semiconductorsandbandtheoryh_tcm4-658243

8/11/2019 SemiconductorsAndBandTheoryH_tcm4-658243

1/23

NATIONAL QUALIFICATIONS CURRICULUM SUPPORT

Physics

Semiconductors and

Band Theory

Support Materia

!"I#"$R%


2/23

The Scottish Quai&ications Authority re'uary

re(ie)s the arran'ements &or Nationa

Quai&ications* Users o& a NQ support materias+

)hether pu,ished ,y Learnin' and Teachin'

Scotand or others+ are reminded that it is their

responsi,iity to chec- that the support materias

correspond to the re.uirements o& the current

arran'ements*

Acknowledgement

Learnin' and Teachin' Scotand 'rate&uy ac-no)ed'es this contri,ution to the

Nat iona Quai&ications support pro'ramme &or Physics*

I 'rate&uy ac-no)ed'e the -ind 'uidance and ad(ice I ha(e recei(ed &rom Caro

Tra'er/Co)an o& the Uni(ersity o& Strathcyde*

0 Learnin' and Teachin' Scotand 1233

This resource may ,e reproduced in )hoe or in part &or educationa purposes ,y

educationa esta,ishments in Scotand pro(ided that no pro&it accrues at any sta'e*

1 S$MICON4UCTORS AN4 BAN4 T"$OR5 6"+ P"5SICS7



3/23

Contents

Electrical conductivity and band theory 8

Summary of band theory 9

Intrinsic semiconductors :

Extrinsic semiconductors 33

Student Activity 1 Thermistor investigation 3;

Summary of intrinsic and extrinsic semiconductors 38

n !unctions 3ampe+ therma e>citations and con(entiona eectric circuit (ota'es )ithin

a materia pro(ide ener'ies that are smaer than 3 e on an atomic scae* It

)oud ,e necessary to e>pose an insuator to eectric &ieds o& the order o&

3232 mG3 in order to 'i(e the (aence eectrons enou'h ener'y to Hump

across the 'ap to the conduction ,and+ since this coud pro(ide ener'y in the

order o& a &e) eectron (ots on an atomic scae* This is )hat happens )hen

there is dieectric ,rea-do)n*

Contrastin'y+ conductors ony ha(e one ,and+ and the top o& this ,and is ony

partiay &i ed+ permittin' eectr ica conduction* This means that there are

penty o& near,y ener'y e(es a(aia,e &or eectrons to mo(e into* They can

&o) easiy &rom one atom to another )hen a potentia di&&erence is appied

across the conductin' materia*

Li-e insuators+ semiconductors ha(e a competey &u (aence ,and and so

eectrons are not a,e to &aciitate conduction at o) temperatures* "o)e(er+

&or semiconductors+ the &or,idden ener'y e(e Eone ,et)een the t)o ,ands is

su&&icienty sma to ma-e it much easier &or si'ni&icant num,ers o& eectrons

to mo(e across this 'ap and 'o &rom the (aence ,and to the conduction ,and*This can happen i& su&&icient ener'y is suppied+ &or e>ampe i& there is some

therma e>citation* As a resut+ semiconductors e>hi,it increased conducti(ity

)ith increasin' temperatures* In many semiconductors+ a temperature

increase o& 32 ? )i permit a dou,in' o& the num,ers o& eectrons in the

conduction ,and*

In order to increase the conducti(ity o& semiconductors+ sma amounts o&

dopin' materia can ,e used* This resuts in si'ni&icant increases in

conducti(ity as a resut o& the narro)in' o& the 'ap ,et)een the conduction

and (aence ,ands*

S$MICON4UCTORS AN4 BAN4 T"$OR5 6"+ P"5SICS7 =



8/23

SE+IC,-&.CT,*S A-& /A-& T0E,*

Summary of band theory

In soids+ permitted eectron ener'y e(es are or'anised as ,ands* The valence bandcontains eectrons that can ,e considered to ,e ,ound to

