Material Science SRM 1st year Unit 1 LECTURE NOTES-6

(1)

LECTURE 2



_{SEMICONDUCTORS AND ITS}

CLASSIFICATION AND



FERMI ENERGY LEVEL DISTRIBUTION

IN INTRINSIC SEMICONDUCTORS



VARIATION OF FERMI LEVEL WITH

TEMPERATURE IN EXTRINSIC

SEMICONDUCTORS

(2)

Semicondc!o"#

In!"odc!ion



The materials The materials are classified are classified on on the bthe basis of asis of conductiit!conductiit!

and resistiit!"



#emiconductors are the materials $hich has#emiconductors are the materials $hich has

conductiit!% resistiit! alue in bet$een conductor and

insulator "



The resistiit! of semiconductor is in the order of 10The resistiit! of semiconductor is in the order of 10−−&& toto

0"5 'hm(metre"



It It is is not not that% that% the the resistiit! resistiit! alone alone decides decides $hether $hether aa

substance

substance is is a a semiconductor semiconductor )or* )or* not not % % because because somesome

allo!s

allo!s hae hae resistiit! resistiit! $hich $hich are are in in the the ran+e ran+e ofof

semiconductor,s resistiit!" -ence there are some .ro.erties

li/e band +a. $hich distin+uishes the materials as

(3)



 semi(conductor semi(conductor is is a a solid solid $hich $hich has has the the ener+! ener+! bandband

similar to

similar to that that of of an an insulatorinsulator" " It It acts acts as as an an insulator insulator atat

absolute

absolute ero ero and and as as a a conductor conductor at at hi+h hi+h tem.eratures tem.eratures andand

in the .resence of im.urities"

#emiconductors are materials $hose electronic .ro.erties

are intermediate bet$een those of metals and insulators"

These intermediate .ro.erties are determined b! the

cr!stal structure% bondin+ characteristics and electronic ener+!

bands"

The!

The! are are a a +rou. +rou. of of materials materials hain+ hain+ conductiities conductiities bet$eenbet$een

those of metals and insulators"

(4)

C$%##i&ic%!ion o& #emicondc!o"#

C$%##i&ic%!ion o& #emicondc!o"# Acco"din' !oAcco"din' !o

!(e con#!i!en! %!om#

Elemental semiconductor:



ll the

ll the constituent atoms

constituent atoms

are of the same /ind

)i"e* com.osed of sin+le

s.ecies of atoms" )e+* +ermanium and silicon"

Compound semiconductor:

The! are com.osed of

t$o or

t$o or more different elements )

more different elements )

e+* a#% 

e+* a#% ls

ls

etc"%

(5)

C")#!%$ #!"c!"e o& #i$icon %nd

C")#!%$ #!"c!"e o& #i$icon %nd 'e"m%nim'e"m%nim

The structure of #i and e% $hich are hain+

coalent bondin+" Coalent bondin+s are stereo

s.ecific3 i"e" each bond is bet$een a s.ecific .air of

atoms"

The .air of atoms share a .air of electrons )of

o..osite ma+netic s.ins*"

(6)

Three

Three dimensional dimensional re.resentation re.resentation of of the the structures structures #i%#i%

and e% $ith the bonds sho$n in belo$ fi+ure% the re+ion of

hi+h electron .robabilit! )shaded*"

*%+

*%+ *,+*,+

S!"c!"e o& *%+ #i$icon %nd

(7)

ll

ll atoms atoms hae hae coordination coordination number number &3 &3 each each material material hashas

an aera+e of & alence electrons .er atom%

an aera+e of & alence electrons .er atom% and t$o electronsand t$o electrons

.er bond"

Each

Each atom atom of of a a material material is is coordinated coordinated $ith $ith itsits

nei+hbours"

*%+

*%+ *,+*,+

S!"c!"e o& *%+ #i$icon %nd

(8)

The

The thermal thermal ibrations ibrations on on one one atom atom influence influence thethe

ad4acent atoms3 the dis.lacement of one atom b!

mechanical forces% or b! an electric field% leads to

ad4ustments of the nei+hbourin+ atoms"

The number of coordinatin+ nei+hbours that each atom

has is im.ortant" Coalent bonds are er! stron+"

