One-dimensional band-edge absorption in a on 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 on an n-type modulation-doped Tshaped single quantum wire with a gate to tune electron densities. We find that the With non-degenerate 1D electron gas,
band-edge absorption of 1D electron systems exhibits a sharp band-edge-divergence peak structure of induced by the
singularity of 1D density of states (DOS) divergence. 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 1Delectron-gas filling. We show that these results can be explained by the free-particle-model with inverse square root 1D
DOS and carrier distribution functions.
Optical spectroscopy of 1D electron gas formed in ntype doped semiconductor quantum wires has been a
subject of exciting challenges intense research in the
past two decades [1-11]. Pioneering tTheoreticalies
works have pointed out some interesting kinds of
phenomena inherent in 1D electron gas, such as
appearance/disappearance
of
band-edgebottom
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 one has
achieved the direct observation of 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 study clarify such fundamental properties
the lineshape of DOS in detail by optical spectroscopy,
we need to measure both emission and absorption
spectra at various temperatures and electron densities.
This is because emission and absorption the optical
spectra of in doped systems selectively occur for
occupied and unoccupied conduction-band states,
respectively. exhibit not only DOS but also the effect
of carrier distribution. 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 temperaturedependent absorption spectra of 1D electron systems at
various electron densities. To investigate this
unexplored subject field, we developed a measurement
system of resonant high-resolution photoluminescenceexcitation (PLE) spectra measurement system, which
allows us to get a clear lineshapes of absorption
spectruma 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. Our
interpretations are supported by good agreements
between the experimental results and free-particlemodel calculations with inverse square root 1D DOS
and carrier distribution functions.
The sample structure of an n-type doped GaAs
quantum wire is illustrated in the inset of Fig. 1. A
single T-shaped quantum wire was formed at the crosssectional
area
of
14nm-thick
for
the
Al0.07Ga0.93As/Al0.33Ga0.67As quantum well (stem well)
and 6 nm-thick for the GaAs/Al0.45Ga0.55As quantum
well (arm well). Delta doping of Si at a spacer distance
of 100 nm from the stem well induced resulted in the
formation of 2D electron gas with a density of 1 x 10 11
cm-2 in the stem well. By applying DC gate voltage
(Vg) 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]-
Fig. 1 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.
polarization direction to cut intense laser scattering.
Normalized PLE spectra at various temperatures in
the presence of dense 1D electron gas are shown by as
solid curves in Fig. 1 (a). The gate voltage was fixed to
0.7V, which corresponds to the electron density of
about almost 6 x 105 cm –1 in the quantum wire. At low
temperature (5K), we observed a single absorption
onset (FE) 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
disappeared 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 (BE) at
50K. We assigned this BE peak to the band-edge (BE)
singularity induced by the inverse square root 1D-DOS
divergence.
Dotted curves in Fig.1 (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. Here wWe 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 kind of red shifts 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.
To check the validity of our assignment of FE as
Fermi edge and BE as band edge, wWe calculated
optical spectra with a free-particle - model formulae.
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 any kinds of many-body
Coulomb interactions. Figure 1 (b) shows Nnormalized
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, are shown in Fig. 1 (b).
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. 1 (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 are analogous to
these free-particle-model calculations, which supports
our interpretations of BE as the band edge and FE as
the Fermi edge. 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. 2 (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. 1
(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. 3 (a).
At Vg = 0.4V, band-edge another absorption onset
appeared at low-energy side (1.566eV). At V g = 0.35V,
this low-energy onset increased its intensity, and so
that 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 low-energy
peak, and formed a single asymmetrical absorption
peak structure at Vg = 0.2V.
This asymmetrical peak became a symmetrical peak
(X-) at Vg = 0.15V, which is we 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 sharp 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 full-width-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. 3 (a), we plot peak energies of X- (solid triangles)
and X (solid circles).
Dotted curves in Fig. 2 (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
observed broad PL peak which shifts to higher energy
with decreasing electron density, which represents the
band-gap-renormalization shift. The photon energyies
of the BEPL peak at BE are plotted by solid squares in
Fig. 3 (a). At 0-0.15V, we observed PL spectra also
show sharp PL peaks of trions (X-) and excitons (X).
The Stokes shift between the PL and PLE peaks of
excitons was less than 0.2meV.
Figure 2 (b) shows Here we want to demonstrate the
free-particle-model calculationsed too. Nnormalized
emission (dotted curves) and absorption (solid curves)
spectra calculated for with the free-particle model
assuming various electron densities (ne) and with
parameters of Te (=Th) = 8K,  = 0.4 meV are shown in
Fig. 2 (b). 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. 3
8me
(b) as blank squares and blank circles, respectively.
The calculated emission spectra exhibit almost no
change with ne. Thus, they do not reproduce the change
in the experimental PL data. However, we found good
agreements between the experimental PLE spectra at
Vg > 0.2V and the calculated absorption spectra with
the free-particle model. In particular, the characteristic
double peak structures of the band-edge and the Fermiedge absorptions at Vg = 0.35-0.4 V are almost
completely reproduced by the calculations. The
calculated absorption curve for ne < 1.0 x 105 cm-1
represents the inverse-square-root 1D-DOS shape with
broadening of 0.5 meV. It is remarkable that observed
optical-absorption responses of electron gas with
estimated densities above 1.0 x 105 cm-1 are apparently
the same as those of free electrons except for band-gap
renormalization.