the atom* In insuators and semiconductors the (aence ,and is &u*

The conduction bandis a re'ion o& permitted ener'y e(es that is empty

in insuators and semiconductors+ ,ut partiay &ied in conductors*

Ony partiay &ied ,ands may permit conduction*

There is a &or,idden Eone that &orms an energy ga,et)een the (aence

and conduction ,ands in insuators and semiconductors*

That ener'y 'ap must ,e Humped i& an eectron is to mo(e to the

conduction ,and+ and this is not normay possi,e in insuators ,ecause

the 'ap is too ar'e*

In semiconductors+ the &or,idden Eone is much smaer and eectrons can

Hump the 'ap to the conduction Eone as a resut o& therma e>citation*

&oingo& semiconductors can si'ni&icanty reduce the )idth o& the ener'y

'ap*

For &urther in&ormation on this topic+ try this hi'h/e(e simuation@

http@phet*coorado*eduensimuation,and/structure

There is aso &urther in&ormation &rom the "yperphysics )e,site@

http@hyperphysics*phy/astr*'su*eduh,asesoids,and*htm

Many in-s ead &rom this+ athou'h it shoud ,e noted that some 6other)ise

(ery use&u7 resources descri,e an o(erap ,et)een (aence and conduction

,ands in metas* This is miseadin' and shoud ,e treated )ith caution*


http://phet.colorado.edu/en/simulation/band-structurehttp://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.htmlhttp://phet.colorado.edu/en/simulation/band-structurehttp://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html


9/23

SE+IC,-&.CT,*S A-& /A-& T0E,*

Intrinsic semiconductors

Pure+ undoped siicon and 'ermanium are t)o simpe e>ampes o& intrinsicsemiconductors 6Fi'ure 87* They are ,oth in #roup I o& the Periodic Ta,e+

and &orm a tetrahedra crystaine structure+ simiar to diamond* $ach atom o&

siicon and 'ermanium has &our eectrons in its outermost eectron she+ and

each o& these eectrons is used in a co(aent ,ond )ith one o& the atoms &our

nei'h,ours*

2igure 3T)o/dimensiona iustration o& a crysta o& pure undoped Si* I& any indi(idua atom

o& siicon is considered+ it can ,e seen that each o& its &our (aence eectrons is used in

maintainin' co(aent ,onds )ith the atoms nei'h,ours* These eectrons are there&ore

una(aia,e &or conduction*

Since a (aence eectrons are in(o(ed in ,ondin'+ pure siicon and

'ermanium may ,e e>pected to ,e 'ood insuators* "o)e(er+ reati(ey sma

ener'ies are re.uired to mo(e a (aence eectron across the ener'y 'ap to the

conduction ,and* This is 3*3 e &or siicon+ and ony 2*= e &or 'ermanium*This means that a si'ni&icant num,er o& eectrons are a(aia,e in the

conduction ,and+ e(en at room temperature 6Fi'ure


10/23

SE+IC,-&.CT,*S A-& /A-& T0E,*

2igure 4It is possi,e &or si'ni&icant num,ers o& eectrons to cross the ener'y 'ap in

semiconductors*

It must ,e noted at this sta'e that athou'h most therma e>citation in(o(es

ener'ies much ess than e(en 2*= e+ .uantum mechanics ceary sho)s that

there is a sma ,ut si'ni&icant pro,a,iity o& an eectron ,ein' a,e to Humpthe ener'y e(e 'ap+ e(en at reati(ey o) temperatures* As pre(iousy

discussed+ this pro,a,iity increases rapidy )ith temperature*

Once an eectron Humps up to the conduction ,and in the crysta attice+ it

ea(es ,ehind a hoe in the co(aent ,ond* This hoe can ena,e another

nei'h,ourin' (aence ,and eectron to mo(e into it* As such+ a hoe ,eha(es

rather i-e a positi(e char'e carrier+ e(en thou'h it is actuay a (acancy &or

an eectron* A hoe can tra(e throu'h the crysta attice o& the semiconductor*

A hep&u anao'y mi'ht ,e to consider a .ueue o& cars on a road* I& a space

appears at the &ront o& the .ueue+ cars may mo(e &or)ard in turn* $ach time a

car mo(es &or)ard+ it ea(es a space ,ehind it+ into )hich the ne>t car may

no) mo(e* An o,ser(er &rom a,o(e mi'ht consider that the cars are mo(in'

