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One-dimensional band-edge absorption in a doped quantum wire
T. Ihara1, Y. Hayamizu1, M. Yoshita1, H. Akiyama1, L. N. Pfeiffer2, and K. W. West2
1
Institute for Solid State Physics, University of Tokyo and CREST, JST, Chiba 2778581, Japan
2
Bell Laboratories, Lucent Technologies, Murray Hill, NJ 07974, USA
Abstract. Low-temperature photoluminescence-excitation 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 (DOS). When the dense 1D electron gas is degenerate at a
low temperature, we observed a Fermi-edge absorption onset without power-law singularity. In stark contrast to
theoretical predictions (and to non-doped-wire experiments), excitonic (or correlation) effects in the optical spectra are
suppressed by 1D-electron-gas filling.
Optical spectroscopy of 1D electron gas formed in ntype doped semiconductor quantum wires has been a
subject of exciting challenges in the past two decades
[1-11]. Theories have pointed out some interesting
phenomena inherent in 1D electron gas, such as
appearance/disappearance of band-edge singularity
induced by inverse square root 1D-DOS divergence,
and also strong 1D many-body interaction effects [4-7].
Experimentally, observations of strong Fermi-edge
power-law singularity effects [8,9] and 1D band-gap
renormalization effects [10,11] have been reported.
However, no experiment has shown band-edge
singularity induced by 1D-DOS divergence. Thus, a
question of whether the 1D band-edge singularity
appears in optical spectra still remains unanswered.
In order to clarify such fundamental properties by
optical spectroscopy, we need to measure both
emission and absorption spectra at various
temperatures and electron densities. This is because
emission and absorption in doped systems selectively
occur for occupied and unoccupied conduction-band
states, respectively. However, it is difficult to measure
absorption spectra of quantum wires because of its
small volume. Thus, there have been no systematic
experimental studies of temperature-dependent
absorption spectra of 1D electron systems at various
electron densities. To investigate this unexplored
subject, we developed a measurement system of
resonant photoluminescence-excitation (PLE) spectra,
which allows us to get clear lineshapes of absorption
spectra of a single quantum wire.
This letter reports the first observation of band-edge
absorption singularities induced by 1D DOS
divergence probed by the low-temperature PLE
measurements on an n-type doped single quantum wire
with a gate to tune electron densities. The sharp bandedge absorption peaks appear in the PLE spectra when
the 1D electron gas is not degenerate at high
temperature, or at low electron density. In the presence
of dense electron gas at low temperature (5K), we
observe an absorption onset at the Fermi edge of
degenerate 1D electron gas. The absorption lineshapes
agree very well with free-pariticle calculations, but
surprisingly not with more advanced calculations
including many-body Coulomb interactions.
The sample structure of an n-type doped GaAs
quantum wire is illustrated in Fig. 1. A single T-shaped
quantum wire was formed at the cross-sectional area of
14nm-thick Al0.07Ga0.93As/Al0.33Ga0.67As quantum well
(stem well) and 6 nm-thick GaAs/Al0.45Ga0.55As
quantum well (arm well). Delta doping of Si at a
distance of 100 nm from the stem well induced 2D
electron gas with a density of 1 x 10 11 cm-2 in the stem
well. By applying DC gate voltage (V g) to a gate layer
on the top of the arm well relative to 2D electron gas in
the stem well, we tuned electron concentrations in the
1D wire. A more detailed description of the sample
preparation is given in ref. 10.
In our micro-PL and PLE measurements, excitation
light from a continuous-wave Titanium-sapphire laser
with polarization parallel to the [001] direction
(perpendicular to the wire axis) was focused into a 1m spot by a 0.5 numerical aperture objective lens on
the top (110) surface of the sample. The PL emission in
the [001] direction was detected via a 0.5 numerical
aperture objective lens and a polarizer set in the [1-10]polarization direction to cut intense laser scattering.
