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.

Chair of Physics Department Physics Mechanics and Electrical Engineering Montanuniversität Leoben Franz Josef Strasse 18 8700 Leoben Austria

Chemical Engineering Department Delft University of Technology Van der Maasweg 9 NL 2629 HZ Delft The Netherlands

Department of Electronic and Electrical Engineering Trinity College Dublin 2 Dublin 2 Ireland

Department of Inorganic Chemistry University of Chemistry and Technology Prague Technická 5 Prague 6 166 28 Czech Republic

Department of Physics Faculty of Sciences University of Oviedo C Leopoldo Calvo Sotelo 18 33007 Oviedo Asturias Spain

i3N CENIMAT Faculty of Science and Technology Universidade NOVA de Lisboa Campus de Caparica 2829 516 Caparica Portugal

Materials Research and Development Toyota Motor Europe B1930 Zaventem Belgium

School of Physics CRANN and AMBER Research Centres Trinity College Dublin Dublin 2 Ireland

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Chandrasekaran S, Jayakumar A, Velu R. A Comprehensive Review on Printed Electronics: A Technology Drift towards a Sustainable Future. Nanomaterials. 2022;12:4251. doi: 10.3390/nano12234251. PubMed DOI PMC

Gulzar U, Glynn C, O'Dwyer C. Additive manufacturing for energy storage: Methods, designs and material selection for customizable 3D printed batteries and supercapacitors. Curr. Opin. Electrochem. 2020;20:46–53. doi: 10.1016/j.coelec.2020.02.009. DOI

Schiessl SP, et al. Polymer-Sorted Semiconducting Carbon Nanotube Networks for High-Performance Ambipolar Field-Effect Transistors. ACS Appl. Mater. Interfaces. 2015;7:682–689. doi: 10.1021/am506971b. PubMed DOI PMC

Lu S, Smith BN, Meikle H, Therien MJ, Franklin AD. All-Carbon Thin-Film Transistors Using Water-Only Printing. Nano Lett. 2023;23:2100–2106. doi: 10.1021/acs.nanolett.2c04196. PubMed DOI

Graf A, Murawski C, Zakharko Y, Zaumseil J, Gather MC. Infrared Organic Light-Emitting Diodes with Carbon Nanotube Emitters. Adv. Mater. 2018;30:1706711. doi: 10.1002/adma.201706711. PubMed DOI

Richter M, Heumüller T, Matt GJ, Heiss W, Brabec CJ. Carbon Photodetectors: The Versatility of Carbon Allotropes. Adv. Energy Mater. 2017;7:1601574. doi: 10.1002/aenm.201601574. DOI

De S, et al. Silver Nanowire Networks as Flexible, Transparent, Conducting Films: Extremely High DC to Optical Conductivity Ratios. ACS Nano. 2009;3:1767–1774. doi: 10.1021/nn900348c. PubMed DOI

Hu L, Kim HS, Lee J-Y, Peumans P, Cui Y. Scalable Coating and Properties of Transparent, Flexible, Silver Nanowire Electrodes. ACS Nano. 2010;4:2955–2963. doi: 10.1021/nn1005232. PubMed DOI

Lin S, et al. Room-temperature production of silver-nanofiber film for large-area, transparent and flexible surface electromagnetic interference shielding. npj Flex. Electron. 2019;3:6. doi: 10.1038/s41528-019-0050-8. DOI

Zhu Y, et al. Flexible Transparent Electrodes Based on Silver Nanowires: Material Synthesis, Fabrication, Performance, and Applications. Adv. Mater. Technol. 2019;4:1900413. doi: 10.1002/admt.201900413. DOI

Witomska, S., Leydecker, T., Ciesielski, A., Samori, P. Production and Patterning of Liquid Phase-Exfoliated 2D Sheets for Applications in Optoelectronics. Adv. Funct. Mater.29, 1901126 (2019).

Kelly AG, O’Suilleabhain D, Gabbett C, Coleman JN. The electrical conductivity of solution-processed nanosheet networks. Nat. Rev. Mater. 2022;7:217–234. doi: 10.1038/s41578-021-00386-w. DOI

Zhu X, et al. Hexagonal Boron Nitride-Enhanced Optically Transparent Polymer Dielectric Inks for Printable Electronics. Adv. Funct. Mater. 2020;30:2002339. doi: 10.1002/adfm.202002339. PubMed DOI PMC

Zhang, J., et al. Scalable Manufacturing of Free‐Standing, Strong Ti3C2Tx MXene Films with Outstanding Conductivity. Adv. Mater.32, 2001093 (2020). PubMed

Sannicolo T, et al. Metallic Nanowire-Based Transparent Electrodes for Next Generation Flexible Devices: a Review. Small. 2016;12:6052–6075. doi: 10.1002/smll.201602581. PubMed DOI

Kelly, A. G., et al. Highly Conductive Networks of Silver Nanosheets. Small18, 2105996 (2022). PubMed

Zorn, N. F., Zaumseil, J. Charge transport in semiconducting carbon nanotube networks. Appl. Phys. Rev.8, 041318 (2021).

Zhou X, Park JY, Huang S, Liu J, McEuen PL. Band structure, phonon scattering, and the performance limit of single-walled carbon nanotube transistors. Phys. Rev. Lett. 2005;95:146805. doi: 10.1103/PhysRevLett.95.146805. PubMed DOI

Carey T, et al. High-Mobility Flexible Transistors with Low- Temperature Solution-Processed Tungsten Dichalcogenides. ACS Nano. 2023;17:2912–2922. doi: 10.1021/acsnano.2c11319. PubMed DOI PMC

Song O, et al. All inkjet-printed electronics based on electrochemically exfoliated two-dimensional metal, semiconductor, and dielectric. Npj 2d Mater. Appl. 2022;6:64. doi: 10.1038/s41699-022-00337-1. DOI

Lin Z, et al. Solution-processable 2D semiconductors for high-performance large-area electronics. Nature. 2018;562:254–258. doi: 10.1038/s41586-018-0574-4. PubMed DOI

Radisavljevic B, Radenovic A, Brivio J, Giacometti V, Kis A. Single-layer MoS2 transistors. Nat. Nanotechnol. 2011;6:147–150. doi: 10.1038/nnano.2010.279. PubMed DOI

Perera MM, et al. Improved Carrier Mobility in Few-Layer MoS2 Field-Effect Transistors with Ionic-Liquid Gating. ACS Nano. 2013;7:4449–4458. doi: 10.1021/nn401053g. PubMed DOI

Liu H, Ye PD. MoS2 Dual-Gate MOSFET With Atomic-Layer-Deposited Al2O3 as Top-Gate Dielectric. IEEE Electron Device Lett. 2012;33:546–548. doi: 10.1109/LED.2012.2184520. DOI

Ippolito S, et al. Covalently interconnected transition metal dichalcogenide networks via defect engineering for high-performance electronic devices. Nat. Nanotechnol. 2021;16:592–598. doi: 10.1038/s41565-021-00857-9. PubMed DOI

Ippolito S., et al. Unveiling Charge‐Transport Mechanisms in Electronic Devices Based on Defect‐Engineered MoS2 Covalent Networks. Adv. Mater.35, 2211157 (2023). PubMed

Nirmalraj PN, Lyons PE, De S, Coleman JN, Boland JJ. Electrical connectivity in single-walled carbon nanotube networks. Nano Lett. 2009;9:3890–3895. doi: 10.1021/nl9020914. PubMed DOI

Bellew AT, Manning HG, Gomes da Rocha C, Ferreira MS, Boland JJ. Resistance of Single Ag Nanowire Junctions and Their Role in the Conductivity of Nanowire Networks. ACS Nano. 2015;9:11422–11429. doi: 10.1021/acsnano.5b05469. PubMed DOI

Forró C, Demkó L, Weydert S, Vörös J, Tybrandt K. Predictive Model for the Electrical Transport within Nanowire Networks. ACS Nano. 2018;12:11080–11087. doi: 10.1021/acsnano.8b05406. PubMed DOI

O'Callaghan C, Gomes da Rocha C, Manning HG, Boland JJ, Ferreira MS. Effective medium theory for the conductivity of disordered metallic nanowire networks. Phys. Chem. Chem. Phys. 2016;18:27564–27571. doi: 10.1039/C6CP05187A. PubMed DOI

Tarasevich YY, Vodolazskaya IV, Eserkepov AV. Electrical conductivity of random metallic nanowire networks: an analytical consideration along with computer simulation. Phys. Chem. Chem. Phys. 2022;24:11812–11819. doi: 10.1039/D2CP00936F. PubMed DOI

Biccai S, et al. Negative Gauge Factor Piezoresistive Composites Based on Polymers Filled with MoS2 Nanosheets. ACS Nano. 2019;13:6845–6855. doi: 10.1021/acsnano.9b01613. PubMed DOI

Ponzoni, A. The contributions of junctions and nanowires/nanotubes in conductive networks. Applied Physics Letters114, 153105 (2019).

Bonaccorso F, Bartolotta A, Coleman JN, Backes C. 2D-Crystal-Based Functional Inks. Adv. Mater. 2016;28:6136–6166. doi: 10.1002/adma.201506410. PubMed DOI

De S, King PJ, Lyons PE, Khan U, Coleman JN. Size Effects and the Problem with Percolation in Nanostructured Transparent Conductors. ACS Nano. 2010;4:7064–7072. doi: 10.1021/nn1025803. PubMed DOI

Backes C, et al. Equipartition of Energy Defines the Size-Thickness Relationship in Liquid-Exfoliated Nanosheets. ACS Nano. 2019;13:7050–7061. doi: 10.1021/acsnano.9b02234. PubMed DOI

Nakamura S, Miyafuji D, Fujii T, Matsui T, Fukuyama H. Low temperature transport properties of pyrolytic graphite sheet. Cryogenics. 2017;86:118–122. doi: 10.1016/j.cryogenics.2017.08.004. DOI

Agarwal MK, Nagireddy K, Patel PD. Electrical-Properties of Tungstenite (WS2) Crystals. Krist. Und Tech. Cryst. Res. Technol. 1980;15:K65–K67.

Upadhyayula LC, Loferski JJ, Wold A, Giriat W, Kershaw R. Semiconducting Properties of Single Crystals Of N And P-Type Tungsten Diselenide (WSe2) J. Appl. Phys. 1968;39:4736–4740. doi: 10.1063/1.1655829. DOI

Song TB, et al. Nanoscale Joule Heating and Electromigration Enhanced Ripening of Silver Nanowire Contacts. ACS Nano. 2014;8:2804–2811. doi: 10.1021/nn4065567. PubMed DOI

Lazanas AC, Prodromidis MI. Electrochemical Impedance Spectroscopy-A Tutorial. ACS Meas. Sci. Au. 2023;3:162–193. doi: 10.1021/acsmeasuresciau.2c00070. PubMed DOI PMC

Yim C, McEvoy N, Kim HY, Rezvani E, Duesberg GS. Investigation of the Interfaces in Schottky Diodes Using Equivalent Circuit Models. ACS Appl. Mater. Interfaces. 2013;5:6951–6958. doi: 10.1021/am400963x. PubMed DOI

Irvine JTS, Sinclair DC, West AR. Electroceramics: Characterization by Impedance Spectroscopy. Adv. Mater. 1990;2:132–138. doi: 10.1002/adma.19900020304. DOI

Gerstl M, et al. The separation of grain and grain boundary impedance in thin yttria stabilized zirconia (YSZ) layers. Solid State Ion. 2011;185:32–41. doi: 10.1016/j.ssi.2011.01.008. PubMed DOI PMC

Fleig J, Maier J. The impedance of ceramics with highly resistive grain boundaries: validity and limits of the brick layer model. J. Eur. Ceram. Soc. 1999;19:693–696. doi: 10.1016/S0955-2219(98)00298-2. DOI

Moore D. C., et al. Ultrasensitive Molecular Sensors Based on Real-Time Impedance Spectroscopy in Solution-Processed 2D Materials. Adv. Functional Mater.32, 2106830 (2022).

Gabbett C, et al. Quantitative analysis of printed nanostructured networks using high-resolution 3D FIB-SEM nanotomography. Nat. Commun. 2024;15:278. doi: 10.1038/s41467-023-44450-1. PubMed DOI PMC

Kim, J., et al. All-Solution-Processed Van der Waals Heterostructures for Wafer-Scale Electronics. Adv. Mater.34, 2106110 (2022). PubMed

Gao X, et al. High-mobility patternable MoS2 percolating nanofilms. Nano Res. 2021;14:2255–2263. doi: 10.1007/s12274-020-3218-6. DOI

Heil T, Jossen A. Continuous approximation of the ZARC element with passive components. Meas. Sci. Technol. 2021;32:104011. doi: 10.1088/1361-6501/ac0466. DOI

Boukamp BA. Distribution (function) of relaxation times, successor to complex nonlinear least squares analysis of electrochemical impedance spectroscopy? J. Phys.-Energy. 2020;2:042001. doi: 10.1088/2515-7655/aba9e0. DOI

Aigner W, et al. Intra- and inter-nanocrystal charge transport in nanocrystal films. Nanoscale. 2018;10:8042–8057. doi: 10.1039/C8NR00250A. PubMed DOI

Kelly AG, et al. All-printed thin-film transistors from networks of liquid-exfoliated nanosheets. Science. 2017;356:69–73. doi: 10.1126/science.aal4062. PubMed DOI

Palermo V, Palma M, Samorì P. Electronic Characterization of Organic Thin Films by Kelvin Probe Force Microscopy. Adv. Mater. 2006;18:145–164. doi: 10.1002/adma.200501394. DOI

Yu Y-J, et al. Tuning the Graphene Work Function by Electric Field Effect. Nano Lett. 2009;9:3430–3434. doi: 10.1021/nl901572a. PubMed DOI

Matković A., et al. Interfacial Band Engineering of MoS2/Gold Interfaces Using Pyrimidine‐Containing Self‐Assembled Monolayers: Toward Contact‐Resistance‐Free Bottom‐Contacts. Adv. Electronic Mater.6, 2000110 (2020).

Shlimak I. Is Hopping a Science?: Selected Topics of Hopping Conductivity (World Scientific Publishing, 2015).

Piatti E, et al. Charge transport mechanisms in inkjet-printed thin-film transistors based on two-dimensional materials. Nat. Electron. 2021;4:893–905. doi: 10.1038/s41928-021-00684-9. DOI

Xu Q, Yang GM, Zheng WT. DFT calculation for stability and quantum capacitance of MoS2 monolayer-based electrode materials. Mater. Today Commun. 2020;22:100772. doi: 10.1016/j.mtcomm.2019.100772. DOI

Huo N, et al. High carrier mobility in monolayer CVD-grown MoS2 through phonon suppression. Nanoscale. 2018;10:15071–15077. doi: 10.1039/C8NR04416C. PubMed DOI

Lin M-W, et al. Thickness-dependent charge transport in few-layer MoS2 field-effect transistors. Nanotechnology. 2016;27:165203. doi: 10.1088/0957-4484/27/16/165203. PubMed DOI

Radisavljevic B, Kis A. Mobility engineering and a metal-insulator transition in monolayer MoS2. Nat. Mater. 2013;12:815–820. doi: 10.1038/nmat3687. PubMed DOI

Sze S. M. Semiconductor Devices: Physics and Technology (John Wiley and Sons, 1985).

Jariwala, D. et al. Band-like transport in high mobility unencapsulated single-layer MoS2 transistors. Appl. Phys. Lett.102, 173107 (2013).

Baugher BWH, Churchill HOH, Yang Y, Jarillo-Herrero P. Intrinsic Electronic Transport Properties of High-Quality Monolayer and Bilayer MoS2. Nano Lett. 2013;13:4212–4216. doi: 10.1021/nl401916s. PubMed DOI

Guyot-Sionnest P. Electrical Transport in Colloidal Quantum Dot Films. J. Phys. Chem. Lett. 2012;3:1169–1175. doi: 10.1021/jz300048y. PubMed DOI

Kim JS, et al. Electrical Transport Properties of Polymorphic MoS2. ACS Nano. 2016;10:7500–7506. doi: 10.1021/acsnano.6b02267. PubMed DOI

Qiu H, et al. Hopping transport through defect-induced localized states in molybdenum disulphide. Nat. Commun. 2013;4:2642. doi: 10.1038/ncomms3642. PubMed DOI

Xue J, Huang S, Wang JY, Xu HQ. Mott variable-range hopping transport in a MoS2 nanoflake. RSC Adv. 2019;9:17885–17890. doi: 10.1039/C9RA03150B. PubMed DOI PMC

Backes C, et al. Guidelines for Exfoliation, Characterization and Processing of Layered Materials Produced by Liquid Exfoliation. Chem. Mater. 2017;29:243–255. doi: 10.1021/acs.chemmater.6b03335. DOI

Barwich S, Khan U, Coleman JN. A Technique To Pretreat Graphite Which Allows the Rapid Dispersion of Defect-Free Graphene in Solvents at High Concentration. J. Phys. Chem. C. 2013;117:19212–19218. doi: 10.1021/jp4047006. DOI

Backes C, et al. Production of Highly Monolayer Enriched Dispersions of Liquid-Exfoliated Nanosheets by Liquid Cascade Centrifugation. ACS Nano. 2016;10:1589–1601. doi: 10.1021/acsnano.5b07228. PubMed DOI

Ueberricke L., Coleman J. N., Backes C. Robustness of Size Selection and Spectroscopic Size, Thickness and Monolayer Metrics of Liquid-Exfoliated WS2. Phys. Status Solidi B Basic Solid State Phys.254, 1700443 (2017).

Backes C, et al. Spectroscopic metrics allow in situ measurement of mean size and thickness of liquid-exfoliated few-layer graphene nanosheets. Nanoscale. 2016;8:4311–4323. doi: 10.1039/C5NR08047A. PubMed DOI

Synnatschke K, et al. Length- and Thickness-Dependent Optical Response of Liquid-Exfoliated Transition Metal Dichalcogenides. Chem. Mater. 2019;31:10049–10062. doi: 10.1021/acs.chemmater.9b02905. DOI

Scardaci V, Coull R, Lyons PE, Rickard D, Coleman JN. Spray Deposition of Highly Transparent, Low-Resistance Networks of Silver Nanowires over Large Areas. Small. 2011;7:2621–2628. doi: 10.1002/smll.201100647. PubMed DOI

Lee K, et al. Highly conductive and long-term stable films from liquid-phase exfoliated platinum diselenide. J. Mater. Chem. C. 2023;11:593–599. doi: 10.1039/D2TC03889G. DOI

Cinquanta, E., Pogna, E. A. A., Gatto, L., Stagira, S., Vozzi, C. Charge carrier dynamics in 2D materials probed by ultrafast THzspectroscopy. Adv. Phys. X8, 2120416 (2023).

Lloyd-Hughes J, Jeon TI. A Review of the Terahertz Conductivity of Bulk and Nano-Materials. J. Infrared Millim. Terahertz Waves. 2012;33:871–925. doi: 10.1007/s10762-012-9905-y. DOI

Spies JA, et al. Terahertz Spectroscopy of Emerging Materials. J. Phys. Chem. C. 2020;124:22335–22346. doi: 10.1021/acs.jpcc.0c06344. DOI

Naftaly M, Gregory A. Terahertz and Microwave Optical Properties of Single-Crystal Quartz and Vitreous Silica and the Behavior of the Boson Peak. Appl. Sci. 2021;11:6733. doi: 10.3390/app11156733. DOI

Schindelin J, et al. Fiji: an open-source platform for biological-image analysis. Nat. Methods. 2012;9:676–682. doi: 10.1038/nmeth.2019. PubMed DOI PMC

Klein CA, Straub WD. Carrier densities and mobilities in pyrolytic graphite. Phys. Rev. 1961;123:1581–1583. doi: 10.1103/PhysRev.123.1581. DOI

Solution-processed negative gauge factor PtSe2 strain sensors

Carrier Multiplication and Photoexcited Many-Body States in Solution-Processed 2H-MoSe2

Using Electrical Impedance Spectroscopy to Separately Quantify the Effect of Strain on Nanosheet and Junction Resistance in Printed Nanosheet Networks

Production of Ultrathin and High-Quality Nanosheet Networks via Layer-by-Layer Assembly at Liquid-Liquid Interfaces