I. Core Research Summary

• General One-Dimensional/Two-Dimensional Nanonetwork Conductivity Analytical Model

We derive resistivity formulas applicable to both nanowires and nanosheets, enabling simultaneous separation solely through DC resistivity measurements of nanofilms with varying dimensions. Nanobody resistance R_NP and Inter-chip node resistance R_J , eliminating the need for single‑nanotube micro‑measurements; experiments confirm that all nanonetworks belong to a node‑limited conductive system, with nodes serving as the primary barriers to charge transport.

• Quantification of order-of-magnitude differences in node resistance among different materials

In metallic systems, the resistance of silver nanosheets is only 5 Ω, while that of silver nanowires is approximately 254 Ω; in semimetallic graphene, the junction resistance is on the order of several kiloohms; and in the semiconductor WS₂, the junction resistance can reach as high as 24 GΩ. These findings confirm that junction resistance is strongly correlated with the material’s bandgap and carrier concentration, establishing an intrinsic relationship between material properties and junction resistance.

• Electrochemical impedance spectroscopy simultaneously resolves dual conduction mechanisms.

A nano‑junction串联 Randles equivalent circuit is proposed, enabling direct decomposition of two transport mechanisms from impedance spectra: intra‑nanosheet band‑type transport (with resistance decreasing as temperature rises) and inter‑nanosheet hopping transport (dominated at low temperatures). Temperature‑dependent measurements clearly reveal the critical transition region where these two mechanisms switch.

• Aerosol Jet–Based Fabrication of High-Precision IDE Test Electrodes

AJP direct‑print micrometer‑scale silver fork‑finger electrodes are employed, delivering uniform patterns with sharp edges, and enabling precise electrical characterization of ultrathin two‑dimensional semiconductor nanofilms while avoiding the high costs and lengthy processing times associated with evaporation and photolithography.

• Micro-Potential Visualization Verification of the Theoretical Model

In situ KPFM scanning directly reveals abrupt potential drops at the nodes of the nanonetwork, and quantitative analysis of the fraction of node‑level potential drops yields results that closely match those obtained from AC–DC model fitting, thereby validating the reliability of the entire quantitative methodology.

II. Complete Process Flow for the Preparation of Aerosol-Sprayed Electrodes.

(1) Complete Preparation Procedure

• Ultrasonic cleaning of the glass substrate and plasma activation enhance the adhesion of the silver film.
• Commercial silver nanoparticle ink is diluted with deionized water and ultrasonically dispersed to eliminate particle agglomeration.
• The aerosol jet system employs ultrasonic atomization, a 150 μm ceramic nozzle, and maintains a constant 3 mm standoff distance for direct printing of micron-scale interdigitated electrodes.
• Cured by low-temperature baking at 120°C to remove surface-active agents from the ink.
• A nano‑network functional layer is sequentially deposited, and a probe station is assembled to perform DC/AC temperature‑dependent electrical measurements.

(II) Five Core Advantages of Aerosol-Based Processes (Comparison with Lithography and Evaporation Deposition)

• Maskless Digital Rapid Customization of Interdigital Electrodes

CAD allows free adjustment of line width, spacing, and channel length, and enables rapid electrode‑size changes for different two‑dimensional thin films, reducing sample‑preparation time per batch by 70%.

• Low-temperature, gentle forming that does not damage the ultra-thin nanofunctional layer.

The entire process employs post‑treatment at 120°C, avoiding high‑temperature vapor deposition and harsh photolithography‑based lift‑off steps, thereby preserving the performance of oxidation‑prone two‑dimensional materials such as WS₂ and MoS₂.

• Non-contact deposition does not damage the porous nanonetwork.

Without mechanical pressure, the nanoplatelet‑based loosely stacked structure remains undistorted, faithfully preserving the film’s intrinsic electrical conductivity.

• Low consumable costs and high cost-effectiveness for small-batch R&D.

Only the target area is subjected to localized silver deposition, while full‑area evaporation of precious metals results in significant material waste; this approach substantially reduces the cost of laboratory mechanistic studies.

• Fabrication of Test Electrodes Compatible with Irregular-Shaped and Flexible Substrates

PI, paper, and other flexible substrates can be directly printed with IDEs, enabling in-situ electrical characterization of flexible nanoelectronic devices.

III. Five Key Technological Innovations

Innovation 1: A General Dual-Resistance Analytical Model for One-Dimensional/Two-Dimensional Nanonetworks

Innovation 2: A Dual-Dimensional Quantitative Characterization Paradigm for AC–DC Hybrid Systems

Innovation: A Theoretical Framework Distinguishing Three Dual-Conduction Mechanisms

Innovation 4: High-Precision Aerosol Electrode–Based Nanomaterial Characterization Protocol

Innovation: Correlation Rules of Five-Node Resistive Materials

IV. Current Industry Challenges in the Process and Corresponding Breakthrough Solutions

Challenge 1: Nanoscale devices exhibit poor performance, yet it is difficult to distinguish whether the issue stems from intrinsic nanoscale effects or from interface-induced barriers.

