The potential barrier height accross a p-n junction is known as the built in potential and also as the junction potential.

The potential energy that this potential barrier correspond is

biV

p – n junction barrier height,biV

biqV• Electron energy is positive upwards in the energy level

diagrams, so electron potentials are going to be measured positive downwards.

• The hole energies and potentials are of course positive in the opposite directions to the electrons

EC

EV

Ef

p-type n-type

EC

EV

Ef

Depletion region

Ei

Ei

biqV

pqV

nqV

Ele

ctrı

on e

nerg

y

Ele

ctro

n po

tent

ial

p – n junction barrier height

Current Mechanisms, Diffusion of the carriers

cause an electric in DR.

Drift current is due to the presence of electric field in DR.

Diffusion current is due to the majority carriers.

Drift current is due to the minority carriers.

p – n junction in thermal equilibriumE

lect

rıon

ene

rgy

+ + +

+ + +

+ + +

- - - -

- - - -

- - - -

Neutral

p-region

Neutral

n-region

Hole Diffussion

Electron Diffusion

Electron Drift

Hole Drift

Field Direction

Hol

e en

ergu

y

EC

EV

Ef

DR

n – p junction at equilibriumE

lect

rıon

ene

rgy

+ + +

+ + +

+ + +

- - - -

- - - -

- - - -

Neutral

p-region

Neutral

n-region

Hole Diffussion

Electron Diffusion

Electron Drift

Hole Drift

Field Direction

Hol

e en

ergu

y EC

EV

Ef

DR

When electrons and holes are diffusing from high concentration region to the low concentration region they both have a potential barrier. However, in drift case of minority carriers there is no potential barrier.

Built in potential ;

Diffusion :

2ln

i

DAbi n

NN

q

kTV

At fixed , is determined by the number of and atoms.bi A DT V N N

Depletion Approximation, Electric Field and Potential for pn junction

+ + +

+ + +

- - - -

- - - -

p-type n-type

Pote

nti

al

Ele

ctri

c field

Ch

arg

e d

en

sity

+ + +

+ + +- - - -

- - - - biV area

mE

biqV

x

x

x

Depletion

Region

At equilibrium, there is no bias, i.e. no applied voltage.

The field takes the same sign as the charge

The sign of the electric field is opposite to that of the potential ;

nv

dVE

dx

nx px

+ + +

+ + +

- - - -

- - - -

p-typen-type

+ + +

+ + +- - - -

- - - -

biV area mE

x

x

x

Depletion

Region

Field direction is positive x direction

Field direction

Depletion Approximation, Electric Field and Potential for np junction

Pote

nti

al

Ele

ctri

c field

Ch

arg

e d

en

sity

Abrupt junction

+ + +

+ + +

- - - -

- - - -

p-type n-type

Ch

arg

e d

en

sity

+ + +

+ + +- - - -

- - - -

x

Depletion

Region

pxnx

• The amount of uncovered negative charge on the left hand side of the junction must be equal to the amount of positive charge on the right hand side of the metalurgical junction. Overall space-charge neutrality condition;

A p D nN x N x

w

pnDA xxNN when

The higher doped side of the junction has the narrower depletion

width

xn and xp is the width of the depletion layer on the n-side and p-side of the junction, respectively.

Unequal impurity concentration results an unequal depletion layer widths by means of the charge neutrality condition;

Abrupt junction

nDpA xNxN ..

W = total depletion

region

When (unequal impurity concentrations)

and , WD A

p n p

N N

x x x

Abrupt junction

When WA D n p nN N x x x

• Depletion layer widths for n-side and p-side

)(

21

)(

21

DA

DAbiSi

Ap

DA

DAbiSi

Dn

NNq

NNV

Nx

NNq

NNV

Nx

Abrupt junction

For equal doping densities W

Total depletion layer width , W

21 1( )

( )

2 ( )

n p

Si bi A D

A D A D

Si bi A D

A D

x x

V N NW

N N q N N

V N NW

qN N

Abrupt junction

12 permittivity of vacuum 8 85 10

relative permittivity of Silicon 11 9

, and W depends on , and

ln

-Si o r o

r

n p A D bi

Abi

. x F/m

.

x x N N V

kT N NV

q

2

D

in

One-Sided abrupt p-n junction

D

2 21 1

2 obtain a similar equation for W

in the case of N

Si bi A D Si bi A Dn

D A D D A

Si bip

D

A

V N N V N NW x

N q N N N qN

VW x

qN

N

neglegtedsince NA>>ND

One-sided abrupt junction

Appliying bias to p-n junction

p n

+ -

forward bias

p n

- +

reverse bias

How current flows through the p-n junction when a bias (voltage) is applied.

The current flows all the time whenever a voltage source is connected to the diode. But the current flows rapidly in forward bias, however a very small constant current flows in reverse bias case.

There is no turn-on voltage because current flows in any case. However , the turn-on voltage can be defined as the forward bias required to produce a given amount of forward current.

If 1 m A is required for the circuit to work, 0.7 volt can be called as turn-on voltage.

Appliying bias to p-n junction

Vb I0

Vb ; Breakdown voltage

I0 ; Reverse saturation current

Forward BiasReverse Bias

I(current)

V(voltage)

Appliying bias to p-n junction

+ - - +

p n p n p n

biqV

biV

Fbi VVq

Fbi VV

bi rq V V

Rbi VV

+ + + +

- -- -

++

--

+ + + +

- -- -

Pote

nti

al Energ

y

Zero Bias Forward Bias Reverse Bias

Ec

EvEv Ev

Ec Ec

When a voltage is applied to a diode , bands move and the behaviour of the bands with applied forward and reverse fields are shown in previous diagram.

Appliying bias to p-n junction

voltagereverse

voltageforward

R

F

V

V