solid state lectures

7/27/2019 Solid state lectures

1/53

TemperatureDependenceof

CarrierConcentrations(IntrinsicLecture08

.

MdJawaidAlam JIIT,Sect62,Noida,India

Intrinsiccarrierconcwithtempraturefor

Ge,SiandGaAs.RefB

G

Streetman

Fig

318


2/53

TemperatureDependenceofCarrierConcentrations

(ExtrinsicSemiconductors)

Lecture08

Thetemperaturedependenceofelectronconcentrationin

adopedsemiconductorcanbevisualizedasshowninthis

Fig

concentrationNDof1015

cm3.

Atver lowtem eratures

(large1/T),negligible

intrinsicEHPsexist,and the

donorelectronsareboundo e onora oms.

RefBGStreetmanFig319

Between100400Kwheneveryavailable

extrinsicelectronhasbeen transferredtothe

conductionband,n isvirtuallyconstantwith

At higher temperatures ni is

much greater than Nd, and the


temperature untiltheconcentrationofintrinsic

carriersnibecomescomparabletotheextrinsicconcentrationNd.


3/53

CompensationandSpaceChargeNeutrality Lecture08

D i A i,only approximation no=Ndand po= NA is valid.

The exact relationship among the electron, hole, donor, and acceptor

concentrations can be obtained by considering the requirements for space charge

neutrality

If the material is to remain electrostaticall neutral the sum of the ositive

charges (holes and ionized donor atoms) must balance the sum of the negative

charges (electrons and ionized acceptor atoms).


Ifthematerialisdopedntype(n0p0)then


4/53

* 10 3

Lecture08

temperature then

a) findtheequilibriumelectronandholeconcentrationinthedoped

semiconductor.

b) Shiftin

Fermi

level

with

respect

to

intrinsic

Fermi

level.c) If wedopeBinsteadofAsthenrepeatparta)andb).

Prob 2:FindthedopingconcentrationofAsorB(whicheverbesuitable)

sothatFermilevelinthedopedSiliesexactlymiddleofthebandgap.



5/53

Lastlecture.Lecture09



6/53

Lastlecture.Lecture09



7/53

TemperatureDependenceofCarrierConcentrations

(IntrinsicSemiconductors)Lecture09



8/53

Drift and DiffusionDrift and Diffusion Lecture09

We now have some idea of the number density of

semiconductor material from the work we covered inthe last lectures.

ncecurren s e ra e o ow o c arge , we s abe able calculate currents flowing in real devices

since we know the number of charge carriers. There are two current mechanisms which cause

charges to move in semiconductors. The twomechanisms we shall stud in due course are dri tdri tandand diffusiondiffusion.

Md Jawaid Alam JIIT,Sec62,Noida,INDIA


9/53

CarrierDriftCarrierDrift Lecture09

fieldsince thefield exert a forceon charge carriers (electrons and holes).

These movements result a current of ; F E=d

d d

dV

Anq

d

:dV

chargeoftheelectrondriftvelocityofchargecarrier :q

areaofthesemiconductor:A



10/53

CarrierMobility,CarrierMobility, Lecture09

dV E=

:E appliedfieldmobilit ofchar ecarrier

2

[ ]

=SecV

cm isaproportionalityfactor

=E

d

So is ameasurehoweasilychargecarriersmoveundertheinfluenceof .



11/53

ThemobilityhastwocomponentsThemobilityhastwocomponents Lecture09

Themobilityhastwocomponent

Impurityinteraction

component

component



12/53

ThermalvelocityThermalvelocity Lecture09

ssume t at s c crysta s at t ermo ynam c equ r um .e. t ere s noapplied field). What will be the energy of the electron at a finitetemperature?

The electron will have a thermal energy ofkkTT//22 per degree of freedom. So, in 3D, electron will have a thermal energy of

* 23 1 3 3th th

kT kT kT

E m V V = = =

: electronovelocitthermalV

1

2

1

TV th

2mV th



13/53

RandommotionRandommotionresultresultnocurrentnocurrent.. Lecture09

Since there isno applied field,the movement of thechar e carriers will be com letel random. This

randomness resultno net current flow. As a result of

thermal energy there are almostan equal number ofcarriers moving right as left, in as out or up as down.



