Short conductive nanowires are printed at random positions and orientations onto an insulating flexible substrate between two electrode pads (top-down view). Wherever two wires physically overlap they form a junction; a continuous chain of junctions from the left pad to the right pad is a percolating path, and only then can current flow edge-to-edge across the film. Below the critical wire density the network is a set of disconnected islands and the film behaves as an insulator (aside from a tiny tunnelling leakage current across the narrowest remaining gap); above it, one giant connected cluster spans the whole film and conductance jumps sharply.
- Nanowire density — wires per film area. Sweeping it up drives the network across the percolation threshold, where the conducting path appears abruptly rather than growing smoothly.
- Film strain — stretching the substrate pulls at every wire-wire contact. Junctions crossing at a shallow, near-parallel angle have less contact area and let go first; near-perpendicular crossings hold on longest. Losing junctions one by one degrades conductance gracefully — unlike a solid evaporated metal film, which has no redundant paths and instead cracks catastrophically at a single strain threshold, dropping straight to zero (dashed reference curve).
- Highlighted path — the shortest active chain of junctions currently carrying current from pad to pad; its hop count sets the dominant resistance of the film.
This redundancy is exactly why nanowire meshes, rather than solid metal films, are used for stretchable and printed electronics: bendable displays, wearable sensors and flexible interconnects all rely on percolating conductor networks that keep working after many flex cycles.