Normalized PLE spectra at various temperatures in
the presence of dense 1D electron gas are shown by
solid curves in Fig. 2 (a). The gate voltage was fixed to
0.7V, which corresponds to the electron density of
FIG. 1 Schematic view of n-type doped T-shaped
quantum wire sample.
FIG. 2 Normalized experimental (a) and theoretical
(b) spectra of PL (dotted line) and PLE (solid line) for
1D wire at various temperatures. FE and BE
corresponds to Femi edge and band edge, respectively.
about 6 x 105 cm –1 in the quantum wire. At low
temperature (5K), we observed a single absorption
onset at 1.575eV with a long low-energy tail. We
assigned this onset as the Fermi edge (FE), which
separates the occupied and unoccupied state in the
conduction band. A large absorption by the arm well
showed its low-energy tail at around 1.578eV. As the
temperature was increased, the FE onset was smeared
and the low-energy tail increased its intensity. At 30K,
another absorption onset was formed at 1.565eV. At
higher temperature, this onset increased its intensity
and formed a sharp peak structure at 50K. We assigned
this peak to the band-edge (BE) singularity induced by
the inverse square root 1D-DOS divergence.
Dotted curves in Fig. 2 (a) indicate PL spectra. At
5K, we observed an asymmetrical broad PL peak at
1.565eV. We assigned this PL peak to the band-edge
emission. We observed a large energy gap of 10meV
between PL peak and PLE onset at FE. As the
temperature was increased, the PL peak shifted to
lower energy without any remarkable change in its
lineshape. This red shift with increasing temperature
also appears in bulk GaAs [3]. At 50K, we found that
the PL and PLE peak appeared exactly at the same
energy of band edge denoted by BE.
We calculated optical spectra with a free-particle
model. This model includes the 1D joint DOS with the
energy dependence of 1/ E , Fermi distribution
functions for electrons and holes, broadening function
of Gaussian lineshape, but neglects many-body
Coulomb interactions. Figure 2 (b) shows normalized
emission (dotted curves) and absorption (solid curves)
spectra calculated for various temperatures for
electrons and holes, Te (= Th), with parameters of
broadening () of 1.0 meV, the effective mass for
electrons of 0.067 m0 and that for holes of 0.105 m0,
where m0 is electron mass in vacuum, and the electron
density (ne) of 6 x 105 cm–1. The band gap energies at
various temperature, Eg(T), were estimated roughly by
those for bulk GaAs [3]. The absorption spectrum at
8K, shown as bottom solid line in Fig. 2 (b), exhibits an
onset at the energy of Eg + 10meV, which corresponds
to the Fermi edge. The low-energy tail of this onset
corresponds to the slope of Fermi distribution function
at 8K. The emission spectrum exhibits a peak at the
energy of Eg, which corresponds to the band edge. At
higher temperature, the Fermi-edge absorption onset
disappears while another low-energy absorption onset
of the band edge appears at the same energy of
emission peak (Eg). At 40K or 50K, the absorption
spectra exhibit a sharp asymmetrical peak at the band
edge. This peak originates from the 1D-DOS
divergence with broadening of 1.0 meV. We found that
the experimental results agree well with these freeparticle-model calculations. The sharp absorption peak
at 50K clearly demonstrates the 1D band-edge
singularity induced by 1D-DOS divergence.
We also studied electron density dependence of PLE
spectra at low temperature (5K), using the same sample
of a doped quantum wire. The solid curves in Fig. 3 (a)
indicate the normalized PLE spectra at various Vg. The
bottom line at Vg = 0V corresponds to the zero-density.
The top line at Vg = 0.7V corresponds to the highdensity, which is the same as the bottom line of Fig. 2
(a). As we have already mentioned, the single
absorption onset (FE) at Vg = 0.7V corresponds to the
Fermi edge. As the density was decreased, the FE onset
shifted to lower energy. The photon energies of the FE
onset are plotted by solid inverse triangles in Fig. 4 (a).
