Study of semiconductors with positrons V. Bondarenko, R. Krause-Rehberg Martin-Luther-University Halle-Wittenberg, Halle, Germany Introduction Positron trapping into defects Methods of positron annihilation Positron lifetime spectroscopy Outlook: Doppler broadening spectroscopy Coincidence Doppler broadening spectroscopy
Introduction Questions of semiconductor industry Defect types? Defect charge states? Defect concentrations? Answers of positron annihilation Vacancy-like defects and defect complexes Size of a vacancy (mono-, di-, vacancy cluster) Neutral or negatively charged vacancy-complexes Positively charged defects are invisible Sensitivity limits 10 14-10 19 cm -3
Positron in condensed matter γ 0.511 MeV 1.27 MeV Diffusion L + 100 nm γ 22 11 Na 22 10 τ 1/2 = 3.7 ps γ 1274 kev Ne + 22 Na + e e + +υ 22 11 Na β + 90.4 %, EC 9.5 % β + 0.06 % Thermalization 3 ps E 300 kev k b T 100 µm γ 0.511 MeV e - 22 10 Ne
Positron trapping - Vacancy Perfect lattice Atom potential in GaAs (110) plane Positron wave function in GaAs (110) plane Positrons are repelled by positive atom cores
Positron trapping - Vacancy Mono-vacancy Vacancy represents a positron trap due to the missing nuclei (potential well for a positron)
Methods of positron annihilation Sensitive to electron density distribution L Positron Annihilation Lifetime Spectroscopy (PALS) + = D + τ b λ = 1/ τ = π r0 c ψ ( r) ψ ( r) γ dr b τ b positron bulk lifetime λ - positron annihilation rate the lower the electron density is, the higher is the positron lifetime + Sensitive to electron momentum distribution energy and momentum conservation leads to Angular Correlation of Annihilation Radiation (ACAR) Doppler Broadening of annihilation line Spectroscopy (DOBS) Coincidence Doppler Broadening
Methods of Positron Annihilation γ 22 Na Positron lifetime spectroscopy 1.27 MeV e + Thermalization 3 ps E 300 kev k b T 100 µm E1 = 0.511MeV + plc Diffusion L + 100 nm p p T / 2 p L θ E p T / m 0 c Θ Angular correlation of annihilation radiation Doppler broadening spectroscopy 2 2 = m0c plc / 2
Technique of positron lifetime spectroscopy PM photomultiplier SCA Single Channel Analyzer TAC Time to Amplitude Converter MCA Multichannel Analyzer
Positron Annihilation Lifetime Spectroscopy (PALS) probability n(t) that e + is alive at time t: λ - positron annihilation rate Positron lifetime spectrum in bulk: (no trapping of positrons) bulk dn ( t) dt = λ n( t) n( 0) = 1 λ b = 1 τ b n( t) = e λ bulk t annihilation radiation λ - slope of the exponential decay
Positron Annihilation Lifetime Spectroscopy model of trapping into a defect annihilation from bulk with λ b =1/τ b s -1 trapping to vacancy-defect with K s -1 annihilation from the defect with λ d =1/τ d two-component lifetime spectrum Nt ( ) = I/ τ exp( t/ τ ) + I / τ exp( t/ τ ) 1 1 1 2 2 2 analysis by non-linear fitting bulk trapping trapping rate K λ d 1 = τ d annihilation radiation λ b 1 = τ b Information vacancy type (mono-, di-, vacancy cluster) τ 2 reflects the electron density defect concentration C K = I I 1 τ b τ 2 2 1 1 C τ av = Iiτ i i
The Nature of EL2 defect in GaAs one of the most frequently studied crystal lattice defects at all responsible for semi-insulating properties of GaAs: large technological importance is deep donor, compensates shallow acceptors, e.g. C - impurities defect shows metastable state after illumination at low temperatures IR-absorption of defect disappears during illumination at T < 100 K ground state recovers during annealing at about 110 K many structural models proposed Dabrowski, Scheffler and Chadi, Chang (1988): simple As Ga -antisite defect responsible must show a metastable structural change stabil metastabil (Dabrowski 1988, Chadi 1988)