14/53

CalculationCalculation Lecture09

Calculate the velocity of an electron in a piece of ntype silicon

due to its thermal energy at RT and due to the application of an

*= = =

e ec r c e o m across e p ece o s con.

2? 1000 / 0.15 /( )

t e

dV E V m m V s= = =

53 1.08 10 / secth th

kTV V x m

= =

150 / secV E V m= =



15/53

MicroscopicunderstandingofmobilityMicroscopicunderstandingofmobility?? Lecture09

Howlon doesacarriermoveintimebeforecollision?

Theaveragetimetakenbetweencollisionsiscalledasrelaxation

time, (ormeanfreetime)

v

collision?

Theaveragedistancetakenbetweencollisionsiscalledasmean

freepath, . l



16/53


Driftvelocity=AccelerationxMeanfreetime

*dFV

m=

Forceisduetotheappliedfield, F=qE

* *d

qV

m m = =

d

qV E

= =



17/53


a cu a e e mean ree me an mean ree pa or e ec ronsin a piece of ntype silicon and for holes in a piece of ptypesilicon.

*

2 2

? ? 1 .1 8 0 .5 90 .1 5 / 0 .0 4 5 8 /

e o h ol m m m m

m V s m V s

= = = == =

1 2 1 31 0 sec 1 .5 4 1 0 sece e h he h

m mx

q q

= = = =

5 51 .0 8 1 0 / 1 .0 5 2 1 0 /elec h o leth th

v x m s v x m s= =

5 1 2 7(1 .0 8 1 0 / )(1 0 ) 1 0elece th e

l v x m s s m = = =

5 1 3 8 .h o l eh th h

. .



18/53

Saturated DriftSaturated DriftVelocities(EffectatHighElectricField)Velocities(EffectatHighElectricField)Lecture09

dV E=

Soonecanmakeacarriergoasfastaswelikejustbyincreasing

theelectricfield!!!

dV forefore

or o esor o es

E E

a mp ca ono a oveeqn. a ura on r ve oc y



19/53

Saturated DriftVelocitiesSaturated DriftVelocities Lecture09

The equation of does not imply thatVVdd increasesEVd .=linearly with applied fieldEE..

dd

at some value ofVVdd which is closeVVthth at higher values ofEE.

Any further increase in EE after saturation point does not

increaseVVdd instead warms up the crystal.



20/53

LastLectureLecture10

I n V A=

dV E=

So is ameasurehoweasilychargecarriersmoveundertheinfluenceof

anappliedfieldor determineshowmobile the chargecarriersare.

Themobilityhastwocomponent

Impurityinteraction

component

Latticeinteraction

component


21/53

MobilityvariationwithtemperatureMobilityvariationwithtemperature Lecture10

L I

TTTT

Hightemperature Lowtemperature

)ln(1 1 1

Peakdependsonthedensityof

impuritiesI

LT L I

=

ln(T)ln(T)Thisequationiscalled as

Mattheisensrule.Md Jawaid Alam JIIT,Sec62,Noida,INDIA


22/53

For lightly doped samples (e.g., the

MobilityvariationwithtemperatureMobilityvariationwithtemperature Lecture10

sample with doping of 1014 cm3), the

lattice scattering dominates, and the

mobility decreases as the temperature

For heavily doped samples, the effect

of impurity scattering is most

pronounced at low temperatures. The

mobility increases as the temperature

increases, as can be seen for the19

For a given temperature, the mobility

decreases with increasing impurity

Electronmobilityinsiliconversustemperaturefor

impurity scattering

var ous onorconcen ra ons. nser s ows e

theoreticaltemperaturedependenceofelectron

Mobility


23/53

ConceptofMeanfreetimeandMeanFreePathlengthLLecture10

Driftvelocity=AccelerationxMeanfreetime

*dFV

m=

Forceisduetotheappliedfield, F=qE

* *d

qV

m m = =

d

qV E

= =


24/53

Conductivity Lecture10

Anq

d

I

d d dI nqV A V E= =

dJ

A m

= =

d d2

x d x x

nqJ nqV nq E J E

m

= = =

2 1n x xm = = =


25/53

OhmsLaw Lecture10

1x

x xx

I IV VJ E

A L A L = = =

VA V

L R= =

Prob: Assumin that mobilit of electron is three times mobilit of holes insilicon at 300K prove that a silicon sample has maximum resistivity when it isslightly ptype. Also find the doping concentration for maximum resistivity.