At Vg = 0.4V, band-edge absorption onset appeared at
low-energy side (1.566eV). At Vg = 0.35V, this lowenergy onset increased its intensity, and a characteristic
double peak structure was formed. As the density was
further decreased, the Fermi edge peak merge into the
tail of the band-edge peak, and formed a single
asymmetrical absorption peak structure at V g = 0.2V.
This asymmetrical peak became a symmetrical peak
(X-) at Vg = 0.15V, which is assigned to trions (a bound
state of two electrons and a hole). This X- peak lost its
intensity as the density approached to zero. Instead,
another asymmetrical peak appeared at higher energy
(1.569eV), which became a sharp peak (X) at 1.569eV
at Vg = 0V. We assigned this X peak to neutral excitons
(a bound state of an electron and a hole). The fullwidth-of-half-maximum of X peak was 0.9 meV. The
splitting of the X peak is probably due to monolayer
thickness fluctuations in the stem well. In Fig. 4 (a), we
plot peak energies of X- (solid triangles) and X (solid
circles).
Dotted curves in Fig. 3 (a) indicate PL spectra,
which are almost same as those we reported in detail in
a previous paper [10]. At Vg from 0.7V to 0.2V, we
Fig. 4 (a) The position of peaks and (b) estimated
electron density and corresponding Fermi energy are
plotted as a function of gate voltage.
FIG. 3 ormalized experimental (a) and theoretical
(b) spectra of photoluminescence (PL: dotted lines)
and PL excitation (PLE: solid lines) for 1D quantum
wire at various electron densities. X is assigned to
excitons and X- is assigned to trions. BE and FE
corresponds to the band edge and the Fermi edge,
respectively.
observed broad PL peak which shifts to higher energy
with decreasing electron density, which represents the
band-gap-renormalization shift. The energies of the PL
peak at BE are plotted by solid squares in Fig. 4 (a). At
0-0.15V, PL spectra also show sharp peaks of trions (X ) and excitons (X). The Stokes shift between the PL
and PLE peaks of excitons was less than 0.2meV.
Figure 3 (b) shows calculated normalized emission
(dotted curves) and absorption (solid curves) spectra
with the free-particle model assuming various electron
densities (ne) and parameters of Te (=Th) = 8K,  = 0.4
meV. The assumed electron density (ne) in the
calculations and corresponding Fermi energy,
 2  2 ne 2
Ef 
are plotted as a function of Vg in Fig. 4
8me
(b) as blank squares and blank circles, respectively.
The calculated absorption spectra for ne = 1 – 5.9 x
105 cm-1 show good agreements with the experimental
PLE spectra at Vg > 0.2V. In particular, the
characteristic double peak structures of the band-edge
and the Fermi-edge absorptions at Vg = 0.35-0.4 V are
almost completely reproduced by the calculations. The
sharp band-edge absorption originates from 1D-DOS
divergence, and it appears in the PLE spectra when the
1D electron gas is not degenerate at low density. We
have already demonstrated, in Fig. 2 (a), the
appearance of band-edge divergence in the PLE spectra
at high temperature (50K). These results confirm our
insistence that the divergence of 1D DOS appears in
the PLE spectra in the presence of non-degenerated
electron gas at low density, or at high temperature.
On the contrary, the sharp symmetrical absorption
peaks of trions and excitons observed at V g = 0 – 0.15V
are out of explanation of this free-particle model. In
other words, we need to take into account Coulomb
interactions between conduction electrons and a
valence hole to explain these bound complexes. In 1D
systems, this excitonic effect becomes strong due to its
large quantum confinement [someya]. However, it has
not been fully understood how the 1D excitonic effect
is weakened by screening or phase-space-filling effects
caused by the 1D electron gas. Our experiments
provided a quantitative value of the electron density
where the excitonic effects have to be taken into
account. The value was ne < 1 x 105 cm-1, which
corresponds to the Fermi energy of Ef < 0.15 meV and
mean distances between carriers of rs < 8aB, where aB
(=12.7 nm) is the Bohr radius of bulk GaAs. Above this
density, the PLE spectra exhibited free-particle
behavior.
Let us now discuss the 1D many body effects that
appear in PL and PLE spectra at high electron densities.
