^{1,a)}

### Abstract

The dispersion in the dot size, shape, and composition leads to a difficult comparison with experimental spectroscopy and transport data even if the growth conditions are similar. In this work, an extensive analysis of the influence of the dot size and shape on the electron and hole energy states and on transition energies is carried out using a unified model of the semiconductor band structure. In this study we obtain the electron energy spectra for three-dimensional small quantum dots of several different truncated shapes described in the literature: tetrahedral, pyramidal with base of different geometry, etc. Also, in order to give an idea of the flexibility of the method, the icosahedral geometry is analyzed. The combination of theoretical results using a unified model for all the geometries with structural techniques will allow a more precise analysis of experimental samples.

This work has been supported by the GENESIS FW project of the National Spanish program CONSOLIDER (CSD2006-0004), by the European Commission through the funding of the project IBPOWER (Grant Agreement No. 211640), and by La Comunidad de Madrid through the funding of the project NUMANCIA (Ref. No. S-0505/ENE/0310).

I. INTRODUCTION

II. RESULTS AND DISCUSSION

A. Tetrahedral QD

B. Pyramidal QD

C. Icosidodecahedral shape QD

III. CONCLUSIONS

### Key Topics

- Quantum dots
- 71.0
- Effective mass
- 7.0
- Electron spectroscopy
- 4.0
- Semiconductor device modeling
- 4.0
- Semiconductors
- 4.0

## Figures

Energy of the ground and first electronic states (with respect to the potential barrier) for tetrahedral-shaped QD embedded in an cube of (a) , (b) , (c) , (d) , (e) , and (f) . is the truncating parameter of the tetrahedral QD with ( corresponds to the tetrahedron without truncation and correspond to the point in the center of the cube). In the upper panel the truncated tetrahedral QD is represented. The tetrahedron without truncation is imbedded in a cube of edge . The tetrahedron is truncated by the planes perpendicular to the vectors from the origin to the vertices of the cube and that they contain the points , , , , where .

Energy of the ground and first electronic states (with respect to the potential barrier) for tetrahedral-shaped QD embedded in an cube of (a) , (b) , (c) , (d) , (e) , and (f) . is the truncating parameter of the tetrahedral QD with ( corresponds to the tetrahedron without truncation and correspond to the point in the center of the cube). In the upper panel the truncated tetrahedral QD is represented. The tetrahedron without truncation is imbedded in a cube of edge . The tetrahedron is truncated by the planes perpendicular to the vectors from the origin to the vertices of the cube and that they contain the points , , , , where .

Energy of the firstly electronic states (with respect to the potential barrier) for a truncated tetrahedral-shaped QD embedded in an cube of (a) , (b) , (c) , (d) , (e) , and (f) as a function of the QD volume.

Energy of the firstly electronic states (with respect to the potential barrier) for a truncated tetrahedral-shaped QD embedded in an cube of (a) , (b) , (c) , (d) , (e) , and (f) as a function of the QD volume.

Energy of the first allowed transitions [ and , according to the Table I] for a truncated tetrahedral-shaped QD embedded in a cube of as a function of the QD volume. For the hole levels the parametrization has been used: and (Ref. 22).

Energy of the first allowed transitions [ and , according to the Table I] for a truncated tetrahedral-shaped QD embedded in a cube of as a function of the QD volume. For the hole levels the parametrization has been used: and (Ref. 22).

Energy of the ground and first electronic states with respect to the potential barrier for the square base pyramid with dimensions of and heights of 4 (a), 6 (b), 8 (c), 10 (d), and (e), and with dimensions of and heights of 4 (f), 6 (g), 8 (h), 10 (i), and (j). is the truncating parameter of the pyramid height (, pyramid without truncation). In the upper panel the truncated pyramidal QD is represented. The pyramid base is a polygon with edges ( triangular, , square, pentagonal, hexagonal, etc). The truncated pyramid has a , where the height of the original pyramid and is the truncating parameter.

Energy of the ground and first electronic states with respect to the potential barrier for the square base pyramid with dimensions of and heights of 4 (a), 6 (b), 8 (c), 10 (d), and (e), and with dimensions of and heights of 4 (f), 6 (g), 8 (h), 10 (i), and (j). is the truncating parameter of the pyramid height (, pyramid without truncation). In the upper panel the truncated pyramidal QD is represented. The pyramid base is a polygon with edges ( triangular, , square, pentagonal, hexagonal, etc). The truncated pyramid has a , where the height of the original pyramid and is the truncating parameter.

Energy of the first allowed transitions ( and , according to Table I) for a truncated pyramidal-shaped QD with square base of and heights of 4, 6, 8, and as a function of the truncating parameter . For the hole levels the parameterization has been used: and (Ref. 22). The transition with lower energy for each height corresponds to the transition.

Energy of the first allowed transitions ( and , according to Table I) for a truncated pyramidal-shaped QD with square base of and heights of 4, 6, 8, and as a function of the truncating parameter . For the hole levels the parameterization has been used: and (Ref. 22). The transition with lower energy for each height corresponds to the transition.

Energy of the firstly electron energy levels, labeled with index , of the icosidodecahedron QD imbedded in spheres of 15, 20, and .

Energy of the firstly electron energy levels, labeled with index , of the icosidodecahedron QD imbedded in spheres of 15, 20, and .

## Tables

Allowed transitions for the QD with different symmetries. The second column indicates the irreducible representations (IR), denoted by , of the point group. The allowed transitions are indicated as , where and are the IR of the allowed transitions and is the polarization.

Allowed transitions for the QD with different symmetries. The second column indicates the irreducible representations (IR), denoted by , of the point group. The allowed transitions are indicated as , where and are the IR of the allowed transitions and is the polarization.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content