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

LECTURE 2 

SEMICONDUCTORS AND ITS CLASSIFICATION AND



FERMI ENERGY LEVEL DISTRIBUTION IN INTRINSIC SEMICONDUCTORS



VARIATION OF FERMI LEVEL WITH TEMPERATURE IN EXTRINSIC SEMICONDUCTORS 15PY102L UNIT 1 LECTURE 2

Semicondc!o"# In!"odc!ion The

materials are classified on the basis basis of conductiit! and resistiit!" #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 10 −& to 0"5 'hm(metre" It is not that% the resistiit! alone decides $hether a substance is a semiconductor )or* not % because some allo!s hae resistiit! $hich are in the ran+e of semiconductor,s resistiit!" -ence there are some .ro.erties li/e band +a. $hich distin+uishes the materials as conductors% semiconductors and insulators" 15PY102L UNIT 1 LECTURE 2

semi(conductor is a solid $hich has the ener+! band similar to that of an insulator insulator"" It acts as an insulator at absolute ero and as a conductor at hi+h tem.eratures and 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! are a +rou. of materials hain+ conductiities bet$een those of metals and insulators" 15PY102L UNIT 1 LECTURE 2

C$%##i&ic%!ion o& #emicondc!o"# Acco"din' !o !(e con#!i!en! %!om# Elemental semiconductor:  llll the 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 more different elements )e+* ) e+* a#% ls ls etc"% 15PY102L UNIT 1 LECTURE 2

C")#!%$ #!"c!"e o& #i$icon %nd '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*" 15PY102L UNIT 1 LECTURE 2

Three dimensional re.resentation of the structures #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$icon %nd *,+ 'e"m%nim c")#!%$# 15PY102L UNIT 1 LECTURE 2

ll atoms hae coordination number &3 each material has an aera+e of & alence electrons .er atom% and t$o electrons .er bond" Each atom of a material is coordinated $ith its nei+hbours"

*%+

*,+


The thermal ibrations on one atom influence the 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+"

*%+

*,+


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

In semiconductors and insulators% $hen an eternal electric field is a..lied the a..lied the conduction is not .ossible as .ossible as there is a forbidden +a.% +a.% $hich is absent in metals" In order to conduct% the electrons from the to. of the full alence band hae to moe into the conduction band% b! crossing the forbidden gap " The field that needs to be a..lied to do this $or/ $ill be etremel! lar+e" 15PY102L UNIT 1 LECTURE 2

E+6 #ilicon $here the forbidden +a. is about 1 e7 e7"" The distance bet$een these t$o locations is about 1 8 )10 m*"

−10

 field field +radient of a..roimatel! 179 )10 10 m* : 10107m 1 is necessar! to moe an electron from the to. of the alence band to the bottom of the conduction band" −

15PY102L UNIT 1 LECTURE 2

−

The other .ossibilit! b! $hich this transition can be brou+ht about is b! thermal excitation" 

t room tem.erature% the thermal ener+! that is aailable can ecite a limited number of electrons across the ener+! +a."" This limited number accounts for semi(conduction" +a. semi(conduction" 

;hen the ener+! +a. is lar+e as in diamond% the number of electrons that can be ecited across the +a. is etremel! small" 


In intrinsic semiconductors% the conduction is due to the intrinsic .rocesses )without the influence of impurities) " 



 .ure cr!stal of silicon or +ermanium is an intrinsic 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 number of electrons ecited across the +a. can be calculated from the

f )E * :

1 1 + {exp[ E − E F ) / k BT ]}

The mid$a! in mid$a! in the forbidden +a." +a." > The .robabilit! of findin+ an electron here electron here is 50? 50?%% een thou+h ener+! leels at this .oint are forbidden" forbidden " >

Then )E −E F * is e@ual to E g 92% $here E g is the ma+nitude of the ener+! +a." 15PY102L UNIT 1 LECTURE 2

>
T(e Fe"mi $e-e$ in %n in!"in#ic #emicondc!o" $ie# in !(e midd$e o& !(e ene"') '%./ 15PY102L UNIT 1 LECTURE 2

>

The .robabilit! f )E *of *of an electron occu.!in+ ener+! leel E becomes f )E * : e.)−E g 9 2k BT *"

