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Modelling electrical conduction in nanostructure assemblies through complex networks


Carrier transport processes in assemblies of nanostructures rely on morphology-dependent and hierarchical conduction mechanisms, whose complexity cannot be captured by current modelling approaches. Here we apply the concept of complex networks to modelling carrier conduction in such systems. The approach permits assignment of arbitrary connectivity and connection strength between assembly constituents and is thus ideal for nanostructured films, composites and other geometries. Modelling of simplified rod-like nanostructures is consistent with analytical solutions, whereas results for more realistic nanostructure assemblies agree with experimental data and reveal conduction behaviour not captured by previous models. Fitting of ensemble measurements also allows the conduction properties of individual constituents to be extracted, which are subsequently used to guide the realization of transparent electrodes with improved performance. A global optimization process was employed to identify geometries and properties with high potential for transparent conductors. Our intuitive discretization approach, combined with a simple solver tool, allows researchers with little computational experience to carry out realistic simulations.

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Fig. 1: Complex network modelling approach.
Fig. 2: Modelling rod-like constituents.
Fig. 3: Complex assemblies and comparison with experiments.
Fig. 4: Prediction of high-performance TCF materials.

Data availability

The datasets generated during and/or analysed during the current study are available online at

Code availability

Sample code employed in this work is available in the Supplementary Information and additional examples are available at


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M.H. acknowledges funding from the Ministry of Science and Technology (107-2112-M-002 -004 -MY3). Y.-P.H. acknowledges funding from Academia Sinica (AS-iMATE-108-32) and the Ministry of Science and Technology.

Author information




H.Y. developed methodology, software and analysis and wrote the original draft, Y.-P.H. provided methodology, experimental resources, revisions and supervision, J.K. contributed conceptualization, experimental ressources and critical review, M.H. aided in formal analysis, visualization, project management and revision.

Corresponding authors

Correspondence to Ya-Ping Hsieh or Mario Hofmann.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary text, Table 1 and Figs. 1–5.

Supplementary Video 1

Animated visualization of percolation pathways in composite of resistive matrix with conductive fillers corresponding to the inset of Fig. 3a.

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Yao, H., Hsieh, YP., Kong, J. et al. Modelling electrical conduction in nanostructure assemblies through complex networks. Nat. Mater. 19, 745–751 (2020).

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