Transcript Document

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)
(b)
(c)
(d)
Case Western Reserve University
Columbia University
Rowan University
University of Leiden/AMOFL
Research supported by NSF
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 TimeDomain 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
• 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)
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, …
Probing Transient Conductivity by THz
Time-Domain Spectroscopy
Optical pump Sample
E(t)

Detector



THz Probe
E(t)X100



E

Conductivity  ( ) 
E  
Experimental Setup
Ti:S Regen
1 KHz, 1 mJ
150 fs, 810 nm
Emitter
Sample
Tripling
UV: 270 nm
40 J
Lock-in
amplifier
Detector
-
Charge Transport in Liquids
eQuasi-free state
0
Energy (eV)
eLocalized bound states
-8.6
0
2 nm
• Inject electrons with fs UV pulses
• Probe with pulsed THz at a variable delay
Distance
THz E-field and Pump Induced Changes
in n-Hexane
-3
6x10
1.0
4
E(t)
0.5
2
0.0
0
-2
-0.5
E(t) [kV/cm]
E(t) [kV/cm]
E(t)
-4
-1.0
0
1
2
3
4
5
6
7
Time [ps]
• 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
[x 10-3]
2
e' ; e"
Data
Drude model
0
e"
1
 2p
e    e 0 
   ig o 
p2 = nee2/(eom*) - Plasma frequency
g0 - Scattering rate
-1
e
-2
(ne)quasi-free = 1013 - 1015 cm-3
0.4
0.6
0.8
n [THz]
1.0
1.2
go = (270  50 fs)-1
f = e/(m*go) =470 cm2V-1s-1
Comparison with Complementary
Measurement
Electron Mobility
• THz TDS:
f = e/(m*go) =470 cm2V-1s-1
go = (270  50 fs)-1
m*=m0
• Radiolysis studies1:
X-ray, e-
e- M+
hexane
- - - - - - - - -
• Two-state model of
solvated electrons2,3
1N.
current
+++++++++
= 0.074 cm2V-1s-1
(average)
time
f = 30 - 300 cm2V-1s-1
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.
Dynamics of Quasi-Free Electrons
- > Non-geminate
6
Fluence = 0.3J/cm2
Decay 360 ps
4
recombination mechanism
3
2
1
½ fluence
Decay > 1 ns
4
0
200
400
600
800
Delay time (ps)
Electron trap
binding energy Ea
~ 150 meV
3
e
0
[a. u.]
Ea
n
ne [a.u.]
5
20
Arrhenius fit:
- E /kT
e
a
3.20
3.30
3.40
1000/T [T in K]
3.50
Charge Transport in Sapphire
e
- - - - -
Ec
8.9 eV
h + + +++
EV
• Important optical and electonic material
• High quality samples available
• Model ionic material with polaronic effects
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
Electron Scattering Rate and Mobility
in Sapphire at Room Temperature
Drude Model fit:
Scattering rate:
Mobility:
γ0 = ( 95 fs )-1
μe=e/(m*γ0)= 610 cm2/V-s (m* ≈ 0.27 m0)
Relation between conductivity
and dielectric function
P
J
t
J  iP
  i  i (e  1) / 4
Electron Scattering Rate and Mobility
in Sapphire at Room Temperature
Drude Model fit:
Scattering rate:
Mobility:
γ0 = ( 95 fs )-1
μe=e/(m*γ0)= 610 cm2/V-s (m* ≈ 0.27 m0)
Temperature Dependence of Scattering
Rate in High Purity Sapphire
Scattering Rate (THz)
20
μe= 610 cm2/V-s
15
10
μe= 30,000 cm2/V-s
5
0
0
100
200
Temperature (K)
300
Scattering Mechanism of Electrons in
Sapphire
• Acoustic phonon scattering
• Optical phonon scattering (polaron theory)
• Impurity scattering
~
T 3/ 2
~
e

 LO
kT
g 0 (T )  g acoustic(T )  g optical (T )  g impurity
A Closer Look at the Theory
Temp.
dependence
gacoustic
T3/2
a
Known
parameters
Unknown
parameters
ed : deformation
cii: elastic constant
potential
m*: effective mass
LO: optical phonon
gopticalb
exp(-E/kT)
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)
Temperature Dependence of Scattering
Rate in High Purity Sapphire
Scattering Rate (THz)
20
m* = 0.3 m0
edef = 19 eV
15
LO-phonon
~e

 LO
kT
10
Acoustic phonon
3/ 2
scattering ~ T
5
0
0
100
200
Temperature (K)
300
Impurity Scattering in Sapphire
g 0 (T )  g acoustic(T )  g optical (T )  g impurity
Scattering Rate (THz)
20
15
10
5
Ionic impurities
High purity
0
0
100
200
Temperature (K)
300
Interpretations Based on Various
Polaron Models
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
Numerical simulations
• Electron band mass4: 0.3 - 0.4 m0
• Deformation potential5: 19 - 20 eV
1.
2.
3.
4.
5.
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).
Fluence Dependence of Carrier
Lifetime in n-Hexane
6
Fluence = 0.3J/cm2
Decay 360 ps
ne [a.u.]
5
4
3
½ fluence
Decay > 1 ns
2
1
0
0
200
400
600
Delay time (ps)
800
 Non-geminate recombination
Fluence Dependence of Carrier
Lifetime in Sapphire
Signal (a.u.)
1.0
Fluence (mJ/cm2)
0.1
0.2
0.3
0.4
0.5
0.5
0.0
-20
0
20
Time (ps)
40
60
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
T=294K
=190 ps
0.4
nf (a.u.)
n f (a.u.)
0.8
T = 294 K
6
 = 22 ps
4
2
0.0
0
0
60
120
Delay (ps)
180
0
30
60
delay (ps)
90
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