Diffusion Capacitance of PN Junction Diode

Diffusion Capacitance (C_D)

• During forward biased condition, an another capacitance comes into existence called diffusion capacitance or storage capacitance, denoted as C_D.

• In forward biased condition, the width of the depletion region decreases and holes from p side get diffused in n side while electrons from n side move into the p‒side.

• As the applied voltage increases, concentration of injected charged particles increases.

• This rate of change of the injected charge with applied voltage is defined as a capacitance called diffusion capacitance.

 C_D = dQ / dV

     ……. (2.14.1)

• The diffusion capacitance can be determined by the expression

 C_D = τI / ηV_T

          ... (2.14.2)

• So diffusion capacitance is proportional to the current.

• For forward biased condition, the value of diffusion capacitance is of the order of nano farads to micro farads while transition capacitance is of the order of pico farads. So C_D is much larger than C_T.

• However in forward biased condition, C_D appears in parallel with the forward resistance which is very very small. Hence the time constant which is function of product of the forward resistance and C_D is also very small for ordinary signals.

Key Point: For normal signals C_D has no practical significance but for fast signals C_D must be considered.

• The graph of C_D against the applied forward voltage is shown in Fig. 2.14.1.

• As applied forward voltage increases, current I increases hence diffusion capacitance C_D increases.

Derivation of Expression for Diffusion Capacitance

• In a p‒n junction the total current at the junction (x = 0) is given by,

    I = I_pn(0) + I_np(0)A

where

I_pn(0) = Current due to holes diffusing from p to n side

I_np(0) = Current due to holes diffusion from n to p side

• Let p side is heavily doped with respect to other hence I_np(0) is negligible compared to I_pn(0).

 I = I_np(0)

• The diffusion current density is given by,

 J_p(x) = ‒q D_p (dp_n/dx)

where

Dp = Diffusion constant

dp_n/dx = Concentration gradient

• Also

J = Current / Area = I/A

i.e. I_p(x) = Jp(x) A

I_p(x) = ‒q A D_p (dp_n/dx)

       ...(2.14.3)

• For a p‒n junction,

 P_n(x) = P_n (0) e^‒x/Lp

       ...(2.14.4)

where

Lp = Diffusion length for holes

• From equation (2.14.4) D_pn (x)/dx = P_n(0) e^‒x/Lp (‒1/Lp)

 I_p(x) = ‒ q A D_p P_n(0) e^‒x/Lp (‒1/Lp)

 I_p(x) = q A (D_p/Lp) P_n(0) e^‒x/Lp

• At x = 0, I_p(x) = I_pn(0) = I

i.e.

 I = qAD_pP_n(0) / L_p

            ...(2.14.5)

P_n(0) = IL_p / qAD_p

            ...(2.14.6)

• The excess minority charge Q exists only on n side and given by,

Q = ₀∫^∞ AqP_n(0) e^‒x/Lp dx

 = [AqP_n(0) ( e^‒x/Lp / ‒1/L_p ) ]₀^∞

= AqL_pP_n(0)

            ...(2.14.7)

Using equations (2.14.6) in (2.14.7)

 Q = AqL_pIL_p / qAD_p = L_p²I / D_p

             ...(2.14.8)

• But L²/D_p = τ = Mean life time of charge carriers.

 Q = τI

and C_D = dQ/dV = dQ/dl . dl/dV

• But dQ/dI = τ hence C_D = τ dI/dV

• From diode current equation,

 I = I₀ e^V/ηVT

       …………… Neglecting 1 from equation

dI/dV = I₀ e^V/ηVT . 1/ ηV_T = 1 / ηV_T

               ….....(2.14.10)

CD = τI / ηV_T  = Diffusion capacitance

Review Questions

1. Explain the concept of diffusion capacitance of a p‒n junction diode.

2. Derive the expression for the diffusion capacitance of p‒n junction diode.