Basics and Means of Positron Annihilation

Transcription

1 Basics and Means of Positron Annihilation Positron history Means of positron annihilation positron lifetime spectroscopy angular correlation Doppler-broadening spectroscopy Near-surface positron experiments: Monoenergetic slowpositron beams Determination of defect concentrations: The trapping model Conclusions

2 1928 positron predicted by Dirac Positron History 1932 positron found in cosmic radiation by Anderson 1940ties interation of positrons with matter first studies of electronic structure of solids by angular correlation establishment of Doppler-broadening and lifetime techniques end of 60 s annihilation parameters are sensitive to lattice imperfections: positron trapping (thermal vacancies in metals, plastic deformation, ionic crystals) 1968 first LINAC-based positron generation 1982 positron moderation & slow-positron beams 1998 first positron microprobe under operation Number of papers Positron studies of Defects Defects in semiconductors Publication year

3 Sources of positrons Positrons are obtained either by: - β + decay: 22 Na 22 Ne + β + + ν e + γ (1.27MeV) (half life: 2.6 years, up to 10 6 e + /s) - pair production using a beam of MeV electrons onto a target Bremsstrahlung creates positrons; >10 9 e + /s; discontinuous positron beam - nuclear reaction: 113 Cd(n,g) 114 Cd + three g rays pair production continuous positron beam; >10 10 e + /s (planned at new Forschungsreaktor München)

4 Effect of Positron Trapping in Crystal Lattice Defects γ radiation 1.27 MeV annihilation radiation MeV positron wave function is localized at vacancy site until annihilation positron annihilation parameters change when annihilating in a defect defects can by detected (identification and quantification)

5 Positron Trapping Potential attractive potential mainly due to missing ion (repelling core is absent) in semiconductors: additional Coulomb tails (µ1/r rather extended) no positron trapping by positive vacancies

6 Possible Positron Traps open-volume defects: - vacancies & vacancy clusters - dislocations (defects at dislocation line) - grain boundaries (if grain size is smaller 1 µm) - surface non-open-volume defects: - precipitation's - negatively charged impurities e.g. in semiconductors Positron trapping at a surface Positron lifetime [ps] Vacancy Clusters theoretical calculation by Saito, Oshiyama (1996) Hakala et al. (1997) Puska, Corbel (1988) Vacancy cluster size Positron trapping in Precipitates

7 Methods of Positron Annihilation: Positron Lifetime Annihilation γ MeV

8 The Positron Lifetime Measurement - Positron lifetime is measured as time difference between 1.27 MeV quantum (b + decay) and MeV quanta (annihilation process) - PM=photomultiplier; SCA=single channel analyzer (constant-fraction type); TAC=time to amplitude converter; MCA= multi channel analyzer

9 Positron Lifetime Spectra Counts t b = 218 ps As grown Cz Si Plastically deformed Si t 2 = 320 ps t 3 = 520 ps Time [ns] - lifetime spectra consist of exponential decay components - positron trapping in open-volume defects leads to long-lived lifetime components - spectra analysis is performed by nonlinear fitting routines after source and background subtraction - result: lifetimes t i and intensities I i k + 1 Ii Nt () = exp- å t i = 1 i F HG t t i I KJ

10 The Methods of Positron Annihilation

11 Angular Correlation of Annihilation Radiation - ACAR Coincidence counting rate N z c : s N ( Q, Q ) = A ( Q mc, Q mc, p ) p c x y c x y z d z

12 2D-ACAR of defect-free GaAs (Tanigawa et al., 1995)

13 Theory 2D-ACAR of Copper Experiment 3D-Fermi surface can be reconstructed from measurements in several directions of a single crystal p z along [100] Fermi surface of copper p y along [010] (Berko, 1979)

14 Methods of Positron Annihilation: Doppler broadening Normalized intensity e + annihilation in GaAs FWHM» 2.6 kev defectfree defect-rich 85 Sr FWHM = 1.4 kev g-ray energy [kev]

15 Measurement of Doppler Broadening - electron momentum in propagation direction of 511 kev g-ray leads to Doppler broadening of annihilation line - can be detected by conventional energy-dispersive Ge detectors and standard electronics

16 Line Shape Parameters S parameter: S=A S /A 0 W parameter: W=A W /A 0 W parameter mainly determined by annihilations of core electrons (chemical information)

17 Doppler Coincidence Spectroscopy - coincident detection of second annihilation g reduces background - use of a second Ge detector improves energy resolution of system

18 Doppler Coincidence Spectra GaAs:Zn Relative intensity g-ray energy [kev] E 1 +E 2 = 2 m 0 c 2 =1022 kev

19 Thermalization in Solids - broad positron emission spectrum from b sources - deep implantation into solids - no use for study of defects in thin layers - moderation produces monoenergetic positrons Mean (maximum) implantation depth of unmoderated positrons (1/e 0.999) Si: 50µm (770µm) GaAs: 22µm (330µm) PbS: 15µm (220µm)

20 Moderation of Positrons moderation efficiency: 10-4

21 Implantation Profiles of monoenergetic Positrons depth resolution is function of implantation depth exact implantation profiles are obtained by Monte- Carlo simulations depth resolution limited for larger positron energies surface can be removed by sputtering or etching (but: not any more non-destructive) L mz F m z PzE (, ) = exp m z - HG I - 1 NM z K J 0 0 m O QP z = f (E,ρ) z 0 = const. m = 2 (Makhov, 1961)

22 The Positron Beam System at Halle University spot diameter: 5mm time per single Doppler measurement: 15 min time per depth scan: 6 hours

23 The Diffusion of Positrons Diffusion can be described by the time-dependent diffusion equation: l t n t D 2 + ( r, ) = + Ñ n + ( r, t )-Ñ v n + ( r, t ) - n + ( r, t d eff ). n + (r,t)... positron density ν d... drift velocity (electric field) λ eff =1/τ b + κ(r)... effective annihilation rate κ = µc µ... trapping coefficient C... defect density Mean free path l and positron diffusion length L + in semiconductors is mainly determined by acoustic phonon scattering Þ D µ T -0.5 at 300 K: l [nm] Si L + [nm] GaAs

24 Positron Trapping in a Single Defect Type dnb () t dt dnd () t dt b =- l + k n b d b () t =- l n () t + k n () t g d d d b solution: positron decay spectrum abbreviations: t 1 1,, = t = l + k 1 2 b d ld I 1 I, I = - = l - l + k k d b d d The t i F HG t Dt () = Iexp - I exp 1 I F HG KJ + 2 t - 1 t 2 and Ii are measured Þ k is obtained: F I k d = m d = HG C - I1 t b t d I KJ t I KJ

25 Determination of absolute Defect Densities Trapping rate [s -1 ] Average positron lifetime t d V - t b V - Sensitivity range V 2- V 0 V + V 2- V 0 V Vacancy concentration the trapping coefficient µ k = µc must be determined by an independent method positron trapping may be strongly temperature-dependent Þ µ= f (T) defect in Si 300K µ (10 15 s -1 ) V - 1 V 2-2 V V + < 0.1 dislocation 1 cm 2 s -1 vacancy cluster n µ 1V

26 Conclusions positron annihilation is a powerful tool for defect studies on a nanoscopic scale applicable in almost all materials which are important in material science non-destructive technique very sensitive (one vacancy in 10 7 Si atoms) advanced tools for defect identification suitable for study of bulk and near-surface properties of solids R. Krause-Rehberg, H.S. Leipner Positron Annihilation in Semiconductors Springer-Verlag, 1999 ISBN this talk can be found as PowerPoint HTML export at: