Space-Charge-Limited Currents in Solids

TLDR

These currents are the direct analog of space‑charge‑limited currents in a vacuum diode. The shape of the current–voltage curve, influenced by traps, allows determination of trap energy distribution, temperature dependence, and capture cross sections, and also provides a mechanism for electrical breakdown in insulators. In thin, nearly perfect insulating crystals, space‑charge‑limited currents far exceed ohmic currents but are reduced from the ideal by the free‑to‑trapped carrier ratio, making them a sensitive probe of crystal imperfections down to one part in 10^15, while traps also alter the current–voltage curve from a square law to a higher‑power dependence.

Abstract

Currents, far in excess of ohmic currents, can be drawn through thin, relatively perfect insulating crystals. These currents are the direct analog of space-charge-limited currents in a vacuum diode. In actual crystals, the space-charge-limited currents are less than their theoretical value for an ideal crystal by the ratio of free to trapped carriers. Space-charge-limited currents become, therefore, a simple tool for measuring the imperfections in crystals even in the range of one part in ${10}^{15}$.The presence of traps not only reduces the magnitude of space-charge-limited currents, but also is likely to distort the shape of the current-voltage curve from an ideal square law to a much higher power dependence on voltage. The particular shape can be used to determine the energy distribution of traps.The presence of traps tends to uniformize the charge distribution between electrodes, to introduce a temperature dependence of the current, and to give rise to certain transient effects from which capture cross sections of traps may be computed.Space-charge-limited currents offer another mechanism for electrical breakdown in insulators.