Question

) With the aid of a diagram, explair the formation of the depletion region in a P-n junction diode in thermal equilibrium. State the equilibrium condition for the currents flowing across the junction. Draw the band diagram of a forward biased p-n junction diode. On the diagram sketch the variation of the conduction band edge energy Ec and the valence band edge energy Ey. Sketch the variation of the electric field and potential across the p-n junction. State the changes in the width, energy band slope and voltage drop depletion region compared to a p-n junction in thermal equilibrium. across the b) Explain the mechanism injection electroluminescence? What type of semiconductor produces very efficient devices based on injection electroluminescence? Give an example of one such device. c) A forward biased GaP diode is connected in series with a 1 kn resister. The e.m.f in the circuit is 10 V. Assuming that the built-in voltage of the GaP diode is 2 V, (i) calculate the current flowing in the circuit. (ii) determine the band-gap energy of GaP given that the diode emits light at 562 nm. (iii) calculate the optical power emitted by the diode assuming 20 % recombination efficiency and current flow due to electrons.

Answer 1

Solution :

a)

The following steps highlight the formation of depletion region in pn junction :

step 1) P-n junctions are formed by joining n-type and p-type semiconductor materials, as shown below. Since the n-type region has a high electron concentration and the p-type a high hole concentration, electrons diffuse from the n-type side to the p-type side.

p-type n-type hole diffusion electron difusion

step 2) When N-doped and P-doped semiconductors are placed together to form a junction, free electrons in the N-side conduction band migrate (diffuse) into the P-side conduction band, and holes in the P-side valence band migrate into the N-side valence band. The diffused electrons come into contact with holes and are eliminated by recombination in the P-side.
Similarly the diffused holes are recombined with free electrons so eliminated in the N-side.

uncovered space charges n-type p-type hole drift electron drift

The net result is that the diffused electrons and holes are gone. In a N-side region near to the junction interface, free electrons in the conduction band are gone due to :

(1) the diffusion of electrons to the P-side
  (2) recombination of electrons to holes that are diffused from the P-side.

Holes in a P-side region near to the interface are also gone by a similar reason. As a result, majority charge carriers (free electrons for the N-type semiconductor, and holes for the P-type semiconductor) are depleted in the region around the junction interface, so this region is called the depletion region or depletion zone.

So in the end a depletion region is as formed below :

space charge region neutral region neutral region holes electrons p-doped n-doped E-field "Diffusion force" on holes "Diffusion force" on electrons E-field force on holes E-field force on electrons carrier concentration [log scale]

Please note that under equilibrium :

---- The electron diffusion current is balanced by the equal and opposite electron drift current

---- The hole diffusion current is balanced by the equal and opposite hole drift current

So the net currents of both the electrons as well as the holes go to zero …. and equilibrium is established!!

b)

Consider a pn junction under forward bias. This is achieved by connecting the p side to the positive terminal of an external power source and the n side to the negative terminal.:

A P-doped ww a N-doped Na

In forward bias, the depletion regions shrink, and the electric field in the junction also decreases in magnitude.

The effect of this is that the net potential at the junction is lowered. In the presence of an external potential the Fermi levels no longer line up but are shifted :

Vn Vo VP EFn EFp

The application of the external potential, in forward bias, shifts the n side up with respect to the p side,

Vn Vo Vext Vo Vp frved Efn EFn eVext EFn EFp Efp

or

Drift p-type Diffusion Forward bias Ep n-type CA-)6 Diffusi on E F.p Drift thermal eq.

c)

under thermal equilibrium electric field and potential are like :

Ast h- (a) e E(x) W. Nelrel n-region Nevtral p-realor ELECTRIC FIELD E V(x) Ve ELECTRIC POT 5pace charge region Wa login), log p) Pr PE(x) eVa POTENTIAL ENERGY Hoin PE(x) Pei (b) x0 Pm Electron PE(x N V w.. X N (D