheet resistance, conductivity and mobility measurements, collapse all physics into a single effective value, obscuring the complex interplay between the inter-particle and intra-particle transport. This thesis reframes electrical characterisation around the two elemental contributions that govern conduction in nanomaterial networks: the nanoparticle (intra-particle) resistance, RNP, and the junction (inter-particle) resistance, RJ. We develop a simplistic, geometry-independent resistor-chain model that relates network resistivity to the resistance of an average nanoparticle-junction (NP-J) pair and show how it yields two complementary, practical and quantitative routes to decouple and extract both terms. First, DC nanomaterial size-dependent studies (nanowire length for 1D, nanosheet thickness for 2D) enable extraction of nanoparticle resistivity, �NP and junction resistance, RJ. Second, AC impedance spectroscopy is used by converting the network impedance spectra into the impedance of an average NP-J pair allowing extraction of RNP and RJ. Using the DC route, we validate the scaling predictions on silver nanowire (AgNW) networks and liquid-phase-exfoliated (LPE) graphene nanosheet networks. For AgNWs, network resistivity scales with the inverse nanowire length, as predicted by our model, yielding nanowire resistivities ~10-8 �m (close to bulk Ag) and typical junction resistances ~200 �, with RNW/RJ � 0.03 - 0.7, confirming predominantly junction-limited transport. For graphene, network resistivity scales with nanosheet thickness, providing values of �NS = (3.5 � 0.6) � 10-5 �m and RJ� = 7.8 � 0.5 k�. RJ/RNS rises from 0.56 to 6.11 across size fractions, indicating a transition from mixed to strongly junction-limited regimes as the nanosheets get thicker. These measurements establish a broadly applicable DC methodology for separating intra- from inter-particle contributions. To overcome the extensive sample preparation demands using DC size-dependent studies, we establish a rapid, single-sample AC impedance-spectroscopy route. Our model enables the conversion of network impedance spectra into a single average NP-J pair representation. Fitting a modified Randles circuit (RNS in series with RJ, CPE pair) to the NP-J impedance spectra permits extraction of RNS, RJ and CJ rapidly. Applied to liquid-liquid-interface-deposited (LLID) networks of electrochemically exfoliated (EE) MoS2, this method yields RJ = 2.9 � 0.1 M�, RNS = 0.67 � 0.07 M�, CJ = 8.4 � 0.4 fF and n = 0.985. The extracted RJ/RNS = 4.4 � 0.2 indicates these dense, aligned EE networks are not strongly junction limited. Independent verifications (field-effect and THz mobilities and in-operando KPFM mapping) are consistent with the impedance-extracted parameters. We also determine the practical window for this technique, bounded at high frequency by analyser bandwidth and at large impedances by IDE parasitic capacitance. We extend both approaches to temperature-dependent studies, enabling mechanistic transport assignments to RNS and RJ, separately. In AgNW networks, plotting �Net versus 1/lNW at each T isolates �NW(T) and RJ(T). �NW follows Bloch�Gr�neisen behaviour while RJ(T) confirms metallic silver junctions expected after annealing, with consistent Debye temperatures, residual resistivities and electron-phonon coupling constants for both the junctions and the nanowires; evidence that junctions are effectively sintered metallic contacts rather than tunnelling barriers. In LPE-graphene networks, the extracted �NS(T) is weakly thermally activated and is well captured by two parallel semiconducting channels associated with Bernal (2H) and rhombohedral (3R) stacking in graphite. Fitting yields Eg � 42 meV (Bernal) and � 195 meV (3R), consistent with graphite literature. Junction transport shows a distinct power-law behaviour with an exponent = 0.1866 � 0.0005, consistent with hopping just above a mobility edge in partially disordered systems. Temperature-dependent impedance reveals band-like nanosheet transport with an exponent � 1.1, characteristic of phonon-limited conduction at elevated carrier densities, while junctions exhibit a 3D-VRH to thermally activated crossover with Ea = 55 � 2 meV and T0 = (471 � 37) � 103 K. A CJ/AJ � 2 �F cm-2 matches geometric capacitance estimates with ~0.6 nm inter-sheet spacing. Together these results separate intra- from inter-flake transport behaviour, replacing previous network-only analyses that conflate the two. Overall, this work turns network optimisation from intuition into measurement-driven design. The DC methodology is simple and universal but sample-intensive while the AC route is rapid and information-rich, but instrument and device limited. Together, they provide complementary methods to quantify RJ and RNS across materials systems and temperatures, to pinpoint the true rate-limiting element, and to prescribe targeted improvements. Because the underlying model is independent of particle and network geometry, these strategies are transferable across printed conductors and semiconductors, offering a general framework for rationally engineering the electrical properties of nanomaterial networks.