p –n junctionbgonul/dersnotlari/sc/CHAPTER_5.pdf · Idealized pIdealized p--n junction n junction...

p – n junctionp – n junction

Prof.Dr.Beşire GÖNÜLProf.Dr.Beşire GÖNÜL

� The p-n junction is the basic element of allbipolar devices. Its main electrical property isthat it rectifies (allow current to flow easily in onedirection only).The p-n junction is often justcalled a DIODE. Applications;

p p –– n junctionn junction

>photodiode, light sensitive diode,

>LED- ligth emitting diode,

>varactor diode-variable capacitance diode

� The p-n junction can be formed by pushing apiece of p-type silicon into close contact with apiecce of n-type silicon. But forming a p-njunction is not so simply. Because;

1) There will only be very few points of contactand any current flow would be restricted tothese few points instead of the whole surface

The formation of pThe formation of p--n junction :n junction :

these few points instead of the whole surfacearea of the junction.

2) Silicon that has been exposed to the air alwayshas a thin oxide coating on its surface calledthe “native oxide”. This oxide is a very goodinsulator and will prevent current flow.

3) Bonding arrangement is interrupted at thesurface; dangling bonds.

To overcome these surface states problems

p-n junction can be formed in the bulk of the

Surface states

p-n junction can be formed in the bulk of the

semiconductor, away from the surface as

much as possible.


EC

EĐ

EV

Ef

p-type n-typeEC

EĐ

EV

Ef

There is a big discontinuity in the fermi level accross the p-n junction.

EC

EĐ

EV

Ef

EC

EĐ

EV

Ef

p-type n-type

+++++

+++++

+++++

+++++

+++++

+++++

- - - - -

- - - - -

- - - - -

- - - - -

- - - - -

- - - - -

Hole

Movement

n-type p-type

+++++

+++++

+++++

- - - - -

- - - - -

- - - - -

Electron

Movement

++++

++++

++++

Fixed positive space-charge

- - - -

- - - -

- - - -

Fixed negativespace-charge

Ohmic end-contact

Metallurgical junction

� Lots of electrons on the left hand side of thejunction want to diffuse to the right and lots ofholes on the right hand side of the junction wantto move to the left.

� The donors and acceptors fixed,don’t move(unless you heat up semiconductors, so they can


(unless you heat up semiconductors, so they candiffuse) because they are elements (such asarsenic and boron) which are incorporated tolattice.

� However, the electrons and holes that come fromthem are free to move.

� Holes diffuse to the left of the metalurgical junction andcombine with the electrons on that side. They leave behindnegatively charged acceptor centres.

� Similarly, electrons diffusing to the right will leave behindpositively charged donor centres. This diffusion process cannot go on forever. Because, the increasing amount of fixedcharge wants to electrostatically attract the carriers that aretrying to diffuse away(donor centres want to keep theelectrons and acceptor centres want to keep the holes).

Idealized pIdealized p--n junctionn junction

electrons and acceptor centres want to keep the holes).Equlibrium is reached.

� This fixed charges produce an electric field which slowsdown the diffusion process.

� This fixed charge region is known as depletion region orspace charge region which is the region the free carriershave left.

� It is called as depletion region since it is depleted of freecarriers.

� Energy level diagram for the p-n junction in thermal equilibrium

EC

E

p-type n-type

EC

E

Electron Diffusion

Electron Drift

Neutral p-region

EV

Ef

EV

Ef

Depletion region

Hole Diffussion

Hole Drift

Neutral n-region

2

( ) ( ) 0 (1)

( )

p p p

p

J J drift J diffusion

AJ is the hole current density

cm

= + =

Thermal equilibrium; no applied field; no net current Thermal equilibrium; no applied field; no net current

flowflow

Drift current is due toelectric field at thejunction; minoritycarriers.

Diffusion current is

0 (2)

1( )

p p x p

pix p

dpJ q pE qD

dx

where

kTdEE D Einstein relation

q dx q

µ

µ

= − =

= =

Diffusion current isdue the toconcentrationgradient; majoritycarriers.