> The fraction of electrons at ener+! E is e@ual to the .robabilit! f )E *" *" The number n of electrons .romoted .rom oted across the +a.% e.)−E g 9 2k BT * n : N e.) $here N is is the number of electrons aailable for ecitation from the to. of the alence band"


The .romotion of some of the electrons across the +a. leaes some acant electron sites in the alence band" These are called holes" n intrinsic semiconductor contains an equal number of holes in the alence band and electrons in the conduction band % that is ne : nh"

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" 15PY102L UNIT 1 LECTURE 2

t the same time% the holes in the alence band also moe% but in a direction opposite to that of electrons" The conductiit! of the intrinsic semiconductor de.ends on the concentration of these char+e carriers% ne and nh" 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% µe and µh% as the drift elocit! ac@uired b! them under unit field +radient" 15PY102L UNIT 1 LECTURE 2

The conductiit! σ of an intrinsic semiconductor sem iconductor as σi

: ne e

µe

B nh e

µh

$here e is the electronic char+e% ne and nh are concentrations of electrons and holes .er unit olume"


Fermi level

The number of free electrons .er unit olume in an intrinsic semiconductor is 3 / 2

 2π m*e kT    n = 2   h 

ex p

2

 E F − E c     kT 

The number of holes .er unit olume in an intrinsic semiconductor is p :

 2m ∗π k T  2  2  h  h

3

2

 E − E   KT  

. exp

V

F

#ince n : . in intrinsic semiconductors" 15PY102L UNIT 1 LECTURE 2

 2  

3

(m ) ∗

e

3

2

exp

h

( E − E ) F

C

3

 2  E F − E c   2π mh∗k T  2  Ev − E F   ex p  exp  = 2  2   kT kT h       

* 2π me k T 2

 Ev − E  =   m ∗   exp    KT  3

2

F

h

kT

3

or

2 E F

e

kT

 m ∗  2  E + E  =  *  exp   kT m     h

v

e

Ta/in+ lo+ on both sides% 2 E F kT

=

2 E F kT

3 2

 mh∗    E v + E c    log exp +    e   *   kT     me 

log e 

 mh∗   E v + E c  = log e  *    +  2  me   kT  3

or Ef :


3kT 4

 mh∗ log e   *  me

  E v + E c   +    2   

c

If $e assume that% E F

E + E  =    2   v

c

*

me

= m*h

 since lo+e1 : 0D

Thus% the
Po#i!ion o& Fe"mi $e-e$ in %n in!"in#ic #emicondc!o" %! -%"io# !em.e"%!"e# *%+ %! T 0 1 3 !(e Fe"mi $e-e$ in !(e midd$e o& !(e &o",idden '%. *,+ %# !em.e"%!"e inc"e%#e#3 E F #(i&!# .4%"d# 15PY102L UNIT 1 LECTURE 2

EXTRINSIC SEMICONDUCTOR

In an etrinsic semiconductin+ material% the char+e carriers ori+inate from im.urit! atoms added to the ori+inal material is called im.urit! orD etrinsic semiconductor semiconductor""  This #emiconductor obtained b! do.in+ TRI7LENT and PENT7LENT im.urities in a TETR7LENT semiconductor"" The electrical conductiit! of semiconductor .ure semiconductors ma! be chan+ed een $ith the addition of fe$ amount of im.urities"


='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 addition of im.urit! $ould $ould increases the no" of free electrons and holes holes in a semiconductor semiconductor and hence increases its conductiit!" SORTS OF SEMICONDUCTOR accordin+

'< IMPURITIES n(t!.e semiconductor .(t!.e semiconductor 15PY102L UNIT 1 LECTURE 2

to ==ITI'N

N – type semiconductor

;hen .entaalent im.urit! is added to the intrinsic semiconductors% n t!.e semi conductors are formed"

n 5 !).e #emicondc!o"

A! T 0 1


;hen small amounts of .entaalent im.urit! im.urit! such as .hos.horous are added durin+ cr!stal formation% the im.urit! atoms loc/ into the cr!stal lattice see aboe
Consider a silicon cr!stal $hich is do.ed $ith a fifth column element such as P% s or #b" 



