Electronic structure of cleaved-edge-overgrowth strain-induced quantum wires
M. Grundmann, O. Stier, A. Schliwa, and D. Bimberg
Institut fu ¨r Festko ¨rperphysik, Technische Universita ¨t Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
Received 8 June 1999; revised manuscript received 21 July 1999
The electronic properties of strained cleaved-edge-overgrowth quantum wires are calculated for structures in
which the 001 quantum well has a larger lattice constant and band gap than the barrier and imposes tensile
strain on the 110 quantum well. The lateral charge-carrier confinement is entirely due to strain effects and not
due to heterostructure barriers. Large localization energies of up to 90 meV are predicted from eight band
k• p calculations. Symmetric, asymmetric, and interdiffused geometries in the In
0.2
Al
0.8
As/Al
0.35
Ga
0.65
As/GaAs
system are investigated.
Cleaved-edge overgrowth CEO has been used in recent
years to fabricate quantum wires QWRRefs. 1 and 2 and
quantum dots.
3–5
The inclusion of strained layers in such
structures introduces a new dimension in band-gap engineer-
ing and may strongly modify confinement effects. Theoreti-
cal investigations of the electronic states for structures con-
sisting of lattice matched materials have been presented by
several groups.
3,6–9
The confinement in this case is a conse-
quence of the configuration of the heterostructure barriers. In
Ref. 10, the effects of compressively strained material for
both the 001 and 110 layers in the conventional T-shape
geometry have been theoretically analyzed. No distinctive
enhancement of carrier confinement at the juncture due to
strain effects was identified.
In this work we study the configuration proposed in Ref.
11 and sketched in Fig. 1. The 001 layer
(In
0.2
Al
0.8
As/Al
0.35
Ga
0.65
As) is compressively strained by
the GaAs substrate and exerts tensile strain on the 110
quantum well QWL and barrier, in our case
GaAs/Al
0.35
Ga
0.65
As. The band gap of the 001 In
0.2
Al
0.8
As
layer is sufficiently high that the charge carriers are confined
to the 110 GaAs layer. This configuration of the CEO
structure creates a new physical situation: The lateral charge-
carrier localization along 110 is not due to heterostructure
barriers but solely due to the induced tensile strain in the
110 layer.
First the strain for the given structure is calculated by
minimizing the strain energy. Here we use the continuum
mechanical CM model.
10,14
The material parameters used
in the calculations are shown in Table I. The extension of the
strained region used for the CM calculations in the 110
direction is large about 180 nm and only a fraction close to
the QWR is shown in all graphs. In the 001 direction, pe-
riodic boundary conditions i.e., a superlattice are assumed.
A comparison with a single QWR will also be made. In Fig.
2, three strain components
xx
,
zz
, and
xy
and the hy-
drostatic strain
H
=
xx
+
yy
+
zz
around the juncture are
shown. The results from CM strain relaxation will be com-
pared with the ‘‘pseudomorphic strain’’ PS model in which
two subsequent pseudomorphic growth steps are assumed,
first in the 001 direction and then in the 110 direction.
The PS model yields several regions of constant strain with-
out allowing for proper strain relaxation.
The band-structure calculation is carried out within eight-
band k• p theory, used by us previously for V-groove quan-
tum wires.
15
The model accounts for valence-band mixing
and conduction-band–valence-band interaction. The k• p
Hamiltonian is solved on 4040 nm
2
areas. First we calcu-
late electron and hole levels for a symmetric geometry where
both layers have the same width ( d
100
=d
110
=10 nm), for
the two cases of a 001 superlattice 30-nm Al
0.35
Ga
0.65
As
barriers and a single QWR. Additionally, asymmetric wires
and the effect of intermixing indium diffusion from the
In
x
Al
1 -x
As layer into the 110 GaAs quantum well are
investigated.
Significant differences between the CM and PS strain
models are found. In particular, the hydrostatic strain, re-
sponsible for the shift of the conduction band, differs near
the junction by about 0.012. In Fig. 3, line scans of
zz
and
of the hydrostatic strain are shown along the 110 direction.
Using eight-band k• p theory we find the levels given in
Table II. Also given is the optical recombination energy
without Coulomb effects. The wave functions in the QWR
are shown in Fig. 4. As expected, the wave functions are
entirely confined to the 110 GaAs QWL and do not pen-
etrate into the In
x
Al
1 -x
As layer.
Due to the different strain distributions, the positions of
the electron and hole levels differ between the cases of a
superlattice and a single QWR. However, the optical recom-
bination energy is very similar. With respect to the quantum-
well energy levels, which act as barriers for the localized
QWR states, both the electrons and holes are predicted to
have about 30 meV localization energy. The numerical re-
sults are shown in Table III, together with the values for
FIG. 1. Geometry of strained CEO quantum wire. Numerical
examples are calculated for the In
0.2
Al
0.8
As/Al
0.35
Ga
0.65
As/GaAs
system.
PHYSICAL REVIEW B 15 JANUARY 2000-I VOLUME 61, NUMBER 3
PRB 61 0163-1829/2000/613/17444/$15.00 1744 ©2000 The American Physical Society