^{1,a)}

### Abstract

A model to determine the electronic structure of self-assembled quantum arbitrarily shaped dots is applied. This model is based principally on constant effective mass and constant potentials of the barrier and quantum dot material. An analysis of the different parameters of this model is done and compared with those which take into account the variation of confining potentials, bands, and effective masses due to strain. The results are compared with several spectra reported in literature. By considering the symmetry, the computational cost is reduced with respect to other methods in literature. In addition, this model is not limited by the geometry of the quantum dot.

The author wants to thank Professor A. Luque and Professor A. Martí for their fruitful discussions. This work was supported by the European Commission through the funding of the project FULLSPECTRUM (Contract No. SES6-CT-2003-502620).

I. INTRODUCTION

II. THEORETICAL MODEL

III. RESULTS

IV. CONCLUSIONS

### Key Topics

- Quantum dots
- 73.0
- Effective mass
- 13.0
- Ground states
- 9.0
- Wave functions
- 7.0
- Self assembly
- 5.0

## Figures

Model to obtain the states of QD of dimensionality , volume , inside a barrier material . The volume , of the dimensionality and limited by the surface , contains the barrier and QD material . On this surface is applied to the hard boundary conditions (HBC).

Model to obtain the states of QD of dimensionality , volume , inside a barrier material . The volume , of the dimensionality and limited by the surface , contains the barrier and QD material . On this surface is applied to the hard boundary conditions (HBC).

Variation in the energy for the first four electronic states (symmetry , , , and in increasing order of energy) of the rectangular pyramid of base dimensions and in height with the basis set size (see text). The legend box indicates the symmetry of the states.

Variation in the energy for the first four electronic states (symmetry , , , and in increasing order of energy) of the rectangular pyramid of base dimensions and in height with the basis set size (see text). The legend box indicates the symmetry of the states.

Energy (eV) variation of the electronic ground states with the height (Å) for pyramidal QD with (a) square basis of side 60, 80, 120, and and (b) rectangular basis of side , , , and .

Energy (eV) variation of the electronic ground states with the height (Å) for pyramidal QD with (a) square basis of side 60, 80, 120, and and (b) rectangular basis of side , , , and .

Energy (eV) variation of the hole ground states with the height (Å) for pyramidal QD with square basis of side 60, 80, 120, and and parametrizations and (see text).

Energy (eV) variation of the hole ground states with the height (Å) for pyramidal QD with square basis of side 60, 80, 120, and and parametrizations and (see text).

Energy (eV) variation of the ground a four firstly electronic (, , , , and ) and hole (parametrization ) states (, , , , and ) with the height (Å) for pyramidal QD with a square base of side .

Energy (eV) variation of the ground a four firstly electronic (, , , , and ) and hole (parametrization ) states (, , , , and ) with the height (Å) for pyramidal QD with a square base of side .

Variation in the energy for the electronic ground state of cylindrical QD with respect to radius (height constant equal to ) and height (radius constant equal to ). represents the radius or the height, respectively.

Variation in the energy for the electronic ground state of cylindrical QD with respect to radius (height constant equal to ) and height (radius constant equal to ). represents the radius or the height, respectively.

Difference between the electronic ground state energy of the cylindrical QD of Ref. 25 and the method presented here. is the quotient between the radius and the lattice parameter of the HgS . The cylindrical QD has the height equal to the radius.

Difference between the electronic ground state energy of the cylindrical QD of Ref. 25 and the method presented here. is the quotient between the radius and the lattice parameter of the HgS . The cylindrical QD has the height equal to the radius.

Energy difference between the cylindrical and tetrahedral electronic ground state with respect to the energy of the pyramidal electronic ground state with equal volume. For this comparison a squared pyramid with sides of 120 and has been chosen. The curves corresponding to the energy ground state difference between sphere and pyramid, and curves by the tetrahedral and pyramid.

Energy difference between the cylindrical and tetrahedral electronic ground state with respect to the energy of the pyramidal electronic ground state with equal volume. For this comparison a squared pyramid with sides of 120 and has been chosen. The curves corresponding to the energy ground state difference between sphere and pyramid, and curves by the tetrahedral and pyramid.

Energy difference between the electronic ground and first excited states (, , , , and ) for QD of pyramidal shape with square basis of side , with and without truncation.

Energy difference between the electronic ground and first excited states (, , , , and ) for QD of pyramidal shape with square basis of side , with and without truncation.

Energy difference between experimental values of Ref. 27 by pyramidal QD and this model for transitions between electron and hole excited states with .

Energy difference between experimental values of Ref. 27 by pyramidal QD and this model for transitions between electron and hole excited states with .

## Tables

Comparison between the results obtained with this model for pyramidal QD transitions and experimental values from PL spectra in Ref. 26.

Comparison between the results obtained with this model for pyramidal QD transitions and experimental values from PL spectra in Ref. 26.

Comparison between the results obtained with this model for the PL transitions of Refs. 18 and 19 for pyramidal QD.

Comparison between the results obtained with this model for the PL transitions of Refs. 18 and 19 for pyramidal QD.

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