On the correct interpretation of the low voltage regime in intrinsic single-carrier devices

We discuss the approach of determining the charge-carrier density of a single-carrier device by combining Ohm’s law and the Mott-Gurney law. We show that this approach is seldom valid, due to the fact that whenever Ohm’s law is applicable the Mott-Gurney law is usually not, and vice versa. We do this using a numerical drift-diffusion solver to calculate the current density-voltage curves and the charge-carrier density, with increasing doping concentration. As this doping concentration is increased to very large values, using Ohm’s law becomes a sensible way of measuring the product of mobility and doping density in the sample. However, in the high-doping limit, the current is no longer governed by space-charge and it will no longer be possible to determine the charge-carrier mobility using the Mott-Gurney law. This leaves the value for the mobility as an unknown in the mobility-doping density product in Ohm’s law. We also show that, when the charge-carrier mobility for an intrinsic semiconductor is known in advance, the carrier density is underestimated up to many orders of magnitude if Ohm’s law is used. We finally seek to establish a window of conditions where the two methods can be combined to yield reasonable results.