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’07 5/8 QTuL4 @ QELS
Density tuning of one-dimensional electron gas
in a doped T-shaped quantum wire
( studied by photoluminescence-excitation spectra )
Toshiyuki Ihara, Masahiro Yoshita, Hidefumi Akiyama
Loren N. Pfeiffer, Ken W. West
Institute for Solid State Physics, University of Tokyo, and CREST, JST, Japan
Bell Laboratories, Lucent Technologies, 600 Mountain Avenue, Murray Hill, New Jersey 07974
Outline
Ⅰ
Ⅱ
Ⅲ
Ⅳ
Introduction / Sample / Optical setup
Results for high-density 1D electron gas
Results for electron-density dependences
Summary
Introduction : Low-dimensional electron systems in semiconductor
I    Ek    f kC 1  f kV 
k
A    Ek   1  f kC  f kV
k
1986 Asada et. al., IEEE J. Quantum Electron.
Interests in Fundamental physics and Applications in Low-dimensional system
Sharp density of states (DOS)
Quantum wire Laser diode
M. Okano et al., App. Phys. Lett. 90, 091108 (2007).
Quantum (Fermi / Bose) statistics
S. Liu et al., Jpn. J. Appl. Phys. 46, L330 (2007).
Many-body effect (Exciton, Trion, FES, BGR)
Early works of experiments on Low-dimentional electron systems
2D electron system
’87 M. S. Skolnick, PRL
Fermi edge singularity (FES)
’93 K. Kheng, PRL
Trions (Charged excitons)
’99 V. Huard, PRL
evolution from trions to FES
’00 R. Kaur, PSS(b) [1]
’02 T. Ogawa, Nonlinear Opt.
’91 J. M. Calleja, SSC
1D FES effect
’01 D. Y. Oberli, Physica E
’02 H. Akiyama, SSC
1D BGR effect
calculations (FES theory)
[1]
Electron density
low
FES
1D electron system
high
Excitons (X)
Experimental Difficulties in
sample growth
optical measurement
Trions (X-)
Small number of
experimental works
Band-to-Band
recombination
 Density-tuning of 2DEG by gate
 Absorption measurements
 Interesting physics
< Targets of our investigation >
 High-quality single quantum wire
 Density-tuning of 1DEG by gate
 Absorption measurements
T-wire fabricated by Cleaved edge overgrowth method
Epitaxy was done by Dr. L. N. Pfeiffer in Lucent-Bell lab in U.S.
①
②
③
④
[1]
＜wire size＞
14 x 6nm x 4mm (single)
＜doping [2]＞
①Si modulation doping
②gate electrode
→tunable density
[1] M. Yoshita, H. Akiyama, L. N. Pfeiffer, and K. W. West, Jpn. J. Appl. Phys. 40, L252 (2001).
[2] H. Akiyama, L. N. Pfeiffer, A. Pinczuk, K. W. West, and M. Yoshita, Solid State Commun. 122, 169 (2002).
Optical setup
PL (photoluminescence) - emission
PLE (PL-excitation)
- absorption
Point 1 keep excitation power stable
Point 2 set excitation and detection
perpendicular to each other
Point 3 set the sample angle tilted and
cut laser scattering by iris
Point 4 set polarization of excitation and
detection perpendicular to each other
We succeeded
PLE measurement on a ground state of a single T-wire
Results for high-density 1D electron gas
Exc.
5K
Pex = 40mW
Small hole density
We observed PL peak at Band edge and PLE onset at Fermi edge
Estimation of carrier temperature from PL/PLE ratio
  
