Networks of nanowires, nanotubes, and nanosheets are important for many applications in printed electronics. However, the network conductivity and mobility are usually limited by the resistance between the particles, often referred to as the junction resistance. Minimising the junction resistance has proven to be challenging, partly because it is difficult to measure. Here, we develop a simple model for electrical conduction in networks of 1D or 2D nanomaterials that allows us to extract junction and nanoparticle resistances from particle-size-dependent DC network resistivity data. We find junction resistances in porous networks to scale with nanoparticle resistivity and vary from 5 Ω for silver nanosheets to 24 GΩ for WS₂ nanosheets. Moreover, our model allows junction and nanoparticle resistances to be obtained simultaneously from AC impedance spectra of semiconducting nanosheet networks. Through our model, we use the impedance data to directly link the high mobility of aligned networks of electrochemically exfoliated MoS₂ nanosheets (≈ 7 cm² V⁻¹ s⁻¹) to low junction resistances of ∼2.3 MΩ. Temperature-dependent impedance measurements also allow us to comprehensively investigate transport mechanisms within the network and quantitatively differentiate intra-nanosheet phonon-limited bandlike transport from inter-nanosheet hopping.

In this work, we have examined the optical properties of exfoliated graphene on an ${\text{Si}/\text{SiO}}_2$ substrate using spectroscopic imaging ellipsometry in the visible range (360–800 nm). Measured spectra were analyzed by an optical model based on the Fresnel coefficient equations. The optical model was supported by correlated Raman and atomic force microscopy measurements. The complex refractive index of graphene was obtained by inversion of the measured ellipsometry data. The Fano line-shape was used to parameterize the optical properties. Measurements were highly reliable due to the numerous advantages of the spectroscopic imaging ellipsometric technique combined with the proper choice of substrate and experimental set-up. Thickness maps of the graphene sample were obtained from spatially resolved imaging ellipsometry spectra with a spot size of 1 μm. The data showed the presence of a water layer on the surface of the sample, and the thickness was mapped showing the distribution of water over graphene in ambient conditions.

Tapping mode atomic force microscopy (AFM) is employed for dynamic plowing lithography of exfoliated graphene on silicon dioxide substrates. The shape of the graphene sheet is determined by the movement of the vibrating AFM probe. There are two possibilities for lithography depending on the applied force. At moderate forces, the AFM tip only deforms the graphene and generates local strain of the order of 0.1%. For sufficiently large forces the AFM tip can hook graphene and then pull it, thus cutting the graphene along the direction of the tip motion. Electrical characterization by AFM based electric force microscopy, Kelvin probe force microscopy and conductive AFM allows us to distinguish between the truly separated islands and those still connected to the surrounding graphene.