Solids and Semiconductor Devices 1

7/23/2019 Solids and Semiconductor Devices 1

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SOLIDS AND SEMICONDUCTOR DEVICES - I

1. Energy Bands in Solids

2. Energy Band Diagra

!. Me"als# Sei$ond%$"ors and Ins%la"ors

&. In"rinsi$ Sei$ond%$"or

'. Ele$"rons and (oles

). Do*ing o+ a Sei$ond%$"or

,. E"rinsi$ Sei$ond%$"or

. N-"y*e and /-"y*e Sei$ond%$"or

0. Carrier Con$en"ra"ion in Sei$ond%$"ors

1.Dis"in$"ion e"3een In"rinsi$ and E"rinsi$ Sei$ond%$"ors11. Dis"in$"ion e"3een Sei$ond%$"or and Me"al

12.Cond%$"i4i"y o+ a Sei$ond%$"or

S(ER SIN5(# /5T /(6SICS# 7ENDRI6A VID6ALA6A SAN5AT(AN


2/18

Energy Bands in Solids8

A$$ording "o 9%an"% Me$:ani$al La3s# ":e energies o+ ele$"ronsin a+ree a"o $an no" :a4e ari"rary 4al%es %" only soe de+ini"e;.

B%" in ":e o%"eros" s:ells# odi+i$a"ion is a**re$ialee$a%se ":eele$"rons are s:ared y any neig:o%ring a"os.

D%e "o in+l%en$e o+ :ig: ele$"ri$ +ielde"3een ":e $ore o+ ":e a"os and":e s:ared ele$"rons# energy le4els are s*li"-%* ors*read o%" +oringenergy ands.

Consider a single $rys"al o+ sili$on :a4ing N a"os. Ea$: a"o $an e

asso$ia"ed 3i": a la""i$e si"e.

Ele$"roni$ $on+ig%ra"ion o+ Siis 1s2# 2s2# 2*)#!s2# !*2. ;A"oi$ No. is 1&>


3/18

O

1s2

2s2

2*)

!*2

!s2

In"er a"oi$ s*a$ing ;r>

Energy

a $ d

Cond%$"ion Band

Valen$e Band

?oridden Energy 5a*

Ion

$ore

s"a"e

?ora"ion o+ Energy Bands in Solids8


4/18

Ea$: o+ N a"os :as i"s o3n energy le4els. T:e energy le4els are iden"i$al#

s:ar*# dis$re"e and dis"in$".

T:e o%"er "3o s%-s:ells ;!s and !* o+ M s:ell or n @ ! s:ell> o+ sili$on a"o

$on"ain "3o s ele$"rons and "3o * ele$"rons. So# ":ere are 2N ele$"rons$o*le"ely +illing 2N *ossile s le4els# all o+ 3:i$: are a" ":e sae energy.

O+ ":e )N *ossile * le4els# only 2N are +illed and all ":e +illed * le4els :a4e

":e sae energy.

;ii> O$ r Od8

T:ere is no 4isile s*li""ing o+ energy le4els %" ":ere de4elo*s a "enden$y+or ":e s*li""ing o+ energy le4els.

;iii> r @ O$8

T:e in"era$"ion e"3een ":e o%"eros" s:ell ele$"rons o+ neig:o%ring

sili$on a"os e$oes a**re$iale and ":e s*li""ing o+ ":e energy le4els

$oen$es.

;i> r @ Od ; Oa>8

;i4> O r O$8

T:e energy $orres*onding "o ":e s and * le4els o+ ea$: a"o ge"s slig:"ly

$:anged. Corres*onding "o a single s le4el o+ an isola"ed a"o# 3e ge" 2N

le4els. Siilarly# ":ere are )N le4els +or a single * le4el o+ an isola"ed a"o.


5/18

Sin$e N is a 4ery large n%er ; 120 a"os !> and ":e energy o+ ea$: le4el

is o+ a +e3 eV# ":ere+ore# ":e le4els d%e "o ":e s*reading are 4ery $losely

s*a$ed. T:e s*a$ing is 1-2!eV +or a 1 $!$rys"al.

T:e $olle$"ion o+ 4ery $losely s*a$ed energy le4els is $alled anenergy and.

;4> r @ O8

T:e energy ga* disa**ears $o*le"ely. N le4els are dis"ri%"ed

$on"in%o%sly. e $an only say ":a" &N le4els are +illed and &N le4els are

e*"y.

;4> r @ Oa8T:e and o+ &N +illed energy le4els is se*ara"ed +ro ":e and o+ &N %n+illed

energy le4els y an energy ga* $alled +oridden ga*or energy ga*or

and ga*.

