positron and positronium interactions with...
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POSITRON AND POSITRONIUM INTERACTIONS WITH CONDENSED MATTER
Paul Coleman University of Bath
POSITRON-SURFACE INTERACTIONS
positron backscattering
E = 30 keV
ATOMIC NUMBER0 20 40 60 80
BA
CK
SCA
TTER
ED F
RA
CTI
ON
0
5
10
15
20
25
30
35
40
GOLD
INCIDENT POSITRON ENERGY (keV)0 10 20 30 40 50
BA
CK
SCA
TTER
ED F
RA
CTI
ON
05
10152025303540
THE FATE OF POSITRONS IN CONDENSED MATTER
POSITRON-SURFACE INTERACTIONS
secondary electron emission
ELECTRON ENERGY (eV)100 200 300 400 500 600
dN/d
E (a
rbitr
ary
scal
e)
2 keV ELECTRONS IN
2 keV POSITRONS IN
COPPER
THE FATE OF POSITRONS IN CONDENSED MATTER
POSITRON-SURFACE INTERACTIONS
low-energy positron diffraction
θ2 θ1
THE FATE OF POSITRONS IN CONDENSED MATTER
Auger electron emission
POSITRON-SURFACE INTERACTIONS THE FATE OF POSITRONS IN CONDENSED MATTER
positron surface trapping, re-emission, positronium formation
POSITRON-SURFACE INTERACTIONS
thermal or epithermal positrons
ENERGY (eV)0 5 10
CO
UN
TS (a
rb. u
nits
)
0.0
0.5
1.0100eV200eV500eV3000eV
THE FATE OF POSITRONS IN CONDENSED MATTER
positron implantation
POSITRON-SOLID INTERACTIONS
mono-energetic e+
β+
P(z) = α exp(-αz), with α (cm) ≈ 16ρEm-1.4 (ρ = density in gcm-3, Em = maximum beta positron energy in keV)
α exp(-αz)
2(z/z02)exp(-z2/z0
2)
P(z) = 2(z/z02)exp(-z2/z0
2) where zo = (40/ρ)E1.6 with density ρ in gcm-3 and E in keV
depth distributions at thermalisation (after ~ps):
THE FATE OF POSITRONS IN CONDENSED MATTER
in-flight annihilation
POSITRON-SOLID INTERACTIONS
2.65MeV e+s in Au
THE FATE OF POSITRONS IN CONDENSED MATTER
positron diffusion and annihilation
POSITRON-SOLID INTERACTIONS
free annihilation
defect trapping
THE FATE OF POSITRONS IN CONDENSED MATTER
positronium formation – insulators, nanoporous materials
2γ
Ps (3γ)
POSITRON-SOLID INTERACTIONS
** see later talks in this session **
THE FATE OF POSITRONS IN CONDENSED MATTER
POSITRON SOURCES
The perennial problem – not enough positrons…
• Relatively long half-life (2.6 years)
• Relatively short biological half-life (3 days)
• 1.274 MeV γ can be used as a ‘start’ signal
RADIOACTIVE ISOTOPES – eg 22Na
• Relatively long half-life (2.6 years)
• Relatively short biological half-life (3 days)
• 1.274 MeV γ can be used as a ‘start’ signal
RADIOACTIVE ISOTOPES – eg 22Na POSITRON SOURCES
LINEAR ACCELERATORS – eg KEK, Japan
~ 102 MeV electrons
bremstrahhlung
pair production
RESEARCH REACTORS – eg NEPOMUC, Munich
n capture
gamma emission
pair production
= probability that a pair of annihilation gamma rays has total (ie ~ e-) momentum p
2-D ANGULAR CORRELATION
DOPPLER BROADENING SPECTROSCOPY
LIFETIME SPECTROSCOPY
POSITRON SPECTROSCOPIES
ρ(px,py) = ∫ρ(p) dpz
ρ(pz) = ∫∫ρ(p) dpx dpy
λ = ∫∫∫ρ(p) dpx dpy dpz
ρ(p)
ANGULAR CORRELATION OF ANNIHILATION RADIATION
δθ ≈ pt /mc (~ 5-20 mrad)
where p t is the component of momentum of the annihilating pair in a direction transverse to the gamma emission
C of M FRAME LAB FRAME
θ0 θ0
θ1 θ2
γ1
γ2
γ1
γ2
Bristol 2D-ACAR lab
e+ 2D-ACAR – quartz ↑
← 2D Fermi surface
electron momentum densities
POSITRON LIFETIME SPECTROSCOPY
electron densities
∑ )λexp(=)(i
ii tItI
positronium (Ps): e+-e- bound state
-formed in insulators
- para-Ps lives 125 ps in vacuum
- ortho-Ps lives 142 ns in vacuum
- typical Ps lifetime in solids ~ ns
e+
γ
LIFETIME (ns)
0.1 1 10 100
Metals & alloys
Semi- conductors
Polymers
Mesoporous materials
POSITRONS POSITRONIUM
POSITRON LIFETIME MEASUREMENT
DOPPLER BROADENING SPECTROSCOPY
e+ Doppler shift in the photon energy = ± cpz /2
If pz is from a 5eV electron cpz/2 = 1130 eV (~ the resolution of a high-purity Ge detector) Doppler broadening around 511keV is measured Good for rapid, low-resolution measurements of e- momenta vs time, temperature etc.
