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Jie Shan (a) , Feng Wang (b) , Ernst Knoesel (c) , Mischa Bonn (d) , and Tony F. Heinz (b)

Conductivity in Photo-Excited Insulators Probed by THz Time-Domain Spectroscopy. Jie Shan (a) , Feng Wang (b) , Ernst Knoesel (c) , Mischa Bonn (d) , and Tony F. Heinz (b) (a) Case Western Reserve University (b) Columbia University (c) Rowan University

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Jie Shan (a) , Feng Wang (b) , Ernst Knoesel (c) , Mischa Bonn (d) , and Tony F. Heinz (b)

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  1. Conductivity in Photo-Excited Insulators Probed by THz Time-Domain Spectroscopy • Jie Shan(a),Feng Wang(b), Ernst Knoesel(c), Mischa Bonn(d) , and Tony F. Heinz(b) • (a) Case Western Reserve University • (b) Columbia University • (c) Rowan University • (d) University of Leiden/AMOFL • Research supported by NSF

  2. Relevant Published Papers • E. Knoesel, M. Bonn, J. Shan, and T. F. Heinz, “Charge Transport and Carrier Dynamics in Liquids Probed by THz Time-Domain Spectroscopy,” Phys. Rev. Lett. 86, 340 (2001). • E. Knoesel, M. Bonn, J. Shan, F. Wang, and T. F. Heinz, “Transient Conductivity of Solvated Electrons in Hexane Investigated with Time-Domain THz Spectroscopy,”J. Chem. Phys 121, 394 (2004). • J. Shan, F. Wang, E. Knoesel, M. Bonn, and T. F. Heinz, “Measurement of the Frequency-Dependent Conductivity of Sapphire,” Phys. Rev. Lett. 90, 247401 (2003). • F. Wang, J. Shan, E. Knoesel, M. Bonn, and T.F. Heinz, “Electronic Charge Transport in Sapphire Studied by Optical-Pump/THz-Probe Spectroscopy,” SPIE Proceedings (in press). • E. Hendry, F. Wang, J. Shan, T. F. Heinz, and M. Bonn, “Electron Transport in TiO2 Probed by THz Time-Domain Spectroscopy,” Phys. Rev. B 69,  081101 (2004).

  3. Charge Transport in Insulators • Electrical breakdown • Optical breakdown  laser micromachining • Basis of radiation detectors • Fundamentals of electrons and their transport • Polaron = electron + virtual phonon cloud This study: prototype crystalline and amorphous material Sapphire (Al2O3), MgO: Liquid n-hexane (Bandgap 9-5 eV) (Ionization potential 8.6 eV)

  4. Difficulties in Probing Insulators • Very low intrinsic conductivity • Problems with contacts • Short carrier lifetime  Optical pump/THz probe spectroscopy Also powerful technique for semiconductors, superconductors, …

  5. E(t)X100 E(t) Conductivity Probing Transient Conductivity by THz Time-Domain Spectroscopy Sample Optical pump  Detector       Current (j=E) radiates THz Probe

  6. Detector Emitter Sample - Tripling UV: 270 nm 40 J Lock-in amplifier Experimental Setup Ti:S Regen 1 KHz, 1 mJ 150 fs, 810 nm

  7. e- Quasi-free state e- 0 Localized bound states Energy (eV) ~ ~ -8.6 0 2 nm Distance Charge Transport in Liquids • Inject electrons with fs UV pulses • Probe with pulsed THz at a variable delay

  8. -3 1.0 6x10 E(t) 4 D E(t) 0.5 2 0.0 0 E(t) [kV/cm] DE(t) [kV/cm] -2 -0.5 -4 -1.0 0 1 2 3 4 5 6 7 Time [ps] THz E-field and Pump Induced Changes in n-Hexane • Measured THz waveform with and without uv pump radiation. • Delay time betweenUV-pump and THz-probe:  = 67 ps. Knoesel et al. PRL 86, 340 (2001)

  9. Data Drude model ] -3 2 p2= nee2/(eom*) - Plasma frequency 0 - Scattering rate [x 10 De " 1 " 0 De • (ne)quasi-free = 1013 - 1015 cm-3 go= (270  50 fs)-1 ' ; -1 De De -2 0.4 0.6 0.8 1.0 1.2 n [THz] mf = e/(m*go) =470 cm2V-1s-1 Electronic Conductivity in n-Hexane

  10. THz TDS: mf = e/(m*go) =470 cm2V-1s-1 go = (270  50 fs)-1 m*=m0 • = 0.074 cm2V-1s-1 (average) • Radiolysis studies1: + + + + + + + + + e- current X-ray, e- M+ hexane time - - - - - - - - - • Two-state model of solvated electrons2,3 mf = 30 - 300 cm2V-1s-1 1N. Gee. Chem. Phys. 89 (1988) 3710; R. C. Munoz, J. Phys. Chem. 91 (1987) 4639 2Y. A. Berlin, J. Chem. Phys. 69 (1978) 2401; 3Mozumder, Chem. Phys. Lett. 233 (1995) 167. Comparison with Complementary Measurement Electron Mobility