&or)ards or that the space is mo(in' ,ac-)ards*

Some semiconductors+ i-e pure siicon or 'ermanium+ are -no)n as intrinsic

semiconductors* Intrinsic semiconductors must a)ays contain e.ua num,ers

o& conduction eectrons and hoes* I& an eectron can mo(e &rom its pace then

it must ea(e ,ehind a hoe 6Fi'ure D7*



Silic

on

Germanium

Conduction

band

Valence

band

Electrons

moving

across

energy gap

due to

thermal

excitation


11/23

SE+IC,-&.CT,*S A-& /A-& T0E,*

2igure 5In intrinsic semiconductors i-e pure siicon or 'ermanium+ e(ery eectron that

mo(es up to the conduction ,and must ea(e a hoe in the (aence ,and* $ectrons and hoes

e>ist in e.ua num,ers and ,oth contri,ute to conduction* There are no maHority char'e

carriers in intrinsic semiconductors*

Extrinsic semiconductors

O&ten+ it is more use&u to contro the properties o& a #roup I semiconductor

,y dei,eratey introducin' (ery sma proportions o& a #roup III or #roup

eement* This is -no)n as dopin' and resuts in )hat is -no)n as an e>trinsic

semiconductor* $>trinsic semiconductors ha(e maHority char'e carriers thatmay ,e either eectrons or hoes*

Consider a semiconductor that is doped )ith a #roup III eement 6Fi'ure =7*

$ach atom o& the dopin' a'ent )i ha(e ony three eectrons in its outer

she* This is insu&&icient to &orm the &our co(aent ,onds )ith its #roup I

nei'h,ours and there&ore resuts in a hoe* Countess hoes are no) ,uit into

the semiconductors crysta attice* It may ,e re&erred to as a p/type

semiconductor as the maHority char'e carriers are positi(ey char'ed hoes* As

a resut o& the dopin' process+ it )i re.uire much ess ener'y to ao)

char'e to &o) throu'h the semiconductor and so its conducti(ity is 'reatyenhanced* Uni-e metas+ a p/type semiconductors conduction occurs in the

(aence ,and* In e&&ect+ the dopin' a'ent adds an e>tra ener'y e(e Hust

a,o(e the (aence ,and+ sometimes caed an acceptor ,and*

S$MICON4UCTORS AN4 BAN4 T"$OR5 6"+ P"5SICS7 33


electro

nshole

s


12/23

SE+IC,-&.CT,*S A-& /A-& T0E,*

2igure 6Introducin' sma .uantities o& #roup III atoms into a siicon attice 6in practice

ony around one part in a miion7 ea(es hoes ,uit into the (aence ,and*

Technicay+ there )i aso sti ,e a sma de'ree o& intrinsic ,eha(iour+ as

eectrons ea(e ,ehind hoes+ ,ut this is not considered to ,e si'ni&icant in

comparison )ith the o(er)hemin' num,er o& maHority char'e carriers*

A simiar process is in(o(ed i& a #roup eement is used &or dopin'* This

'i(es an e>tra eectron+ surpus to co(aent ,ondin' re.uirements+ &or each

atom o& the dopin' a'ent* These eectrons are ne'ati(ey char'ed and so an

n/type semiconductor has ,een produced* In an n/type semiconductor+ the

maHority char'e carriers are eectrons* The conducti(ity has ,een 'reaty

enhanced as ,e&ore+ ,ut this time conduction occurs in an e>tra ener'y e(e

Hust ,eo) the conduction ,and+ )hich is somet imes caed the donor ,and*There&ore+ in p/type and n/type semiconductors conduction can occur easiy

