^{1,a)}, Tilmann Hickel

^{1}and Jörg Neugebauer

^{1}

### Abstract

We have performed systematic studies of wurtzite GaN/AlN quantum dots grown on polar and nonpolar surfaces. For this purpose, experimentally observed quantum dot geometries have been employed within an eight-band model. The spatial separation of electrons and holes due to polarization potentials is found to be much larger in nonpolar than in polar grown quantum dots. In order to improve the electron-hole overlap and thus the recombination rates, we have varied the shape, size, and the periodic arrangement of nonpolar quantum dots. We observed the strongest improvement of the charge carrier overlap in nonpolar quantum dots that have a reduced dimension. If the size is reduced below 60% of the dimensions reported recently in literature, this increase is clearly more pronounced than for the polar quantum dots, indicating much better recombination rates in smaller nonpolar quantum dots.

Financial support by the Deutsche Forschungsgemeinschaft (research group “Physics of nitride-based, nanostructured, light emitting devices,” Project No. Ne 428/6-3) is gratefully acknowledged.

I. INTRODUCTION

II. APPLIED METHODS

III. SHAPE OF POLAR AND NONPOLAR QDS

IV. RESULTS

A. Electronic properties of polar and nonpolar QDs and the influence of the piezoelectric constant

B. Influence of the QD shape

C. Periodicity of the system along growth direction

D. Influence of the QD size

V. SUMMARY

### Key Topics

- Quantum dots
- 118.0
- Polarization
- 22.0
- Charge carriers
- 20.0
- Piezoelectric constants
- 10.0
- Electrons
- 8.0

## Figures

The polar reference QD. The growth direction [0001] is highlighted.

The polar reference QD. The growth direction [0001] is highlighted.

The nonpolar reference QD. The growth direction is highlighted.

The nonpolar reference QD. The growth direction is highlighted.

Polarization potential for shear piezoelectric constants in cases A and B for a polar (left) and a nonpolar (right) grown QD.

Polarization potential for shear piezoelectric constants in cases A and B for a polar (left) and a nonpolar (right) grown QD.

Polarization potential for the cases A and B plotted along [0001] direction in a polar (top) and a nonpolar (bottom) grown QD for the original system geometries. The upper and lower edge of the QD are marked with vertical lines. For the polar QD, the [0001] axis crosses the wetting layer (dashed vertical line).

Polarization potential for the cases A and B plotted along [0001] direction in a polar (top) and a nonpolar (bottom) grown QD for the original system geometries. The upper and lower edge of the QD are marked with vertical lines. For the polar QD, the [0001] axis crosses the wetting layer (dashed vertical line).

Charge density of the first three electron and hole states in a polar QD for case A (outer surface: 90%, inner surface: 50%).

Charge density of the first three electron and hole states in a polar QD for case A (outer surface: 90%, inner surface: 50%).

Charge density of the first three electron and hole states in a nonpolar QD for case A (outer surface: 90%, inner surface: 50%).

Charge density of the first three electron and hole states in a nonpolar QD for case A (outer surface: 90%, inner surface: 50%).

Polarization potential in a nonpolar QD plotted along [0001] direction for different cell sizes along growth direction . The piezoelectric constants are those in case A. Vertical lines indicate the QD boundaries.

Polarization potential in a nonpolar QD plotted along [0001] direction for different cell sizes along growth direction . The piezoelectric constants are those in case A. Vertical lines indicate the QD boundaries.

Overlap matrix element between electron ground state and the hole states , , and (top) and correspondingly for the hole ground state and the electron states , , and (bottom) as a function of characteristic dimensions of the nonpolar and the polar QD. For the polar QD, the overlap behaves antiproportional to the QD size.

Overlap matrix element between electron ground state and the hole states , , and (top) and correspondingly for the hole ground state and the electron states , , and (bottom) as a function of characteristic dimensions of the nonpolar and the polar QD. For the polar QD, the overlap behaves antiproportional to the QD size.

Second excited electron state for the original nonpolar dot (left) and for a dot with dimensions reduced to 60% of the original size (right).

Second excited electron state for the original nonpolar dot (left) and for a dot with dimensions reduced to 60% of the original size (right).

## Tables

Material parameters for wurtzite GaN and AlN. Effective masses, the ’s, , and are taken from Ref. 25. , , and are taken from Ref. 26. All other parameters are taken from Ref. 27.

Material parameters for wurtzite GaN and AlN. Effective masses, the ’s, , and are taken from Ref. 25. , , and are taken from Ref. 26. All other parameters are taken from Ref. 27.

Overlap between different pairs of electron and hole states for the positive values of (case A, top), and negative (case B, bottom) of a polar QD.

Overlap between different pairs of electron and hole states for the positive values of (case A, top), and negative (case B, bottom) of a polar QD.

Overlap between different pairs of electron and hole states for the positive values of (case A, top), and negative (case B, bottom) of a nonpolar QD. Note that these elements are four orders of magnitude smaller than those of polar QDs.

Overlap between different pairs of electron and hole states for the positive values of (case A, top), and negative (case B, bottom) of a nonpolar QD. Note that these elements are four orders of magnitude smaller than those of polar QDs.

Charge carrier overlap in a nonpolar QD with 60% of its original dimensions.

Charge carrier overlap in a nonpolar QD with 60% of its original dimensions.

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