Ge PRE-AMP AMPLIFIER BIASED AMP DIGITAL STABILISER ADC LN2 CRYO- STAT MCA MEMORY
GAMMA ENERGY (keV)
504 506 508 510 512 514 516 518
CO
UN
T R
ATE
(AR
B U
NIT
S)
C
W1 W2
DOPPLER BROADENING SPECTROSCOPY
PARAMETERS: Sharpness parameter S = C/A Wing parameter W = (W1+W2)/A
where A = total area under photopeak
TRANSITION LIMITED TRAPPING:
High C, deep but narrow traps: K = νC
DIFFUSION LIMITED TRAPPING:
Low C, large traps: K = 4π r DC
NEUTRAL VACANCY: no detrapping, τ > τbulk , less Doppler broadening: no temperature dependence
NEGATIVE VACANCY: no detrapping, τ > τbulk , less Doppler broadening: stronger trap at lower temperatures
SHALLOW TRAP (eg NEGATIVE ION): detrapping below 300K, τ ~ τbulk , little Doppler broadening
OPEN-VOLUME POINT DEFECTS WHAT CAN BE STUDIED?
sensitive to ~ 1 vacancy
per 107 atoms
VACANCIES, VACANCY CLUSTERS, DISLOCATIONS, GRAIN BOUNDARIES, INNER/OUTER SURFACES
DEFECT SIZE
DEPTH (Angstrom)100 101 102 103 104 105 106 107 108
RE
SOLV
ED
DE
FEC
T S
IZE
(Ang
stro
m)
100
101
102
103
104
105
106
107
108
STM/AFM
X-RAYSCATTERINGTEM
OM
nS
POSITRON SPECTROSCOPY
DEFECT CONCENTRATION
DEPTH (Angstrom)100 101 102 103 104 105 106 107 108
DE
FEC
T C
ON
CEN
TRAT
ION
(app
m)
10-1
100
101
102
103
104
105
STM/AFM
POSITRON SPECTROSCOPY
OM TEM
X-RAYSCATTERING
nS
SENSITIVITY TO OPEN-VOLUME POINT DEFECTS
OPEN-VOLUME POINT DEFECTS: EXTRACTING CONCENTRATIONS
∑=i
iiSfS
for two states - bulk or defect:
BBD
BD C
CSSSS
fλ+ν
ν==
- -
GAMMA ENERGY (keV)
504 506 508 510 512 514 516 518
CO
UN
T R
ATE S
)λ∑ exp(λ=)( tItN ii
ii -
for two states - bulk or defect:
)λλ(=µ=κ dbb
ddd I
ICν -
τ2
τ3 τ1
ν is the specific trapping rate
CONCENTRATION
ν is the specific trapping rate – ν depends on charge state of the defect
VACANCY CONCENTRATION (cm-3)
1014 1015 1016 1017 1018 1019 1020
S/S
Si
1.00
1.01
1.02
1.03
1.04
V2-
VV+
OPEN-VOLUME POINT DEFECTS SIZE
τ and S are related to open volume of defect
Vacancy cluster size0 5 10 15 20
S P
aram
eter
for V
n1.00
1.02
1.04
1.06
1.08
1.10
1.12
1.14
Si
CHEMICAL SPECIFICITY - ANNIHILATION LINESHAPE ANALYSIS
GAMMA ENERGY (keV)
506 508 510 512 514 516
CO
UN
TS
annihilation lines for Si Ge
Si0.7Ge0.3 Si0.9Ge0.1
Si0.98Ge0.02
GAMMA ENERGY (keV)
512 514 516 518 520 522 524
SP
EC
TRU
M R
ATI
O
0.8
1.0
1.2
1.4
1.6
1.8
spectrum ratios: Ge/Si Si0.7Ge0.3/Si = 30% of Ge/Si Si0.9Ge0.1/Si = 10% of Ge/Si Si0.98Ge0.02/Si = 2% of Ge/Si
information on chemical environment and affinity
POSITRON MODERATION
NEGATIVE WORK FUNCTION BETA SPECTRUM (0 – 540 keV, PEAK 180 keV) RE-EMITTED POSITRONS (0 – 3eV, PEAK 1.5eV)
POSITRON ENERGY (keV) (LOG SCALE)0.0001 0.001 0.01 0.1 1 10 100 1000
NU
MB
ER
OF
PO
SIT
RO
NS
PE
R e
V BETA POSITRONS FROM 22Na
3eV POSITRONSFROM MODERATOR
EMISSION FROM TUNGSTEN
alternatives include moderation by solid rare gases
LAB-BASED POSITRON BEAMS
Magnetic-transport positron beam system
Depth (z) / nm 0 20 40 60 80 100 120 140
Impl
anta
tion
Pro
files
P(E
,z)
0.00 0.03 0.06 0.09 0.12 0.15
E=0.5 keV
E=1.0 keV E=1.5 keV
E=2.0 keV
Si
LAB-BASED POSITRON BEAMS
Magnetic-transport positron beam system
also: TRAP-BASED BEAMS
PULSED BEAMS
INCIDENT POSITRON ENERGY (keV)0 5 10 15 20 25 30
NO
RM
ALIZ
ED
S P
ARAM
ETER
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1112131415
virgin
FZ Si implanted with 2MeV Si+ ions at 10n cm-2 (n = 0, 11, 12, 13, 14, 15)
depth sensitivity
nSi SAMPLES (MANCHESTER)JUNE-SEPTEMBER 2008
INCIDENT POSITRON ENERGY (keV)
5 10 15 20 25 30
S P
AR
AM
ETE
R
0.92
0.94
0.96
0.98
1.00
1.02
1s5s10s100s1has-imp
POSITRON RESPONSE
INTERFACE TRAPPING
Si-rich SiO2 ANNEALED AT 1100ºC
EXAMPLES OF POSITRON BEAM STUDIES OF SOLIDS 1. SILICON NANOCRYSTALS in SiO2 MATRIX
INCIDENT POSITRON ENERGY (keV)
5 10 15 20 25 30
S P
AR
AM
ET
ER
0.92
0.94
0.96
0.98
1.00
1.02
WITH Er
NO Er
→ Er in interfaces
ERBIUM and nSi
TEM Si Er
3-5nm clusters – Er and Si
EELS responses coincident
ILLUMINATION BY BLUE LEDs
TOTAL LED POWER (W)
0 5 10 15 20 25 30 35 40 45 50
MIN
IMU
M S
PAR
AME
TER
(AT
3 ke
V)
0.955
0.956
0.957
0.958
0.959
0.960
0.961
EXAMPLES OF POSITRON BEAM STUDIES OF SOLIDS 1. SILICON NANOCRYSTALS in SiO2 MATRIX
Ps (3γ)
2γ
INCIDENT POSITRON ENERGY (keV)
0 2 4 6 8 10
Ps
FRA
CTI
ON
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
grown at 120k 10-4torr 20mingrown at 120k 10-7torr
DEPENDENCE ON GROWTH RATE
INCIDENT POSITRON ENERGY (keV)
0 2 4 6 8 10
Ps
FRA
CTI
ON
0.0
0.2
0.4
0.6
0.8at 120Kat 150Kat 170K
DURING SUBLIMATION
T (K)
40 60 80 100 120 140 160
Ps
FRAC
TIO
N (A
RB
UN
ITS
)
0.0
0.1
0.2
0.3
0.4
0.5
PORE COLLAPSE
see poster for more information
CLOSED nm PORES:
Ps DECAY TO 3γ and Ps LIFETIME
DEPEND ON PORE SIZE
INTERCONNECTED PORES:
ESCAPE POSSIBLE, 3γ FRACTION INCREASED,
VACUUM LIFETIME
EXAMPLES OF POSITRON BEAM STUDIES OF SOLIDS 2. NANOPORES in ICE
POSITRON BEAMS: APPLICATIONS IN ASTROPHYSICS
DUST in the ISM
N. Guessoum, P. Jean & W. Gillard Applied Surface Science 252 (2006) 3352
back- scattered
free/ trapped e+
o-Ps Ps
POSITRON BEAMS: APPLICATIONS IN ASTROPHYSICS
DOPPLER BROADENING – CHEMICAL ANALYSIS
IN-FLIGHT ANNIHILATION ON MODEL SYSTEMS
DOPPLER BROADENING – STRUCTURAL ANALYSIS
Ps FORMATION AND DECAY – PORES AND STRUCTURAL ANALYSIS
DUST in the ISM
POSITRON BEAMS: APPLICATIONS IN ASTROPHYSICS
Thanks to past and present members of the Bath positron group
- and to you for your attention