In semiconductor quantum dots, the
three-dimensional (3D) confinement leads to very specific features like
a delta-like density of states. This delta-like density of states which
is similar to that observed in atoms is expected to lead to strong
modifications of the optoelectronic properties Optical transitions can
be observed between the three-dimensionally confined states of the
quantum dots either between the conduction states or
the valence states. These transitions are usually referred to as
intersublevel or intraband transitions. The measurement of the infrared
absorption is the most direct path to observe intersublevel transitions
in quantum dots. Absorption usually results from the transition of
carriers from the ground state of the
dot, either in the conduction band or in the valence band, towards an
excited
state. For the InAs/GaAs self-assembled quantum dots, the absorption
associated
with the intersublevel transitions occurs in the midinfrared and in the
far
infrared spectral range. Intersublevel absorption spectroscopy is a
powerful
technique to get access to a very detailed experimental description of
the
electronic structure of the dots. We emphasize that intersublevel
absorption
spectroscopy is very complementary to interband spectroscopy such as
photoluminescence.
Intersublevel absorption corresponds to a unipolar measurement since it
only
involves one type of carrier (electron or separately hole) while
interband
transitions involve confined excitons. Infrared absorption spectroscopy
directly
provides the difference between confinement energies (i.e. without any
difference
associated with the exciton binding energy). In addition, intersublevel
absorptions
satisfy distinct transition rules as compared to interband transitions.
An
interband transition essentially follows the overlapping integral
between
envelope functions of the initial and final state while an
intersublevel
transition is governed by the dipole matrix element between the initial
and
the final envelope wave functions. Intersublevel absorption may
therefore
give access to states that are not observed in interband measurements.
At
last the information on polarization allows a fine tracking of the main
origin
of the excited levels (in-plane confinement, growth axis confinement).
Beyond the fundamental study of the electronic
structure, intersublevel absorption opens the route to the realization
of quantum dot infrared photodetectors. For this particular
application, one specific advantage of the quantum dots is the
relaxation of the polarization selection rules as compared to
two-dimensional heterostructures. In quantum wells it is
well known that, at least in the conduction band, intersubband
transitions
are always polarized along the growth direction. This polarization
selection
rule prevents any absorption at “normal-incidence”, thus implying
additional
technological steps to couple the infrared light to the intersubband
dipole.
On the contrary, because of the three-dimensional confinement, the
intersublevel
transitions in 0D systems are expected to be polarized either along the
growth
axis or in the layer plane. The in-plane polarization of the
intersublevel
transitions results from the in-plane confinement of the carriers.
Infrared Absorption of
InAs/GaAs self-assembled quantum dots
The figure below shows the mid and far infrared absorption of n-doped
InAs/GaAs self-assembled quantum dots measured by Fourier transform
spectroscopy.
The dots are populated by inserting a Si doping plane 2 nm beneath the
wetting layer. The sheet doping density is nominally chosen to
correspond to 2 and 1.5 electrons per dot in the samples of the left
and right hand side of
the figure respectively. Two different configurations are used.
On the left hand side, the absorption is measured in a normal incidence
configuration in a sample containing 30 quantum dot planes separated by
50 nm GaAs barriers. The temperature is 5 K and the polarization is set
along either cleaved edge directions. Two clear infrared resonances are
observed at 56 and 63 meV. The full width at half maximum is 6 meV.
Following the calculated
electronic structure, these infrared resonances are attributed the
intersublevel
transitions of the electrons from the s ground state to the p excited
state.
The exact agreement (within less than 1 meV) between the predicted
transition
energies and the experiment is fortuitous but demonstrates an overall
validity
of the model and the input parameters. In particular the observed 7 meV
s-p
splitting energy agrees with a 10% elongation of the dot along the
[100]
direction. The broadening of the absorption is attributed to the size
fluctuation
of the dots. According to the multiband 3D simulation, the observed
broadening
correspond to a ±9 % dot size fluctuation in good agreement with
structural
characterizations.
On the right hand side of the figure, the absorption is measured in the
90-400 meV energy range in a wave guide configuration. The sample
contains 40 quantum dot planes inserted into the core of a GaAs/Al
0.9Ga
0.1As
midinfrared waveguide. The light is injected with an infrared
microscope coupled to the Fourier transform spectrometer. Polarization
can be set either TE, in the layer plane, or TM along the growth axis.
In this configuration, spectrally large infrared resonances are
observed around 8-10 µm wavelength. In TM polarization, the
absorption is maximum at 155 meV with a ~ 100 meV full width at half
maximum. In TE polarization, the absorption is maximum at 200 meV with
the same width. Considering the theoretical electronic structure, the
TM resonance is attributed to the bound-to-continuum absorption from
the
s ground state to the delocalized state of the wetting layer continuum.
The
polarization is reasonable since the expected transfer of charge (i.e.
the
dipole) is mostly along the growth axis from the dot to the wetting
layer. The TE resonance on the contrary is attributed to the transition
towards the
bulk GaAs barriers, at a slightly higher energy. The 45 meV difference
between
the TE and TM resonances corresponds roughly to the wetting layer
subband
depth and, as compared to the calculation, integrates the fact that the
oscillator
strength of a bound-to-continuum transition is maximum at higher energy
than
the continuum onset. The 100 meV broadening of the absorption is
attributed
to three factors : the dot size fluctuation, the bound-to-continuum
nature
of the transition, and a possible contribution of the d-states around
120
meV (in TM polarization).