  11. 6 Fluence = 0.3J/cm2 Decay 360 ps 5 4 [a.u.] 3 ne ½ fluence Decay > 1 ns 2 1 4 0 E ~ 150 meV a 0 200 400 600 800 3 [a. u.] Delay time (ps) Arrhenius fit: e n a /kT - E e 20 3.20 3.30 3.40 3.50 1000/T [T in K] Dynamics of Quasi-Free Electrons - > Non-geminate recombination mechanism Electron trap binding energy Ea

  12. e - - - - - Ec 8.9 eV 4.6 eV EV h + + + + + Charge Transport in Sapphire • Important optical and electonic material • High quality samples available • Model ionic material with polaronic effects

  13. Polarons & Polaronic Charge Transport Electrons in crystal are dressed by interaction with optical phonons in strongly polar crystals • New quasi-particle with m* > mband • Model widely studied • Landau, Froehlich, Lee, Pines, Feynman • Specific predictions for transport properties • of polarons, but verified only in a limited class • of materials .

  14. Electron Scattering Rate and Mobility in Sapphire at Room Temperature Drude Model fit: Scattering rate: γ0 = ( 95 fs )-1 Mobility: μe=e/(m*γ0)=610 cm2/V-s (m* ≈ 0.27 m0)

  15. Relation between conductivity and dielectric function

  16. Electron Scattering Rate and Mobility in Sapphire at Room Temperature Drude Model fit: Scattering rate: γ0 = ( 95 fs )-1 Mobility: μe=e/(m*γ0)=610 cm2/V-s (m* ≈ 0.27 m0)

  17. Temperature Dependence of Scattering Rate in High Purity Sapphire μe=610 cm2/V-s μe= 30,000 cm2/V-s

  18. Scattering Mechanism of Electrons in Sapphire • Acoustic phonon scattering • Optical phonon scattering (polaron theory) • Impurity scattering ~ ~

  19. Temp. dependence Known parameters Unknown parameters acoustica T3/2 cii: elastic constant d : deformation potential m*: effective mass opticalb exp(-E/kT) LO: optical phonon frequency (c) Ue-p: electron-optical phonon coupling constant(c) m*: effective mass A Closer Look at the Theory a. J. Bardeen and W. Shockley, Phys. Rev. 80, 72 (1950) b. F.E. Low and D. Pines, Phys. Rev. 98, 414 (1955) c. M. Schubert, T.E. Tiwald and C.M. Herzinger, Phys. Rev. B. 61(12), 8187 (2000)

  20. LO-phonon ~ Acoustic phonon scattering ~ Temperature Dependence of Scattering Rate in High Purity Sapphire m* = 0.3 m0 def = 19 eV

  21. Impurity Scattering in Sapphire Ionic impurities High purity

  22. Interpretations Based on Various Polaron Models • Numerical simulations • Electron band mass4: 0.3 - 0.4 m0 • Deformation potential5: 19 - 20 eV • F. E. Low and D. Pines, Phys. Rev. 98, 414 (1955). • F. Garcia-Moliner, Phys. Rev. 130, 2290 (1963). • Y. Osaca, Progr. Theoret. Phys. 25, 517 (1961). • Y. N Xu and W.Y. Ching, Phys. Rev. B 43, 4461 (1991). • J. C. Boettger, Phys. Rev. B 55, 750 (1997).

  23. 6 Fluence = 0.3J/cm2 Decay 360 ps 5 4 [a.u.] 3 ne ½ fluence Decay > 1 ns 2 1 0 0 200 400 600 800 Delay time (ps) Fluence Dependence of Carrier Lifetime in n-Hexane  Non-geminate recombination

  24. Fluence (mJ/cm2) 1.0 0.1 0.2 0.3 0.4 0.5 Signal (a.u.) 0.5 0.0 -20 0 20 40 60 Time (ps) Fluence Dependence of Carrier Lifetime in Sapphire

  25. Carrier Lifetime in Sapphire • Observations: • Large deviation from sample to sample (sensitive to impurities, defects) • Temperature dependence of carrier lifetime deviates from sample to sample Sapphire window High purity sapphire wafer

  26. Summary • THz Time-Domain Spectroscopy: Measure complex conductivity over broad far-IR spectral range • THz probing of electronic charge transport: • Determine basic transport parameters: carrier density, scattering rate • Doesn’t require contacts • . . . Together with ultrafast excitation • Access nonequilibrium systems and their dynamics • Probe materials without intrinsic conductivity, short-lived carriers • Investigated charge transport in model non-polar liquids (hexane) and model wide-gap insulators (sapphire) • Demonstrated high carrier mobilities • Determined carrier lifetimes and trapping mechanisms • Analyzed scattering mechanism from T-dependent conductivity

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