ProofProof

( ) 0 (3 )

e x p ( ) ( )

0 ( 4 )

ip p

i f fii

f

d E d pJ p k T

d x d x

E E d Ed Ed p pp n

k T d x k T d x d x

d EJ p

µ

µ

= − =

−= ⇒ = −

= = 0 ( 4 )

0

.

0 ( 5 )

f

p p

f

f

n n

d EJ p

d x

d Ew e c o n c lu d e th a t w h ic h s ta te s th a t

d x

th e F e rm i L e v e l i s a C O N S T A N T a t e q u i l ib r iu m

d EJ n

d x

µ

µ

= =

=

= =

� The drift and diffusion currents are flowing all thetime. But, in thermal equilibrium, the net currentflow is zero since the currents oppose each other.

� Under non-equilibrium condition, one of thecurrent flow mechanism is going to dominate

ProofProof

current flow mechanism is going to dominateover the other, resulting a net current flow.

� The electrons that want to diffuse from the n-type layer to the p-layer have potential barier.

� The potential barrier height accross a p-n junction isknown as the built in potential and also as the junctionpotential.

� The potential energy that this potential barrier correspondis

biV

p p –– n junction barrier height,n junction barrier height,biV

qVbiqV

• Electron energy is positive upwards in the energy leveldiagrams, so electron potentials are going to be measuredpositive downwards.

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

EC

E

p-type n-type

EC

E

Ei

biqV

pqV

Electrıon energy

Electron potential

p p –– n junction barrier heightn junction barrier height

EV

Ef

EV

Ef

Depletion region

Ei

pqV

nqV

Electrıon energy

Electron potential

e x p

ln ( 2 )

i f

i

Ap

i

E Ep n

k T

k T NV

q n

− =

=

The intrinsic Fermi Level is a very useful reference level in asemiconductor.

The p The p –– n junction barrier heightn junction barrier height

( ) (1)p i fqV E E= −

2

ln (3 )

,

ln ( 4 )

i

n

Dn

i

A Db i n p

i

q n

S im i la r ly fo r V

kT NV

q n

F o r fu l l io n iz a t io n th e b u i l t in v o l ta g e is a s u m o f

k T N NV V V

q n

=

−

= + =

�� CurrentCurrent MechanismsMechanisms,

� Diffusion of the carrierscause an electric in DR.

� Drift current is due tothe presence of electricfield in DR.

p p –– n junction in thermal equilibriumn junction in thermal equilibriumElectrıon energy

+ + +

+ + +

+ + +

- - - -

- - - -

- - - -

Neutral

p-region

Neutral

n-region

Electron Diffusion

Electron Drift

Field Direction

Hole energuy

DRDR

field in DR.

� Diffusion current is dueto the majority carriers.

� Drift current is due tothe minority carriers.

Electrıon energy

Hole Diffussion

Hole Drift

Hole energuy

EC

EV

Ef

n n –– p junction at equilibriump junction at equilibrium

Electrıon energy+ + +

+ + +

+ + +

- - - -

- - - -

- - - -

Neutral

p-region

Neutral

n-region

Electron Diffusion

Electron Drift

Field Direction

Hole energuy

E

DRDR

Electrıon energy

Hole Diffussion

Electron Diffusion

Hole Drift

Hole energuy

EC

EV

Ef

� When electrons and holes are diffusing from highconcentration region to the low concentration region theyboth have a potential barrier. However, in drift case ofminority carriers there is no potential barrier.

�� BuiltBuilt inin potentialpotential ;;

Diffusion :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 Depletion Approximation, Electric Field and Potential for pn

junctionjunction

+ + +

+ + +

- - - -

- - - -p-type n-type

Pote

ntial

Ele

ctric

field

Charg

e d

ensi

ty

+ + +

+ + +

- - - -

- - - -

biV area =

xx

� At equilibrium, there isno bias, i.e. no appliedvoltage.

� The field takes thesame sign as thecharge

Pote

ntial

Ele

ctric

field

Charg

e d

ensi

ty

mE−

biqVxx

xx

Depletion Region

� The sign of the electricfield is opposite to thatof the potential ;

nv

dVE

dx= −

nx px

� Charge density is negative on p-side and positive on n-side.

