Analytical description of mixed ohmic and space-charge-limited conduction in single-carrier devices

While space-charge-limited current measurements are often used to characterize charge-transport in relatively intrinsic, low-mobility semiconductors, it is currently difficult to characterize lightly or heavily doped semiconductors with this method. By combining the theories describing ohmic and space-charge-limited conduction, we derive a general analytical approach to extract the charge-carrier density, the conduction-band edge, and the drift components of the current density–voltage curves of a single-carrier device when the semiconductor is undoped, lightly doped, or heavily doped. The presented model covers the entire voltage range, i.e., both the low-voltage regime and the Mott–Gurney regime. We demonstrate that there is an upper limit to how doped a device must be before the current density–voltage curves are significantly affected, and we show that the background charge-carrier density must be considered to accurately model the drift component in the low-voltage regime, regardless of whether the device is doped or not. We expect that the final analytical expressions presented herein to be directly useful to experimentalists studying charge-transport in novel materials and devices.