Derive expression of diffusion capacitance of pn junction diode
Answers
To implement this notion quantitatively, at a particular moment in time let the voltage across the device be {\displaystyle V} V. Now assume that the voltage changes with time slowly enough that at each moment the current is the same as the DC current that would flow at that voltage, say {\displaystyle I=I(V)} {\displaystyle I=I(V)} (the quasistatic approximation). Suppose further that the time to cross the device is the forward transit time {\displaystyle {\tau }_{F}} {\displaystyle {\tau }_{F}}. In this case the amount of charge in transit through the device at this particular moment, denoted {\displaystyle Q} Q, is given by
{\displaystyle Q=I(V){\tau }_{F}} {\displaystyle Q=I(V){\tau }_{F}}.
Consequently, the corresponding diffusion capacitance: {\displaystyle C_{diff}} {\displaystyle C_{diff}}. is
{\displaystyle C_{diff}={\begin{matrix}{\frac {dQ}{dV}}\end{matrix}}={\begin{matrix}{\frac {dI(V)}{dV}}\end{matrix}}{\tau }_{F}} {\displaystyle C_{diff}={\begin{matrix}{\frac {dQ}{dV}}\end{matrix}}={\begin{matrix}{\frac {dI(V)}{dV}}\end{matrix}}{\tau }_{F}}.
In the event the quasi-static approximation does not hold, that is, for very fast voltage changes occurring in times shorter than the transit time {\displaystyle {\tau }_{F}} {\displaystyle {\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 continuing research under the topic of non-quasistatic effects