Femtosecond luminescence measurements of the intersubband scattering rate
in Al
x
Ga
1 x
As/GaAs quantum wells under selective excitation
M. Hartig, S. Haacke, and B. Deveaud
Laboratorie d’Optoe ´lectronique Quantique, Institute for Micro and Optoelectronics, E
´
cole Polytechnique Fe ´de ´rale de Lausanne,
CH-1015 Lausanne, Switzerland
L. Rota
Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
Received 6 May 1996
We have investigated the intersubband scattering of electrons in GaAs quantum wells using luminescence
up-conversion with 100-fs resolution. The decay time of the n =2 electron-to-heavy-hole transition ( e ,hh)
2
depends both on the excess energy of the charge carriers and on the excitation density. A Monte Carlo
simulation allows us to reproduce the experimental data with high accuracy. The intrinsic LO-phonon scatter-
ing rate is found to be 2.010
12
s
-1
for 80-meV subband separation. We show the wave-vector dependence
and explain the density and excess energy dependence. S0163-18299652340-4
In quantum wells, LO-phonon emission is the most im-
portant energy relaxation channel for electrons. The prob-
ability of interaction is proportional to 1/| q |
2
q is the wave
vector of the emitted phonon,
1
and to the overlap of the
wave functions of the initial and final electron states.
2
If the
intersubband separation is larger than the LO-phonon en-
ergy, the intersubband scattering is expected to be
subpicosecond.
1
If, on the contrary, the subband separation is
smaller than 36 meV, the scattering time is due to acoustical
phonons and carrier-carrier CC scattering. In this case and
for carrier densities 10
11
cm
-2
the decay rate should be
greatly reduced.
3
Femtosecond dynamics in quantum wells have been in-
vestigated using different techniques: Raman scattering,
pump-probe, and photoluminescence PL up-conversion.
3–5
A coherent picture emerges for the cooling and capture
rates.
6–8
For intersubband scattering, if a consensus now ex-
ists on the theoretical description of phonons,
9,10
the experi-
mental situation is not clear. Different techniques have de-
livered different values: this is true both for the case of an
intersubband spacing smaller than 36 meV Refs. 4, 11, and
12 and when it is larger than 36 meV.
13–16
A resurgence of the interest in this subject has developed
recently due to the demonstrated feasibility of infrared inter-
subband quantum-well lasers.
17
An exact knowledge of the
intersubband scattering processes is fundamental in order to
understand how these lasers work. Our results are obtained
by PL up-conversion, a technique which allows the direct
and sensitive determination of the dynamics of the photoge-
nerated charge carriers in time- and energy-resolved mea-
surements down to very low densities, keeping a 100-fs time
resolution. In this paper, we will show how the results of the
experiment may be obscured by different mechanisms de-
pending on the excitation density and on the photon energy,
and we will give final results that are in very good agreement
with a Monte Carlo simulation of the experiment including
all the relevant scattering processes.
A resolution of 100 fs is obtained by up-conversion in a
LiIO
3
crystal. Two different laser sources have been used, a
synchronously pumped dye laser at 600 nm and a Ti:sapphire
laser at 705 nm. Multiple quantum-well samples 25 wells
with different well widths have been studied, all with 70-Å
barriers of either AlAs or Al
0.45
Ga
0.65
As. Our samples were
grown by molecular beam epitaxy and the sample parameters
were checked by a combination of PLE measurements and
x-ray-diffraction studies. We concentrate on the results from
similar samples, with well widths between 90 and 135 Å.
The energy spacing between the first and the second confined
electron levels is about 100 meV. Differences in confinement
energy arise from the changes in the Al concentration, as
well as in the width of the well. The excitation density was
varied between 5 10
10
cm
-2
and 10
12
cm
-2
and the lattice
temperature was kept at 77 K, allowing a reasonable thermal
population in the second heavy-hole subband.
Figure 1 shows energy resolved spectra of a 135-Å 92-Å
well sample, with an Al
x
Ga
1 -x
As AlAs barrier, under dif-
ferent excitation conditions density and wavelength. The
spectra are dominated by the ( e ,hh
1
transition at about 1.55
eV. Since the PL intensity is proportional to the joint density
of states and to the product of the Fermi distribution func-
tions of electrons and holes, the spectra yield a variety of
information concerning the carrier thermalization and the de-
gree of thermal equilibrium between the different subbands.
At this point it is important to emphasize that all dynamical
processes concerning the hole population in the QW occur
beyond the resolution of our experiments. The effective hole
thermalization occurs on a time scale less than 50 fs, due to
the small excess energy of the holes and the effectiveness of
hole-hole scattering.
18
As the holes have a small excess en-
ergy and as we keep the lattice temperature above 50 K, their
cooling has a negligible influence on the spectra.
The electron temperature manifests itself as an exponen-
tial slope on the high-energy side of the luminescence.
19
If
the electrons in subbands e
1
and e
2
are in thermal equilib-
rium i.e., same chemical potential, the PL spectra should
show a steplike increase at the onset of the ( e ,hh
2
transition
by a factor of 2 corresponding to the underlying change in
the density of states. Such a situation is observed in the up-
per spectrum of Fig. 1a. On the contrary, nonequilibrium is
evidenced in other spectra displayed in Fig. 1. The lower
PHYSICAL REVIEW B 15 NOVEMBER 1996-II VOLUME 54, NUMBER 20
54 0163-1829/96/5420/142694/$10.00 14 269 © 1996 The American Physical Society