� As seen from the previous diagram, the charge distributionis very nice and abrupt changes occur at the depletionregion (DR) edges. Such a junction is called as an abruptjunction since the doping abruptly changes from p- to n-type at the metallurgical junction (ideal case).


junctionjunction

th e w id th o f th e D R o n n -s id e

th e w id th o f th e D R o n p -s id e

n

p

x

x

→

→

� In reality, the charge distribution tails-off into theneutral regions, i.e. the charge distrubition is notabrupt if one goes from depletion region into theneutral region. This region is called as atransition region and since the transition region isvery thin, one can ignore the tail-off region and


junctionjunction

very thin, one can ignore the tail-off region andconsider the change being abrupt. So thisapproximation is called as DEPLETIONAPPROXIMATION.

� The electric field is zero at the edge of the DR and increasesin negative direction. At junction charge changes its sign sodo electric field and the magnitude of the field decreases (itincreases positively).

Electric Field Diagram :

Potential Diagram :


junctionjunction

� Since the electric field is negative through the wholedepletion region ,DR, the potential will be positive throughthe DR. The potential increases slowly at left hand side butit increases rapidly on the right hand side. So the rate ofincrease of the potential is different an both sides of themetallurgical junction. This is due to the change of sign ofcharge at the junction.

+ + +

+ + +

- - - -

- - - -p-typen-type

+ + +

+ + +

- - - -

- - - -

mE+

xx

Field direction is positive x direction

Field direction

Depletion Approximation, Electric Field and Potential for np Depletion Approximation, Electric Field and Potential for np

junctionjunction

Pote

ntial

Ele

ctric

field

Charg

e d

ensi

ty

biV area =m

xx

xx

Depletion Region

Field direction

Pote

ntial

Ele

ctric

field

Charg

e d

ensi

ty

Abrupt junctionAbrupt junction

+ + +

+ + +

- - - -

- - - -p-type n-type

Charg

e d

ensi

ty

+ + +

+ + +

- - - -xx

• The amount of uncoverednegative charge on the left handside of the junction must beequal to the amount of positivecharge on the right hand side ofthe metalurgical junction.Overall space-charge neutralitycondition;

Charg

e d

ensi

ty

- - - -

- - - -

Depletion Region

pxnx

condition;

A p D nN x N x=

w

pnDA xxNN =⇒=when

The higher doped side of the junction has the narrower depletion width

� xxnn and xxpp is the width of the depletion layer on the n-sideand p-side of the junction, respectively.

� Unequal impurity concentration results an unequaldepletion layer widths by means of the charge neutrality


When (unequal impurity concentrations)

and , W

D A

p n p

N N

x x x

>>

>> ≅

depletion layer widths by means of the charge neutralitycondition;

nDpA xNxN .. =

W = total depletion

region


When WA D n p nN N x x x>> ⇒ >> ⇒ ≅

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

21 DAbiSi NNVx =

ε

)(

21

)(

DA

DAbiSi

A

p

DA

DAbiSi

D

n

NNq

NNV

Nx

NNqNx

+=

+=

ε


F o r e q u a l d o p i n g d e n s i t i e s W

T o t a l d e p le t i o n l a y e r w i d t h , W

21 1( )

n p

S i b i A D

x x

V N NW

ε

= +

= +21 1

( )( )

2 ( )

S i b i A D

A D A D

S i b i A D

A D

V N NW

N N q N N

V N NW

q N N

ε

ε

= ++

+=


12 permittivity of vacuum 8 85 10

relative permittivity of Silicon 11 9

, and W depends on , and

-

Si o r o

r

. x F/m

.

