analy sis of microinhomogeneity of irradiated si by hall and magnetoresistance effects

10 th RD 50 Workshop, Vilnius, 2007.06.04

Analysis of microinhomogeneity of irradiated Si by Hall and

magnetoresistance effects

J.Vaitkus, A.Mekys, J.Storasta

Vilnius University, Institute of Materials Science and Applied Research


V

- + A

B

Scattering by clusters:

0

0

BMM B

rX

HHH BV

Vrf

Basic principle


tNtvStH

0

11

em /*

2 4 6 8 10 12 14 16

10-3

10-2

10-1

J (cm-2s-1)

2,83*1023

1,22*1023

7,04*1022

3,03*1022

1,40*1022

6,02*1021

3,72*1021

1,71*1021

7,38*1020

2,54 s

JV61AK

(-1

cm-1

)

t (s)

0 10 20 30 40 50

-1000

-800

-600

-400

-200

0

J (cm-2s-1)

2,83*1023

1,22*1023

7,04*1022

3,03*1022

1,40*1022

6,02*1021

3,72*1021

1,71*1021

7,38*1020

JV61AK

H (

cm2 /V

s)

t (s)

x

iiii

iiiii

H BEttne

tAtnetE

)()(

)()()1( 2

Transient photo-Hall


4 8 12 16 20 24

10-2

10-1

100

101

283334384042444649505153545657596162636566

67

68

69

70717273

747576777879808182838485868788899091929394

9596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184

185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277

278279280281282283284285286287288289290291292293294

295296297298299300301302303304305306307308309310311312313314315316317318

319320321322323324325326

327328329330331332333334335336337

338339340341342343344

345346347348349350351352353

354355356357358359360361

362363364365366367368369

370371372373374375376377378379380381382383384385386387388389390391392393394395396397

398399400401402403404405406407408409410411412413414415416417418419420

421422423424425426427428429430431432433434435436437438439440441442443444445446

447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477

478479480481482483484485486487488489490

491492493494495496497498499500501502503504505

506507508509510511512513514515516517518519520521522523

524525526527528529530531

532533534535536537538539540541542543544545546547548549550551552553554555

556557558559560561562563564565566567568

569570571572573574575576577578579580581582583584585586587588589590591592593594595

596

597

598

599600601602603604605606

607608609610611612613614615616617618619620621622623624625626627628629630631632633

634635636637638639640641642643644645646647648649650651652

653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683

684685686687688689

690691

692693694

695

696

697

698699700701702703704705706707708

709

710

711

712

713714715716717718719

720

721722

723

724725

726727728729730731732

733

734735

736737

738

739

740

741

742743744745746747748749750751752753754755

756757

758

759760761762763

764

765766767768769770771772773

774

775

776777778

779780

781

782783784785786787788789790791792793794795796797798799

800

801

802

803804

805806807808809810811

812

813814815

816

817

818

819

820

821

822823824825826827828829

830831832833

834835

836

837838839

840841

842

843844845846847848849850851852853854855856857858859860861862863864865866867868869870871872873874875876877878879880881882

883

884885886

887

888889890

891

892

893894

895896

897

898

899900901

902903

904905906

907

908

909910911912913

914915916

917918919920

921

922

923

924925926927928

929930

931932

933

934935

936

937938939

940

941942943944945946947948949950951952

953

954955956957958959

960961

962963964965

966967

968969

970

971

972973

974975

976

977

978

979

980981982983984

985

986987988989990991992993994995996997998999100010011002100310041005100610071008100910101011101210131014101510161017101810191020102110221023102410251026102710281029103010311032103310341035103610371038103910401041104210431044104510461047

1048

1049105010511052105310541055105610571058105910601061106210631064106510661067106810691070107110721073107410751076107710781079108010811082108310841085108610871088108910901091109210931094109510961097109810991100110111021103110411051106

1107

110811091110

1111

11121113111411151116

1117

1118111911201121112211231124112511261127

1128

11291130

11311132

1133113411351136

1137

11381139114011411142114311441145114611471148114911501151

1152

11531154115511561157115811591160116111621163116411651166116711681169117011711172117311741175117611771178117911801181118211831184118511861187118811891190119111921193119411951196119711981199120012011202120312041205

1206

120712081209121012111212121312141215121612171218121912201221122212231224122512261227122812291230123112321233123412351236123712381239124012411242124312441245124612471248

1249

125012511252

1253

12541255

1256

125712581259126012611262

1263

1264

12651266

1267

1268

126912701271

1272

1273

12741275

1276

12771278

1279

12801281

1282

12831284

1285

12861287

1288

12891290

J (cm-2s-1)

2,83*1023

1,22*1023

7,04*1022

3,03*1022

1,40*1022

6,02*1021

3,72*1021

1,71*1021

1 7,38*1020

JV61AK

Y(t)

t (s)

3,6 3,9 4,2

100

0,33 eV

JV63AK

Y (s

)

1000/T (K-1)

1

01

H

H

U

UtY

tYconsttNtS

)/exp(~ kTEY

stssH N

n

n

Y

N

nZvA

n

Y

~2 00

As = 10-12cm-2 for ionized scattering center.

1

0

0000 1

111

H

H

H U

U

vU

wBE

tvSNNSSN

Calculation scheme


Hall factor

22 // CHHr

sEE

Hall scattering factor rH is defined by following expressions:

The relaxation time for individual scattering process often follows a power law:

Mechanism s rH rMP rMG

Ionized impurities -3/2 1.93 2.16 5.89

Neutral impurities 0 1 0 1

Acoustic phonons +1/2 1.18 0.38 1.77

Etc.