,ecause there is e&&ecti(ey un&ied space )ithin either the (aence or the

conduction ,and+ respecti(ey*

Semiconductors are crucia to modern i&e* Accordin' to estimates 6She&&ied

Uni(ersity7 8; o& a semiconductor production 'oes into computers+ 1;

into consumer products+ 3; into communication and 31 into

manu&acturin'*



Electro

n

Hole

Silicon

Group


13/23

SE+IC,-&.CT,*S A-& /A-& T0E,*

In Scotand+ Siicon #en 6)hich is a ar'e proportion o& the centra ,et7 has

,een pioneerin' eectronics production since the 3:82s+ empoyin' around


14/23

SE+IC,-&.CT,*S A-& /A-& T0E,*

Summary of intrinsic and extrinsic semiconductors

Semiconductors ao) conduction ,y means o& ne'ati(e char'e carriers+)hich are eectrons+ or positi(e char'e carriers+ )hich are hoes*

The ener'y ,and 'ap in semiconductors is sma enou'h that therma

e>citation is su&&icient &or si'ni&icant num,ers o& eectrons to ,e a,e to

mo(e up &rom the (aence to the conduction ,and*

Intrinsic semiconductors+ such as pure siicon+ )i a)ays ha(e e.ua

num,ers o& hoes and eectrons since each conduction eectron )i ea(e

,ehind a hoe*

Semiconductors may ,e doed )ith impurities that add either e>tra

eectrons or hoes to the attice*

These doped semiconductors no) ha(e a maHority char'e carrier present

and are -no)n as extrinsic semiconductors*

#roup III dopin' a'ents resut in p/type e>trinsic semiconductors+ )hich

contain e>tra hoes*

#roup dopin' a'ents resut in n/type e>trinsic semiconductors+ )hich

contain e>tra eectrons*

This in- 'i(es you a simuation &or a semiconductor that you can adHust

yourse&@

http@phet*coorado*eduensimuationsemiconductor


http://phet.colorado.edu/en/simulation/semiconductorhttp://phet.colorado.edu/en/simulation/semiconductor


15/23

SE+IC,-&.CT,*S A-& /A-& T0E,*

n !unctions

I& a sin'e semiconductin' crysta is doped in such a )ay that one end isp/type and the other n/type+ then some (ery use&u properties come into pay*

The inter&ace ,et)een the p/type and n/type sections is -no)n as a pGn

Hunction* In this ,oundary re'ion+ eectrons &rom the n/type mater ia may

di&&use across the ,oundary and com,ine )ith hoes &rom the p/type materia+

and (ice (ersa* This resuts in a ac- o& maHority char'e carriers in the

immediate (icinity o& the Hunction and as such the re'ion is -no)n as the

depetion Eone* The pGn Hunction 'reaty a&&ects the conducti(ity o& the

semiconductor as a )hoe* hen eectrons &rom the n/type materia di&&use

into the p/type materia+ they &orm ne'ati(e ions as they com,ine )ith hoes*

Positi(e ions are aso e&t ,ehind in the n/type materia* $(entuay+ this

process resuts in there ,ein' no &urther di&&usion o& eectrons or hoes as a

resut o& Couom, attraction and repusion 6Fi'ures 9a and 9,7*

2igure 7aIn a pGn Hunction a depetion Eone is &ormed ,y the di&&usion o& eectrons &rom the

n/type materia into the p/type materia* As the eectrons com,ine )ith hoes+ ions are&ormed in the depetion Eone*

