Electron Mobility

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Electron mobility - Wikipedia, the free y

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Electron mobility!rom Wikipedia, the free encyclopedia

"n #olid-#tate phy#ic#, the electron mobility characteri$e# ho% &'ickly an electron can mo(e thro')h a metal or #emicond'ctor, %hen p'lled by

an electric field* "n #emicond'ctor#, there i# an analo)o'# &'antity for hole#, called hole mobility* +he term carrier mobility refer# in )eneral

to both electron and hole mobility in #emicond'ctor#*

Electron and hole mobility are #pecial ca#e# of electrical mobility of char)ed particle# in a fl'id 'nder an applied electric field*

When an electric fieldE i# applied acro## a piece of material, the electron# re#pond by mo(in) %ith an a(era)e (elocity called the drift (elocity,

* +hen the electron mobility i# defined a#

*

Electron mobility i# almo#t al%ay# #pecified in 'nit# of cm2./#* +hi# i# different from the S" 'nit of mobility, m

2./#* +hey are related by 1m

2./#

10

4

cm

2

./#*

ond'cti(ity i# proportional to the prod'ct of mobility and carrier concentration* !or eample, the #ame cond'cti(ity co'ld come from a #mall

n'mber of electron# %ith hi)h mobility for each, or a lar)e n'mber of electron# %ith a #mall mobility for each* !or metal#, it %o'ld not typically

matter %hich

of the#e i# the ca#e, #ince mo#t metal electrical beha(ior depend# on cond'cti(ity alone* +herefore mobility i# relati(ely 'nimportant in metal

phy#ic#* n the other hand, for #emicond'ctor#, the beha(ior of tran#i#tor# and other de(ice# can be (ery different dependin) on %hether there are

many electron# %ith lo% mobility or fe% electron# %ith hi)h mobility* +herefore mobility i# a (ery important parameter for #emicond'ctor

material#* 6lmo#t al%ay#, hi)her mobility lead# to better de(ice performance, %ith other thin)# e&'al*

Semicond'ctor mobility depend# on the imp'rity concentration# .incl'din) donor and acceptor concentration#, defect concentration,

temperat're, and electron and hole concentration#* "t al#o depend# on the electric field, part ic'larly at hi)h field# %hen (elocity #at'ration

occ'r#* "t can be determined b

y the 7all effect, or inferred from tran#i#tor beha(ior*

Contents

1 "ntrod'ction

1*1 8rift (elocity in an electric field

1*2 8efinition and 'nit#
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1*3 9elation to cond'cti(ity

2 Eample#

3 Electric field dependence and (elocity #at'ration

4 9elation bet%een #catterin) and mobility

4*1 "oni$ed imp'rity #catterin)

4*2 attice .phonon #catterin)

4*3 Pie$oelectric #catterin)

4*4 S'rface ro')hne## #catterin)

4*5 6lloy #catterin)

4*; "nela#tic #catterin)

4*< Electron=electron #catterin)

4*> 9elation bet%een mobility and #catterin) time

4*? atthie##en@# r'le

4*10 +emperat're dependence of mobility

5 ea#'rement of #emicond'ctor mobility

5*1 7all mobility

5*2 !ield-effect mobility

5*2*1 A#in) #at'ration mode

5*2*2 A#in) the linear

re)ion

; 8opin) concentration dependence in hea(ily-doped #ilic

on

< See al#o

> 9eference#

? Eternal link#

Introduction

Drift velocity in an electric field
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Witho't any applied electric field, in a #olid, electron# .or, in the ca#e of #emicond'ctor#, both electron# and hole# mo(e aro'nd randomly*

+herefore, on a(era)e there %ill be no o(erall motion of char)e carrier# in any partic'lar direction o(er time*

7o%e(er, %hen an electric field i# applied, each electron i# accelerated by the electric field* "f the electron %ere in a (ac''m, it %o'ld be

accelerated to fa#ter and fa#ter (elocitie# .called balli#tic tran#port* 7o%e(er, in a #olid, the electron repeatedly #catter# off cry#tal defect#,

phonon#, imp'ritie#, etc* +herefore, it doe# not accelerate fa#ter and fa#terB in#tead it mo(e# %ith a finite a(era)e (elocity, called the drift (elocity*

+hi# net electron motion i# '#'ally m'ch #lo%er than the normally occ'rrin) random motion*

"n a #emicond'ctor the t%o char)e carrier#, electron# and hole#, %ill typically ha(e different drift (elocitie# for the #ame electric field*

