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

• Published in: Journal of applied physics 2020-10, Vol.128 (16)
• Main Authors: Röhr, Jason A., MacKenzie, Roderick C. I.
• Format: Article
• Language: English
• Subjects: Applied physics; Carrier density; Charge density; Charge materials; Conduction bands; Current carriers; Current density; Drift; Electric potential; Mathematical analysis; Semiconductors; Voltage
• ISSN: 0021-8979; 1089-7550
• DOI: 10.1063/5.0024737

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.