Challenge 2: Single‑channel DC measurements can only yield the overall resistance and cannot elucidate the microscopic charge transport mechanisms.

Challenge 3: The lithography and evaporation electrode‑deposition processes are complex and can cause high‑temperature damage to two‑dimensional nanoscale thin films.

Challenge 4: The throughput of single‑nanotube AFM/KPFM measurements is extremely low, making it impossible to screen ink formulations in bulk.

Challenge 5: Lack of a universal theoretical framework, leaving nanofilm research and development entirely reliant on trial and error.

V. Future Diversified Industrial Application Scenarios

1 Aerosol-printed flexible transparent electrode

2 Two-dimensional semiconductor printed transistors

3 Wearable piezoresistive/gas sensors

4 Flexible Electromagnetic Shielding Film

5. University-Based R&D Platform for Aerosol-Printed Electronics

Figure 1 | Schematic of the model. a shows, under an applied voltage, a network of nanosheets connecting two electrodes and its channel length LCh. The figure depicts a single conductive pathway composed of linearly arranged nanosheets that spans the entire channel length (indicated by the red arrow). The lateral dimension of each nanosheet is lNS. Although this schematic illustrates a nanosheet network, a similar diagram can equally be used to represent a nanowire network. b This conductive pathway can be regarded as a resistor chain, with each pair of resistors comprising one nanosheet resistance RNS and the other representing the inter‑sheet junction resistance RJ.

Figure 2 | Microscopic analysis results of nanoparticles and nanoporous networks. a The relationship between the average length of silver nanowires (AgNWs) selected by ultrasonic‑induced fragmentation and the duration of ultrasonic treatment. The uncertainty for lNW is the mean ± standard error (SE) (n = 100–200). b The dependence of the average nanoplate length (lNS) on centrifugal speed for silver nanoplates (AgNSs), graphene, WS₂, and WSe₂ nanoplates obtained via centrifugal fractionation. For AgNSs (n = 135–251), graphene (n = 210–270), WS₂ (n = 226–443), and WSe₂ (n = 89–227), the uncertainty in lNS is the mean ± SE. c The average aspect ratio (kNS) of nanoplates across all size‑selected fractions of each two‑dimensional material. Inset: Example data showing a linear relationship between nanoplate length and thickness (tNS) for five size‑selected fractions of LPE graphene, consistent with an aspect ratio of kNS ≈ 30 (all data are provided in Supplementary Note 2). The uncertainty in kNS is the root sum of squares (RSS) of the standard errors of the mean values of lNS and tNS (n = 89–443). d Scanning electron microscopy images of the surface of an AgNW network prepared by spray‑casting; representative images of spray‑cast network structures include: (e) AgNSs, (f) graphene, (g) WSe₂, and (h) WS₂ nanoplates.

Figure 3 | Dependence of network resistivity on nanoparticle size. a: Resistivity of spray‑cast silver nanowire (AgNW) networks as a function of the inverse nanowire length, lNW⁻¹. The curve represents a fit to Equation (2); here, the carrier density is sufficiently high that the term in square brackets in the second term of Equation (2) can be neglected. The uncertainty in lNW⁻¹ is given as mean ± standard error (n = 100–200), and ρNet denotes the standard deviation of the network cross‑sectional area ANet and the length LCh. b–e show, respectively, the dependence of the resistivity ρNet of spray‑cast nanoplate networks—(b) AgNSs, (c) graphene, (d) WS₂, and (e) WSe₂—on the nanoplate length lNS. In figures b–e, the curves are fits to Equation (3); in b and c, the carrier density is high enough to neglect the term in square brackets in the second term of Equation (3). Notably, the trends in b and c contradict common expectations—that smaller nanoplates should yield higher resistivity. Fitting the data in figures a–e yields the junction resistance RJ and the nanoparticle resistivity ρNP for each material; combining these with the nanoparticle size allows calculation of the nanoparticle resistance RNP. Figures a–e and Table 1 list the values of RJ, ρNP, and the ratio RJ/RNP for each material. Data are presented as mean ± standard error: lNS (n = 89–443, see Supplementary Note 2) and ρNet (n = 5–29). f: Plot of the junction resistance RJ versus the nanoparticle resistivity ρNP, illustrating a proportional relationship; the uncertainty in RJ reflects the errors associated with the fits to Equations (2) and (3). The uncertainty in ρNP corresponds to the standard error of the mean RJ and SE for tNS (or DNW) across materials (n = 135–443), calculated using the root sum of squares (RSS).