C'a#i-balli#tic tran#port i# po##ible in #olid# if the electron# are accelerated acro## a (ery #mall di#tance .a# #mall a# the mean free path, or for a

(ery #hort time .a# #hort a# the mean free time* "n the#e ca#e#, drift (elocity and mobility are not meanin)f'l*

Definition and units

+he electron mobility i# defined by the e&'ation:

*

%here:

E i# the ma)nit'de of the electric field applied to a material,

vd i# the ma)nit'de of the electron drift (elocity .in other %ord#, the electron drift #peed ca'#ed by the electric field, and

i# the electron mobility*

+he hole mobility i# defined by the #ame e&'ation* Doth electron and hole mobilitie# are po#iti(e by definition*

A#'ally, the electron drift (elocity in a material i# directly proportional to the electric field, %hich mean# that the electron mobility i# a con#tant

.independent of electric field* When thi# i# not tr'e .for eample, in (ery lar)e electric field#, the mobility depend# on the electric field*

+he S" 'nit of (elocity i# m#, and the S" 'nit of electric field i# /m* +herefore the S" 'nit of mobility i# .m#./m m2./#* 7o%e(er,

mobility i# m'ch more commonly epre##ed in cm2./# 10

4m

2./#*

obility i# '#'ally a #tron) f'nction of material imp'ritie# and temperat're, and i# determined empirically* obility (al'e# are typically

pre#ented in table or chart form* obility i# al#o different for electron# and hole# in a )i(en #emicond'ctor*

Relation to conductivity
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+here i# a #imple relation bet%een mobility and electrical cond'cti(ity* et nbe the n'mber den#ity of electron#, and let ebe their mobility* "n

the electric field E, each of the#e electron# %ill mo(e %ith the (elocity (ector , for a total c'rrent den#ity of .%here e i# the

elementary char)e* +herefore, the electrical cond'cti(ity F #ati#fie#:G1H

*

+hi# form'la i# (alid %hen the cond'cti(ity i# d'e entirely to electron#* "n a p-type #emicond'ctor, the cond'cti(ity i# d'e to hole# in#tead, b't

the form'la i# e##entially the #ame: "fp i# the den#ity of hole# and h i# the hole mobility, then the cond'cti(ity i#

*

"f a #emicond'ctor ha# both electron# and hole#, the total cond'cti(ity i#G1H

Examples

+ypical electron mobility for Si at room temperat're .300 I i# 1400 cm2 ./# and the hole mobility i# aro'nd 450 cm

2 ./#*

G2H

/ery hi)h mobility ha# been fo'nd in #e(eral lo%-dimen#ional #y#tem#, #'ch a# t%o-dimen#ional electron )a#e# .28EJ .35,000,000 cm2./# at

lo% temperat're,G3H

carbon nanot'be# .100,000 cm2./# at room temperat're

G4Hand more recently, )raphene .200,000 cm

2 /# at lo%

temperat're*G5H

r)anic #emicond'ctor# .polymer, oli)omer de(eloped th'# far ha(e carrier mobilitie# belo% 10 cm2./#, and '#'ally m'ch

lo%er*

Electric field dependence and velocity saturation

6t lo% field#, the drift (elocity vd i# proportional to the electric fieldE, #o mobility i# con#tant* +hi# (al'e of i# called the low-field mobility*

6# the electric field i# increa#ed, ho%e(er, the carrier (elocity increa#e# #'blinearly and a#ymptotically to%ard# a maim'm po##ible (al'e, called

thesaturation velocity v#at* !or eample, the (al'e of v#at i# on the order of 1K10H

%urface roughness scattering

S'rface ro')hne## #catterin) ca'#ed by interfacial di#order i# #hort ran)e #catterin) limitin) the mobility of &'a#i-t%o-dimen#ional electron# at

the interface* !rom hi)h-re#ol'tion tran#mi##ion electron micro)raph#, it ha# been determined that the interface i# not abr'pt on the atomic

le(el, b't act'al po#ition of the interfacial plane (arie# one or t%o atomic layer# alon) the #'rface* +he#e (ariation# are random and ca'#e

fl'ct'ation# of the ener)y le(el# at the interface, %hich then ca'#e# #catterin)*G>H

