Extended defects in semiconductors studied b positron ...hsl/Talks/Poitiers03.pdf · Dislocations...

Extended defects in semiconductors Extended defects in semiconductors studied by positron annihilationstudied by positron annihilation

Hartmut S. Leipner

Interdisziplinäres Zentrum für Materialwissenschaften

Martin-Luther-Universität Halle–Wittenberg

http://www.cmat.uni-halle.de

Colloquium DES Poitiers 2003

hsl – Poitiers 2003-7-4 2CMAT

Contributors

➢ Reinhard Krause-Rehberg, Halle

➢ Torsten E. M. Staab, Helsinki/Bonn

➢ Christian G. Hübner, Zürich/Mainz

➢ Konrad Petters, Halle

➢ Zhu Wang, Wuhan

➢ Michael Haugk, Paderborn

➢ Jacques Rabier and Jean-Luc Demenet, Poitiers


Overview

➢ Positron techniques

➢ Point defect generation during plastic deformation

➢ What we can learn from positron annihilation about defect structures?

➢ Calculations of vacancy clusters

➢ Low temperature – high temperature deformation

➢ Modell of point defect generation

➢ Implantation-induced defects


➢ Positrons may be captured during their diffusion in lattice defects.➢ Annihilation rate (reciprocal lifetime) depends on the local electron

concentration at the annihilation site.

Positron annihilation

Source Thermalization

Diffusion

Capture in a vacancy

e+


Positron annihilation techniques

Birth -rayE

b = 1.28 MeV

Annihilation -raysE

+ = 0.511 MeV

Angular correlation = p

z/mc

Doppler broadeningE

+ = 0.511 MeV ± ∆E

Positron lifetime

∆t

e+ source

22Na DiffusionL

+ ≈ 100 nm

Thermalizationt+ ≈ 10─12 s

Sample


0 1 2 3 4 5

103

104

105

2 = 320 ps

As-grown Cz Si

Plastically deformed Si

Co

un

ts

Time (ns)

Decomposition of the experimental positron lifetime spectra

➢Undeformed Czochralski Si:

one component, τb = 218 ps

➢Plastically deformed Si:

(3 %, 1050 K)

three components

τ1 = 120 ps (not shown),

τ2 = 320 ps, τ3 = 520 ps

3 = 520 ps

b = 218 ps

Positron lifetime spectrum


Trapping model

➢ Quantitative analysis of positron trapping by a set of rate equations

➢ Solution (lifetime spectrum):

Trapping rate: di = µCdi

Average positron lifetime: τ=∑iI i τi

∑i

I iτiexp− tτi

Trapping

Defect

Positron source

Thermalization

Annihilationb

d

d

Defect-free bulk

Annihilation radiation

τ1 = 1/(λ

d + κ

d), τ

2 = 1/λ

d


Positron capture in defects

open volume ≈ b

Positron potential V+(r) of a neutral and a negatively charged vacancy. The potential of a negatively charged acceptor acting as a shallow positron trap is shown on the right. λ is the annihilation rate (inverse positron lifetime). The trapping rate κ is constant for neutral defects and a function of temperature for charged defects.

V+

r

V+

V+

r r

Coulomb potential Coulomb potential


Point defect density as a function of deformation conditions (i)

Density of vacancies and antisite defectsas a function of the strain. Result of measurements by positron annihilation in plastically deformed GaAs. Uniaxial compression in [110] direction at 773 K, strain rate 1×10−3 s−1.

Plastic strain0.05 0.10

10

20

0.2

0.4

0.6

30

40

Def

ect

de

nsity

(10

cm

)1

6−

3

GaAs

−

Vacancies

ρv=lgc jl b2m

Relation between density of excess vacancies and strain


Total number of vacancies in the bulk (), vacancies bound to dislocations (), as well as number of Ga

As antisites ()

in plastically deformed GaAs. Deformation temperature 773 K, strain 3 %, strain rate 7.5×105 s1 (above), 3×104 s1 (below).