x x N N V

ε ε ε ε

ε

= = =

= =

, and W depends on , and

ln

n p A D bi

Abi

x x N N V

kT N NV

q=

2

D

in

OneOne--Sided abrupt pSided abrupt p--n junctionn junction

+ + +

+ + +

-

-p-type n-type

+ + +

+ + +

-

-

xx

+ + +

+ + +

- - - -

- - - -

DA NN >>heavily doped p-type

nxpx

Depletion Region

Abrupt pAbrupt p--n junctionn junction

neglected becan px


( )2 21 1

2

Si bi A D Si bi A Dn

D A D D A

V N N V N NW x

N q N N N qN

V

ε ε

ε

≅ = =+

neglegted

since NA>>ND

D

2 obtain a similar equation for W

in the case of N

Si bip

D

A

VW x

qN

N

ε≅ ≅

>>

One-sided abrupt junction


+ + +

+ + +

-

-p-type n-type

Pote

ntial

Ele

ctric

field

Charg

e d

ensi

ty

+ + +

+ + +

-

-

biV area =

xx

Electric field

-x directionPote

ntial

Ele

ctric

field

Charg

e d

ensi

ty

mE−

biqVxx

xx

nxpx

Appliying bias to pAppliying bias to p--n junctionn junction

p n

+ -

forward bias

� How current flows through the p-njunction when a bias (voltage) isapplied.

p n

- +

reverse bias

� The current flows all the time whenevera voltage source is connected to thediode. But the current flows rapidly inforward bias, however a very smallconstant current flows in reverse biascase.


VVbb II00

VVbb ; Breakdown voltage

II Reverse saturation current

Forward BiasForward BiasReverse BiasReverse Bias

I(current)

V(voltage)

� There is no turn-on voltage because current flows in anycase. However , the turn-on voltage can be defined as theforward bias required to produce a given amount of forwardcurrent.

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

II0 ;0 ; Reverse saturation current


+ - - +

p n p n p n

biqV( )Fbi VVq −

( )q V V+

+ +

+ +

- -

- -+

+

-

-

+ +

+ +

- -

- -

Zero Bias Forward Bias Reverse Bias

Ec

E Ev Ev

Ec Ecbi

biV

Fbi VV −

( )bi rq V V+

Rbi VV +

Pote

ntial Energ

y

EvEv Ev


voltagereverse

voltageforward

→

→

R

F

V

V

� When a voltage is applied to a diode , bands moveand the behaviour of the bands with appliedforward and reverse fields are shown in previousdiagram.

� Junction potential reduced

� Enhanced hole diffusion from p-side to n-side comparedwith the equilibrium case.

� Enhanced electron diffusion from n-side to p-side comparedwith the equilibrium case.

� Drift current flow is similar to the equilibrium case.

� Overall, a large diffusion current is able to flow.

Forward BiasForward Bias

� Overall, a large diffusion current is able to flow.

� Mnemonic. Connect positive terminal to p-side for forwardbias.

� Drift current is very similar to that of the equilibrium case.This current is due to the minority carriers on each side ofthe junction and the movement minority carriers is due tothe built in field accross the depletion region.

� Junction potential increased

� Reduced hole diffusion from p-side to n-side compared withthe equilibrium case.

� Reduced electron diffusion from n-side to p-side comparedwith the equilibrium case

Reverse BiasReverse Bias

with the equilibrium case

� Drift current flow is similar to the equilibrium case.

� Overall a very small reverse saturation current flows.

� Mnemonic. Connect positive terminal to n-side for reversebias.

Qualitative explanation of forward biasQualitative explanation of forward bias

+ -

p n+

+

-

-

ppnn

� Junction potential is reducedfrom VVbibi to VVbibi--VVFF..

� By forward biasing a largenumber of electrons areinjected from n-side to p-sideaccross the depletion regionand these electrons become

Carr

ier

Densi

ty

ppnono

nnpopo

npnp

p-n junction in forward bias

and these electrons becomeminority carriers on p-side,and the minority recombinewith majority holes so that thenumber of injected minorityelectrons decreases (decays)exponentially with distanceinto the p-side.

Carr

ier

Densi

ty

� Similarly, by forward biasing a large number ofholes are injected from p-side to n-side acrossthe DR. These holes become minority carriers atthe depletion region edge at the n-side so thattheir number (number of injected excess holes)decreases with distance into the neutral n-side.


decreases with distance into the neutral n-side.

