Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1...
Transcript of Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1...
Positron Annihilation Spectroscopy
22Na (e+ Source)
~100µm
θ
(1) Angular Correlation
τ ∝ 1/ne-
(3) Lifetime
γ-ray (1.28MeV)
~ 10-12 s
e+e-
Sampleγ-ray (511keV ±∆E)
(2) Doppler Broadening
Cmp yx
yx0
,, =θ
2zCpE =∆
N
Np
θ
ln(N
)
t (ns)
τ1
τ2
A positron annihilates with an electron giving rise to two 511 keV photons in two opposite directions. Because of the finite momentum of the electron-positron pair, the annihilation energy of 511 keV gets Doppler shifted by an amount ∆E. Since numerous annihilation events are measured to give the complete Doppler spectrum, the energy line is broadened due to the individual Doppler shifts along the annihilation direction.
Doppler Broadening Spectroscopy gives information on the electron momentum distribution in the sample.
γ-ray (511keV ± ∆E)
e+e-
S = Np/NtotalSdefect > Sdefect-free
Doppler Broadening
W = (Nw1+Nw2)/Ntotal
E
NpN Defect-free
Defect
Nw1 Nw2
Doppler broadening spectroscopy
S-parameter corresponds to positron annihilation with the valence electrons and W-parameter corresponds to positron annihilation with the core electrons.
S is sensitive to open volume defects and W is sensitive to the chemical surrounding at the annihilation site.
Increase in S-parameter indicates presence of vacancy defects.
Positron source & sample sandwich
HPGe
LN2
Amplifier
PC based MCA
HV
511 keV + CpL/2
5040 5060 5080 5100 5120 5140 5160 5180 5200
0
5000
10000
15000
20000
25000
30000
35000
Al Ni
Cou
nts
Channel number
Estimate S & W
N
E
Np
S = Np/Ntotal
Nw1 Nw2
W = (Nw1 + Nw2 )/Ntotal
SNi < SAl
Experimental Doppler broadening spectrometer
Since, Doppler energy changes are small (about 20 keV), one needs to use Hyperpure Germanium semiconductor detector (having small energy resolution) to measure the energy spectrum.
( )( )SS
SSCKV
BBV −
−== λµ )/(0 kTE
VV
FVeCC −=
Get EVF
Vacancies in thermal equilibrium
One can determine the vacancy formation energy EVF in metals by plotting ln(K/λB)
versus 1/T. K is the trapping rate, Cv is the concentration of vacancy defects and Cv
0 = Sv/KB, Sv is the entropy of monovacancy formation.
Circles indicate dominant annihilation sites
Conventional Doppler broadening and elemental specificity from Doppler spectrum
Gaussian Core part
Parabolic valence part
Cou
nts
E (keV)
N
E
Np
S = Np/Ntotal
Nw1 Nw2
W = (Nw1 + Nw2 )/Ntotal
W- parameter signifies core electron structureBut still contains valance contribution.
These parts of the DB curve form the fingerprint for Core structurewill reveal the particular element contributing to positron annihilation
Normal Doppler Broadened spectrum
50 100 150 200 250 300 350
Compton edge 1280 + pileups
Insufficient charge collection
Compton edge (511 & 1280)
1280
keV
511
keV
Cou
nts
Channel Number
Core electron contribution (at wing parts) – Completely masked by
background
The core annihilation events contributing to high momentum region (520 – 530 keV) overlap with the background region. This region contains information pertaining to the core-electrons, using which one can deduce elemental specific information.
To overcome this difficulty, the annihilation spectra are recorded using two Gedetectors in coincidence mode. In this way, the peak to the background ratio is dramatically improved in the tail region and the contribution of the core electrons can be easily extracted.
For example, a given vacancy-defect complex is decorated with what type of impurity atom can be deduced by analyzing this region.
Coincidence Doppler Broadening
Eγ1 + Eγ2 = 2m0C2 (1022keV) - e-BE (~keV) - e+
BE (~eV)
Eγ1 - Eγ2 = 2∆E = Cpz
useful conversion factor 1keV = 3.91 x 10-3 m0C = 3.92 mrad
e+e-
Eγ1Eγ2
Dual parameterMCA
Coincidence
HPGe HPGe
Simplified Block diagram
Coincidence Doppler broadening spectrometer
The horizontal and the vertical bands correspond to the intensities of the annihilation gamma rays of the individual detector.
The intense peak at the center corresponds to the counts for E1=E2= 511 keV.
The elliptical region extending diagonally with E1+E2= 1022 keV corresponds to the true Doppler shift which is Eγ1 - Eγ2 . This region is nearly background free.
A two dimensional display of the coincident events collected on Si (100) with 3 x 107 total counts
Det
ecto
r A
Detector B
480 490 500 510 520 530 540101
102
103
104
105
106
Normal Doppler Coincident Doppler
Cou
nts
(arb
. uni
ts)
γ-ray energy (keV)
Peak to background ratio=102
Peak to background ratio=105
Comparison between a conventional Doppler spectrum (blue) and a coincident Doppler spectrum (red) recorded on Si. Note the large reduction in the background (520 to 540 keV) in coincidence Doppler spectrum.
R. Krause-Rehberg and H. S. Leipner, Positron annihilation in Semiconductors, (Springer-Verlag, New York, 1998).
511 512 513 514 5150.0
2.0x105
4.0x105
6.0x105
8.0x105
1.0x106
Cou
nts
(arb
. uni
ts)
γ-ray energy (keV)
Co Ni Al
0 4 8 12 16 20 24 28 32 36 40
0.0
5.0x106
1.0x107
1.5x107
2.0x107
2.5x107
Np L2
pL (10-3 m0c)
Co Ni Al
Coincidence Doppler broadening of pure elements
The orbital electron momentum spectrum (OEMS) is the pL2 weighted counts plotted as a
function of pL. In this plot, the differences in the valence electron contributions are nullified and only the core contributions are shown. It shows the extent of overlap of the positron wavefunction with the orbital electrons.
This plot is different for different elements, proving the chemical sensitivity of the OEMS.
0 5 10 15 20 25 30
1.0
1.5
2.0
2.5R
atio
to A
l
pL (10-3 moc)
Co CoSi CoSi
2 Si
0 5 10 15 20 25 30
0.5
1.0
1.5
2.0
2.5
Rat
io to
Al
pL (10-3 m0c)
Co CoSi CoSi2 Si
(a) (b)
Experimental (a) and theoretical (b) ratio curves of Co, CoSi and CoSi2 obtained by dividing the curves by the curve of Al. For the experimental data beyond about 15 x 10-3 m0c, there is a lot of fluctuations. So, to get clear trends, the curves have been smoothened using 16 point smoothening.
The ratio curves are distinctly different for Co, CoSi, CoSi2 and Si.The peaking around 12 x 10-3 m0c for Co is due to the 3d electrons. For the silicide samples, the peaking decreases. The peaking shifts towards lower momentum values as one goes from a metal to a silicideand finally to silicon.
CDB measurements on bulk cobalt silicidesRatio curves
S. Abhaya and G. Amarendra, XVth International Conference on Positron annihilation (ICPA-15), Saha Institute of Nuclear Physics, Kolkata, 2009.