Point defect density as a function of deformation conditions (ii)

[001] [110] [213]

Deformation axis

Def

ect d

ensi

ty (

101

6 c

m−

3 )

46

61014

4

6

468

10

1020

468

10


Positron lifetimes and capture ratesin deformed GaAs

Lifetime components:

➢ 2 = d3 = (260 ± 5) ps

corresponds to a defect with the open volume of a monovacancy

➢ 3 = d2 = (477 ± 20) ps

corresponds to a defect with a large open volume (vacancy cluster)

➢At low sample temperatures, another positron trap without open volume becomes active (e. g. antisite defects). d1 b

d2

d2

d30

0 100 200

250

270

290

310

330

350

350

450

300 400

0

5

5

10

1510

15

Sample temperature (K)

d3

Trapping rate (10

9 s−

1)

Pos

itron

life

time

(ps)

250


Plastic deformation of silicon

Sample temperature (K)

Deformation at 1073 KDeformation at 1173 KDeformation at 1273 KUndeformed reference

0 100 200 300 400 500

220

240

260

280

300

320A

vera

ge

po

sitr

on

life

time

(ps)

Average positron lifetime a a function of the sample temperature in lightly P-doped FZ Si deformed in [110] direction. 7 % deformation, 2.1×10−5 s−1 strain rate.


Comparison of high and low deformation temperatures

Positron lifetime as a function of the sample temperature in P-doped Si deformed at room temperature in comparison to high-temperature deformation


Thermal stability of deformation-induced defects

Tdef

= 800 °C Tdef

= 20 °C

d2 = 540 ps 460 ps (as deformed)– 530 ps (after annealing)

d3 = 280 ps – (as deformed)280 ps – (after annealing)


Dissociated dislocation in the diamond structure

Dissociation of a perfect 60° dislocation in the glide set in a 30° and a 90° partial dislocation. There is an intrinsic stacking fault between the two partials. The drawing is along the (110) plane.

[111]

-


Vacancy incorporation in dislocations

SF

[111]Incorporation of a vacancy in the core of a 30° partial dislocation as a local transition from glide to shuffle set.


Dislocations as positron traps

V

x

y

+

┴

Positron potential V+(x,y) of a dislocation. The regular dislocation line is a shallow positron trap, while a bound vacancy acts as a deep trap.


Trapping model in deformed crystals

(i = 1/i)

Trapping and detrapping

Regular dislocationsVacancy clusters

Dislocation-bound vacancies

Positron source

Thermalization

Annihilationb v

st

t

t

v

st

Defect-free bulk

Annihilation radiation


Calculation of vacancy clusters

➢Construction of vacancy clusters and relaxation with a self-consistent charge-density-functional-based tight binding (SCC DFTB) method [Elstner et al. 1998]➢Method allows the modeling of large

supercells (512 atoms), which are needed to avoid defect–defect interactions.➢Different vacancy aggregates were examined

in respect of their stability.➢Construction scheme of closed structures

with hexagonal rings of vacancies gives clusters of lowest total energy

Vacancy cluster in Si before and after relaxation


Calculation of vacancy clusters

450

400

350

300

250

20151050

−5

−4

−3

−2

−1

0

375 ps

420 ps 435 ps

Number of vacancies

Energy gained by adding a

monovacancy to an aggregate of

n – 1 vacancies in Si (upper part)

and the corresponding positron

lifetime (lower part).[Staab et al. 1999]

3D vacancy cluster

Vacancy chainP

osi

tro

n li

fetim

e (p

s)Dis

soci

atio

n e

ner

gy

(eV

)


Results of calculations

➢Especially stable structures (n < 18): V12 in GaAs V6, V10, V14 in Si

➢Vacancy chains are not energetically favored structures➢The experimentally observed long-lived positron lifetime

component may be attributed to V12 in GaAs and to V14 in Si.

➢Magic numbers in silicon n = 4i + 2, i = 1, 2, 3, …


Formation of vacancy clusters

Agglomeration of vacancies as a result of jog dragging at screw dislocations

Number of point defects

u

b1 b 2

1

2

Vacancy cluster

C= 1V

1⋅u×2|1⋅u×2 |

b1⋅u×b2


Superjogs

Formation of edge dipoles and prismatic dislocation loops

b

b

JogsScrew

TEM

Edge


Vacancies and interstitials

b

Vacancies Interstitials

Secondary reactions lead to antisites:

IGa + VAs GaAs IAs + VGa AsGa


Room temperature deformation of Si

➢No evidence of dislocations acting as shallow positron traps→ low average dislocation density due to inhomogeneous deformation or due to other dislocation character ?➢Large thermally stable vacancy clusters

→ formation by a jog dragging or cross slip mechanism ?