� In summary, by forward biasing in fact oneinjects minority carriers to the opposite sides.These injected minorites recombine withmajorities.

� How does current flow occur if all the injectedminorities recombine with majorities ?

� If there is no carrier; no current flow occurs.� Consider the role of ohmic contacts at both ends

of p-n junction.


of p-n junction.� The lost majority carriers are replaced by the

majority carriers coming in from ohmic contactsto maintain the charge neutrality.

� The sum of the hole and electron currents flowingthrough the ohmic contacts makes up the totalcurrent flowing through the external circuit.

� “o” subscript denotes the equilibrium carrierconcentration.

Ideal diode equationIdeal diode equation

material. type-pin ion concentratelectron mequilibriu

material. type-nin ion concentratelectron mequilibriu

→

→no

n

n

material. type-nin ion concentrat hole mequilibriu

material. type-pin ion concentrat hole mequilibriu

material. type-pin ion concentratelectron mequilibriu

→

→

→

no

po

po

p

p

n

2. inpn =

� At equilibrium case ( no bias )


)1(.

.

2

2

materialtypennpn

npn

inono

i

−→=

=

)2(.

)1(.

2 materialtypepnpn

materialtypennpn

ipopo

inono

−→=

−→=


2ln assuming full ionization

; majority carriers

A Dbi

i

A po D no

kT N NV

q n

N p N n

=

≅ ≅

2

2

.ln . for n-type

ln exp (3)

po no

bi no no i

i

po bibi po no

no

p nkTV n p n

q n

p qVkTV p p

q p kT

= =

= ⇒ =


2

2

, (2)

.ln .

po no

bi po po i

i

Similarly from equation

p nkTV n p n

q n= =

ln exp (4)no bibi no po

po

n qVkTV n n

q n kT

= ⇒ =

This equation gives us the equilibrium majority carrier concentration.


What happens when a voltage appears across the p-n junction ?

� Equations (3) and (4) still valid but you should drop (0) subscript and change VVbi bi with

i.i. VV –– VV if a forward bias is applied.i.i. VVbibi –– VVF F if a forward bias is applied.

ii.ii. VVbibi + V+ VR R if a reverse bias is applied.if a reverse bias is applied.

VVFF : : forward voltage

VVR :R : reverse voltage

With these biases, the carrier densities change from equilibrium carrier densities to non- equilibrium carrier densities.


� Non-equilibrium majority carrier concentration in forward bias;

( )e x p b i F

p n

q V Vp p

k T

− =

F o r e x a m p le ; f o r r e v e r s e b i a s

( )e x p

n

b i Rn p

n

q V Vn n

k T

+ =

• When a voltage is applied; the equilibrium nno changes to the non equilibrium nn.

Assumption; low level injectionAssumption; low level injection

• For low level injection; the number of injected minorities ismuch less than the number of the majorities. That is theinjected minority carriers do not upset the majority carrierequilibrium densities.

pop

non

pp

nn

≈

≈

pop

• Non equilibrium electron concentration in n-type when a forward bias is applied ,

( )exp non-equilibrium.bi F

n p

q V Vn n

kT

− =


( ) (5)

exp (6)

bi Fn no no p

bino po

q V Vn n n n

kT

qVn n

kT

− ≈ =

= kT

combining (5) and (6)

( )exp expbi F bi

p po

q V V qVn n

kT kT

− =


poexp and subtracting n from both sidesFp po

qVn n

kT

=

� Solving for non-equilibrium electron concentration in p-type material, i.e. np

exp 1

the excess concentration of minority electrons

over the equilibrium concentration at the edge of the DR

p po po n

n

qVn n n

kTδ

δ

− = − =

=


Similarly ,

exp 1 the non-equilibriumn no no p

qVp p p

kTδ

− = − =

the excess concentration of minority holes

over the equilibrium concentration at the edge of the DR

pδ =

Forward-bias diode; injection of minority carriers across DR

+ -

p n+

+

-

-

BB

nnnono

pppopo

point A

point B

p po

n no

n n

p p

→ −

→ −

• is the distance from DR edge into p-side

• is the distance from DR edge into n-side

p

n

l

l

When a forward bias is applied; majoritycarriers are injected across DR andBB

ppnono

nnpopo

AA

lnlp

carriers are injected across DR andappear as a minority carrier at the edgeof DR on opposite side. These minoritieswill diffuse in field free opposite-regiontowards ohmic contact. Since ohmiccontact is a long way away, minoritycarriers decay exponentially withdistance in this region until it reaches toits equilibrium value.