Table 1 | Fitting Parameters of the DC Resistivity Model and the AC Impedance Model in This Study

Fixed and measured parameters are shown in bold. All other values were obtained by fitting Equations (2) (for silver nanowires) and (3) (for silver nanosheets, LPE graphene, WS₂, and WSe₂) to DC data, as well as by fitting Equation (5) (for molybdenum disulfide) to AC data. The aspect ratio kNS of the nanosheets and the diameter DNW of the silver nanowires were determined using atomic force microscopy (AFM) and scanning electron microscopy (SEM), respectively. The network porosity PNet was taken from the studies by Gabbett et al. [47] and Carey et al. [19]; mobility data for WS₂ and WSe₂ nanosheets were cited from Kelly et al. [53], while the graphene mobility used the in‑plane value reported in [83]. The network channel length LCh and cross‑sectional area ANet were calculated based on the known electrode dimensions of each material, combined with profilometry and AFM measurements. For LPE materials, the nanoparticle resistivity ρNP was computed from the nanoparticle mobility μNP and carrier density nNP using the relation ρNP = ðnNPeμNPÞ ¹; given the extremely high nNP values for silver nanowires and nanosheets, the second term in parentheses in Equations (2) and (3) can be neglected, allowing a simple linear fit to yield ρNP and RJ—provided that PNet and either kNS or DNW are known. For electrochemically exfoliated molybdenum disulfide, RNS and RJ were derived via impedance fitting; RNS was then converted to ρNS based on the nanosheet thickness, and finally, the measured carrier density was used to obtain μNS.

Figure 4 | Identification of nanosheets and junction resistance. a SEM surface image of an electrochemically exfoliated (EE) molybdenum disulfide nanosheet network, with arrows pointing to two well-defined junctions. b Field-effect transfer curves of the electrolytically gated EE MoS₂ network at a drain–source voltage of VDS = 1 V. Inset: Plot of the network mobility µNet as a function of gate voltage; after averaging over four devices, the average (peak) mobility is μNet = (6.6 ± 0.6) cm²·V⁻¹·s⁻¹. c Plots of the real (Re) and imaginary (Im) parts of the complex network resistance ρ*Net of the EE MoS₂ nanosheet network as a function of angular frequency ω; inset: circuit elements representing nanosheet–junction pairs, where RNS denotes the nanosheet resistance, and RJ and CJ represent the junction resistance and junction capacitance, respectively. d Plot of the real part Re(ZNSJ) of the nanosheet–junction pair impedance as a function of ω; data are fitted using Equation (5), with contributions from the junction resistance and the nanosheet resistance indicated by arrows; inset: plot of Im(ZNSJ) versus ω, with the solid line showing the fitted curve (see Supplementary Note 13 for the equation and fitting parameters). e Plot of the mobility µNS of a typical single EE MoS₂ nanosheet as a function of gate voltage. Arrows indicate the scanning direction. f Top: AFM topography image of a cross-section of the EE MoS₂ network between source and drain electrodes; bottom: KPFM image under operating conditions. g Top: topographic profile corresponding to the red dashed line in Figure f; bottom: potential distribution curve. Within this channel cross-section, six sharp voltage drops associated with interlayer junctions are observed, labeled J1 through J6; nearly flat regions reflect gradual potential reductions between nanosheets; black lines denote linear fits to these regions. h Shows how the voltage drop across the nanosheet ends varies with the number of junctions observed within a specific channel segment. The voltage‑drop formula is V_NS = (V_NS + V_J), where V_NS and V_J represent the voltage drops across the nanosheet and at the junction, respectively. Inset: histogram of RJ/RNS ratios calculated from the voltage‑drop data in Figure h.

Figure 5 | Measurement of transport properties in networks, nanosheets, and junctions using impedance spectroscopy. a) Real part of the complex network resistivity, Reρ*Net, as a function of angular frequency ω, showing the behavior of MoS₂ nanosheet networks at various temperatures T; the arrow indicates that the DC network resistivity is given by ρNet = Reρ*Net Þ ω^0. b) Temperature dependence of the DC network resistivity ρNet, plotted against 1/T and T^(1/4) (inset). The dashed line represents an activation‑type fit, while the solid line corresponds to a three‑dimensional variable‑range hopping (VRH) model fit. c) Real (c) and imaginary (d) parts of the impedance spectra measured for a single (average) nanosheet–junction pair, ZNS–J, at different temperatures. The curves in c were fitted using Equation (5). e) Temperature dependence of the nanosheet resistance RNS and the junction resistance RJ, extracted from the Re(ZNS–J) spectral fits. Uncertainties for RNS and RJ are given as ± values of the fitting errors. f) Temperature dependence of the nanosheet junction capacitance CJ. Inset: histogram of the nanosheet junction area AJ, obtained from scanning electron microscopy images and plotted as log(AJ/μm²); the distribution yields hAJi = 0.41 μm² (n = 807). The uncertainty for CJ is the ± value of the Re(ZNS–J) spectral fit error. g) Temperature dependence of the average resistivity ρNS of a single nanosheet, derived from RNS (ρNS ≈ 2RNStNS); the solid line denotes a power-law relationship with exponent α = 1.1. The uncertainty for ρNS is the ± value of the standard error (SE) of the mean tNS (n = 674), plus the RNS fitting error. Hollow triangles indicate the terahertz mobility of the nanosheets, converted to resistivity based on a measured carrier density of 3.8 × 10²³ m⁻³. The temperature dependencies of the junction resistance on 1/T and T⁻¹/⁴ are shown in the figure’s inset. The dashed line represents an activation‑type fit described by Equation (6), while the solid line corresponds to a fit based on the 3D‑VRH model (Equation (7)). The uncertainty in RJ equals the absolute value of the Re(ZNS–J) spectral fit error shown in c.