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

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

Relation between conductivity and dielectric function

t

PJ

PiJ

4/)1( ii

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