Transition or Space Charge or Depletion Capacitance

TRANSITION OR SPACE CHARGE OR DEPLETION CAPACITANCE

When PN diode is reverse biased, the majority charge carriers move away from the junction and large immobile carriers are generated near the junction. The width of the space - charge layer increases with increasing reverse voltage.

Thus the increase in uncovered charge with applied voltage is considered as a capacitor. The two parallel layers of oppositely charged immobile ions form the two plates of capacitor, C_T.

Where dQ/dv - change in charge due to change in voltage

The change in voltage dV in a time dt results in current

I = dQ/dt .................(2)

(1) can be written as

C_T = transition, space-charge, barrier or depletion capacitance.

C_T is derived for two cases

i. Step-graded junction

ii. Linearly graded junction

i. Step Graded Junction

A PN junction is formed from a single intrinsic semiconductor by doping part of it with acceptor impurities and the remaining with donors.

There is a sudden step change from acceptor ions on one side to donor ions on the other side. Trivalent Indium is placed against N-type germanium and heated to high temperature.

Some of the Indium dissolves into the Germanium and N-type Germanium is changed to P-type at the junction. This step-graded junction is called an alloy or fusion junction.

Consider a PN diode which is asymmetrically doped at the junction. The net charge is zero,

Where N_A - Acceptor impurity concentration

N_D - Donor impurity concentration

W_p & W_n - Depletion region width of P and N region

q - Magnitude of charge of electron or hole

By poisson's equation,

Integrating the above equation twice

Width of depletion layer, W increases with applied reverse voltage

Total charge density of P-type material

Differentiate above equation with respect to V

Differentiate (4) with respect to V

Substitute (6) in (5)

Where

ε - permittivity of the material

A - Cross sectional area of the junction

W - Width of depletion layer

The depletion width W is given by

When no external voltage is applied, width of PN diode is of the order of 0.5 microns. The majority carriers move across the junction and opposite charges are stored at a distance W apart. This depletion region acts as dielectric between P and N regions. Thus it acts as a parallel plate capacitor with transition capacitance C_T approximately 20 PF with no external bias. C_T ranges from 5 to 200 PF with applied voltage.

ii. Linearly Graded Junction

The charge density varies linearly with the applied voltage.

Linear graded junction is formed by melting Germanium and its type is changed during the drawing process by adding first p-type and then n-type impurities. The charge density becomes absolutely zero at edge distances and W/2 W/2 and varies linearly with distance.

Where k - proportionality constant

Using Poisson's equation

Where V - potential at a distance 'x' from the junction

Integrating (2)

Substitute (4) in (3)

Substitute (5) in (3)

Integrating (6)

The total potential V_J across the junction from - W/2 to W/2 is given by

The total charge on one side of the layer is

From (7)

Substitute (9) in (8)