Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1...

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Transcript of Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1...

Page 1: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons
Page 2: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

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.

Page 3: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

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.

Page 4: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

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.

Page 5: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

( )( )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.

Page 6: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

Circles indicate dominant annihilation sites

Page 7: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

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

Page 8: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

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

Page 9: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

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.

Page 10: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

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

Page 11: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

Coincidence Doppler broadening spectrometer

Page 12: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

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

Page 13: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

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.

Page 14: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

R. Krause-Rehberg and H. S. Leipner, Positron annihilation in Semiconductors, (Springer-Verlag, New York, 1998).

Page 15: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

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.

Page 16: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons
Page 17: Positron Annihilation Spectroscopy DB.pdf · px y x y 0, θ, = 2 ∆E =Cpz N Np θ ln(N) t (ns) τ1 τ2 ¾A positron annihilates with an electron giving rise to two 511 keV photons

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.