Optically active quantum dots (QD) are compound semiconductor structures that confine both electrons and holes in a potential box having a dimension of few tens of nanometers. The electronic and optical properties of these structures are governed by the discrete energy eigenvalues of carriers. The focus of our research has been in strain induced QD's, where a self-assembled stressor island is grown on top of a near surface quantum well (QW). The minimum of the confinement potential is located inside the QW few nanometers below the stressor island. These semiconductor structures have exceptionally high optical quality, which makes them ideal for fundamental research of electronic and optical properties of QD's. In the enclosed project descriptions we describe two subtopics that we have studied especially during 1999.

This work includes extensive domestic and international collaboration, with following laboratories: Optoelectronics Laboratory, HUT; VTT Electronics; Instituto Nazionale di Fisica della Materia, University of Lecce; MegaGauss Laboratory, University of Tokyo; Inst. of Industrial Science, University of Tokyo; Center for Teraherz Science, USCB; Department of theoretical Chemistry, University of Lund; Department of Chemistry, University of Helsinki; Department of Physics, Åbo Academy University; Department of Physics, Ludwig Maximillians University.

**Electron-hole Correlation in Quantum Dots under High Magnetic Field**

Researchers: Risto Virkkala, Kari Maijala, and Jukka Tulkki

In our recent work (Phys. Rev. Lett. **77**, 342 (1996)) we have
demonstrated that the magnetic interaction in quantum dots (QD)
with axially symmetric potential causes lifting of the degeneracy
of states having different values of the angular momentum quantum
number. The resulting Zeeman splitting, observed in the QD
luminescence spectra, is related to the mesoscopic
magnetic momentum of electrons and holes which overwhelmes the
spin splitting. This picture is well reproduced by single particle
Luttinger - Kohn calculations in the low-field limit (below 10 Tesla).
At high fields, the shrinkage of the carrier wavefunctions in the dots
and the increased degeneracy of the electronic levels leads to a strong
enhancement of the electron-electron and electron-hole correlation.
Therefore, the spectroscopic investigation of the optical transition of
strongly confined quantum dots in very high magnetic field becomes
a unique tool for the direct measure of the electron-hole correlation
energy in artificial atoms.

Figure 28:
Comparison between the experimental diamagnetic shift
of the ground Landau level (consisting of the 1 and
m<0 1transitions), and the theoretical shift
calculated in the four bands
single particle approximation (dotted curves) or in the full
Hartree-Fock model taking into account the electron-hole correlation
effects (continuous curves). The symbols and
on the curves indicate the spin orientation. Inset: Comparison
between the experimental data (symbols) and the calculated (lines)
single-particle magnetic field dependence of the ground ()
and excited () quantum dots states. |

In this project we have studied both experimentally and theoretically the magneto-luminescence spectra of InGaAs strain induced quantum dots under optical excitation in the range 0-45T. Our dots are strongly confined (typical intersubband splitting in the range of 15 meV), and neutral, so that a direct measure of the electron-hole correlation is obtained optically and at normal cryogenic temperatures (4K), as opposed to other pioneering papers in which the experiments were conducted well below 1K and in charged dots. The electron hole correlation is found to reduce the diamagnetic shift of the lowest quantum dot Landau levels by over 20 meV at 40 T. Furthermore, a suppression of the state filling and a strong transfer of carriers from the high energy quantum dot Darwin-Fock states into the ground state of the quantum well is observed at fields higher than 20T. Our theory predicts - in excellent agreement with the experiments - that when the zero field QD electron and holes states merge into the electron and hole Landau levels, the increased degeneracy of the electron and hole states allows for increasingly many electrons and holes to occupy the lowest energy level. This is seen in the luminescence spectrum as a gradual increase of the QD ground state luminescence while the excited state luminescence lines fade out at high fields. As a main consequence the e-h correlation increases with increasing the magnetic field and thus the comparison between theory and experiment provides the first determination of such electron-hole correlation energy in neutral dots.

**Piezoelectric Potentials and Carrier Lifetimes in
Quantum Dots **

Researchers: Risto Virkkala, Kari Maijala, and Jukka Tulkki

In strained quantum well (QW) structures the
piezoelectric field strength induced by position dependent
shear strain can be of the order of 150 kV/cm for an
In_{0.2}Ga_{0.8}As/GaAs superlattice grown in (111) direction.
The piezoelectric fields have been predicted
to be important also in self organized semiconductor islands.
The influence of piezo effect on the optical properties
of QD's is however more subtle than in QW's.
A direct measurement of piezoelectric field or potential is
difficult since high spatial accuracy (few nanometers) is
needed for experimental observation of the potential differences.
At long distance piezoelectric effect is weak, since the structure
remains electrically neutral. The field strength decreases faster
than the dipole field .

In this project we have studied the piezoelectric effect
in quantum well dots induced by self assembled InP islands.
The calculation of piezoelectric polarization is based on
elastic continuum model and theory
is used to calculate the confinement energies and carrier
lifetimes of electrons and holes confined in the
piezoelectric potential and the deformation potential minima.
Our calculations show that the carriers confined
in piezoelectric minima have radiative
lifetimes which are 2 x 10^{3} longer
than the lifetime of carriers in the QD ground state.
Under quasi equilibrium conditions
confinement of a free electron and a hole in the piezo
minima is energetically more favourable than
exciton formation followed by confinement in the deformation
potential minima. This suggest that with
inreasing photoexcitation intensity confinement
of electrons and holes in the piezo
minima will largely cancel the piezoelectric
polarization of the structure.

Figure 29:
On the left the 3d FEM model of the strain induced QD
is shown. Geometrical shape and dimensions of the InP island have
been from TEM and AFM pictures. The model includes two mirror planes
and therefore only one fourth of the structure is shown. Figure on
the right shows the piezoelectric charge density at a) one nanometer
above and b) one nanometer below the InP/GaAs interface. |