Exponential decay of injected minority carriers on opposite Exponential decay of injected minority carriers on opposite sidessides

� The excess injected minorities decay exponentially as

( ) (0 ) ex pp

p

n

lp l n

Lδ δ

= −

p

( ) (0 ) ex p

an d L a re d iffu s io n le n g th s

fo r e le c tro n s a n d h o le s

nn

p

n

ln l p

L

L

δ δ

= −

Number of Injected Minority Holes Across The Depletion RegionNumber of Injected Minority Holes Across The Depletion Region

• By means of forward-biasing a p-n junctiondiode, the holes diffuse from left to right accrossthe DR and they become minority carriers.

• These holes recombine with majority electronswhen they are moving towards ohmic constants.

• So, the number of minority holes on the n-regiondecreases exponentially towards the ohmiccontact. The number of injected minoritydecreases exponentially towards the ohmiccontact. The number of injected minorityholes;excess holes;

( ) (0) exp( )nn

p

lp l p

Lδ δ= −

Distance into then region

from the Depletion Region

Diffusion Length for

holes

Number of Injected Minority Holes Across The Depletion RegionNumber of Injected Minority Holes Across The Depletion Region

point A

( ) (0)exp( )

p po

p

p

n

n n

ln l n

Lδ δ

→ −

= −

(0) exp( ) 1

(0) exp 1

po

no

qVn n

kT

qVp p

kT

δ

δ

= −

= −


• Similarly by means offorward biasing a p-njunction, the majorityelectrons are injectedfrom right to left acrossthe Depletion Region.These injected electrons

)exp()0()(n

p

npnL

ll −= δδ

These injected electronsbecome minorities at theDepletion Region edge onthe p-side, and theyrecombine with themajority holes. When theymove into the neutral p-side, the number ofinjected excess electronsdecreases exponentially.

)exp(1)exp()(n

p

popn

n

L

l

kT

qVnl −⋅

−=δ


Diffusion current density for electrons ;

( ) exp 1 exp

( 0) exp 1 Minus sign shows that electron current

density is

n po p

n n n p

n n

n po

n p

n

D n ldn d qVJ qD qD n l q

dx dx L kT L

qD n qVJ l

L kT

δ = = =− − −

− = = − in opposite direction to increasing .That is in the positive x direction.

Similarly for holes;

pl

Similarly for holes;

( 0) exp 1

The total current density;

exp 1

p no

p n p

p

n po p no

Total n p

n p

qD pdp qVJ l qD

dx L kT

D n D p qVJ J J q

L L kT

= = − = −

= + = + −


exp 1 exp 1

multiplying by area ;

n po p no

Total o

n p

D n D p qV qVJ q J

L L kT kT

= + − = −

exp 1o

qVI I

kT

= −


This equation is valid for both forward and reverse biases; just change the This equation is valid for both forward and reverse biases; just change the

sign of V.sign of V.


• Change V with –V for reverse bias. When qV>a few kT;exponential term goes to zero as

oII −= Reverse saturation currentexp 1o

qVI I

kT

− = −

Current

VVBB II00

VVBB ; Breakdown voltage




Voltage

Forward bias current densitiesForward bias current densities

+ -

p n

Ohmic contact

pntotal JJJ +=

Current density

� Jtotal is constant through thewhole diode.

� Minority current densitiesdecreases exponentially intothe the neutral sides whereas

ln=0lp=0

pJnJ

Current density decreases exponentially into

the the neutral sides whereasthe current densities due tothe majorities increase into theneutral sides.

pp--n junction in reverse biasn junction in reverse bias

• Depletion region gets bigger withincreasing reverse bias.

