Two-Carrier Space-Charge-Limited Current in a Trap-Free Insulator

Abstract

The space‐charge‐limited electrical behavior of a trap‐free insulator containing both mobile electrons and holes is investigated under the approximation of neglecting diffusioncurrent. When both contacts are ohmic, the dependence of two‐carrier space‐charge‐limited current on voltage and interelectrode spacing remains the same as in the one‐carrier case; i.e., the current varies as the square of the voltage and as the inverse cube of the spacing. For given voltage and spacing, however, the two‐carrier current is usually orders of magnitude larger than the one‐carrier current. This is in striking contrast to the case of space‐charge‐limited flow of electrons and positive ions in a vacuum. The two‐carrier current in an insulator can be reduced to the size of the one‐carrier current either by making one contact highly blocking or by reducing the mobility of one of the carriers to zero. While the first approach yields in detail the well‐known one‐carrier case, the second approach differs from the one‐carrier case in that no net excess space charge can be injected into the insulator. The intermediate case of a slightly blocking contact shows that, while the current may be carried mainly by one sign of carrier, the net space charge of the insulator can have the opposite sign. When both contacts are blocking, the current saturates for sufficiently high voltages. The current is smaller than the saturation value by an amount proportional to the cube of the interelectrode spacing and the inverse square of the voltage. Near such saturation, the space charge is negligible and the electric field is uniform across the insulator. It is plausible that many of the above results will also be true for an insulator with traps.