T:e lo3er $o*le"ely +illed and ;3i": 4alen$e ele$"rons>is $alled ":e

4alen$e andand ":e %**er %n+illed and is $alled ":e $ond%$"ion and.

No"e8

1. T:e ea$" energy and *i$"%re de*ends on ":e rela"i4e orien"a"ion o+

a"os in a $rys"al.

2. I+ ":e ands in a solid are $o*le"ely +illed# ":e ele$"rons are no" *eri""ed

"o o4e ao%"# e$a%se ":ere are no 4a$an" energy le4els a4ailale.


6/18

Me"als8

Cond%$"ion Band

Valen$e Band

/ar"ially +illed

Cond%$"ion Band

T:e +irs" *ossile energy and diagra

s:o3s ":a" ":e $ond%$"ion and is only

*ar"ially +illed 3i": ele$"rons.

i": a li""le e"ra energy ":e ele$"rons$an easily rea$: ":e e*"y energy

le4els ao4e ":e +illed ones and ":e

$ond%$"ion is *ossile.

T:e se$ond *ossile energy anddiagra s:o3s ":a" ":e $ond%$"ion

and is o4erla**ing 3i": ":e 4alen$e

and.

T:is is e$a%se ":e lo3es" le4els in ":e

$ond%$"ion and needs less energy

":an ":e :ig:es" le4els in ":e 4alen$eand.

T:e ele$"rons in 4alen$e and o4er+lo3

in"o $ond%$"ion and and are +ree "o

o4e ao%" in ":e $rys"al +or

$ond%$"ion.

T:e :ig:es" energy le4el in ":e

$ond%$"ion and o$$%*ied y

ele$"rons in a $rys"al# a" asol%"e

"e*era"%re# is $alled ?eri Le4el.T:e energy $orres*onding "o ":is

energy le4el is $alled ?eri energy.

I+ ":e ele$"rons ge" eno%g: energy

"o go eyond ":is le4el# ":en

$ond%$"ion "aFes *la$e.


7/18

Cond%$"ion Band

Valen$e Band

?oridden Energy 5a*

1 eV

Sei$ond%$"ors8

Eg-Si@ 1.1 eV Eg5e@ .,& eV

A" asol%"e =ero "e*era"%re# no

ele$"ron :as energy "o G%* +ro

4alen$e and "o $ond%$"ion and

and :en$e ":e $rys"al is an ins%la"or.A" roo "e*era"%re# soe 4alen$e

ele$"rons gain energy ore ":an ":e

energy ga* and o4e "o $ond%$"ion

and "o $ond%$" e4en %nder ":e

in+l%en$e o+ a 3eaF ele$"ri$ +ield.

T:e +ra$"ion is * H e-

Eg

FB TSin$e Egis sall# ":ere+ore# ":e +ra$"ion

is si=eale +or sei$ond%$"ors.

As an ele$"ron lea4es ":e 4alen$e and# i" lea4es soe energy le4el in and

as %n+illed.

S%$: %n+illed regions are "ered as :olesJin ":e 4alen$e and. T:ey are

a":ea"i$ally "aFen as *osi"i4e $:arge$arriers.

Any o4een" o+ ":is region is re+erred "o a *osi"i4e :oleo4ing +ro one

*osi"ion "o ano":er.


8/18

Cond%$"ion Band

?oridden Energy 5a*

Valen$e Band

) eV

Ins%la"ors8

Eg-Diaond@ , eV

Ele$"rons# :o3e4er :ea"ed# $an no"

*ra$"i$ally G%* "o $ond%$"ion and

+ro 4alen$e and d%e "o a large

energy ga*. T:ere+ore# $ond%$"ion is

no" *ossile in ins%la"ors.

Ele$"rons and (oles8

On re$ei4ing an addi"ional energy# one o+ ":e ele$"rons +ro a $o4alen" and

reaFs and is +ree "o o4e in ":e $rys"al la""i$e.

:ile $oing o%" o+ ":e $o4alen" ond# i" lea4es e:ind a 4a$an$y naed

:oleJ.

An ele$"ron +ro ":e neig:o%ring a"o $an reaF a3ay and $an $oe "o ":e

*la$e o+ ":e issing ele$"ron ;or :ole> $o*le"ing ":e $o4alen" ond and

$rea"ing a :ole a" ano":er *la$e.

T:e :oles o4e randoly in a $rys"al la""i$e.

