Positron Annihilation Spectroscopy

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2 Positron Annihilation Spectroscopy (1) Angular Correlation θ N x, y = p x, y m C θ γ-ray (511keV ± E) 0 (2) Doppler Broadening Cp E = z 2 θ N p ~100µm 22 Na (e + Source) e - e + ~ s Sample γ-ray (1.28MeV) (3) Lifetime τ 1/n e- 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. ln(n) τ 1 t (ns) τ 2

3 Increase in S-parameter indicates presence of vacancy defects. Doppler broadening spectroscopy e - e + γ-ray (511keV ± E) Doppler Broadening Defect S = N p /N total S defect > S defect-free N N p Defect-free W = (N w1 +N w2) /N total N w1 N w2 E 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.

4 Experimental Doppler broadening spectrometer 511 kev + Cp L /2 Positron source & sample sandwich HPGe HV Amplifier PC based MCA Al Ni LN S Ni < S Al Estimate S & W Counts N N p N w1 N w E Channel number S = N p /N total W = (N w1 + N w2 )/N total 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.

5 Vacancies in thermal equilibrium Get E V F K = µ C = λ V B ( S SB ) ( S S ) V C V = C e F 0 ( EV / kt ) V One can determine the vacancy formation energy E VF in metals by plotting ln(k/λ B ) versus 1/T. K is the trapping rate, C v is the concentration of vacancy defects and C v0 = S v /K B, S v is the entropy of monovacancy formation.

6 Circles indicate dominant annihilation sites

7 Conventional Doppler broadening and elemental specificity from Doppler spectrum Parabolic valence part N N p N w1 N w2 Counts E S = N p /N total W = (N w1 + N w2 )/N total E (kev) Gaussian Core part W- parameter signifies core electron structure But still contains valance contribution. These parts of the DB curve form the fingerprint for Core structure will reveal the particular element contributing to positron annihilation

8 Normal Doppler Broadened spectrum Insufficient charge collection Core electron contribution (at wing parts) Completely masked by background Counts 511 kev Compton edge pileups Compton edge (511 & 1280) 1280 kev Channel Number

9 The core annihilation events contributing to high momentum region ( 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 Ge detectors 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.

10 Coincidence Doppler Broadening E γ1 + E γ2 = 2m 0 C 2 (1022keV) -e - BE (~kev) -e+ BE (~ev) E γ1 -E γ2 = 2 E = Cp z useful conversion factor 1keV = 3.91 x 10-3 m 0 C = 3.92 mrad Simplified Block diagram HPGe E γ1 e - e + E γ2 HPGe Coincidence Dual parameter MCA

11 Coincidence Doppler broadening spectrometer

12 A two dimensional display of the coincident events collected on Si (100) with 3 x 10 7 total counts Detector A Detector B 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 E 1 =E 2 = 511 kev. The elliptical region extending diagonally with E 1 +E 2 = 1022 kev corresponds to the true Doppler shift which is E γ1 -E γ2. This region is nearly background free.

13 Counts (arb. units) 10 6 Normal Doppler Coincident Doppler Peak to background ratio=10 2 Peak to background ratio= γ-ray energy (kev) 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.

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

15 Coincidence Doppler broadening of pure elements Counts (arb. units) 1.0x x x x x γ-ray energy (kev) Co Ni Al Np L 2 2.5x x x x x p L (10-3 m 0 c) Co Ni Al The orbital electron momentum spectrum (OEMS) is the p L2 weighted counts plotted as a function of p L. 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.

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17 CDB measurements on bulk cobalt silicides Ratio curves Co CoSi CoSi 2 Si Co CoSi CoSi 2 Si Ratio to Al 1.5 Ratio to Al p L (10-3 m o c) p L (10-3 m 0 c) (a) (b) Experimental (a) and theoretical (b) ratio curves of Co, CoSi and CoSi 2 obtained by dividing the curves by the curve of Al. For the experimental data beyond about 15 x 10-3 m 0 c, 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, CoSi 2 and Si. The peaking around 12 x 10-3 m 0 c 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 silicide and finally to silicon. S. Abhaya and G. Amarendra, XVth International Conference on Positron annihilation (ICPA-15), Saha Institute of Nuclear Physics, Kolkata, 2009.