The fifth electron cannot ta/e .art in .art in the discrete coalent bondin+"" It is loosel" bound bondin+ bound to to the .arent atom" 15PY102L UNIT 1 LECTURE 2

It is .ossible to calculate an orbit for the fifth electron 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 electron of the .hos.horus atom is moin+ in the electric field of the silicon cr"stal and 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 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 conduction band"




t '% the electronic s!stem is in its lo$est ener+! ener+! state% all the alence electron $ill be in the alence band and all the .hos.horous atoms $ill be un(ionised" 

The ener+! ener+! leels of of the donor donor atoms are are er! close close to the the conduction band" 

In the ener+! leel leel dia+ram% the the ener+! leel of the fifth electron is called donor leel" leel" The donor leel is so close to the bottom of the conduction c onduction band" 

Jost of the donor leel electrons electrons are ecited ecited into the conduction band at room tem.erature and become ma4orit! char+e carriers" 


A! T 7 1

A! T 0 611

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" 15PY102L UNIT 1 LECTURE 2

Fermi energy

The
=

( E c

+ E

d

)

2

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

t 0 %

E F

=

( E c

+ E

d

)

2

e

Variation of Fermi level with temperature

The
=   

E d

 Ed

=  =  

Ed

+ E   + 2  c

+ 2

+ 2

Ec

kT

÷ −

Ec

÷ −

2

ln

N d

 2π m * kT  2 2  h  e

kT

ln

2

kT 2

ln

 N d   N ÷  x  N x  N ÷  d 

3/ 2

Let

−1


 2π m * kT  2  2 h   e

3 / 2

= N

x

V%"i%!ion V% "i%!ion o& Fe"mi $e-e$ 4i!( dono" concen!"%!ion 4i!( !em.e"%!"e

s T increases%
;e can sa! that E< decreases sli+htl! $ith increase in tem.erature" s the tem.erature is increased% more and more donor atoms are ionied"
P -Type Semiconduct Semiconductor or

;hen trialent im.urit! is added to intrinsic semiconductor% P t!.e semi conductors are formed" l has three electrons electrons in the outer orbital" orbital" ;hile substitutin+ for silicon in the cr!stal% it needs an extra# electron to com.lete the tetrahedral arran+ement of bonds around it" The etra electron can come onl! from fr om one of the nei+hbourin+ nei+hbourin+ silicon atoms% atoms% thereb! creatin+ a acant electron site )hole* on the silicon" 15PY102L UNIT 1 LECTURE 2

The aluminium atom $ith the 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"

p - type semiconductor 15PY102L UNIT 1 LECTURE 2

A! T 0 1

#ince the trialent im.urit! acce.ts an electron% the ener+! leel of this im.urit! atom is called acce.tor leel" leel" This acce.tor leel lies 4ust 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"


If the tem.erature is sufficientl! hi+h% in addition to the aboe .rocess% electron(hole .airs are +enerated +enerated due due to the brea/in+ of coalent bonds" Thus holes are more in number than electrons and hence holes are ma4orit! carriers and electrons are minorit! carriers C o n d u c tio n b a n d E c E g

A c c e p to r s h a  e accepted electrons !ro "  a le n c e b a n d

E a E v

V a l en c e b a n d

*%+ A! T 7 1

*,+ A! T 0 611 15PY102L UNIT 1 LECTURE 2

Fe"mi Ene"')

The
=   

E v

+ E  kT ln  − 2  2

t 0 %

a

E F

   N  3 2π m kT   2  2    h    a

*

/

h

=

Ev

   2    

+ E a 2

t 0%
VA!AT!"N VA !AT!"N "F FE#! $EVE$ %!T& TE#PEAT'E

E F

=   

E v

+ E

a

2

  N  − kT  ln   2  2π m *  2  2   h 

a

/

h

$here N " $

   3 2  kT      

2

  

2π mh

h

 E and therefore E F : 

v



 Ev +  2 

:

+ 2

E a

÷ + 

*

2

÷ 

 ÷ 

kT

2

kT

E a

ln

+

kT

2

ln

 N y  N ÷  a

3/ 2

 N y  N ÷  a

Na

Na

T

Variation Va riation of Fermi level with acceptor concentration and temperature

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

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