Physics 306 (Basic Astronomy) Fall 2006 Instructor: Dr. Alexey Belyanin
A. WojcikTAMU X. Wang, D.M. Mittleman, and J. KonoRice S.A. CrookerNHMFL, Los Alamos Alexey Belyanin...
-
date post
18-Dec-2015 -
Category
Documents
-
view
214 -
download
0
Transcript of A. WojcikTAMU X. Wang, D.M. Mittleman, and J. KonoRice S.A. CrookerNHMFL, Los Alamos Alexey Belyanin...
A. Wojcik TAMUX. Wang, D.M. Mittleman, and J. Kono RiceS.A. Crooker NHMFL, Los Alamos
Alexey Belyanin
Texas A&M University
Terahertz studies of collective excitations and microscopic physics in semiconductor
magneto-plasmas
NSF CAREERNSF OISE
N-doped InSb: a classic narrow-gap semiconductor
~ 0.2 eV
~ 0.8 eV
McCombe & Wagner 1975
Strong non-parabolicity;Non-equidistant cyclotron transitions
Small band gapSmall electron mass ~ 0.014 m0
Palik & Furdyna 1970
Many frequency scales in doped semiconductors fall intothe THz spectral range
1 THz = 4.1 meV
• Plasma frequency
• Fermi energy
• Electron scattering rates
• Cyclotron frequency in the magnetic field of ~ 1 Tesla
• Intra-donor transition frequencies
• Phonon frequencies
• Rich information can be extracted from THz spectroscopic studies
• Exotic conditions for atoms and plasma in superstrong magnetic fields
• Potential for optoelectronic devices utilizing THz coherence
THz time-domain spectroscopy
B
TransmitterReceiver
CPA laser1 KHz, 800 nm
CPA laser1 KHz, 800 nm
Current Amplifier
Lock_in amplifier
ZnTe1/4
WC
Delay stage
ZnTe
Sample: n-doped InSb crystalSample #1: density = 2.1E14 cm-3 Sample #2: density = 3.5E14 cm-3Sample #3 density = 6.1E14 cm-3
T = 1.6-300 Kf = 0.1-2.5THzB = 0-10 T
Incident and transmitted THz pulses
15
10
5
0
-5
x10-3
-30 -20 -10 0 10 20 30
1.375 Tesla
main peak1st multiple refleciton (MR) peak (sample)
2nd MR peak (sample)
1st MR peak from inner window
1st MR from outer window
The transmittance contour map of sample # 1
Magnetic field, Tesla
Fre
qu
ency
, T
Hz
• Plasma edge• Cyclotron resonance• Intra-donor transition lines at low T and high B• Interference features
T = 1.6 K T = 40 K
0.4
0.2
0.0210
1.5 Te
0.4
0.2
0.0
1 Td
0.4
0.2
0.0
0.25 Tb
0.4
0.2
0.0
0 T
a
0.4
0.2
0.0
Tra
nsm
ittan
ce
0.5 Tc
Experiment Theory
210
1.5 Tj
1 Ti
0.5 Th
0.25 Tg
0 T
f
Frequency (THz)
Transmittance at 40 K: only free-carrier effects expected
Free-carrier effects: interference of normal magnetoplasmon modes
“Cold” plasma approximation: ,,|| FTVk
FMS
n2
impuritiesphononsii
nhBh
ph
eBe
pee
)()(
222
...)()(
222
hBh
ph
eBe
peo iin
CRI CRA
BEi
~ 16
CRACRI
he
hehpe m
Ne
,
,2
2,
4 cm
Be
hehBe
,,
||
BepeBeoe 22,0 4
2
1
0.4
0.2
0.0210
1.5 Te
0.4
0.2
0.0
1 Td
0.4
0.2
0.0
0.25 Tb
0.4
0.2
0.0
0 T
a
0.4
0.2
0.0
Tra
nsm
ittan
ce
0.5 Tc
Experiment Theory
210
1.5 Tj
1 Ti
0.5 Th
0.25 Tg
0 T
f
Frequency (THz)
Transmittance at 40 K: only free-carrier effects expected
0.5 1 1.5 2 2.5
0.1
0.2
0.3
0.4
0.5 1 1.5 2 2.5
0.1
0.2
0.3
0.4
0.5 1 1.5 2 2.5
0.1
0.2
0.3
0.4
0.5 1 1.5 2 2.5
0.05
0.1
0.15
0.2
CRI
CRA
a
dc
b
experiment
theory
Interference structure is very sensitive to the cyclotron transition energy and the density of free electrons
Yields information on the electron cyclotron mass, band non-parabolicity, compensation ratio, and binding energy on donors (Tellurium) as a function of magnetic field
