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The contact potential is given as


V0 = contact potential

k = Boltzman constant

T = Temperature

Na = Concentration of acceptors

Nd = Concentration of donors

ni = Intrinsic carrier.

Space Charge at Junction

670.png = penetration of space charge region in p- material.

675.png = penetration of space charge region in n- material.

The maximum value of electric field is at x = 0 (i.e at junction)

E0 = 
680.png = 685.png

w = width of depletion region

V0 = contact potential

690.png = width of depletion region.

The width of depletion region can be given as:

w = 695.png 


Na and Nd = concentration of acceptor and donor (in/cm3)

 = permitivity of material used for formation p – n junction diode.

q = electronic charge (1.6 × 10–19 c)

We can also calculate the penetration of transition region into the n and p material

xpo = 700.png = 705.png

xno = 710.png = 716.png

We can see from the above equations that the depletion region is inversely proportional to the square root of concentration. i.e.

w 721.png726.png 

Carrier Injection

Excess holes on the n - side (i.e. Δpn)

                                   Δpn = pn (eqv/kT – 1)

Excess electron on p - side

                                Δnp = np (eqv/kT – 1)


Δpn = excess hole concentration on n side

Δnp = excess electron concentration on p side

pn = equilibrium hole concentration on n side

np = equilibrium electron concentration on p side

So, the resulting excess electron distribution is obtained using following formula

         731.png (xp) = np (eqv/kT – 1) 736.png

Similarly excess hole distribution is

        741.png(xn) = pn (eqv/kT – 1) 746.png

Where, xp = Distance in the p-material measured in the –x direction with xpo as origin.

xn = Distance in the n-material measured in the + x direction with xno as origin.

751.png(xp), 756.png(xn) = Excess carrier at xn and xp

pn = equilibrium hole concentration on n - side

np = equilibrium electron concentration on p - side

Ln, Lp = electron and hole diffusion length.

The total current across the diode is given by,

I = qA 761.png

This equation is also called diode equation where,

Dp, Dn = hole and electron diffusion coefficient respectively.

Capacitance of p - n Junction

Basically two types of capacitances are associated with a junction

  1. Junction capacitance
  2. Charge storage capacitance (Diffusion capacitance)
  1. Junction capacitance :
    The junction capacitance of a diode is easy to visualise from the charge distribution in the transition region. The uncompensated acceptor ion on the p - side provide a negative charge and equal positive charge result from ionized donor on the n side of transition region.
    C = 766.png
    Where C is capacitance
    The junction capacitance is given by the formula.
    CJ = 772.png = 777.png782.png
    Where, Cj = Voltage variable capacitance
    V0 = built - in potential (contact potential)
    V = bias voltage. 
  2. Diffusion Capacitance :
    Diffusion capacitance is the capacitance due to transport of charge carriers between two terminal of a device.
    Let the time to cross the device is the forward transit time tf. So, the amount of charge in transit through device at this particular moment, Q, is given by
    Q = I (V)  
    The corresponding diffusion capacitance Cdiff. is

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