InAs Quantum Dots on Al
x
Ga
1x
As Surfaces and in an Al
x
Ga
1x
As Matrix 77
7.2 1 0
10
c m
2
can readily be achieved. As was shown in Fig. 2.15 the excitonic ground state
energy in the dot can be tuned by varying the Al content of the confi ning matrix. Depending on
the Al content, it was shown to increase about ⬃ 450 meV and can be adjusted from well below
the GaAs band edge to above the GaAs band gap; tuning of the wavelength dependent detector
response over a wide range is possible.
2.6.2 Quantum dot quantum-cascade emitters
Since 1997 it has been a goal to incorporate QDs into a complete quantum cascade emitter
structure [74] to improve the effi ciency and temperature performance. A signifi cant reduction
in the effi ciency of quantum cascade lasers (QCLs) is caused by longitudinal optical (LO) phonon
depletion of the upper laser level. By embedding QDs in the active region of a QCL this scattering
mechanism is expected to be reduced, due to the phonons ’ small energy dispersion and the dis-
crete energy levels [75–77] .
An estimation of the dimensions of the QDs necessary to effi ciently suppress phonon emission
is given by Eq. 2.10:
(3
LO
πω
22 2
2)/( * )mL
(2.10)
To avoid LO-phonon emission the energy level spacing between the excited and ground states in
the dot has to exceed the optical phonon energy
ω
LO
, which amounts to E
QD, LO
⬃ 32 meV in an
InAs QD with strain taken into account [78] . The maximum dot size L can be estimated from the
energy spacing in a square well of size L . For GaAs, with an effective mass m
*
0.067 m, this
implies dots smaller than L ⬇ 20 nm in all three dimensions. Typical QD heights are well above
this limit as can be seen in Fig. 2.7 . Concerning the in-plane dot dimensions, InAs dots grown
on GaAs surfaces show typical diameters of ⬃ 30 nm, as mentioned previously. InAs QDs grown
on AlGaAs or AlAs surfaces have typical diameters at or below the calculated maximum QD
size L [79] .
For the design of devices which exploit intraband transitions in QDs it is necessary to inves-
tigate the intraband relaxation mechanisms in quasi-zero-dimensional QDs. Because of the dis-
crete density of electronic states in QDs and weak energy dispersion of the longitudinal optical
(LO)-phonons it was suggested that effi cient electron non-radiative relaxation is only possible for
energies close to the LO-phonon energy, also known as the phonon bottleneck effect [80] . It has
been shown that the phonon bottleneck effects can be signifi cantly suppressed in QDs, leading
to decay times from excited states to ground states in the range of 10–50 ps [81] . This is due to
the discrete nature of the confi ned states in QDs, which causes a strong coupling between elec-
trons and phonons, so-called polarons. Effi cient relaxation of excited polarons even for quite
large detunings ( ⬃ 20 meV) from the LO-phonon energy has been demonstrated [82] . Recenty,
the effect of strong electron–phonon coupling on the ground state to fi rst excited state transition
energy has been observed in annealed, self-assembled InAs/GaAs QDs [83] .
Mid-infrared luminescence from a resonant tunnelling QD unipolar device was fi rst demon-
strated [84] with a single layer of self-assembled InAs QDs in an AlAs barrier. By using compo-
sition grading, electrons were resonantly injected into the upper QD states. The electrons were
resonantly extracted from the lower QD states through a superlattice miniband. The superlattice
additionally forms an electron fi lter that prevents the carriers from directly tunnelling out of the
dot before relaxing to a lower energy level and thus the emission of a mid-IR photon is encour-
aged. The graded barrier for QD injection limits this to half of a quantum cascade with no engi-
neered population inversion. Emission from this structure also showed anisotropic polarization
due to the anisotropy in QD shape in the growth plane [9] .
Mid-infrared electroluminescence from a quantum-dot-quantum-well cascade structure, con-
sisting of ten periods, with AlInAs QDs in the active region, has also been demonstrated [85] . In
this design the QDs were embedded in the AlGaAs barriers of the structure. The electrolumines-
cence only showed a distinct peak at low currents, where a resonant subensemble of quantum
dots with a small inhomogeneous broadening contributes to the signal. For higher currents a
spectral broadening of the electroluminescence was observed.
CH002-I046325.indd 77CH002-I046325.indd 77 6/23/2008 4:47:46 PM6/23/2008 4:47:46 PM