I

 exp  
A
 k BT 
Sawicki et al., Phys. Rev. A
54, 4837 (1996).
Chatterjee et al., Phys. Rev. Lett. 92,
067402 (2004).
We observed PL peak at Band edge and PLE onset at Fermi edge
Estimated temperature :
9.8±0.5K
（kBT ～ 1meV）
Estimation of electron density by free-particle model calculation
I    Ek    f kC 1  f kV 
k
A    Ek   1  f kC  f kV
k
Asada et. al., IEEE J.
Quantum Electron. (1986)
me  0.067m0
mh  0.105m0
We observed PL peak at Band edge and PLE onset at Fermi edge
Pronounced FES effect was NOT observed
Estimated temperature :
Estimated density :
9.8±0.5K
6x105 cm-1
（kBT ～ 1meV）
（Ef ～ 5meV）
Ef/kBT ～５
Temperature dependence of ＰＬ and ＰＬＥ at 0.7V
T=5K
(Ef/kBT ～ ５)
high
T=50K
temperature
PLE onset
at Fermi edge (FE)
(Ef/kBT ～ 1)
low
sharp PLE peak
at Band edge (BE)
Good agreement with calculations.
Characteristic of 1D systems.
We observed
Signature of 1D DOS singularity
at Band-edge absorption peak
Gate-voltage dependences at 5K
Estimated density :
6x105 cm-1
（Ef ～ 5meV）
Gate voltage
high
low
Non-doped limit at Zero density （Ef ～ 0meV）
Gate-voltage dependences at 5K (0.7 - 0.5 V)
 Red shifting PLE onset at Fermi edge
Red shift of Fermi edge
Decrease of Electron density
Gate-voltage dependences at 5K (0.4 - 0.35 V)
Characteristic double peak structure
We observed
Characteristic double peak PLE structure
with Band edge and Fermi edge
Gate-voltage dependences at 5K (0.3 – 0 V)
 Crossover to excitonic regime (Vg < 0.2V)
from band-to-band recombination regime (Vg > 0.3V)
 Analogous to the results for 2D electron systems
[’99 V. Huard, PRL,
'00 R. Kaur, PSS(b), '02 T. Ogawa, Nonlinear Opt. ]
Gate-voltage dependences at 5K (0.3 – 0 V)
 Crossover to excitonic regime (Vg < 0.2V)
from band-to-band recombination regime (Vg > 0.3V)
 Analogous to the results for 2D electron systems
[’99 V. Huard, PRL,
'00 R. Kaur, PSS(b), '02 T. Ogawa, Nonlinear Opt. ]
 Splitting of X should be due to
ML fluctuations of stem well
PLE at 0V is consistent with that of non-doped quantum wire [ Itoh et al., APL 83, 2043 (2003). ]
0V corresponds to Limit of non dope (zero density)
Comparison whole experimental results with calculations
Vg = 0.7 - 0.4 V
ne=6x105cm-1 ～ 3x105cm-1
Electron density
high
low
Degenerated 1D electron gas (Ef/kBT > 2)
Vg = 0.4 - 0.35 V
ne=3x105cm-1 ～ 2.5x105cm-1
Non-degenerated 1D electron gas (Ef/kBT < 2)
Double peak induced by 1D DOS
Vg < 0.2 V
ne < 1.5x105cm-1
Limit of non dope (zero density)
Signature of 1D DOS singularity also appears
in the characteristic double peak structure at 0.35-0.4V !!
Differences between 2D and 1D systems
2D electron system
1D electron system
’87 M. S. Skolnick, PRL
strong FES
’93 K. Kheng, PRL
charged exciton (Trions)
’99 V. Huard, PRL
evolution from trions to FES
Characteristic double peak structure with
band edge and Fermi edge
’00 R. Kaur, PSS(b) [1]
’01 G. Yusa, PRL
Trions with Fractional QHE
[1]
Electron density
low
FES
high
Excitons (X)
Trions (X-)
Band-to-Band
recombination
 Density-tuning of 2DEG by gate
 PL and PLE measurements
 Interesting physics
 Signature of 1D DOS singularity
Unique feature of High-quality
1D electron systems
Summary
Variable-density 1D electron gas was realized
in a T-shaped quantum wire with a gate structure.
PLE measurements on a 1D ground states
were achieved on an isolated single quantum wire.
We observed a signature of 1D DOS
represented by an absorption peak at the band edge,
which indicates a high uniformity of our sample.
The tunable density range covers
from 0 to 6x105cm-1
Future investigation
 Remove ML fluctuations in the stem well (g ～0.2meV)
 Measurements at much lower temperature (T＜5K)
 Measurements under magnetic field (B～10T)
PLE measurement on ground states absorption peak
The amount of laser scattering is smaller than that of PL
 We can set the PLE window for the ground state emission !!
M. S. Skolnick et al., Phys. Rev. Lett. 58, 2130 (1987).
 PL of doped InGaAs quantum wells at various Temperature
 Observation of
strong FES effects
K. Kheng et al., Phys. Rev. Lett. 71, 1752 (1993).
 Absorption of dilute-doped CdTe quantum wells
under magnetic field
 Observation of
negatively charged excitons
V. Huard et al., Phys. Rev. Lett. 84, 187 (1999).
 Absorption of doped CdTe wells at various density
under magnetic field
 Observation of
crossover from X- to FES
R. Kaur et al., Phys. Status Solidi B 178, 465 (2000).
 PLE spectra on doped GaAs quantum wells with a gate
 Density-tuning of 2DEG by gate
 PLE measurements
J. M. Calleja et al., Solid State Commun. 79, 911 (1991).
 PL and PLE spectra on doped GaAs quantum wires
 Investigation of
1D FES effects
D. Y. Oberli et al., Physica E 11, 224 (2001).
 PL and PLE spectra on doped V-groove quantum wires
 FES effect can be strong due to extrinsic origin
such as higher subband, hole localization.
H. Akiyama et al., Solid State Commun. 122, 169 (2002).
 PL spectra on single doped T-wire at various density
 Investigation of
1D BGR effects
M. Yoshita et al., Jpn. J. Appl. Phys. 40, L252 (2001).
 Succeeded to improve the uniformity of
the second QW (Arm well)
S. Chatterjee et al., Phys. Rev. Lett. 92, 067402 (2004).
 time-resolved PL spectra
in conjunction with absorption spectra




