Capacitance is the ratio of the change in an electric charge in a system to the corresponding change in its electric potential.
There are two type of PN junction capacitance:
- Transition or depletion or space charge Capacitance.
- Diffusion capacitance
Transition or depletion or space charge capacitance:
During the reverse bias the minority carriers move away from the junction, thereby, having uncovered immobile carriers on either of the junction. Hence the thickness of the space-charge layer at the junction increases with reverse voltage. This increase in uncovered charge with applied voltage may be considered a capacitive effect. We may define an incremental capacitance CT by
Where is the increase in charge caused by a change in voltage. It follows from this definition that change in voltage in a time will result in a current
Therefore, knowledge of CT is important in considering a diode ( or a transistor) as a circuit element. The quantity CT is referred to as the transition, space-charge barrier, or depletion-region, capacitance. For the step-graded1 junction we know that.
However, under bias condition the junction voltage becomes Cj =V0 –VD where VD=VF for forward bias and VD = -VRfor reverse bias, thus the Eqn.(3) for the reverse bias becomes,
This can also be written in terms of Vj = V0 + VR as
Diffusion capacitance: For a forward bias a capacitance which is much larger than the transition capacitance CT comes into play. The origin of the largest capacitance lies in the injected charge stored near the junction outside the transition region. It is convention to introduce an incremental capacitance, defined as the rate of change of injected charge with voltage, called diffusion or storage, capacitance CD.
We now make the quantitative study of CD.
In writing the above equation, we have considered only the effect of holes, i.e.,
NA ≻≻ ND. Now substitution Eqn.(15) in (14) we get.
Where the diode incremental conductance g = Di/DV. Substituting the expression for the diode incremental resistance r = 1/g given in the Eqn.(5).
We see that the diffusion capacitance is proportional to the current I. In derivation above we have assumed that the diode current I is due to holes only. If this assumption is not satisfied, Eqn.(16) give the diffusion capacitance of CD due to holes only, and a similar expression can be obtained for the diffusion capacitance CDp and CDn, given by
For a reverse bias, g is very small and CD may be neglected compared with CT.For a forward current, on the other hand, CD is usually much larger than CT. For example for Ge ( ƞ = 1) at I = 26 mA , g = 1Ʊ and CD= τ. If say τ= 20 µs, then CD = 20µF a value which is about a million times larger than the transition capacitance.