2/1
*2||
22
||2
1
22
1
4
Bg
m
knE
EE B
eBeg
gn
]2/exp[~ TkENN Bbindne
3/13/12*
2
~)(
~ Bra
eE
BBohrstbind
eB
crB
2 A
ema
e
stBohr 600~~
2
2*
a
dc
bexperiment
theory
Temperature map at B = 0.9 T
0.20
0.15
0.10
0.05
0.00
Tra
nsm
ittan
ce
250200150100500
Temperature (K)
e
experiment
-0.2
-0.1
0.0
0.1
0.2
Tra
nsm
itted
Fie
ld
250200150100500
Temperature (K)
b
ordinary extraordinary interference
100
80
60
40
20
0
Imag
inar
y n e
, o
250200150100500
Temperature (K)
d
ne
no
400
300
200
100
0
Rea
l ne,
o
250200150100500
Temperature (K)
c
ne
no
0.20
0.15
0.10
0.05
0.00
Tra
nsm
ittan
ce
250200150100500
Temperature (K)
f
theory
5x1014
4
3
2
1
0
n i (
cm-3
)
20016012080
Temperature (K)
a
doping density
Position of the peak is very sensitive to thermal band gap EgT :
]2/exp[~ 2/3 TkETn BgTi
EgT = 0.215 eV
Electron scattering rate
0.4
0.3
0.2
0.1
0.0
(T
Hz)
3002001000Temperature (K)
(a)
8x105
6
4
2
0
(c
m-2
/Vs)
3002001000
Temperature (K)
(b)
Temperature dependence at B = 0.9 T
Impurity scattering
Polar optical phononsElectron-hole scattering
Scattering mechanisms:
• Ionized and neutral impurities• Acoustic deformation potential• Piezoelectric• Optical deformation potential• Polar optical phonons• intrinsic carriers
Electron-”ion” scattering in a strong magnetic field
http://hyperphysics.phy-astr.gsu.edu
TkEb
e
Tk
eb
b
LbrLbB
BkinsstBst
s
s
DsBDs
~~from~where
,ln~:or,0
22
2
Debye radius pe
FermiTD
VVL
],max[
~
s
BsDBs b
rbLrb ln~: 2Gyroradius:
classical~
quantum
pe
ThermalB
B
Vr
eB
cr
2
)(~from~where~:
223/1
2
23/42 effBe
effststeffeffDsB
bm
b
e
B
mcbBbLbr
Similar to magnetic white dwarfs and neutron stars!
Low-temperature effects: donor absorption lines and field-induced localization
measurements
1.6 K 40 KNn = 2.1x1014 cm-3
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Tra
nsm
ittan
ce (a.
u)
1.00.80.60.40.2
Frequency (THz)
2T
2.5T
3T
4T
5T
6T
7T
8T
8.5T
9T
9.5T
10T
Donor (tellurium) transition lines
McCombe & Wagner 1975
CRA 1s-2p+ transition (000)-(110)
CRI 1s-2p- transition (000)-(0-10)
Cyclotron resonance
Low-temperature effects: field-induced localization
T = 1.6 K, Nn = 2.1x1014 cm-3
Quantum phase transition metal-insulator?
Gradual magnetic freeze-out of carriers?
25.0~*3/1Bohrn aN
B = 0: Nn ~ 6x1013 cm-3
Edwards & Sienko 1978
T1~3/1*2*
cBohrBBohr Bara
Gao et al., APL 2006Shayegan et al. PRB 1988
]2/exp[~ TkENN Bbindne
3/13/12*
2
~)(
~ Bra
eE
BBohrbind
Mani et al., PRB 1989,1991
Freeze-out picture:
3/1]/1ln[~ln BNexx
Low-temperature effects: field-induced localization
T = 1.6 K, Nn = 2.1x1014 cm-3
Not compatible with a gradual magnetic freeze-out?
Trying scaling behavior of dielectric constant … scBB
Efros & Shklovskii 1976 etc.
“Releasing” electrons at B ~ Bc
• Coherent time-domain THz spectroscopy provides quantitative
information on the band structure, electron scattering processes,
and collective excitations
• Intriguing low-temperature behavior of the dielectric response;
nature of the magnetic field-induced localization is still unclear
• Also for future studies: dispersion , deviation from ideal
plasma, kinetic effects near the cyclotron resonance
Conclusions
)(k