multi (20) quantum wells
non-doped system
pulse excitation
non-resonant excitation
(13.6meV higher energy)
H. Itoh et al., App. Phys. Lett. 83, 2043 (2003).
X
 0V is consistent with the results for non-doped quantum wire
Abstract figure 2 : results for the 1D wire
 PL and PLE spectra for doped T-wire at 0.7V and 0V
Abstract figure 3 : results for the 2D Arm well
 PL and PLE spectra for Arm well at 0.8V and 0.2V
Characterization ～ PL and PLE spectra overview
 A clear PLE peak of wire ground state
stokes shift ＜0.2meV
We assigned the peaks by PL and PLE measurement at various position
Free particle model calculation (C-V expression)
I    Ek    f 1  f
C
k
k
V
k
A    Ek   1  f kC  f kV
k




I   1D  '  f C 1  f V  B   'd '
0



A   1D  '  1  f C f V  B   'd '
0
 1D DOS, Effective mass approximation, k-conservation
1D    1 / 
 2 kC
C 
2me
2
   C  V
 2 kV
V  
2 mh
2
kC  kV
 Fermi distribution functions, Carrier densities
fC  C   1  exp C  mC  / kBT 
1
me  0.067m0
mh  0.105m0
fV V   1  expV  mV  / kBT 
1

ni   1D   f i  d
0
 Broadening functions
i  C,V 
    '2 
B    '  exp 

2
g


Free particle model calculation (e-h expression)
I    Ek    f 1  f
C
k
k
V
k
A    Ek   1  f kC  f kV
k


I   1D  '  f e f h  B   'd '
0




A   1D  '  1  f e 1  f h  B   'd '
0
 1D DOS, Effective mass approximation, k-conservation
1D    1 / 
2
 2 ke
e 
2me
  e  h
2
 2kh
h 
2mh
ke  k h
Fermi distribution functions, Carrier densities
f e  e   1  exp e  me  / kBT 
1
me  0.067m0
mh  0.105m0
f h  h   1  exp h  mh  / kBT 
1

ni   1D   f i  d
0
 Broadening functions
i  C,V 
    '2 
B    '  exp 

2
g


Processing on T-shaped quantum wire