microsoft powerpoint - 1. chapter_1 [compatibility mode]

p – n junction

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;

>photodiode, light sensitive diode,>LED- ligth emitting diode,>varactor diode-variable capacitance diode

pp –– n junctionn junction

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 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.

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

To overcome these surface states problems

p-n junction can be formed in the bulk of thesemiconductor, away from the surface as

much as possible.

Surface states


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

EC

Eİ

EV

Ef

EC

Eİ

EV

Ef

EC

Eİ

EV

Ef

p-type n-typeEC

Eİ

EV

Ef

p-type n-type

++++++++++++++++++++++++++++++++++++++++

- - - - -- - - - -- - - - -- - - - -- - - - -- - - - -- - - - -- - - - -

HoleMovement

ElectronMovement

++++++++++++

Fixed positivespace-charge

- - - -- - - -- - - -

Fixed negativespace-charge

Ohmicend-contact

n-type p-type

Metallurgicaljunction

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 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).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.

Idealized pIdealized p--n junctionn junction

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

EC

EV

Ef

p-type n-type

EC

EV

Ef

Depletion region

Hole Diffussion

Hole Drift

Electron DiffusionElectron Drift

Neutral p-region

Neutral n-region

2

( ) ( ) 0 (1)

( )

0 (2)

1 ( )

p p p

p

p p x p

pix p

J J drift J diffusion

AJ is the hole current densitycm

dpJ q pE qDdx

wherekTdEE D Einstein relation

q dx q

Thermal equilibrium; no applied field; no net currentThermal equilibrium; no applied field; no net currentflowflow

Drift current is due toelectric field at thejunction; minoritycarriers.

Diffusion current isdue the toconcentrationgradient; majoritycarriers.

ProofProof

( ) 0 ( 3 )

e x p ( ) ( )

0 ( 4 )

0

.

0 ( 5 )

ip p

i f fii

fp p

f

fn n

d E d pJ p k Td x d x

E E d Ed Ed p pp nk T d x k T d x d x

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 xth e F e r m 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

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 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.

ProofProof

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

pp –– n junction barrier height,n junction barrier height, biV

biqV• 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

EV

Ef

p-type n-type

EC

EV

Ef

Depletion region

Ei

Ei

biqV

pqVnqV

Ele

ctrıo

n en

ergy

Ele

ctro

n po

tent

ial

pp –– n junction barrier heightn junction barrier height

2

e x p

ln ( 2 )

ln (3 )

,

ln ( 4 )

i fi

Ap

i

n

Dn

i

A Db i n p

i

E Ep n

k Tk T NVq n

S im i la r ly fo r Vk T NVq 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 fk T N NV V Vq n

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

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

( ) (1)p i fqV E E

CurrentCurrent MechanismsMechanisms,

Diffusion of the carrierscause an electric in DR.

Drift current is due tothe presence of electricfield in DR.

Diffusion current is dueto the majority carriers.

Drift current is due tothe minority carriers.

pp –– n junction in thermal equilibriumn junction in thermal equilibriumE

lect

rıon

ener

gy

+ + ++ + ++ + +

- - - -- - - -- - - -

Neutralp-region

Neutraln-region

Hole Diffussion

Electron Diffusion

Electron Drift

Hole Drift

Field Direction

Hol

e en

ergu

y

EC

EV

Ef

DRDR

nn –– p junction at equilibriump junction at equilibrium

Ele

ctrıo

n en

ergy

+ + ++ + ++ + +

- - - -- - - -- - - -

Neutralp-region

Neutraln-region

Hole Diffussion

Electron Diffusion

Electron Drift

Hole Drift

Field Direction

Hol

e en

ergu

y

EC

EV

Ef

DRDR

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 :

2lni

DAbi n

NNq

kTV

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

Depletion Approximation, Electric Field and Potential for pnDepletion Approximation, Electric Field and Potential for pnjunctionjunction

+ + ++ + +

- - - -- - - -p-type n-type

Pote

ntia

l

Ele

ctric

field

Cha

rge

dens

ity

+ + ++ + +

- - - -- - - -

biVarea

mE

biqVxx

xx

xx

DepletionRegion

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

The field takes thesame sign as thecharge

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

nv

dVEdx

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).

