The effect of injection properties of contacts on the dynamics of unipolar space-charge limited currents

The influence of the carrier injection properties of electrode contacts on unipolar space-charge limited currents (SCLC) in perfect insulators is theoretically studied. The usual electric transport model consisting of the charge continuity equation and the Poisson equation is supplemented by boundary conditions describing carrier injection. The dependence of the electric behavior on the saturation current density, which is the most important parameter of the boundary condition, is investigated, mainly with FEM simulations. The scenarios in the focus are transient DC current when a constant voltage is switched on, and dielectric (or impedance) spectroscopy (AC). For the latter, higher harmonics up to the 5
^th
order are relevant due to the intrinsic nonlinearity of SCLC. A simplified ordinary differential equation model for transient contact charging is derived, in an analogous way as it is usually done for the early SCLC transient with ideal ohmic contacts. Finally, a specific case with traps that may quench the transit-time peak is briefly discussed to illustrate trapping effects. It turns out that the SCLC dynamics can be separated in three time (or frequency) regimes. Two of them are separated as usual by the time of flight, τ
_tof
, of carriers through the sample. A third region at shorter times t<;τ
_c
<;<;τ
_tof
(or higher frequencies) exists, where τ
_c
characterizes the time for space charge formation at the injecting contact. The contact injection properties thus mainly influence the short-time and high-frequency behavior, where the characteristic time decreases with increasing saturation current. This behavior is reflected by the appearance of specific structures in the absorption current and the impedance spectrum. For instance, an additional current maximum associated with the fast diffusive expansion of the locally injected space charge may appear at early times.