We plotted the electron density (ne) and
 2  2 ne 2
corresponding Fermi energy, E f 
as a
8me
function of Vg in Fig. 3 (b) as blank squares and blank
circles, respectively. The top lines of Fig. 2 (b)
correspond to high-density (5.9 x 105 cm-1), which
exhibit the Fermi-edge absorption onset and the bandedge emission peak. As the density decreases, the
Fermi edge absorption onset shifts to lower energy due
Fig. 2 Normalized 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.
to the decreasing Fermi energy. At ne = 4.2 and 2.9 x
105 cm-1, an absorption onset appears at lower-energy
side, which corresponds to the band edge. At ne = 2.2 x
105 cm-1, a characteristic double peak structure of the
band-edge and the Fermi-edge absorptions appears. At
lower densities, the Fermi-edge absorption merges into
the high-energy tail of band-edge absorption. At ne <
1.0 x 105 cm-1, the solid curve exhibits an asymmetrical
band-edge absorption peak. The lineshape of this peak
represents the inverse square root 1D-DOS with
broadening of 0.5 meV. The emission spectra exhibit
almost no change with decreasing ne.
We found good agreements between the
experimental PLE spectra at Vg > 0.2V and the freeparticle-model calculations for ne = 1 – 5.9 x 105 cm-1.
This indicates that the PLE structures in the presence of
electron gas with density of more than 1.0 x 10 5 cm-1
can be understood by the free-particle model without
any kinds of many-body effects. From this point of
view, the sharp low-energy peaks at Vg = 0.2 – 0.35V
corresponds to the 1D band-edge singularities induced
by 1D-DOS divergence. And the higher-energy peaks,
or onsets, which evolved from FE onset at V g = 0.7V,
corresponds to the Fermi edge. Hence, the double peak
Fig. 3 (a) The position of peaks and (b) estimated
electron density and corresponding Fermi energy are
plotted as a function of gate voltage.
structure at Vg = 0.35V corresponds the coexistence of
band-edge and Fermi-edge absorption peaks.
On the contrary, the free-particle model cannot
explain the sharp symmetrical absorption peaks of
trions and excitons observed at Vg = 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. It is
interesting that these excitonic peaks appear only at
such low electron density. Qualitatively speaking, the
absorption peak of excitons completely disappeared at
ne < 1.0 x 105 cm-1. This small value of the density of
1.0 x 105 cm-1 corresponds to the Fermi energy (Ef) of
0.15meV, and also corresponds to mean distances rs
between carriers of 8aB, where aB (=12.7 nm) is the
Bohr radius of bulk GaAs. Note that it is hard to
determine the density at which the trions disappear
from the PLE spectra, since the trion peak evolves
continuously to the band-to-band structures of BE and
FE at Vg > 0.2V.
Here we want to remark two important findings in
Fig. 2 (a), which are inherent in 1D electron systems.
One is the strong band-edge absorption observed at Vg
= 0.2 - 0.35V. As we have mentioned, this band-edge
absorption peak originates from the inverse square root
divergence of 1D DOS. The other one is the
remarkable decrease of exciton intensities, which is
symbolized by the fact that the exciton peak
disappeared at low electron density (1.0 x 105 cm-1).
This indicates the strong effects of phase-space-filling
and/or screening induced by dilute electron gas in 1D
systems.
As shown above, we demonstrated the first
observation of the band-edge absorption singularities
induced by 1D-DOS divergence. We expect that this
result could not be achieved without the fabrication
technique of high-quality doped quantum wire samples
[13] and the development of high-resolution PLE
method. Thanks to these techniques, we could achieve
the observation of 1D band-edge absorption with less
modification by carrier localization effects induced by
interface roughness of hetero junctions. Note that the
1D-DOS divergence did not appear even in PLE
spectra of high-quality non-doped quantum wires
[14,15]. In the case of non-doped 1D system, the
continuum absorption onset exhibited a step-functional
lineshape due to small Sommerfeld factor [16,17]. In
this sense, n-type doping was one of the important
factors for the observation of 1D DOS.
Finally, we want to comment on the comparisons
with pioneering experiments reported by other groups.
It has been pointed out that strong FES effects appear
in the PL (or PLE) spectra of heavily doped 1D
electron systems [8,9]. This result is in contrast with
our observation of no remarkable many-body
modifications at the Fermi-edge absorption onset. We
speculate that this inconsistency is due to the difference
of sample structures that determine the condition of 1D
electron gas and a valence hole. In fact, some of the
pioneering works of experiments [12] and theories
[4,5] have indicated the necessity of hole localizations,
and also empty higher subbands near the Fermi energy,
for the observation of strong FES effects. Thus, it is not
striking that the pronounced strong FES effect was not
observed in our quantum wire, which contains 1D limit
electron gas, with small carrier localization effects.
メモ
ファイ HF レベル計算や高際計算も試みたが、
フェルミレベルのところが強くモディファイされ
実験にあわない。小川理論では、実際、1 次元で
はパワーローFES は強く表れると期待されている。
しかし、実験はそうなっていない。
温度ではないはず。
構造揺らぎでもないはず。
解らないが、何か本質的な理由があって、フェ
ルミレベルでのクーロンエンハンスメントが消失
して自由粒子的になっているのではないか？
これらのおそらく１D 特有の実験結果が出たの
は試料の高品質が必須。
発光では特に局在は重要。
局在が発光ピーク位置を BE から FE にする理論
実験もそうなっているみたいだ。
エキシトンやトリオンがクエンチ
vs
エキシトンがトリオンに移ってクエンチ
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. We found that the freeparticle-model with inverse square root 1D DOS can
explain the PLE spectra in the presence of dense
electron gas with the density of more than 1 x 10 5 cm-1.
We believe that our observation of 1D DOS, and also
the observation of remarkable decrease of exciton
absorption intensities in the presence of dilute 1D
electron gas, indicates the progress in fabrication of
ideal 1D electron systems formed in doped quantum
wires.
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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