P-N junction Diodes

Abrupt p-n junction

Fig.10.3

Built-in potential=

At equilibrium

Thus

Thus minority carrier in n side

minority carrier in p side

Thermal equilibrium E field in neutral regions=0

Thus Total-ve charge in P side-total + ve charge in n side

Fig.11.4

Poissons Equation

In n side

.

Integrating

Maxwell's field at x=0(junction)

Also we obtain

W=Total depletion region width

Eliminating from previous 3 equations.

More accurate expression for depletion region width

      If one side is heavily doped the depletion region is in weakly doped place) Depletion -layer capacitance per unit area

, Incremental increase in charge per unit area for a voltage increase of

Inside depletion layer assuming the following

.  Boltzman relation is an approximation

.  Abrupt Depletion Layer

.  Low injection (injected minority carrier < majority carrier)

.  No generation current inside depletion layer

where and

When voltage is applied the minority carrier densities on both sides are changed and

are imrefs or quasi Fermi level for electrons and holes (E Fn and E Fp ) under nonequilibrium condition as applied voltage/bias or optical field as shown in Fig. 10.4

Forward bias

Reversed bias

Now =

Similarly

Electron and hole current densities is proportional to gradient of quasi Fermi level.

Now applied voltage across the junction. Now at the boundary of depletion layer at p side i.e. at

We have from (A) & (B)

Where is the equilibrium electron density on the p side.

Where is the equilibrium hole density on the p side.

n side Continuity equation in steady state

Let recombination rate

Then in 1-D we obtain

for n side

Charge neutrality holds approximately

ultiplying first by and second equation by and taking Einstein relation as

Neutral region 

Now Boundary condition (injection)

assuming large structure

exponential decay of electron and hole current components in the Depletion region as shown in Fig. 10.5