26/53

CalculationCalculationLecture10

a cu a e e mean ree me an mean ree pa or e ec ronsin a piece of ntype silicon and for holes in a piece of ptypesilicon.

*

2 2? ? 1 .1 8 0 .5 9

0 .1 5 / 0 .0 4 5 8 /

e o h ol m m m mm V s m V s

= = = == =

1 2 1 31 0 sec 1 .5 4 1 0 sece e h he h

m mx

q q

= = = =

5 51 .0 8 1 0 / 1 .0 5 2 1 0 /elec h o leth th

v x m s v x m s= =

5 1 2 7(1 .0 8 1 0 / )(1 0 ) 1 0elece th e

l v x m s s m = = =

5 1 3 8 .h o l eh th h

. .



27/53

HallEffect Lecture11

The carrier concentration in a semiconductor may be different

from the impurity concentration, because the ionized impurity

density depends on the temperature and the impurity energy

level.

To measure the carrier concentration directly, the most

.

Hall measurement is also one of the most convincing methodsto show the existence of holes as charge carriers, because the

measurement can ive directl the carrier t e.


28/53

HallEffectCont Lecture11

Anelectricfieldappliedalongthexaxis

AmagneticfieldappliedalongthezaxisHallCoefficient

Consideraptypesemiconductorsample

where


29/53

HallEffectCont Lecture11

AmeasurementoftheHallvoltageforaknowncurrentandmagneticfieldyields

whereallthequantitiesinthelighthandsideoftheequationcanbemeasured.


30/53

n(x)DiffusionCurrent Lecture11

F1ofelectronscrossingplane

x=0fromtheleftisthen

Similarly,theaveragerateofelectronflow

perun area 2o e ec ronsa x= cross ng

planex=0fromtherightis

xWhere

* 23 1 3 3th th

kT kT kT E m V V

= = =


31/53

Lecture11

Thenetrateofcarrierflowfromlefttorightis

firsttwotermsofaTaylorseriesexpansion,

weobtain

Where

is calledthediffusioncoefficientalsocalled

F

.

Becauseeachelectroncarriersacharge q


32/53

LastLecture Lecture12

Prob:Assumethat,inanntypesemiconductoratT

=300

K,

the

electron

concentration

variesLinearlyfrom1x1018 to7X1017cm3 overadistanceof0.1cm.Calculatethe

diffusioncurrentdensityiftheelectrondiffusioncoefficientisDn=22.5cm2/s.

Current L t 12


33/53

Current

TotalCurrentdensity Lecture12

n(x)Electrondiffusion

x

Current

p(x)

x

40 L t 12


34/53

EinsteinRelation40 Lecture12

40

L t 13


35/53

Module4: Excesscarriersgeneration&recombination

processesandsemiconductordeviceequations.

Lecture13

Intrinsic Doped

OnlyinthermalequilibriumtheTheprocessofintroducingexcesscarriersis

i

.

calledcarrier

injection.

Wecanintroduceexcesscarriersby

Optica excitation

forwardbiasingapnjunction

Electronbombardment

Lecture 13


36/53

DirectRecombination Lecture13

Numberofelectronholepairsgeneratedpercm3 per

second: GthNumberofelectronholepairsRecombinedper

cm3 persecond:Rth

andatthermalequilibriumRth=Gth

nn0nn0 nn =nn0+ nn0

Thermalequilibrium

pn0pn =pn0+ pn0

n0

Lecture 13


37/53

DirectRecombination Lecture13

therateofchangeofholes withtimeinthisdynamicsystemwillbe

Insteadystate,

whereUisthenetrecombinationrate.

