Band-edge divergence and Fermi-edge singularity in an n-type doped T-shaped quantum wire

1
Band-edge divergence and Fermi-edge
singularityin an n-type doped T-shaped quantum
wire
06 07/25 ICPS TuA3o.3 Tue 1730 Poster

• T. Ihara1, M.Yoshita1, H. Akiyama1, L. N.
  Pfeiffer2 and K.W. West2
• 1Institute for Solid State Physics, University of
  Tokyo and CREST, JST, Chiba 2778581, Japan
• 2Bell Laboratories, Lucent Technologies, Murray
  Hill, NJ 07974, USA

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Introduction
Inverse-square-root divergence Density of state
(DOS)
Interesting phenomena appear. Large exciton
binding energy. Strong absorption of exciton
groundstate. High speed optical modulation
device. High performance laser device.
3
Researches on 1D doped quantum wires
Experiments
91 J. M. Calleja et al. (PL PLE)93 M. Fritze
et al. (PL)01 D. Y. Oberli et al. (PL PLE)
Experimental investigationson the 1D FES effect.
Experimental investigationson the 1D BGR effect.
02 S. Sedlmaier et al. (PL)02 H. Akiyama et
al. (PL)
Theories
92 T. Ogawa et al.96 Y. Oreg et al.96 H.V.
Grünberg et al.
Calculations of the critical exponentsof Fermi
edge power-law singularity.
Calculations ofthe Band Gap renormalization
effect.
92 Das Sarma et al.01 M. Stopa et al.
92 J.F. Mueller et al.92 P. Hawrylak et al.
93 F.J. Rodriguez et al.
Calculation of optical spectrawith 1D DOS and
many-body effect.
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Our recent results and motivations
carrier temperature 10KHigh electron density
6x105 cm-1
Higher temperature
Band-edge absorption ?
04 T. Ihara et. al.
Band edge Fermi edge induced by 1D DOS
andFermis golden rule
Low density
Band-edge absorption ? Band gap renormalization
?Metal-Insulator crossover ? Bound states ? 1D
screening ?
Lower temperature
Fermi edge singularity ?
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Sample structure of n-type doped T-wire
ltfabricationgt MBE with cleaved edge overgrowth
method ltsize of wiregt 14 x 6nm x
4mm(single) ltdopinggt ?Si modulation doping ?FET
gate structure ?tunable electron
density ltmeasurementgt Temperature-elevated
micro-PL spectra resonant PLE spectra
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Results PL and PLE spectra at various
temperature
T50K (kBT/Ef 1) non-degenerate 1DEG
high
A sharp absorptionpeak (BE) appears.
Temperature
T10K (kBT/Ef 0.2) degenerate 1DEG
low
Fermi-edge absorption onset (FE) appears.
Sharp absorption peak at 50K
- Same energy with PL peak. - Good agreements
with calculations.- Characteristic of 1D
electron systems
Band-edge absorption peak induced by 1D DOS
divergence !!
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Results PL and PLE spectra at various electron
density
ne6x105cm-1 3x105cm-1 degenerate 1DEG
(kBT/Ef lt 0.5)
high
-Fermi edge absorption onset-Band edge
emission-Band gap renormalization
Electron density
ne3x105cm-1 1.5x105cm-1 non-degenerate
1DEG (kBT/Ef gt 0.5)
Sharp band-edge absorption
low
ne lt 1.5x105cm-1
Discrete peaks of bound states
Sharp band-edge absorption appears at ne
1.5x105cm-1 3x105cm-1 Discrete symmetrical
peaks appear only at low densities (ne lt
1.5x105cm-1 )
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Results PL and PLE peak energy plot with Ef and
ne plot
Band gap renormalization ? Eb13meV (for
neutral exciton)
0cm-1 2x105cm-1 6x105cm-1
0meV(1.56850.013) -15meV(1.5665) -17meV (1.5645)

Discrete peak of bound states
-Exciton peak disappears ne lt 1.5x105cm-1
Problem
Sharp asymmetrical absorption peak (?) at the
lowest energy (1.5665eV) ? almost 2 meV below
the neutral excitons
Band-edge absorption ? Bound states ? Many-body
objects ? or Mixture of them ?
Our assignment
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Discussion What is the asymmetrical absorption
peak (?)?
Asymmetrical absorption peak (?) at the lowest
energy ? almost 2 meV below the neutral excitons
The asymmetrical peak structure is observed even
at high temperature (50K).

Band edge divergence
Bound states with continuum
?
Many-body object (FES)
Sharp asymmetrical peak at Vg0.2V seems to
originate from Band-edge divergence.
? 1D bound states disappear at such low density
(1.5x105 cm-1) !?
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Discussion Difference between 1D and 2D systems.
Asymmetrical absorption peak (?) at the lowest
energy ? almost 1.5 meV below the neutral
excitons
In the case of 2D electron systems
The asymmetrical peak structure is not observed
at high temperature (50K).
Band edge divergence
Bound states with continuum
Many-body object (FES)

Sharp asymmetrical peak at Vg0.4V seems to
originate from many-body effect.
? The origin of the lowest energy peak (?) is
different in 1D and 2D systems !?
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Summary
Low-temperature PL and PLE spectra are studied in
an n-type modulation-doped T-shaped single
quantum wire with a gate to tune electron
densities. With non-degenerate 1D electron gas,
band-edge absorption exhibits a sharp
band-edge-divergence of 1D density of
states. When the dense 1D electron gas is
degenerate at a low temperature, we observe a
band-edge emission peak and a Fermi-edge
absorption onset.
Problems (Further investigation )
- Bound state and/or Band edge - PL and PLE
measurement at lower temperature (1K) - 1D / 2D
electron system with large hole effective mass
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? In the case of 2D electron systems
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? Estimation of Carrier Temperature
temperature
PL (I)
PLE
with T10K
with T5K
with T15K
Good agreements between PLE and PLexpß(??) at
T10K