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

n

p

xx


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 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 :

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

+ + ++ + +

- - - -- - - -

biVarea mE

xx

xx

xx

DepletionRegion

Field direction is positive x direction

Field direction

Depletion Approximation, Electric Field and Potential for npDepletion Approximation, Electric Field and Potential for npjunctionjunction

Pote

ntia

l

E

lect

ric

field

Cha

rge

dens

ity

Abrupt junctionAbrupt junction

+ + ++ + +

- - - -- - - -p-type n-type

Cha

rge

dens

ity + + ++ + +

- - - -- - - -

xx

DepletionRegion

pxnx

• 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;

A p D nN x N x

w

pnDA xxNN when

The higher doped side of the junctionhas 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 neutralitycondition;


nDpA xNxN ..

W = total depletionregion

When (unequal impurity concentrations) and , W

D A

p n p

N Nx x x


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

NNqNNV

Nx

NNqNNV

Nx


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( )( )

2 ( )

n p

S i b i A D

A D A D

S i b i A D

A D

x x

V N NWN N q N N

V N NWq N N


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 NVq

2D

in

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

+ + ++ + +

--p-type n-type

+ + ++ + +

--

xx

nxpx

+ + ++ + +

- - - -- - - -

DepletionRegion

Abrupt pAbrupt p--n junctionn junction

DA NN heavily doped p-type

neglectedbecanpx


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 xN q N N N qN

VW xqN

N

neglegtedsince NA>>ND

One-sided abrupt junction


+ + ++ + +

--p-type n-type

Pote

ntia

l

E

lect

ric

field

Cha

rge

dens

ity

+ + ++ + +

--

biVarea

mE

biqVxx

xx

xx

nxpx

Electric field

-x direction

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

p n

+ -

forward bias

p n

- +

reverse bias

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

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.

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.


VVbb II00

VVbb ; Breakdown voltage

II0 ;0 ; Reverse saturation current

Forward BiasForward BiasReverse BiasReverse BiasI(current)

V(voltage)


+ - - +

p n p n p n

biqV

biV

Fbi VVq

Fbi VV

bi rq V V

Rbi VV

+ ++ +

- -- -

++

--

+ ++ +

- -- -

Pote

ntia

l Ene

rgy

Zero Bias Forward Bias Reverse Bias

Ec

EvEv Ev

Ec Ec

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


voltagereverse voltageforward

R

F

VV

Junction potential reduced Enhanced hole diffusion from p-side to n-side compared

with the equilibrium case. Enhanced electron diffusion from n-side to p-side compared

with the equilibrium case. Drift current flow is similar to the equilibrium case. Overall, a large diffusion current is able to flow. Mnemonic. Connect positive terminal to p-side for forward

bias.

Forward BiasForward Bias

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 with

the equilibrium case. Reduced electron diffusion from n-side to p-side compared

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 reverse

bias.

Reverse BiasReverse Bias

Qualitative explanation of forward biasQualitative explanation of forward bias

+ -

p n++

--

ppnn

ppnono

nnpopo

npnp

p-n junction in forward bias

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 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.

Car

rier

Den

sity

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.

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. 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-ninionconcentratholemequilibriu

material.type-pinionconcentratholemequilibriu

material.type-pinionconcentratelectronmequilibriumaterial.type-ninionconcentratelectronmequilibriu

no

po

po

no

ppnn

2. inpn

At equilibrium case ( no bias )


)2(.

)1(.

.

2

2

2

materialtypepnpnmaterialtypennpn

npn

ipopo

inono

i


2

22

ln assuming full ionization

; majority carriers

.ln . for n-type

ln exp (3)

A Dbi

i

A po D no

po nobi no no i

i

po bibi po no

no

kT N NVq n

N p N n

p nkTV n p nq n

p qVkTV p pq p kT


22

, (2)

.ln .

ln exp (4)

po nobi po po i

i

no bibi no po

po

Similarly from equation

p nkTV n p nq n

n qVkTV n nq 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 VVbibi with

i.i. VVbibi –– VVFF if a forward bias is applied.ii.ii. VVbibi + V+ VRR if a reverse bias is applied.if a reverse bias is applied.

VVFF :: forward voltageVVR :R : reverse voltageWith these biases, the carrier densities change from equilibrium

carrier densities to non- equilibrium carrier densities.