Variation of Hall scattering factor with total impurity density Nimp. In n-type Si.

Experimantal points: -x- 77K, -o- 300K. Solid curves: calculated (from Kirnas et al., 1974)


Inhomogeneities

R. H. Bube model :

l2VH

grain l1

l1

VA

1

2

2

1

21

l

lrH

[R. H. Bube, Appl. Phys. Lett. 13, 136 (1968)]

21


Inhomogeneities

V. G. Karpov, A. J. Shik and B. I. Schklovskij (1982):

kTb

H

exp0

The cells of typical clusters: I, II and III. Dashed lines indicates the equipotential lines


Inhomogeneities

J. D. Albrecht et al. (1999):

3222 315210608)2/(1/1exp

8

KrH

When the mobility is limited solely by dislocation scattering and this process can be modeled by scattering form a line charge, rH can be estimated by computing the

average momentum relaxation time. It follows from the analytic expression:

2

2*8

Bkm

Specifically, rH is smaller than but close to 1.93

K2 is the second order modified Bessel function and is

the Debye screening length

In summary, it is clear that to assume rH =1 in analyzing low-

field Hall data often leads to errors of 30% (and occasionally as much as 100%) in carrier density and mobility


Mobility from magnetoresistivity (cm2/Vs) at different B direction

Sample No.

Dose (cm-2) Hall mobility (cm2/Vs)

“B+” “B-“

Conductivity (S/cm)

Resistivity (kcm)

61 1E12 1128 1152 1150 2000 0.500 62 1E13 748 891 832 833 1,201 63 1E14 483 850 860 79,2 12,62 64 3E14 374 608 451 102 9,771 54 1E15 461 727 693 37,2 26,90 56 3E15 366 695 602 20,9 47,92 58 1E16 275 800 810 14,0 71,28 60 3E16 209 627 421 11,8 84,58


220 230 240 250 260 270 280 290

1000

2000

3000 61 62 63 64 54 56 58 60

m (

cm2/V

s)

T (K)

100 120 140 160 180 200 220 240 260 280 300

0

200

400

600

800

1000

1200

H (

cm2 /V

s)

61 62 63 64 54 56 58 60

T (K)

Magnetoresistivity does not see the ionized scattering centers –regions where the the current flows are scatters different way.

This is not bipolarity, clusters barriers block the Hall voltage.


1,4 1,5 1,6 1,7 1,8

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

,

-1cm

-1

61 62 63 64 54 56 58 60

(1000/T)1/4

(K)-1/4

4 5 6 7 8 9 10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

0,36 eV

61 62 63 64 54 56 58 60

,

-1cm

-1

1000/T (K-1)

Mr. Mott was here…At higher dozes, amorphous zones appeared.

~0,36 eV activation found at the highest irradiation doze. The activation developed from lower value – that is not doping level, that is barrier.


'4 20

ne

kTrDebye

Cluster’s potential overlaps when n’ decreases to 1011

cm-3 at irradiation doses above 1014 cm-2

Screening

EC

EV

EB1 EB2


1012

1013

1014

1015

1016

10-6

10-5J (cm-2s-1)

2,83*1023

1,22*1023

7,04*1022

3,03*1022

1,40*1022

6,02*1021

3,72*1021

1,71*1021

7,38*1020

Y

(s

)

(cm-2)

The photo-carriers are trapped between barriers that they screen! EFFECTIVE darkness concentration seems low.


1012

1013

1014

1015

1016

10-7

10-6

J (cm-2s-1)

2,83*1023

1,22*1023

7,04*1022

3,03*1022

1,40*1022

6,02*1021

3,72*1021

1,71*1021

7,38*1020

(

s)

(cm-2)

Photoconductivity relaxation


FTIR

1000 200 0 3000 4 000 5000

0,9 5

1,0 0

1,0 5

T

(a.u

.)

1/ (cm-1)

62/61 63/61 64/61 54/61 56/61 58/61 60/61


Annealing 80C

0 6 11 17 22680

700

720

740

760

780

800

820

840

=3*1014 cm-2

m (

cm2 /V

s)

t (hrs)

B+ B-


0 6 11 17 22500

520

540

560

580

600

620

H (

cm2 /V

s)

t (hrs)


0 6 11 17 220,0004

0,0005

0,0006

0,0007

0,0008

0,0009

(S

/cm

)

t (hrs)


210 280 350

0

200

400

600

initia l + 4 min 80C + 26 min 80C +24 hrs 80C

H (

cm

2 /Vs

)

T (K)


T

/ S

/ N S /

kV

{$A+,B-,D-,E+,F-,G+,I-,L-,N+{$M 32768,0,65536}uses defaul,invisi,LPTproc,Hcokeithhol;Const KEITHLEY=1;W301_2=var TKl,temp1,temp2,temp3:sin

33.14159 mA20.0000 V

N2

N2

N /+

-

+-

+-

Time resolved photo-Hall


THANK YOU FOR YOUR ATTENTION

Acknowledgments: I am grateful to Gunnar Lindstroem for complicated and interesting samples

analy sis of microinhomogeneity of irradiated si by hall and magnetoresistance effects

Documents

hall mobility cm2vs

individual scattering

hall voltage

variation of hall

factor rh

clusters barriers

mobility sample

lowfield hall data