S!"c!"e o& *%+ #i$icon %nd

S!"c!"e o& *%+ #i$icon %nd *,+ 'e"m%nim c")#!%$#*,+ 'e"m%nim c")#!%$#

*%+

(9)

In!"in#ic

In!"in#ic SemicondcSemicondc!o"#!o"#

In semiconductors and insulators% $hen an

In semiconductors and insulators% $hen an eternaleternal electric field is a..lied

electric field is a..lied the the conduction is not .ossibleconduction is not .ossible as there as there

is a forbidden +a.

is a forbidden +a.% $hich is absent in metals"% $hich is absent in metals"

In

In order order to to conduct% conduct% the the electrons electrons from from the the to. to. of of thethe

full alence band hae to moe into the conduction band% b!

crossing the forbidden gap

crossing the forbidden gap""

The field that needs to be a..lied to do this $or/ $ill

be etremel! lar+e"

(10)

E+6

E+6 #ilicon #ilicon $here $here the the forbidden forbidden +a. +a. is is about about 1 1 e7e7""

The distance bet$een these t$o locations is about 1 8 )10

The distance bet$een these t$o locations is about 1 8 )10−−1010

m*"

 fie

 field +radient of ld +radient of a..roimatel! 179 )10a..roimatel! 179 )10−−1010 m* : 10 m* : 1010107m7m−−11

is necessar! to moe an electron from the to. of the alence

band to the bottom of the conduction band"

(11)



 The The other other .ossibilit! .ossibilit! b! b! $hich $hich thisthis transitiontransition can becan be

brou+ht about is b!

brou+ht about is b! thermal excitationthermal excitation""



 t t room room tem.erature% tem.erature% the the thermal thermal ener+! ener+! that that is is aailableaailable

can ecite a

can ecite a limited number of electrons across the ener+!limited number of electrons across the ener+! +a.

+a." This limited number" This limited number accounts for semi(conductionaccounts for semi(conduction""



 ;hen ;hen the the ener+! ener+! +a. +a. is is lar+e lar+e as as in in diamond% diamond% the the numbernumber

of electrons that can be ecited across the +a. is etremel!

small"

(12)



 In In intrinsic intrinsic semiconductors% semiconductors% the the conduction conduction is is due due toto

the intrinsic .rocesses )

the intrinsic .rocesses )without the influence of impurities)without the influence of impurities)"" 

   .ure .ure cr!stal cr!stal of of silicon silicon or or +ermanium +ermanium is is an an intrinsicintrinsic

semiconductor" The electrons that are ecited from the to. of

the alence band to the bottom of the conduction band b!

thermal ener+! are res.onsible for conduction"



 The The number number of of electrons electrons ecited ecited across across the the +a. +a. cancan

be calculated from the <ermi(=irac .robabilit! distribution"

(13)

f f ))E E * :* : ]} ]} T T k k / / ) ) E E E E {exp[ {exp[

−−

_F_F _B_B

++

1 1 1 1 >

> TheThe <ermi leel<ermi leel E E _F_F for an for an intrinsic semiconductor intrinsic semiconductor lies lies

mid$a!

mid$a! in the in the forbidden +a.forbidden +a.""

>

> TheThe .robabilit! of findin+ an electron.robabilit! of findin+ an electron here is here is 50?50?% een% een

thou+h

thou+h ener+! leels at this .oint are forbiddenener+! leels at this .oint are forbidden""

>

> Then Then ))E E −−E E _F_F* is e@ual to* is e@ual to E E _g_g 92%92%

$here

(14)

T(e Fe"mi $e-e$ in %n in!"in#ic #emicondc!o" $ie# T(e Fe"mi $e-e$ in %n in!"in#ic #emicondc!o" $ie# in !(e midd$e o& !(e ene"') '%./

in !(e midd$e o& !(e ene"') '%./

>

> <or <or a a t!.ical t!.ical semiconductor semiconductor li/eli/e siliconsilicon%% E+ : 1"1 e7E+ : 1"1 e7% so% so

that

that ))E E −−E E _F_F* is 0"55 e7* is 0"55 e7% $hich is more than t$ent! times% $hich is more than t$ent! times

lar+er than the thermal

lar+er than the thermal ener+!ener+! k k _B_BT T at room tem.erature at room tem.erature

):0"02A e7*"

(15)

>

> The The .robabilit!.robabilit! f f ))E E *of an electron occu.!in+ ener+! leel*of an electron occu.!in+ ener+! leel E

E becomesbecomes f f ))E E * : e.)* : e.)−−E E _g_g9 29 2k k _B_BT T *"*"

>

> The The fraction fraction of of electrons electrons at at ener+!ener+! E E is e@ual to the is e@ual to the

.robabilit!

.robabilit! f f ))E E *" The number n of electrons .rom*" The number n of electrons .romoted across theoted across the

+a.%

n

n :: N N e.) e.)−−E E _g_g 9 29 2k k _B_BT T **

$here

$here N N is the number of is the number of electrons aailable for ecitation fromelectrons aailable for ecitation from

the to. of the

(16)

The .romotion of some of the electrons across the +a.

leaes some acant electron sites in the alence band" These

are called

are called holesholes""



n intrinsic semiconductor contains an equal number ofn intrinsic semiconductor contains an equal number of holes in the alence band and electrons in the conduction holes in the alence band and electrons in the conduction band

band % that is% that is n n_e_e : : nn_h_h""

Under an eternall! a..lied field% the electrons% $hich

are ecited into the conduction band b! thermal means% can

accelerate usin+ the acant states aailable in the conduction

band"

(17)

t

t the the same same time% time% the the holes holes in in the the alence alence band band alsoalso

moe% but in a direction

moe% but in a direction oppositeopposite to that of electrons"to that of electrons"

The conductiit! of the intrinsic semiconductor de.ends

on the concentration of these char+e carriers%

on the concentration of these char+e carriers% n n_e_e and and nn_h_h""

In the case of metals% the drift elocit! ac@uired b! the

free electrons in an a..lied field"

The mobilit! of conduction electrons and holes%

The mobilit! of conduction electrons and holes% µµ_e_e and and

µ

µ_h_h% as the drift elocit! ac@uired b! them under unit field% as the drift elocit! ac@uired b! them under unit field

+radient"

(18)

The

The conductiit!conductiit! σσ of an intrinsic sem of an intrinsic semiconductor asiconductor as

σ

σ_i_i :: nn_e_e ee µµ_e_e BB nn_h_h ee µµ_h_h

$here

$here ee is the electronic char+e% is the electronic char+e% nn_e_e and and nn_h_h are are

concentrations of electrons and holes .er unit olume"

(19)

Fermi

Fermi level level

The number of free electrons .er unit olume

The number of free electrons .er unit olume in an intrinsicin an intrinsic

semiconductor is semiconductor is            −−              == kT kT E E E E p p kT kT m m nn F F cc / / ** ee _ex_ex h h 2 2 2 2 2 2 3 3 2 2 π π The

The number number of of holes holes .er .er unit unit olume olume in in an an intrinsicintrinsic

semiconductor is semiconductor is            −−         ∗∗ KT KT E E E E h h T T k k m m_h_h _V_V _F_F exp exp .. 2 2 2 2 2 2 3 3 2 2 π π p p : : #ince n : . in

(20)

           −−              ==            −−               ∗∗ kT kT E E Ev Ev h h T T k k m m kT kT E E E E p p h h T T k k m m_e_e** _F_F _c_c _h_h _F_F exp exp 2 2 2 2 ex ex 2 2 2 2 2 2 3 3 2 2 2 2 3 3 2 2 π π π π ( ( )) ( ( ))     −−            = = − − ∗∗ ∗∗ KT KT E E Ev Ev m m kT kT E E E E m m F F h h C C F F e

e expexp expexp

2 2 3 3 2 2 3 3 or or            ++              = = ∗∗ kT kT E E E E m m m m e e vv cc e e h h kT kT E E _F_F exp exp 2 2 3 3 * * 2 2

Ta/in+ lo+ on both sides%

                 ++ + +               = = ∗∗ kT kT E E E E exp exp log log m m m m log log kT kT E E _v_v _c_c e e * * e e h h e e F F 2 2 3 3 2 2            ++ ++               == ∗∗ kT kT E E E E m m m m og og kT kT E E _v_v _c_c * * e e h h e e F F ll 2 2 3 3 2 2            ++ ++               ∗∗ 2 2 log log 4 4 3 3 e e c c v v * * e e h

h E E E E

m m m m kT kT or or EE_f_f : :

(21)

