Analytical Description of Mixed Ohmic and Space-Charge-Limited Conduction.

By combining the theory put forward by Mott, Gurney and Simmons, we here derive a series of analytical expressions that accurately describe the charge-carrier density, conduction-band edge and current density of a single-carrier device when the semiconductor is either undoped, lightly doped or heavily doped. We give a simple condition for how doped a semiconductor in a single-carrier device must be before the J-V curves are significantly affected and the doping can be detected. We also show that both the background charge-carrier density and doping density must be taken into account to accurately model the J-V curves in the low-voltage regime. Finally, the model is expanded to cover both the low-voltage regime and the Mott-Gurney drift regime. The analytical expressions presented herein can be fitted to data obtained from space-charge-limited current measurements to simultaneously yield the charge-carrier mobility and the doping density.