The Nature of EL2 defect in GaAs in metastable state at low temperature: Ga vacancy should disappear during annealing at about 110 K confirmed by positron lifetime measurements kinetics of recovery of ground state is identical for IR- und positron experiment: E A = (0.37 ± 0.02) ev evidence of the vacancy in metastable state confirms the proposed structural model Recovery time t 1/2 [s] 10 4 10 3 10 2 Positron annihilation IR absorption 8 9 10 1000/ [K ] T a 1 Krause et al., Phys. Rev. Lett. 65 (1990) 3329
Temperature dependence of positron trapping Compensation in GaAs:S formation of S As -V Ga complex increase of τ av to low T is due to the trapping into negative shallow Rydberg potential of the defect V + (r) 13.6a 0 4.8a 0 r 0.1eV 3.5eV 1 ε 0r observed S As -V Ga complex is negatively charged
Positron trapping shallow traps negative ions are also positron trapping centers due to small negative Coulomb potential (J. Gebauer et al. 1997) term shallow relates to the positron binding energy (few mev). therefore the trapping is significant at low temperatures only the electron density is not reduced: τ st = τ b
Annihilation-Line Doppler broadening spectroscopy Doppler effect electron momentum in propagation direction of 511 kev γ-ray leads to Doppler broadening of annihilation line γ 1 p L p 1.0 e + annihilation 85 Sr θ p T Technique γ 2 Normalized intensity 0.8 0.6 0.4 0.2 in GaAs FWHM 2.6 kev FWHM = 1.4 kev 0.0 506 508 510 512 514 516 518 520 γ ray energy [kev] E 1 -E 2 =p L c E 1, E 2 energy of γ quanta
Annihilation-Line Doppler broadening spectroscopy Data Treatment Line Parameters Shape parameter S = A A s 0, A = E + E Wing parameter s 0 s N E E 0 s D de W = A A w 0, A w = E 2 E 1 N D de Information Both S and W are sensitive to the concentration and defect type W is sensitive to chemical surrounding of the annihilation site, due to high momentum of core electrons participating in annihilation
Coincidence Doppler broadening spectroscopy Technique Both γ - quanta are detected coincidence time is 0.5 µs
Doppler coincidence spectroscopy 10 0 Relative intensity 10-1 10-2 10-3 10-4 10-5 Simple Coincidence Coincidence with E 1 +E 2 =2m 0 c 2 Without coincidence background is dramatically reduced by coincident detection of second annihilation γ-quantum this opens a possibility to investigate the high momentum part of the energy spectrum, i.e. annihilation with core electrons the atoms thus the chemical surrounding of a positron trap can be studied 500 505 510 515 520 525 γ ray energy [kev]
Doppler coincidence spectroscopy chemical sensitivity of energy spectra ρ(p) [10 3 (m 0 c) -1 ] 10-2 Elemental Si Ga As 10-3 Te 10-4 10-5 Ratio to bulk GaAs 1,5 1,0 0,5 Te Ga As Si 10-6 0 10 20 30 Electron momentum p L (10-3 m 0 c) 0 10 20 30 Electron momentum p L (10-3 m 0 c)
Nature of vacancy complexes in Si and Te doped GaAs positron lifetime spectroscopy Doppler coincidence Ratio to bulk GaAs 1,0 0,8 1,0 0,8 Experiment Theory V Ga -Te As Vacancy in GaAs:Te V Gā Si Ga V As V Ga Measurement temperature V Ga -Si Ga in GaAs:Si τ 2 = 260 ps V Ga -Te As in GaAs:Te τ 2 = 253 ps V Ga -Si Ga 10 20 30 Electron momentum p L (10-3 m 0 c) J. Gebauer et al., Phys. Rev. B 60, 1464 (1999)
Conclusion positron annihilation is a sensitive tool for investigation of vacancy-like defects in semiconductors information on type and concentration of vacancies can be obtained temperature dependence of positron trapping is governed by the charge state of the defects chemical surrounding of the annihilation site can be studied with the help of coincidence Doppler broadening technique positively charged defects are invisible for positrons This presentation can be found as a pdf-file file on our Websites: http://positron.physik.uni-halle.de http://positronannihilation.net