If $e assume that% If $e assume that% ** h h * * e e mm m m

=

           ++ = = 2 2 c c v v F F E E E E E E

Thus% the <ermi leel is

Thus% the <ermi leel is located half $a! bet$een thelocated half $a! bet$een the

alence and conduction band and its .osition

alence and conduction band and its .osition is inde.endentis inde.endent

of tem.erature" #ince

of tem.erature" #ince mm_h_h! ! is +reater than is +reater than mm_e_e! ! %% E E _F_F is 4ust is 4ust

aboe the middle% and rises sli+htl! $ith

aboe the middle% and rises sli+htl! $ith increase inincrease in

tem.erature

 since lo+

(22)

Po#i!ion o& Fe"mi $e-e$ in %n in!"in#ic #emicondc!o" %! -%"io# Po#i!ion o& Fe"mi $e-e$ in %n in!"in#ic #emicondc!o" %! -%"io# !em.e"%!"e#

!em.e"%!"e# *%+ %! T 0 1

*%+ %! T 0 1 3 !(e Fe"mi $e-e$ in !(e midd$e o& !(e &o",idden '%.3 !(e Fe"mi $e-e$ in !(e midd$e o& !(e &o",idden '%. *,+ %# !em.e"%!"e inc"e%#e#3

(23)

EXTRINSIC

EXTRINSIC SEMICONDUCTORSEMICONDUCTOR

In

In an an etrinsic etrinsic semiconductin+ semiconductin+ material% material% the the char+echar+e

carriers ori+inate from im.urit! atoms added to the ori+inal

material is called

material is called im.urit! orD etrinsicim.urit! orD etrinsic semiconductorsemiconductor""



 This #emiconductor obtained b! do.in+ TRI7LENT and This #emiconductor obtained b! do.in+ TRI7LENT and

PENT7LENT im.urities in a TETR7LENT

semiconductor

semiconductor" " The The electrical electrical conductiit! conductiit! of of .ure.ure

semiconductors

semiconductors ma! ma! be be chan+ed chan+ed een een $ith $ith the the additionaddition

of fe$ amount of im.urities"

(24)

='PIN

The

method

of

addin+

im.urities

to a

.ure

semiconductor is /no$n as ='PIN% and the

im.urit!

added is called the do.in+ a+ent)E(r%#b%P%e and

l*"

The

The addition

addition of

of im.urit! $

im.urit! $ould

ould

increases

increases the

the no"

no"

of

free

free electrons

electrons and h

and h

oles in

a semicond

a semiconductor and

uctor and

hence increases its conductiit!"

SORTS OF SEMICONDUCTOR

accordin+ to

==ITI'N

'<

IMPURITIESIMPURITIES

n(t!.e

n(t!.e semiconductor

semiconductor

.(t!.e

(25)

N

N – – type type semiconductor semiconductor

;hen .entaalent im.urit! is added to the intrinsic

semiconductors% n t!.e semi conductors are formed"

n

(26)



 ;hen ;hen small small amounts amounts ofof .entaalent im.urit!.entaalent im.urit! such as such as

.hos.horous are added durin+ cr!stal formation% the im.urit!

atoms loc/ into the cr!stal

atoms loc/ into the cr!stal lattice see aboe <i+*"lattice see aboe <i+*"



 Consider Consider a a silicon silicon cr!stal cr!stal $hich $hich is is do.ed do.ed $ith $ith a a fifthfifth

column element such as P% s or #b"



 <our of the fie electrons in the outermost orbital of the<our of the fie electrons in the outermost orbital of the .hos.horus atom ta/e .art in the tetrahedral bondin+

.hos.horus atom ta/e .art in the tetrahedral bondin+ $ith the $ith the

four silicon nei+hbours"



 The The fifth electronfifth electron cannot ta/e .artcannot ta/e .art in the discrete in the discrete coalentcoalent

bondin+

(27)



 It It is is .ossible .ossible to to calculate calculate an an orbit orbit for for the the fifth fifth electronelectron

assumin+ that it reoles around the .ositiel! char+ed

.hos.horus ion% in the same $a! as for the F1sG electron around

the h!dro+en nucleus"



 The The electron electron of of the the .hos.horus .hos.horus atom atom is is moin+ moin+ inin thethe electric field of the silicon cr"stal

electric field of the silicon cr"stal and not in free s.ace% as is theand not in free s.ace% as is the

case in the h!dro+en atom"



 This brin+s in the dielectric constant of the cr!stal into theThis brin+s in the dielectric constant of the cr!stal into the

orbital calculations% and the radius of the electron orbit here

turns out to be er! lar+e% about H0 8% as a+ainst 0"5 8 for the

h!dro+en orbit" #uch a lar+e orbit eidentl! means that the fifth

electron is almost free and is at an ener+! leel close to the

(28)



 t '% t '% the electronic the electronic s!stem is in s!stem is in its lo$est eits lo$est ener+! state% ner+! state% allall

the alence electron $ill be in the alence band and all the

.hos.horous atoms $ill be

.hos.horous atoms $ill be un(ionised"un(ionised"



 The ener+The ener+! leels o! leels of the dof the donor atoms anor atoms are er! clore er! close to thse to thee

conduction band"



 In the In the ener+! leeener+! leel dia+ram% thl dia+ram% the ener+! e ener+! leel of leel of the fifththe fifth

electron is called

electron is called donor leeldonor leel" The donor leel is so close " The donor leel is so close to theto the

bottom of the c

bottom of the conduction band"onduction band"



 Jost of Jost of the donor the donor leel electroleel electrons are ens are ecited into cited into thethe

conduction band at room tem.erature and become ma4orit!

char+e carriers"

(29)

If the thermal ener+! is sufficientl! hi+h% in addition to the

ioniation of donor im.urit! atoms% brea/in+ of coalent

bonds ma! also occur thereb! +iin+ rise to +eneration of

electron hole .air"

A! T 0 611 A! T 0 611 A! T 7 1

(30)

Fermi energy

The <ermi ener+! for n

The <ermi ener+! for n K t!.e semiconductor is +ien b!K t!.e semiconductor is +ien b!

                              + + + + = = ₃₃_//₂₂ 2 2 * * 2 2 2 2 ln ln 2 2 2 2 ) ) ( ( h h kT kT m m N N kT kT E E E E E E e e d d d d c c F F π π t 0 % t 0 % 2 2 )) (( _c_c _d_d F F E E E E E E == ++

Variation of Fermi level with temperature

The <ermi ener+!

The <ermi ener+! is +ien b!%is +ien b!%

2 2 // 3 3 2 2 * * 2 2 2 2 ln ln 2 2 2 2     + +            ++ = = h h kT kT m m N N kT kT E E E E E E e e d d c c d d F F π π

Let

x x / / e e N N h h kT kT * * m m = =       33 22 2 2 2 2 2 2 π π 1 1 ln ln 2 2 22 ln ln 2 2 22 d d c c d d x x d d c c xx E E E E kT kT N N N N E E E E kT kT N N N N −−     ++     = = _{ } _÷÷ −− _{  ÷÷}     _{   }     ++     = = _{ } _÷÷ −− _{  ÷÷}     _{   }

(31)

s

s T T increases% increases% <ermi <ermi leel leel dro.s" dro.s" lso lso for for a a +ien+ien

tem.erature the <ermi leel shift u.$ard as the

concentration increases"

V%

(32)

;e can sa! that E

;e can sa! that E_<_< decreases sli+htl! $ith increase in decreases sli+htl! $ith increase in

tem.erature"

s

s the the tem.erature tem.erature is is increased% increased% more more and and more more donordonor

atoms are ionied" <or a .articular tem.erature all the

donor% atoms are ionied"

<urther increase in tem.erature results in +eneration of

electron(hole .airs due to the brea/in+ of coalence

bonds and the material tends to behae in intrinsic

manner" The <ermi leel +raduall! moes to$ards the

intrinsic <ermi leel

(33)

P

P -Type -Type SemiconductSemiconductor or

;hen trialent im.urit! is added to intrinsic semiconductor% P

t!.e semi conductors are formed"

l has three electron

l has three electrons in the outer orbitas in the outer orbital" ;hile substitutin+l" ;hile substitutin+

for silicon in the cr!stal% it

for silicon in the cr!stal% it needs an extra# needs an extra# electronelectron toto

com.lete the tetrahedral arran+ement of bonds

com.lete the tetrahedral arran+ement of bonds around it"around it"

