hopping conduction
/ HOP-ing kun-DUK-shun /
Imagine crossing a wide river not on a bridge but by leaping from one stepping stone to the next, where the stones are scattered unevenly. You cannot stroll across; you have to make discrete jumps, and how far apart the stones are decides how easily you progress. In a disordered material, trapped electrons get from place to place in much the same way — by hopping from one trapping spot to another. That stop-and-go transport is hopping conduction.
Hopping conduction is the way electric current flows through a material whose electrons are localized — pinned to particular spots by disorder rather than free to roam. Instead of gliding as smooth waves, each electron sits trapped at one site until a lucky thermal kick lets it quantum-mechanically jump to a nearby empty site. The current is the sum of countless such hops. Because each hop needs a thermal nudge, hopping conduction grows stronger as the material warms and dies away as it cools — the opposite of an ordinary metal, where cooling improves conduction. At low temperatures electrons often hop farther to reach an easier landing spot, a refinement called variable-range hopping.
Hopping conduction matters because it is how electricity moves through amorphous semiconductors, doped insulators, and many disordered materials used in solar cells, sensors, and printed electronics — wherever the carriers are localized. The subtle point is that hopping is a fundamentally different mechanism from the smooth band transport of crystals: it relies on disorder and thermal energy together, and its telltale signature is conduction that improves with heating, fading toward zero at the lowest temperatures.
Amorphous silicon, the disordered material in many thin-film solar panels and old calculator screens, carries current largely by hopping conduction. Its electrons are trapped at scattered sites in the jumbled atomic network, and only thermal jumps move them along. Chill such a film and its conductivity plummets; warm it and the conductivity climbs — the exact reverse of a copper wire, and a clear fingerprint of localized carriers hopping their way through disorder.
In amorphous silicon, trapped electrons hop site to site; conductivity rises with heating — the opposite of a metal.
Hopping conduction relies on disorder, so do not confuse it with the ordinary heating-up of a metal's resistance. A metal conducts better when cooled, because its electrons are free waves slowed only by jiggling atoms. A hopping conductor conducts worse when cooled, because its electrons are trapped and need thermal energy just to make each jump.