&lloy scattering

"n compo'nd .alloy #emicond'ctor#, %hich many thermoelectric material# are, #catterin) ca'#ed by the pert'rbation of cry#tal potential d'e to the

random po#itionin) of #'b#tit'tin) atom #pecie# in a rele(ant #'blattice i# kno%n a# alloy #catterin)* +hi# can only happen in ternary or hi)her alloy#

a# their cry#tal #tr'ct're form# by randomly replacin) #ome atom# in one of the #'blattice# .#'blattice of the cry#tal #tr'ct're* Jenerally, thi#

phenomenon i# &'ite %eak b't in certain material# or circ'm#tance#, it can become dominant effect limitin) cond'cti(ity* "n b'lk material#,

interface #catterin) i# '#'ally i)nored*G>HG?HG10HG11HG12H

Inelastic scattering

8'rin) inela#tic #catterin) proce##e#, #i)nificant ener)y echan)e happen#* 6# %ith ela#tic phonon #catterin) al#o in the inela#tic ca#e, the potential

El t bilit Wiki di th f
http://en.wikipedia.org/wiki/Electron_mobilityhttp://en.wikipedia.org/wiki/Electron_mobilityhttp://en.wikipedia.org/wiki/Electron_mobilityhttp://en.wikipedia.org/wiki/Electron_mobility


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aro'#e# from ener)y band deformation# ca'#ed by atomic (ibration#* ptical phonon# ca'#in) inela#tic #catterin) '#'ally ha(e the ener)y in the ran)e

30-50 me/, for compari#on ener)ie# of aco'#tic phonon are typically le## than 1 me/ b't #ome mi)ht ha(e ener)y in order of 10 me/* +here

i# #i)nificant chan)e in carrier ener)y d'rin) the #catterin) proce##* ptical or hi)h-ener)y aco'#tic phonon# can al#o ca'#e inter(alley or

interband #catterin), %hich mean# that #catterin) i# not limited %ithin #in)le (alley*G>H

Electronelectron scattering

8'e to the Pa'li ecl'#ion principle, electron# can be con#idered a# non-interactin) if their den#ity doe# not eceed the (al'e 101o_

p)P630>* ambrid)e Ani(er#ity Pre##* pp* 30;5-< .hbk*, "SDN 0-4-0>;;-5 .pbk*
http://adsabs.harvard.edu/abs/2008SSCom.146http://adsabs.harvard.edu/abs/2008SSCom.146http://adsabs.harvard.edu/abs/2008SSCom.146http://adsabs.harvard.edu/abs/2008SSCom.146http://dx.doi.org/http://dx.doi.org/http://books.google.com/bookshttp://books.google.com/bookshttp://books.google.com/bookshttp://books.google.com/bookshttp://books.google.com/bookshttp://books.google.com/bookshttp://adsabs.harvard.edu/abs/2008SSCom.146http://adsabs.harvard.edu/abs/2008SSCom.146http://dx.doi.org/http://books.google.com/bookshttp://books.google.com/books


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External links

#emicond'ctor )lo##ary entry for electron mobility. ht t p : # e m ic ond ' c t o r ) lo ## a r y *c o m d e f a ' lt *a # p^

#earchtermelectronmobility 9e#i#ti(ity and obility alc'lator from the DYA leanroom

. h t tp : %% % * e e * b y ' * e d ' c lea n r oo m 9 e # i# t i( ity a l* pht m l

nline lect're- obility.ht tp: na noh'b*or) r e#o'rce #;151from an atomi#tic point of (ie%

9etrie(ed from O ht t p : e n *% ik ip e d ia *o r ) % ind e *php^titleElectronRmobility_oldid;0>42>0?:55*

+et i# a(ailable 'nder the reati(e ommon# 6ttrib'tion-Share6like icen#eB additional term# may apply* Dy '#in) thi# #ite, yo' a)ree to the

+erm# of A#e and Pri(acy Policy* Wikipedia` i# a re)i#tered trademark of the Wikimedia !o'ndation, "nc*, a non-profit or)ani$ation*
http://semiconductorglossary.com/default.asphttp://semiconductorglossary.com/default.asphttp://www.ee.byu.edu/cleanroom/ResistivityCal.phtmlhttp://nanohub.org/resources/6151http://nanohub.org/resources/6151http://en.wikipedia.org/w/index.phphttp://en.wikipedia.org/w/index.phphttp://en.wikipedia.org/w/index.phphttp://semiconductorglossary.com/default.asphttp://www.ee.byu.edu/cleanroom/ResistivityCal.phtmlhttp://nanohub.org/resources/6151http://en.wikipedia.org/w/index.php

Electron Mobility

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