Non-equilibrium majority carrier concentration in forwardbias;

( )e x p

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

b i Fp n

n

b i Rn p

q V Vp pk T

n

q V Vn nk T

• When a voltage is applied; the equilibrium nno changes tothe 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

ppnn

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

( )exp non-equilibrium.bi Fn p

q V Vn nkT


( ) (5)

exp (6)

bi Fn no no p

bino po

q V Vn n n nkT

qVn nkT

combining (5) and (6)

( )exp expbi F bip po

q V V qVn nkT kT


poexp and subtracting n from both sides

exp 1

the excess concentration of minority electronsover the equilibrium concentration at the edge of the DR

Fp po

p po po n

n

qVn nkT

qVn n nkT

Solving for non-equilibrium electron concentration in p-typematerial, i.e. np


Similarly ,

exp 1 the non-equilibriumn no no pqVp p pkT

the excess concentration of minority holes

over the equilibrium concentration at the edge of the DRp

Forward-bias diode; injection of minority carriers across DR

+ -

p n++

--

BB

ppnono

nnpopo

AA

nnnono

pppopo

point A

point Bp po

n no

n np p

lnlp

• is the distance from DR edge into p-side

• is the distance from DR edge into n-sidep

n

ll

When a forward bias is applied; majoritycarriers 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 oppositeExponential decay of injected minority carriers on oppositesidessides

The excess injected minorities decay exponentially as

p

( ) (0 ) e x p

( ) (0 ) e x p

a n 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

pp

n

nn

p

n

lp l n

L

ln l pL

L

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 minorityholes;excess holes;

( ) (0) exp( )nn

p

lp l pL

Distance into then regionfrom the Depletion Region

Diffusion Length forholes

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

point A

( ) (0)exp( )

(0) exp( ) 1

(0) exp 1

p po

pp

n

po

no

n n

ln l n

L

qVn nkT

qVp pkT


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

)exp()0()(

n

ppopn

n

pnpn

Ll

kTqVnl

Ll

l

Ideal diode equationIdeal diode equationDiffusion current density for electrons ;

( ) exp 1 exp

( 0) exp 1 Minus sign shows that electron current

density is

n po pn n n p

n n

n pon p

n

D n ldn d qVJ qD qD n l qdx dx L kT L

qD n qVJ lL kT

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

Similarly for holes;pl

( 0) exp 1

The total current density;

exp 1

p nop n p

p

n po p noTotal n p

n p

qD pdp qVJ l qDdx L kT

D n D p qVJ J J qL L kT


exp 1 exp 1

multiplying by area ;

exp 1

n po p noTotal o

n p

o

D n D p qV qVJ q JL L kT kT

qVI IkT


This equation is valid for both forward and reverse biases; just change theThis equation is valid for both forward and reverse biases; just change thesign of V.sign of V.


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

VVBB II00

VVBB ; Breakdown voltage



Reverse BiasReverse Bias

oII Reverse saturation currentexp 1oqVI IkT

Current

Voltage

Forward bias current densitiesForward bias current densities

+ -

p n

ln=0lp=0

Ohmic contact

pntotal JJJ

pJnJCur

rent

den

sity

Jtotal is constant through thewhole diode.

Minority current densitiesdecreases exponentially intothe 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. 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.

- +

p n

ln=0lp=0

pntotal JJJ

pJnJ

Cur

rent

den

sity

Car

rier d

ensi

ty

pnnp

pnonpo

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.

VVbb II00

VVBB ; Breakdown voltage



Reverse BiasReverse BiasDrift current

I(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 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 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.


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

WW (DR width varies width applied voltage VV )

VQC

Charge stored incoloumbs

Voltage across thecapacitor in volts

Capacitancein farads


2

Capacitance per unit area of a diode ;

For one-sided abrupt junction; e.g.

SiDEP

A D n n

A p D n

FCW cm

N N x W xN x N x

2 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 E P n A D

n D

S i S i DD E P

b i RS i b i R

D

VC x N NW x q N

q NCV VV V

q N

Depletion CapacitanceDepletion Capacitance2

2

If one makes measurements and draw 1against the voltage ; built-in voltage anddoping density of low-doped side of the diode fromthe intercept and slope.

2( )1

2

R

bi R

Si D

S

C - V /CV obtain

V VC q N

slopeq

2 ln( )A Dbi

i D i

kT N NVN q n

microsoft powerpoint - 1. chapter_1 [compatibility mode]

Documents

apiecce of n

pp n junctionn junction

ptype silicon

junction wantto

idealized pidealized

fixed charge region

current flow

left hand