200 nm(111)

[110][132]− −

−

Perfect shuffle set dislocations nucleated during plastic deformation of Si under conditions of very high stress and low temperatures

[Rabier et al. 2002]

TEM


Summary

The formation of point defects during plastic deformation of semiconductors can be related to dislocation motion.

The basic mechanism is the emission of vacancies and interstitials by screw dislocations containing jogs.

Formation of long rows of vacancies is energetically unfavorable.

Stable three-dimensional vacancy agglomerates are formed in a primary process by atomic re-arrangement directly at the climbing jog.

Dislocations are combined positron traps with the regular dislocation line representing a shallow positron trap and bound vacancies as deep traps.


Doppler-broadening spectroscopy

➢ Momentum conservation during annihilation

→ Doppler shift of the annihilation energy: ΔE = pzc/2

➢ Doppler spectrum consists of 106 events

→ Doppler-broadening of the annihilation line

GeDetector

MCA

ADC

Stabilizer

Memory

LN2

22 Nasource

Sample+

511 keV 511 keV

e+

e−−


Line-shape parameters

506 508 510 512 514 516

AS

Deformed

Reference

-ray energy (keV)

514 515

AW

Inte

nsi

ty (

arb

itra

ry u

nits

)

Open-volume defects

➢S parameter ➢W parameter

Different sensitivity➢S parameter – valence

electron annihilation

→ open volume➢W parameter – core

electron annihilation

→ chemical environment


Monoenergetic positrons

Positron energy (eV)

β+ emission spectrum of 22Na

10−1

dN

+/d

E (

1/e

V)

Monoenergetic positrons

after moderation in a W foil

100 101 102 103 104 105 106

10−8

10−7

10−6

10−5

10−4

10−3

10−2

The broad emission positron emission spectrum of a radioactive source (mean

e+ penetration depth in silicon of 50 µm) can be moderated in a tungsten foil.


Gettering centers in self-implanted Si

➢After high-energy (3.5 MeV) self-

implantation of Si (5×1015 cm−2)

and RTA annealing (900 °C, 30 s)

two gettering zones appear at Rp

and Rp/2

(Rp projected range of Si+)

➢Visible by secondary ion mass

spectrometry profiling after

intentional Cu contamination

0.95

1.00

1.05

1.10

1.15

W/W

b at

7.5

ke

V

0.995

1.000

1.005

1.010

1.015

S/S

b at

10

ke

V

0 1 2 3 4 5 6

1016

1017

P o s itro n

A n n ih ila tio n

S IM S

Cu

de

ns

ity

(c

m3 )

Depth (µm)

TEM


Positron lifetime microscopy

0 1 2 3 4 5 6260280300260

Ave

rag

e p

osi

tro

n li

fetim

e (p

s)

Depth (µm)

280

300

320

340

360

380

350

400

450

2 (

ps)

Depth (µm)0 1 2 3 4 5 6

Rp

Rp/2

➢ At Rp/2, d = 450 ps

(vacancy clusters, V14

)

➢ At Rp, d = 320 ps

(divacancy-type defect,

related to dislocation

loops)

Defect profile using the Munich

positron lifetime microscope[Krause-Rehberg et al. 2001]


Variable-energy positron beam

e+ source E×B filter Collimator Accelerator Sample

0...50 kV

B

Magneticguidance field

Moderator

➢ Penetration depth in the sample: 0...5 µm➢ Spot diameter: 5 mm➢ Time per single Doppler broadening measurement: 20 min➢ Time per depth scan: 8 h➢ No lifetime measurements possible without bunching


Defect profiling

Scan direction

Positron microbeam8 keV

Lateral resolution1 ... 2 µm

Scan width0 1 mmP

osi

tro

n li

fetim

e

d

b

Defect depth10 µm

0.6°

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