HOLE MOBILITY IN SEMICONDUCTOR NANOWIRES:TEMPERATURE AND STRAIN EFFECTS

Mariama Rebello de Sousa Dias

Advisor: Prof. Dr. Victor Lopez Richard

SUMARY Electron phonon interaction via deformation

potential; Interaction potential; Matrix element calculation; Deformation Potential;

Transition Rate; Lifetime; Mobility; Strain; Results; Molecular Dynamics Simulation.

ELECTRON PHONON INTERACTION VIA DEFORMATION POTENTIAL;

Wave function of an infinite nanowire: jqii mJn ,

ziyx

ziyx

iyx

iyx

mJ j

2)(6

121,

23

2)(6

121,

23

)(2

123,

23

)(2

123,

23

:,

yx

Zikyx

npn

ziknpn

npn

zikinnpn

i LLeynsenxnsen

Jr

ensenr

J

Jr

eer

J

SquareerSemicylindCylinder

z

zz

22

22

zz qiq

qiq

qq

qIe

eaeaV

qqUzV

ˆˆ

2)()()(

2/1~

Interaction potential

iqi

qIeiiqi

qIeiqq

qpezz eaqUeaqU

VqH

ˆ)(ˆ)(

2)( ''

2/1

zz

zz

kpnqiz

kpnqqqjIej

kpnqiz

kpnqqqjIej

qqpe

enanmJqUmJ

enanmJqUmJMH

,,,','

,,,','

'

'

ˆ1,)(','

ˆ1,)(',')(

Interaction element calculation

11ˆ

1ˆ

qqqq

qqqq

nnna

nnna

qkknnnnknnqi

knn

qkkppnnkpnqi

kpn

qkkppnnkpnqi

kpn

zzyyxxzyx

z

zyx

zzz

z

z

zzz

z

z

e

e

e

,',,,,,,

,'',',,,,','

,'',',,,,','

,,',,

'

'

)()(2

3)(0

zDzDa

qU heIe

Deformation Potential

where and are proportional to)(zDe )(zDh r

0

03

100

310

23,

23

03

10000

31

21,

23

00

3100

03

121,

23

000

31

03

1023,

23

23,

23

21,

23

21,

23

23,

23,','

y

x

z

y

x

z

z

y

x

z

y

x

jj

DiD

iD

DiD

iD

iDD

iDiD

DiD

mJrmJ

For the valence band

0srs For the conduction band

In the direction [001]LHHH couples with

qzze

qzza

zz kEkEHkEkEHkkSpepe

)()'()()'(2)',(22

qzzqkkqqzzqkkqq q

zz kEkEnkEkEnaVqdkkS

zzzz

)()'(1)()'(4

)',( ,','20

220

qkk

zqqkk

zq

qq zzzzpe a

iDna

iDnMH

,'0

,'0 2

12

)(

So,

22 )2/()()'(2/1)()'(

qzz

qzz kEkEkEkE

Replace the Dirac delta by a Lorentzian,

TRANSITION RATE CALCULATION

And using the momentum conservation,

22,'

22,'

20

220

)2/()()'(2/11

)2/()()'(2/1

4)',(

qzzqkkq

qzzqkkq

q qzz

kEkEn

kEkEn

aVqdkkS

zz

zz

qzzqz kEqkEkEkEz

)()()()( ,

2... 1,nwith 11112

2... 1,nwith 11112

2... 1, 0,nwith 11112

22

22

2

222

0

2

22

22

0

2

2

122

22

0

2

qzizf

zify

y

x

x

zf

z

zf

qzzizf

np

ifzf

z

zf

qzzz

np

ifzf

z

zf

mmk

mmLn

Ln

mqk

mq

mSquare

kmmrmmm

qkmq

merSemicylind

kmmrmmm

qkmq

mCylinder

a b c

dAdqqkSve

VqkSkkSk z

qz

kzz

z z

),(.

),()',()(

1 3/1

'

aaacb

bacia

aacb

baciaqdcbqaq

q2)2/(44

2)2/(2

)2/(44

2)2/(2)2/(

2/2

2

2

2

222

2

C

LIFETIME CALCULATION

ea2

0

20

3/1

C1C4..)(

1

qq

qz

nnaV

dAdve

Vk

2

23/1 rV yxLLV 3/1

4

23/1 rV)(

* zkme

MOBILITY

STRAIN

Subband HH Displacment Subband HL

where

qzz kEqkE )()(

QPEhh

qizfz EkEEqkE )()(

solh

QQPE

22

||11

12112

cccaaP cv ||

11

1211 2

cccbQ

Elastic moduliDeformation Potential

Spin-orbit split-off energy

RESULTS

MOLECULAR DYNAMICS SIMULATION

•Will provide values of strain field distribution in the wires