Lecture 13


38/53

Lecture13

And

u

For lowlevel in ection

Where

Lecture 13


39/53

Thephysicalmeaningoflifetimecanbestbe

Lecture13

adeviceafterthesuddenremovalofthelight

source.

Consideranntypesample,asshown

inFigthatisilluminatedwithlightand

inwhichtheelectronholepairsare

generateduniformlythroughoutthe

samplewithagenerationrateGL

Insteadystate GLmustbeequaltoNet

recombinationU

Lecture13


40/53

Lecture13

Ifatanarbitrarytime,say

t=0,thelightissuddenly

Willreduceto


41/53

andthesolutionis Lecture13

Prob:ASisamplewithnn0=1014 cm3 isilluminatedwithlightand1013 electronhole

pairs/cm3arecreatedeverymicrosecond.Iftn=tp=1uSec,findthechangeintheminority

carrierconcentration.

Ifthelightisturnedoffatt=0sec,i.e GL=0att=0, thenfind theholeconcentrationatt=1u

sec,

t=2u

sec,

t=4u

sec

and

t=10u

sec

Indirect Recombination Lecture14


42/53

IndirectRecombination

recombinationcenters

Lecture 14

Traplevel

NetRecombination

rate

(U)

depends

on ee ec ronor o ecap urecross

section.

Auger recombination Lecture14


43/53

Augerrecombination Lecture 14

Usually,Augerrecombinationisimportantwhenthecarrierconcentrationisveryhigh

asaresultofeitherhighdopingorhighinjectionlevel.BecausetheAugerprocess

vo ve eep e , o u o o x

TheproportionalityconstantBhasastrongtemperaturedependence

CONTINUITY EQUATION Lecture14


44/53

CONTINUITYEQUATION Lecture 14

In the revious lectures we considered individual effects such as drift due to an

electricfield,diffusionduetoaconcentrationgradient,andrecombinationofcarriersthroughintermediatelevelrecombinationcenters

, ,

simultaneouslyinasemiconductormaterial.Thegoverningequationiscalledthe

continuityequation.



45/53

CONTINUITYEQUATION

Toderivetheonedimensionalcontinuityequationforelectrons,consideraninfinitesimal

Thenumberofelectronsintheslicemay

thesliceandthenetcarriergeneration

intheslice

Theoverallrateofelectron

increaseisthealgebraicsumof

fourcomponents:thenumberof

,

minusthenumberofelectrons

flowingoutatx+dx,plustherate

atwhichelectronsaregenerated,

minustherateatwhichtheyare

recombined withholesintheslice.



46/53

CONTINUITYEQUATION

atx+dx inTaylorseriesyields

Wethusobtainthebasiccontinuityequation

forelectrons:

Asimilarcontinuityequationcanbederived

forholes,

CONTINUITYEQUATION Lecture14


47/53

Q

Intermsofmobilityanddiffusiontheonedimensionalcaseunderlowinjectioncondition,continuityequationsforminoritycarriersbecomes

YouMustkeepinmindthebasic

requirementofPoissonsEquation

Lecture15SteadyStateInjectionfromOneSide


48/53

IntheFigureanntypesemiconductor

whereexcesscarriersareinjectedfromonesideasaresultofillumination.Itis

assumedthatlight penetrationisnegligibly

small i.e. the assum tions of zero field

andzerogenerationforx>0).

thereisaconcentrationgradientnearthe

sur acean tw sat s y ont nu ty

equationgivenby.

Atsteadystatesolutionofthedifferentialequationfor

t em nor tycarr ers ns et esem con uctor s

Lecture15


49/53

o ut ono t e or er erent a equat on s

Thelength isequalto andiscalledthediffusionlength.ppDL p

Minority Carriers at the Surface Lecture15


50/53

MinorityCarriersattheSurface

Lecture15


51/53

Assignment1Dateofsubmission:onorbefore23rdofFebruary

Answer

Lecture15


52/53

W

Uniqueness ofFermilevelinbulksemiconductor


53/53

solid state lectures

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