Date post: | 31-Dec-2015 |
Category: |
Documents |
Upload: | amadahy-mitchell |
View: | 27 times |
Download: | 1 times |
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
Conductivity in Photo-Excited Insulators Conductivity in Photo-Excited Insulators Probed by THz Time-Domain Probed by THz Time-Domain
SpectroscopySpectroscopy
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).
Charge Transport in Insulators
• Electrical breakdown• Optical breakdown laser micromachining• Basis of radiation detectors
This study: prototype crystalline and amorphous material Sapphire (Al2O3), MgO: Liquid n-hexane(Bandgap 9-5 eV) (Ionization potential 8.6 eV)
• Fundamentals of electrons and their transportPolaron = electron + virtual phonon cloud
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, …
Optical pump
THz Probe
Sample
Detector
Probing Transient Conductivity by THz Time-Domain Spectroscopy
E(t)
E(t)X100
Current (j=E) radiates
E
E)(Conductivity
Experimental Setup
-
Emitter Detector
Ti:S Regen1 KHz, 1 mJ
150 fs, 810 nm
Lock-inamplifier
Sample
Tripling
UV: 270 nm40 J
• Inject electrons with fs UV pulses• Probe with pulsed THz at a variable delay
Charge Transport in LiquidsE
ner
gy
(e
V)
Distance2 nm0
0
-8.6
~~
e-
e-
Localized bound states
Quasi-free state
THz E-field and Pump Induced Changes in n-Hexane
-1.0
-0.5
0.0
0.5
1.0
E(t
) [
kV/c
m]
76543210Time [ps]
E(t)
6x10-3
4
2
0
-2
-4
E
(t) [kV/c
m]
E(t)
• Measured THz waveform with and without uv pump radiation. • Delay time between UV-pump and THz-probe: = 67 ps.
Knoesel et al. PRL 86, 340 (2001)
Electronic Conductivity in n-Hexane
1.21.00.80.60.4 [THz]
2
1
0
-1
-2'
;
"
[x
10-
3 ]
"
(ne)quasi-free = 1013 - 1015 cm-
3o = (270 50 fs)-1
Data Drude model
op
i
2
0
p2
= nee2/(eom*) - Plasma frequency 0 - Scattering rate
f = e/(m*o) =470 cm2V-1s-1
Comparison with Complementary Measurement
1N. Gee. Chem. Phys. 89 (1988) 3710; R. C. Munoz, J. Phys. Chem. 91 (1987) 46392Y. A. Berlin, J. Chem. Phys. 69 (1978) 2401; 3Mozumder, Chem. Phys. Lett. 233 (1995) 167.
• Radiolysis studies1: + + + + + + + + +
- - - - - - - - -
X-ray, e- e-M+
time
curr
ent
hexane
= 0.074 cm2V-1s-1
(average)
Electron Mobility
o = (270 50 fs)-
1
m*=m0
f = e/(m*o) =470 cm2V-1s-1
• THz TDS:
• Two-state model of solvated electrons2,3
f = 30 - 300 cm2V-1s-1
Dynamics of Quasi-Free Electrons
Fluence = 0.3J/cm2
Decay 360 ps
6
5
4
3
2
1
0
n e [a
.u.]
8006004002000 Delay time (ps)
½ fluenceDecay > 1 ns
20
3
4
ne
[a.
u.]
3.503.403.303.201000/T [T in K]
E a ~ 150 meV
Arrhenius fit:
e- Ea /kT
Electron trap
binding energy Ea
- > Non-geminate
recombination mechanism
Charge Transport in Sapphire
8.9 eV
EV
e
h
Ec
4.6 eV
+ + + + +
- -- - -
• Important optical and electonic material• High quality samples available• Model ionic material with polaronic effects
Polarons & Polaronic Charge Transport
• New quasi-particle with m* > mband
• Model widely studiedLandau, Froehlich, Lee, Pines, Feynman
• Specific predictions for transport properties of polarons, but verified only in a limited class of materials
.
Electrons in crystal are dressed by interactionwith optical phonons in strongly polar crystals
Drude Model fit:
Scattering rate: γ0 = ( 95 fs )-1
Mobility: μe=e/(m*γ0)= 610 cm2/V-s (m* ≈ 0.27 m0)
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)
Electron Scattering Rate and Mobility in Sapphire at Room Temperature
Temperature Dependence of Scattering Rate in High Purity Sapphire
0 100 200 300
0
5
10
15
20
Sca
tter
ing
Rat
e (T
Hz)
Temperature (K)
μe= 610 cm2/V-s
μe= 30,000 cm2/V-s
impurityopticalacoustic TTT )()()(0
• Acoustic phonon scattering
• Optical phonon scattering (polaron theory)
• Impurity scattering
2/3T kTLO
e
Scattering Mechanism of Electrons in Sapphire
~ ~
Temp.dependence
Knownparameters
Unknown parameters
acoustica
T3/2 cii: elastic constantd : deformation
potentialm*: effective mass
opticalb exp(-E/kT)
LO: optical phonon
frequency (c)
Ue-p : electron-optical
phonon coupling constant (c)
m* : effective mass
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)
A Closer Look at the Theory
Temperature Dependence of Scattering Rate in High Purity Sapphire
0 100 200 300
0
5
10
15
20
Scatt
eri
ng
Rate
(T
Hz)
Temperature (K)
2/3TAcoustic phonon scattering ~
kTLO
e
LO-phonon
~
m* = 0.3 m0
def = 19 eV
Impurity Scattering in Sapphire
0 100 200 300
0
5
10
15
20
Sca
tter
ing
Rat
e (T
Hz)
Temperature (K)
Ionic impuritiesHigh purity
impurityopticalacoustic TTT )()()(0
Model Electron band mass (m0 )
Effective mass (polaron) (m0 )
Deformation potential (eV)
Pines & Low1 0.25 0.30 19
Garcia-Moliner2 0.38 0.48 14
Osaca3 0.65 0.92 8.3
1. F. E. Low and D. Pines, Phys. Rev. 98, 414 (1955). 2. F. Garcia-Moliner, Phys. Rev. 130, 2290 (1963).3. Y. Osaca, Progr. Theoret. Phys. 25, 517 (1961).4. Y. N Xu and W.Y. Ching, Phys. Rev. B 43, 4461 (1991).5. J. C. Boettger, Phys. Rev. B 55, 750 (1997).
Interpretations Based on Various Polaron Models
Numerical simulations• Electron band mass4: 0.3 - 0.4 m0
• Deformation potential5: 19 - 20 eV
Fluence = 0.3J/cm2
Decay 360 ps
6
5
4
3
2
1
0
n e [a
.u.]
8006004002000
Delay time (ps)
½ fluenceDecay > 1 ns
Non-geminate recombination
Fluence Dependence of Carrier Lifetime in n-Hexane
Fluence Dependence of Carrier Lifetime in Sapphire
-20 0 20 40 600.0
0.5
1.0S
igna
l (a.
u.)
Time (ps)
0.4
0.3
0.5
0.2
0.1
Fluence (mJ/cm2)
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
0 60 120 1800.0
0.4
0.8
T=294K
=190 ps
nf (
a.u
.)
Delay (ps)
High purity sapphire wafer Sapphire window
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 mobilitiesDetermined carrier lifetimes and trapping mechanismsAnalyzed scattering mechanism from T-dependent conductivity