Positron Annihilation Lifetime Spectroscopy (PALS)

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1 Positron Annihilation Lifetime Spectroscopy (PALS) Javier Puertas 12/12/12

2 Contents 1. Introduction General idea of the process. 3. PALS: Experimental results What is a positron? 3.1. Math. Model How can we obtain it? PLEPS. 2. PALS: interaction with solids Vacancy Formation and Migration Thermalization Vacancy Identification Diffusion Trapping 4. References

3 Introduction General idea of the process.

4 What is a positron? Theoretical prediction (Dirac, 1928). - Non-relativistic QM: 2 p E= 2m - Relativistic QM: E= (( mc ) +( pc) ) It seems that negative energies are possible. This led to the idea of antiparticles.

5 What is a positron? Experimental discovery: C.D. Anderson (1932)

6 What is a positron? It was the first antiparticle found experimentally. It is similar to the electron but its charge: q = e An electron and a positron annihilate producing two photons (511 kev each). Pair production: High energetic photons interacting with matter might create a positron electron pair.

7 How can we obtain it? Beta + decay: converts a proton into a neutron, a positron and an electron neutrino. It can only happen within matter because this process needs energy due to the neutron's mass being greater than the proton's.

8 How can we obtain it? Na decay scheme - High e+ yield (90.4%). - Half-life = 2.6 years. - The MeV photon is essential for PALS. - Broad energy distribution (from 0.1 ev to 540 KeV aprox.).

9 How can we obtain it? NEPOMUC -First a neutron beam hits the Cd(113) sample creating Cd(114) in an excited state. -Cd(114) decays to its ground state emitting photons. -This photons create positrons by pair production in Pt. - The resulting beam is mono-energetic and has the world's highest intensity for a mono-energetic positron beam.

10 How can we obtain it? Comparison between the two beams.

11 PALS: Interaction with solids We measure the time between the positron's creation and its annihilation. This time provides information about the type of defects present in the sample.

12 PALS: Interaction with solids PALS' objective is to detect defects in solids, so understanding the interaction between positrons and matter is essential.

13 Thermalization Positrons lose part of their initial kinetic energy due to interactions with the lattice and the electrons. Thermalization lasts a few ps ( s).

14 Diffusion The positrons start to behave as charged particles inside a lattice: Bloch states. The probability density in interstitial regions is higher.

15 Trapping - The positrons may be trapped in the lattice's defects, this allows us to detect these defects. - The trapping rate k (number of positrons trapped per time unit) links Bloch states (diffusion) with localized states (trapping).

16 Trapping Relation between the trapping rate and the defect concentration. κ=μc C is the defect concentration μ is the positron trapping coefficient (it depends on the type of defect).

17 Mathematical Model Following this model, we will obtain k through PALS technique.

18 Mathematical Model Differential equation for the model. Nb= # e+ in the bulk. Nd= # e+ in the defect. Λb= annihilation rate in the bulk. Λd= annihilation rate in the defect. Kd= trapping rate of the defect. Starting conditions: nb(0)=n ; nd(0)=0.

19 Mathematical Model Solution of the equation: (nb+nd ) D(t )= N This model can be generalized to various defects

20 Mathematical Model Number of positrons in the sample (k defects): What we measure in PALS is:

21 PALS: Experimental Results The slopes in the logaritmic plot are the different positrons lifetimes.

22 PALS: Experimental Results Important relation

23 PALS: Experimental Results Experimental procedure.

24 PALS: Experimental Results Experimental scheme.

25 PALS: Experimental Results Sample-source sandwich arrangement.

26 PLEPS: Pulsed Low Energy Positron beam System

27 PLEPS: Pulsed Low Energy Positron beam System

28 Vacancy Formation and Migration Study of vacancy formation and migration using PALS. The s-shape curve is due to the thermal vacancy formation

29 Vacancy Formation and Migration Study of vanacy formation through rapid cooling.

30 Vacancy Formation and Migration Trapping coefficient variation as a function of temperature.

31 Vacancy Identification Identification of A- and B-Site Cation Vacancy Defects in Perovskite Oxide Thin Films. We can see the variation in the vacancy concentration as a function of the laser fluence.

32 References Positron Annihilation in Semiconductors. R.Krause-Rehberg, H.S.Leipner. Wikipedia. Status of the pulsed low energy positron beam system (PLEPS) at the Munich Research Reactor FRM-II. (May 2008). P. Sperr, W. Egger, G. Kögel, G. Dollinger, C. Hugenschmidt, R. Repper, C. Piochacz. Simultaneous Study of Vacancy Formation and Migration at High Temperatures in B2-Type Fe Aluminides. (January 1995). R. Würschum, C. Grupp, and H. E. Schaefer. Identification of A- and B-Site Cation Vacancy Defects in Perovskite Oxide Thin Films. (November 2010). D. J. Keeble, S. Wicklein, R. Dittmann, L. Ravelli, R. A. Mackie, and W. Egger.

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