S$MICON4UCTORS AN4 BAN4 T"$OR5 6"+ P"5SICS7 3pected to ha(e much 'reater on'e(ity than con(entiona i'ht

sources* L$4 and OL$4 Ts are e>pensi(e ,ut )ith o) po)er usa'e and

hi'h reia,iity they are set to ,ecome more common in &uture*

In&rared L$4s are used in remote contros ,ecause o& their reia,iity and o)

po)er consumption* Utra(ioet L$4s can ,e used &or detect in' counter&ei tnotes and e(en &or steriisation procedures*

L$4s ha(e e>tremey &ast s)itchin' speeds+ )hich means that they are

particuary use&u &or appications )here i'ht sources mus t ,e pused+

stro,ed or simpy s)itched on and o&& rapidy )ith reia,iity* Additionay+

they )or- )e at o) temperatures+ are shoc- resistant and contain &e)er

haEardous materias than ener'y/sa(in' i'ht ,u,s*

Summary of n !unctions) $E&s and hotovoltaic cells

The inter&ace ,et)een p/type and n/type materia is caed the pGn

Hunction*

MaHority char'e carriers di&&use to)ards the Hunction and eectrons

com,ine )ith hoes+ &ormin' ions*

This ac- o& char'e carriers resuts in a depetion Eone across the pGn

Hunction+ )ith positi(e ions on the n/type side and ne'ati(e ions on the p/

type side*

I& the p/type materia is connected to the positi(e termina o& a suppy and

the n/type to the ne'ati(e termina+ then the Hunction is forward biased*


http://www.chemistry.wustl.edu/~courses/genchem/Tutorials/LED/bands_06.htmhttp://www.chemistry.wustl.edu/~courses/genchem/Tutorials/LED/bands_06.htmhttp://www.chemistry.wustl.edu/~courses/genchem/Tutorials/LED/bands_06.htmhttp://www.chemistry.wustl.edu/~courses/genchem/Tutorials/LED/bands_06.htm


23/23

SE+IC,-&.CT,*S A-& /A-& T0E,*

I& the potentia di&&erence across the Hunction is su&&icient to &orce

eectrons to cross the depetion Eone+ then the Hunction )i conduct*

I& the terminas are re(ersed+ the Hunction is reverse biasedand cannotconduct*

L$4s emit photons o& i'ht as eectrons &a &rom the conduction ,and o&

the n/type materia into hoes in the (aence ,and o& the p/type materia*

The ,i''er the ener'y 'ap ,et)een the ,ands+ the 'reater the ener'y+ and

there&ore the &re.uency+ o& the emitted photons*

Photo(otaic ces use the ener'y o& a,sor,ed photons to separate eectrons

and hoes and thus produce a potentia di&&erence*

*eferences and further reading

5ou )i &ind a 'reat dea o& &urther readin' on the internet and in speciaist

eectronics ,oo-s* The &oo)in' sources are recommended@

http@)))*chemistrye>pained*comRu/SpSemiconductors*htm

http@hyperphysics*phy/astr*'su*eduh,asesoids,and*htm

http@)))*educypedia*,eeducationsoarceanimations*htm

and many other in-ed pa'es associated )ith this topic &rom "yperphysics*

http@en*)i-ipedia*or')i-iP/nHunction

In addition+ &or those )ith a sense o& humour+ the some)hat eccentric

http@,ritneyspears*acphysics,asics,asics*htm
http://www.chemistryexplained.com/Ru-Sp/Semiconductors.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.htmlhttp://www.educypedia.be/education/solarcellanimations.htmhttp://en.wikipedia.org/wiki/P-n_junctionhttp://britneyspears.ac/physics/basics/basics.htmhttp://www.chemistryexplained.com/Ru-Sp/Semiconductors.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.htmlhttp://www.educypedia.be/education/solarcellanimations.htmhttp://en.wikipedia.org/wiki/P-n_junctionhttp://britneyspears.ac/physics/basics/basics.htm

semiconductorsandbandtheoryh_tcm4-658243

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