Space Charge - Mott-Gurney Law

Mott-Gurney Law

In the low-field regime, velocity of injected carriers can be represented by

Where is the applied electric field, is the carrier mobility, and is the carrier velocity. If the current is limited by the drift component of inject carriers, the space-charge-limited conduction current density can be written as

where is the applied voltage, and is the length of the plane-parallel sample. This expression is known as the Mott-Gurney law.

In the velocity-saturation regime, this equation takes the following form

Note the different dependence of on in each of the two cases. Interestingly, in the ballistic case (assuming no collisions), the Mott-Gurney equation takes the form of the more familiar Child-Langmuir law.

It should be noted that the above derivations make the following assumptions:

1. There is only one type of charge carrier present.
2. The material has no intrinsic conductivity, but charges are injected into it from one electrode and captured by the other.
3. The carrier mobility and the dielectric permittivity are constant throughout the sample.
4. The electric field at the charge-injecting cathode is zero.

As an application example, the steady-state space-charge-limited current across a piece of silicon with a charge carrier mobility of 1500 cm2/V-s, a dielectric constant of 11.9, an area of 10-8cm2 and a thickness of 10-4cm can be calculated by an on line calculator as 126.4mA at voltage 3V.