As we have mentioned, the pioneering works have
pointed out interesting many-body effects, such as the
FES effects [4-9] and the BGR effects [10,11]. The
FES theory [4-7] predicts a sharp FES peak, or a
power-law singularity, at low-energy (high-energy)
shoulder of absorption (emission) spectra. This effect
results from multiple scattering processes involving
electrons near the Fermi level. The BGR theory [*]
predicts an energy shift of band-edge emission peak
with increasing the electron density, which results from
the electronic correlation effects. In our experiments, as
shown in Fig. 3 (a), or Fig. 4 (a), the BGR effect was
observed as the red shifts of the band-edge PL peak
(BE) with increasing electron density.
However, the FES effect in the PLE spectra was
surprisingly small. No sharp peak, or no power-law
singularity, was observed at the Fermi edge of the PLE
spectra. We should notice that the inhomogeneous
broadening is small (0.9 meV) and the temperature is
low (5-8 K), which are favorable conditions for strong
FES effects. Even under these conditions, the FES
effect was found to be weak. This indicates that the
strength of FES effects are governed by not only
dimensions and temperatures, but also other factors. As
pointed out by pioneering works [4,5,12], we guess the
carrier localization and the existence of empty higher
subband are necessary for strong FES effects. In this
sense, the free particle behavior without FES effect
could be the essential character inherent to 1D electron
gas formed in the high quality 1D limit quantum wires.
We want to focus here on the carrier localization
effect, which is also one of the interesting topics for 1D
electron systems [*]. Generally speaking, the effect of
localization is strong when the carrier density is small,
because of its weak screening effect. Even in the
presence of dense electron gas, the localization of
valence holes needs to be taken into account. In fact,
our experimental results of PL spectra at high density
(Vg > 0.5V) shows inhomogeneous structures, such as
the appearance of multiple peak structures at higher
energy tail of BE, as shown in our previous paper [10].
We guess this indicates that a part of valence holes are
localized to the inhomogeneous potential fluctuations.
This is consistent to the theoretical prediction that hole
localization causes the strong FES effects in PL spectra
[4,5]. On the contrary, the lineshape of PLE structures
at high density, such as band-edge and Fermi-edge
peaks, have no dependence on the position of the wire.
These facts indicate that a small amount of hole
localization modifies the PL, but not PLE.
The present work is the first convincing observation
of the 1D DOS divergence, and also provides new
findings for optical response of 1D electron gas. We
want to notice that these findings were provided as a
result of following experimental progresses. First of all,
the high-quality sample fabrication method [13] cannot
be omitted. Without this, the sharp 1D DOS peak, and
also sharp excitonic peaks, would be broadened. The
development of resonant PLE measurement system is
also important. This enables us to observe the lineshape
of band-edge absorption peaks of a single quantum
wire. In addition, n-type doping is one of the important
factors for the observation of 1D DOS. In the case of
non-doped wire [14,15], the continuum onset exhibited
a step-functional lineshape due to the small
Sommerfeld factor [16,17], even though it’s quality is
as good as our doped samples. Thanks to these
experimental improvements, we confirmed our
progress to the fabrication of ideal 1D electron gas
formed in the semiconductor quantum wire.
In conclusion, we performed low-temperature PLE
measurements on an n-type doped quantum wire and
achieved the first observation of 1D band-edge
absorption singularities. The 1D excitonic effects were
found to be suppressed by the electron gas at the
density of 1 x 105 cm-1, so that the PLE spectra above
this density exhibited free-particle behavior without
many-body modifications. Compared to PL spectra, the
PLE spectra were less modified by the small amount of
localization of valence holes. These new findings
confirm our progress to the fabrications of ideal 1D
electron gas formed in the semiconductor quantum
wire.
This work was partly supported by a Grant-in-Aid
from the Ministry of Education, Culture, Sports,
Science, and Technology, Japan. We wish to thank T.
Ogawa, M. Takagiwa, and K. Bando for valuable
discussions.
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