Diffusion capacitance

Diffusion capacitance is the capacitance due to transport of charge carriers between two terminals of a device, for eample, the diffusion of carriers from anode to cathode in forward bias mode of a diode or from emitter to base (forward biased junction in active region) for a transistor. In a semiconductor device with a current flowing through it (for example, an ongoing transport of charge by diffusion) at a particular moment there is necessarily some charge in the process of transit through the device. If the applied voltage changes and the current changes, a different amount of charge will be in transit. The change in the amount of transiting charge divided by the change in the voltage causing it is the diffusion capacitance. The adjective "diffusion" is used because the original use of this term was for junction diodes, where the charge transport was via the diffusion mechanism. See Fick's law.

To implement this notion quantitatively, suppose the time to cross the device is the forward transit time ${\tau }_{F}$. At a particular moment in time let the voltage across the device be $V$. Now assume that the voltage changes with time slowly enough that in time ${\tau }_{F}$ virtually no change occurs (the quasi-static approximation). In this case the current $I$ through the device is given by the DC current-voltage relation $I=I(V)$, so the amount of charge in transit through the device $Q$ is given by

$Q=I(V){\tau }_{F}$.

Consequently, the corresponding diffusion capacitance:$C(diff)$. is

$C(diff)={\frac {dQ}{dV}}={\frac {dI(V)}{dV}}{\tau }_{F}$.

In the event the quasi-static approximation does not hold, that is, for very fast voltage changes occuring in times shorter than ${\tau }_{F}$, the equations governing time-dependent transport in the device must be solved to find the charge in transit, for example the Boltzmann equation. That problem is a subject of continuuing research under the topic of non-quasi-static effects. See Liu , and Gildenblat et al.