T:e $o*le"ion o+ a ond ay no" e ne$essarily d%e "o an ele$"ron +ro a

ond o+ a neig:o%ring a"o. T:e ond ay e $o*le"ed y a $ond%$"ion

and ele$"ron. i.e.# +ree ele$"ron and ":is is re+erred "o as ele$"ron K :olere$oina"ionJ.


9/18

In"rinsi$ or/%re Sei$ond%$"or8

C.B

V.B

Eg .,& eV

(ea" Energy

5e 5e

5e 5e

5e 5e

5e 5e

5e 5e

5e 5e

5e 5e

5e 5e

BroFen Co4alen" Bond

?ree ele$"ron ; - >

Valen$e ele$"rons

Co4alen" Bond

(ole ; >


10/18

In"rinsi$ Sei$ond%$"or is a *%re sei$ond%$"or.

T:e energy ga* in Si is 1.1 eV and in 5e is .,& eV.

5e8 1s2# 2s2# 2*)#!s2# !*)# !d1# &s2# &*2. ;A"oi$ No. is !2>

Si8 1s2# 2s2# 2*)#!s2# !*2. ;A"oi$ No. is 1&>

In in"rinsi$ sei$ond%$"or# ":e n%er o+ ":erally genera"ed ele$"ronsal3ays e (ea"ing ":e $rys"al in ":e *resen$e o+ do*an" a"os.

ii> Adding i*%ri"y a"os in ":e ol"en s"a"e o+ sei$ond%$"or.

iii> Boarding sei$ond%$"or y ions o+ i*%ri"y a"os.


11/18

E"rinsi$ orI*%re Sei$ond%$"or8N - Ty*e Sei$ond%$"ors8

5e 5e 5e

5e

5e

5e

5e 5e

As

.&' eVEg @ .,& eV

C.B

V.B

Donor le4el

-

:en a sei$ond%$"or o+ 5ro%* IV ;"e"ra 4alen"> s%$: as Si or 5e is do*ed

3i": a *en"a 4alen" i*%ri"y ;5ro%* V eleen"s s%$: as /# As or S># N K

"y*e sei$ond%$"or is +ored.

:en gerani% ;5e> is do*ed 3i": arseni$;As># ":e +o%r 4alen$e

ele$"rons o+ As +or $o4alen" onds 3i": +o%r 5e a"os and ":e +i+":

ele$"ron o+ As a"o is loosely o%nd.


12/18

T:e energy re i*%ri"y ion is 3eaFened y ":e diele$"ri$ $ons"an" o+ ":e

edi%.

So# s%$: ele$"rons +ro i*%ri"y a"os 3ill :a4e energies slig:"ly less":an ":e energies o+ ":e ele$"rons in ":e $ond%$"ion and.

T:ere+ore# ":e energy s"a"e $orres*onding "o ":e +i+": ele$"ron is in ":e

+oridden ga* and slig:"ly elo3 ":e lo3er le4el o+ ":e $ond%$"ion and.

T:is energy le4el is $alled donor le4elJ.

T:e i*%ri"y a"o is $alleddonorJ.

N K "y*e sei$ond%$"or is $alleddonor K "y*e sei$ond%$"orJ.


13/18

:en in"rinsi$ sei$ond%$"or is do*ed 3i": donor i*%ri"ies# no" only does

":e n%er o+ ele$"rons in$rease# %" also ":e n%er o+ :oles de$reases

elo3 ":a" 3:i$: 3o%ld e a4ailale in ":e in"rinsi$ sei$ond%$"or.

T:e n%er o+ :oles de$reases e$a%se ":e larger n%er o+ ele$"rons*resen" $a%ses ":e ra"e o+ re$oina"ion o+ ele$"rons 3i": :oles "o in$rease.

Conse


14/18

/ - Ty*e Sei$ond%$"ors8

:en a sei$ond%$"or o+ 5ro%* IV ;"e"ra 4alen"> s%$: as Si or 5e is do*ed3i": a "ri 4alen" i*%ri"y ;5ro%* III eleen"s s%$: as In# B or 5a># / K "y*e

sei$ond%$"or is +ored.

:en gerani%;5e> is do*ed 3i": indi% ;In># ":e ":ree 4alen$e

ele$"rons o+ In +or ":ree $o4alen" onds 3i": ":ree 5e a"os. T:e

4a$an$y":a" eis"s 3i": ":e +o%r": $o4alen" ond 3i": +o%r": 5e a"o

$ons"i"%"es a :ole.

