Space-charge-limited current in a film

Space-charge-limited current is considered in a thin-film n-i-n diode. It is assumed that impenetrable barriers limit the current flow to a film of thickness D. Because the electric field of injected electrons spreads out of the film, the level of injection is substantially higher than in the bulk case described by the classical Mott-Gurney law. As a consequence, the current density in a thin diode can be an order of magnitude larger than in a bulk diode of the same length. It is shown that, in the limit of small D, the total current is independent of D because the decreasing film thickness is exactly compensated by increasing injection. In this limit analytic expressions of the current-voltage characteristics are obtained for several model electrode configurations. The analytic results are confirmed by a numerical simulation of the diode within a drift-diffusion model assuming a field-independent mobility. The numerical results also describe a transition with decreasing D from the Mott-Gurney law to the new law governing space-charge-limited current in a film