• Reverse bias prevents largediffusion current to flow throughthe diode.

• However; reverse bias doesn’tprevent the small current flowdue to the minority carrier. The

- +

p n

Current density Carrier density

p

pnonpo

due to the minority carrier. Thepresence of large electric fieldacross the DR extracts almost allthe minority holes from the n-region and minority electronsfrom the p-region.

• This flow of minority carriersacross the junction constitudes I0,the reverse saturation current.

• These minorities are generatedthermally.

ln=0lp=0

pntotal JJJ +=

pJnJCurrent density Carrier density

pnnp

pp--n junction in reverse biasn junction in reverse bias

• The flow of these minorities produces the reversesaturation current and this current increasesexponentially with temperature but it is independent ofapplied reverse voltage.


I(current)

VVbb II00

VVBB ; Breakdown voltage



Drift current

V(voltage)

Junction breakdown or reverse breakdownJunction breakdown or reverse breakdown

• An applied reverse bias (voltage) will result in a smallcurrent to flow through the device.

• At a particular high voltage value, which is called asbreakdown voltage VB, large currents start to flow. If thereis no current limiting resistor which is connected in seriesto the diode, the diode will be destroyed. There are twophysical effects which cause this breakdown.

1)1) ZenerZener breakdownbreakdown is observed in highly doped p-njunctions and occurs for voltages of about 5 V or less.

2)2) AvalancheAvalanche breakdownbreakdown is observed in less highly dopedp-n junctions.

Zener breakdownZener breakdown

• Zener breakdown occurs at highly doped p-njunctions with a tunneling mechanism.

• In a highly doped p-n junction the conductionand valance bands on opposite side of theand valance bands on opposite side of thejunction become so close during the reverse-biasthat the electrons on the p-side can tunnel fromdirectly VB into the CB on the n-side.

Avalanche BreakdownAvalanche Breakdown

• Avalanche breakdown mechanism occurs whenelectrons and holes moving through the DR andacquire sufficient energy from the electric fieldto break a bond i.e. create electron-hole pairsby colliding with atomic electrons within thedepletion region.

• The newly created electrons and holes move inopposite directions due to the electric field andthereby add to the existing reverse bias current.This is the most important breakdownmechanism in p-n junction.

Depletion CapacitanceDepletion Capacitance

• When a reverse bias is applied to p-n junction diode, thedepletion region width, W, increases. This cause an increasein the number of the uncovered space charge in depletionregion.

• Whereas when a forward bias is applied depletion regionwidth of the p-n junction diode decreases so the amount ofwidth of the p-n junction diode decreases so the amount ofthe uncovered space charge decreases as well.

• So the p-n junction diode behaves as a device in which theamount of charge in depletion region depends on the voltageacross the device. So it looks like a capacitor with acapacitance.


V

QC =

Charge stored incoloumbs

Voltage across thecapacitor in volts

Capacitance in farads

� Capacitance of a diode varies with WW (Depletion Region width)

�� W W (DR width varies width applied voltage V V )

capacitor in volts


2

Capacitance per unit area of a diode ;

For one-sided abrupt junction; e.g.

SiDEP

A D n n

A p D n

FC

W cm

N N x W x

N x N x

ε=

>> ⇒ >> ≅

=

2 Vε ε ε2 fo r

T h e ap p lica tio n o f reve rse b ia s ;

2 ( )2 ( )

S i S i S i b iD EP n A D

n D

S i S i DD EP

b i RS i b i R

D

VC x N N

W x qN

q NC

V VV V

qN

ε ε ε

ε εε

= ≅ ⇒ = >>

= =++


2If one makes measurements and draw 1

against the voltage ; built-in voltage and

doping density of low-doped side of the diode from

the intercept and slope.

2( )1

R

C -V /C

V obtain

V V+2

2( )1

2

bi R

Si D

S

V V

C q N

slopeq

ε

ε

+=

=2

ln( )A Dbi

i D i

kT N NV

N q n=

p –n junctionbgonul/dersnotlari/sc/CHAPTER_5.pdf · Idealized pIdealized p--n junction n junction...

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