5e 5e 5e

5e

5e

5e

5e 5e

In .' eVEg @ .,& eV

C.B

V.B

A$$e*"or le4el


15/18

T:e :ole 3:i$: is deliera"ely $rea"ed ay e +illed 3i": an ele$"ron +ro

neig:o%ring a"o# $rea"ing a :ole in ":a" *osi"ion +ro 3:ere ":e ele$"ron

G%*ed.

T:ere+ore# ":e "ri 4alen" i*%ri"y a"o is $alleda$$e*"orJ.

Sin$e ":e :oleis asso$ia"ed 3i": a *osi"i4e $:argeo4ing +ro one *osi"ion"o ano":er# ":ere+ore# ":is "y*e o+ sei$ond%$"or is $alled

/ K "y*e sei$ond%$"or.

T:e a$$e*"or i*%ri"y *rod%$es an energy le4el G%s" ao4e ":e 4alen$e and.

T:is energy le4el is $alleda$$e*"or le4elJ.

T:e energy di++eren$e e"3een ":e a$$e*"or energy le4el and ":e "o* o+ ":e

4alen$e and is %$: saller ":an ":e and ga*.

Ele$"rons +ro ":e 4alen$e and $an# ":ere+ore# easily o4e in"o ":e a$$e*"or

le4el y eing ":erally agi"a"ed.

/ K "y*e sei$ond%$"or is $alleda$$e*"or K "y*e sei$ond%$"orJ.

In a / K "y*e sei$ond%$"or# :olesare ":e aGori"y $:arge $arriersand ":e

ele$"ronsare ":e inori"y $:arge $arriers.

I" $an e s:o3n ":a"# n * @ ni *i@ ni2


16/18

Dis"in$"ion e"3een In"rinsi$ and E"rinsi$ Sei$ond%$"or8

S. No. In"rinsi$ SC E"rinsi$ SC

1 /%re 5ro%* IV eleen"s. 5ro%* III or 5ro%* V eleen"sare in"rod%$ed in 5ro%* IVeleen"s.

2 Cond%$"i4i"y is only slig:". Cond%$"i4i"y is grea"lyin$reased.

! Cond%$"i4i"y in$reases 3i": risein "e*era"%re.

Cond%$"i4i"y de*ends on ":eao%n" o+ i*%ri"y added.

& T:e n%er o+ :oles is al3ays

e


17/18

Dis"in$"ion e"3een Sei$ond%$"or and Me"al8

S. No. Sei$ond%$"or Me"al

1 Sei$ond%$"or e:a4es liFe an

ins%la"or a" 7. I"s $ond%$"i4i"yin$reases 3i": rise in"e*era"%re.

Cond%$"i4i"y de$reases 3i":

rise in "e*era"%re.

2 Cond%$"i4i"y in$reases 3i": risein *o"en"ial di++eren$e a**lied.

Cond%$"i4i"y is an in"rinsi$*ro*er"y o+ a e"al and is

inde*enden" o+ a**lied *o"en"ialdi++eren$e.

! Does no" oey O:Js la3 oronly *ar"ially oeys.

Oeys O:Js la3.

& Do*ing ":e sei$ond%$"ors 3i":i*%ri"ies 4as"ly in$reases ":e$ond%$"i4i"y.

MaFing alloy 3i": ano":er e"alde$reases ":e $ond%$"i4i"y.

El " i l C d "i i" + S i d "


18/18

@ e ;nee n::>Or

Ele$"ri$al Cond%$"i4i"y o+ Sei$ond%$"ors8

E

IeI:I @ Ie I:

Ie@ neeA4e I:@ n:eA4:

So#I @ neeA4e n:eA4:

I+ ":e a**lied ele$"ri$ +ield is sall#

":en sei$ond%$"or oeys O:Js la3.

V

R@ neeA4e n:eA4:

@ eA ;ne4e n:4:>

OrV A

l@ eA ;ne4e n:4:>

sin$eA

lR @

E

@ e ;ne4e n:4:> sin$e E @ lV

Moili"y ;> is de+ined as ":e dri+"

4elo$i"y *er %ni" ele$"ri$ +ield.

1

@ e ;nee n::>

No"e8

1. T:e ele$"ron oili"y is :ig:er ":an ":e :ole oili"y.

2. T:e resis"i4i"y $ond%$"i4i"y de*ends no" only on ":e

ele$"ron and :ole densi"ies %" also on ":eir oili"ies.

!. T:e oili"y de*ends rela"i4ely 3eaFly on "e*era"%re. End o+ S P SC - I

I

Documents

Solids and Semiconductor Devices 1