The etra electron can come onl! fr

The etra electron can come onl! from one ofom one of

the ne

the nei+hbourin+ i+hbourin+ silicon atosilicon atoms% thereb! ms% thereb! creatin+ a creatin+ a acantacant

electron site )hole* on the silicon"

(34)

The aluminium atom $ith

The aluminium atom $ith the etra electron becomes athe etra electron becomes a

ne+atie char+e and the hole $ith a .ositie char+e can be

considered to resole around the aluminium atom% leadin+ to

the same orbital calculations as aboe T"

(35)

#ince

#ince the the trialent trialent im.urit! im.urit! acce.ts acce.ts an an electron% electron% thethe

ener+! leel of this im.urit! atom is called

ener+! leel of this im.urit! atom is called acce.tor leelacce.tor leel""

This acce.tor leel lies 4ust

This acce.tor leel lies 4ust aboe the alence bond"aboe the alence bond"

Een at relatiel! lo$ tem.eratures% these acce.tor

atoms +et ionied ta/in+ electrons from alence bond and

thus +iin+ to holes in the alence bond for conduction"

=ue to ioniation of acce.tor atoms% onl! holes and no

electrons are created"

(36)

V a l e V a l en c e bn c e b a n da n d C C o n do n d u c tu c tiio n b a n do n b a n d E E _v_v E E _g_g E E _a_a E E _c_c A A c c e p tc c e p to r s o r s h a  eh a  e a c c e p t e d e l e c t r o n s a c c e p t e d e l e c t r o n s ! !rro " o "  a l a le n c e b a n de n c e b a n d

If the tem.erature is sufficientl! hi+h% in addition to the

aboe .rocess%

aboe .rocess% electron(hole electron(hole .airs .airs are are +enerated+enerated due to the due to the

brea/in+

brea/in+ of of coalent coalent bonds"bonds"

Thus holes are more in number

Thus holes are more in number than electrons and hencethan electrons and hence

holes are ma4orit! carriers and electrons are minorit! carriers

(37)

Fe"mi Ene"')

The <ermi ener+! for .

The <ermi ener+! for . K t!.e semiconductor is +ien b!K t!.e semiconductor is +ien b!

                          − −            ++ = = ₃₃ ₂₂ 2 2 2 2 2 2 2 2 2 2 ** / / h h a a a a v v F F h h kT kT m m N N ln ln kT kT E E E E E E π π t 0 % t 0 % 2 2 v v aa F F E

E E E E

E

=

+

t 0% <ermi leel is ea

t 0% <ermi leel is eactl! at the middle of the accctl! at the middle of the acce.tore.tor

leel on the to. of the alence band"

(38)

$here $here N N _"_" $ $ 3 3 // 22 2 2 2 2 ** 2 2 m m hh kT kT h h π π       ÷÷     and therefore

and therefore E E _F_F : : lnln 2 2 22 y y v v aa a a N N E

E E E kT kT

N N     ++    _{ ++}   ÷÷   ÷÷     __{ }_

<rom the aboe e@n% it is

<rom the aboe e@n% it is seen thatseen that E E _F_F increases increases sli+htl! sli+htl!

as the

as the tem.erature increasestem.erature increases""

s the

s the tem.erature increases% more and more acce.tortem.erature increases% more and more acce.tor                                   − −            ++ = = ₃₃ ₂₂ 2 2 2 2 2 2 2 2 2 2 _h_h / / a a a a v v F F h h kT kT * * m m N N ln ln kT kT E E E E E E π π lnln 2 2 22 y y v v aa a a N N E

E E E kT kT

N N     + +   _{ ++}   ÷÷   ÷÷     __{ }_ : : VA

VA!AT!"N !AT!"N "F "F FE#! FE#! $EVE$ $EVE$ %!T& %!T&

TE#PEAT'E

(39)

E E N N a a N N a a

<or a .articular tem.erature all the acce.tor

atoms are ionied"

<urther increase in tem.erature

<urther increase in tem.erature results in results in +eneration of+eneration of

electron(hole .air

electron(hole .air due to the brea/in+ of due to the brea/in+ of coalent bondscoalent bonds and and

the material tend to

the material tend to behae in intrinsic mbehae in intrinsic manneranner""

The

The <ermi <ermi leel leel +raduall! +raduall! moes moes to$ards to$ards thethe

intrinsic <ermi leel"