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"

*%+

*,+

S!"c!"e o& *%+ #i$icon %nd *,+ 'e"m%nim c")#!%$# 15PY102L UNIT 1 LECTURE 2

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+"

*%+

*,+

S!"c!"e o& *%+ #i$icon %nd *,+ 'e"m%nim c")#!%$# 15PY102L UNIT 1 LECTURE 2

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" 

15PY102L UNIT 1 LECTURE 2

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

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"

15PY102L UNIT 1 LECTURE 2

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"

15PY102L UNIT 1 LECTURE 2

Fermi level 

The number of free electrons .er unit olume in an intrinsic semiconductor is   n = 2   

h

3 /  2

      

* 2π  me kT  2

 E  F  − E c     ex p     kT   

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

 2m ∗π  k T  2   h 2  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 

=    m∗  

h

kT 

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

3

2

 Ev −  E      exp     KT   F 

or 

e

kT 

3

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

2 E F 

h

v

e

Ta/in+ lo+ on both sides% 2 E  F  kT 

  mh∗      E  +  E c   log e  exp v = log e  *   +     kT  2 m        e  

2 E  F  kT 

3

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

or Ef  :

15PY102L UNIT 1 LECTURE 2

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