^{1}, S. P. Purohit

^{1,a)}and K. C. Mathur

^{1}

### Abstract

Electronic transitions in the quantum confined states in the conduction band of spherical ZnO semiconductor quantum dot are studied. Photoabsorption spectra and oscillator strengths have been obtained for various sizes of quantum dot using effective mass approximation. Electric quadrupole effect has been included in addition to the electric dipole effect. The nonlinear contribution to photoabsorption spectra has also been studied. Results for transition energies of the quantum confined states are found to be in good agreement with the available experimental data.

We thank the Jaypee Institute of Information Technology, Noida for providing facilities and support to carry out this work.

I. INTRODUCTION

II. WAVE FUNCTIONS AND ENERGY LEVELS

A. Infinite barrier height

B. Finite barrier height

C. Absorption coefficient and oscillator strength

III. RESULTS AND DISCUSSION

IV. CONCLUSIONS

### Key Topics

- Quadrupoles
- 38.0
- II-VI semiconductors
- 31.0
- Quantum dots
- 30.0
- Photoabsorption
- 20.0
- Oscillators
- 17.0

## Figures

The confined energy levels , , , and for at dot radius R = 20 .

The confined energy levels , , , and for at dot radius R = 20 .

The variation of transition energy for (1S-1P), (1P-1D), and (1D-1F) transitions as a function of the dot radius. Solid line: infinite confinement; dashed line: finite confinement; dotted line: tight binding (TBA); ^{ 23 } solid dot: experimental data. ^{ 23 }

The variation of transition energy for (1S-1P), (1P-1D), and (1D-1F) transitions as a function of the dot radius. Solid line: infinite confinement; dashed line: finite confinement; dotted line: tight binding (TBA); ^{ 23 } solid dot: experimental data. ^{ 23 }

The variation of linear absorption coefficient as a function of photon energy for electron in initial 1S state.

The variation of linear absorption coefficient as a function of photon energy for electron in initial 1S state.

The variation of linear absorption coefficient as a function of photon energy for electron in initial 2S state.

The variation of linear absorption coefficient as a function of photon energy for electron in initial 2S state.

The variation of linear absorption coefficient as a function of photon energy for electron in initial 1P state.

The variation of linear absorption coefficient as a function of photon energy for electron in initial 1P state.

The variation of linear absorption coefficient as a function of photon energy for electron in initial 1D state.

The variation of linear absorption coefficient as a function of photon energy for electron in initial 1D state.

The variation of photoabsorption coefficient for (1S-1P) transition at (a) R = 25 , (b) R = 30 , and (c) R = 35 at intensities I = 0.1 × 10^{12} W/m^{2}, I = 0.3 × 10^{12} W/m^{2}, and I = 0.5 × 10^{12}W/m^{2} as a function of the incident photon energy. Dotted line: linear; dashed line: nonlinear; solid: total.

The variation of photoabsorption coefficient for (1S-1P) transition at (a) R = 25 , (b) R = 30 , and (c) R = 35 at intensities I = 0.1 × 10^{12} W/m^{2}, I = 0.3 × 10^{12} W/m^{2}, and I = 0.5 × 10^{12}W/m^{2} as a function of the incident photon energy. Dotted line: linear; dashed line: nonlinear; solid: total.

The variation of photoabsorption coefficient for (2S-2P) transition at (a) R = 25 , (b) R = 30 , and (c) R = 35 at intensities I = 0.1 × 10^{12} W/m^{2}, I = 0.3 × 10^{12} W/m^{2}, and I = 0.5 × 10^{12}W/m^{2} as a function of the incident photon energy. Dotted line: linear; dashed line: nonlinear; solid line: total.

The variation of photoabsorption coefficient for (2S-2P) transition at (a) R = 25 , (b) R = 30 , and (c) R = 35 at intensities I = 0.1 × 10^{12} W/m^{2}, I = 0.3 × 10^{12} W/m^{2}, and I = 0.5 × 10^{12}W/m^{2} as a function of the incident photon energy. Dotted line: linear; dashed line: nonlinear; solid line: total.

The variation of photoabsorption coefficient for (1S-1D) transition at (a) R = 25 , (b) R = 30 , and (c) R = 35 at intensities I = 0.1 × 10^{16} W/m^{2}, I = 0.3 × 10^{16}W/m^{2}, and I = 0.5 × 10^{16}W/m^{2} as a function of the incident photon energy. Dotted line: linear; dashed line: nonlinear; solid line: total.

The variation of photoabsorption coefficient for (1S-1D) transition at (a) R = 25 , (b) R = 30 , and (c) R = 35 at intensities I = 0.1 × 10^{16} W/m^{2}, I = 0.3 × 10^{16}W/m^{2}, and I = 0.5 × 10^{16}W/m^{2} as a function of the incident photon energy. Dotted line: linear; dashed line: nonlinear; solid line: total.

The variation of photoabsorption coefficient for (2S-2D) transition at (a) R = 25 , (b) R = 30 , and (c) R = 35 at intensities I = 0.1 × 10^{16}W/m^{2}, I = 0.3 × 10^{16} W/m^{2}, and I = 0.5× 10^{16} W/m^{2} as a function of the incident photon energy. Dotted line: linear; dashed line: nonlinear; solid line: total.

The variation of photoabsorption coefficient for (2S-2D) transition at (a) R = 25 , (b) R = 30 , and (c) R = 35 at intensities I = 0.1 × 10^{16}W/m^{2}, I = 0.3 × 10^{16} W/m^{2}, and I = 0.5× 10^{16} W/m^{2} as a function of the incident photon energy. Dotted line: linear; dashed line: nonlinear; solid line: total.

The variation of quadrupole oscillator strength versus confinement radius for the transitions ( ).

The variation of quadrupole oscillator strength versus confinement radius for the transitions ( ).

The variation of quadrupole oscillator strength versus confinement radius for the transitions ( ).

The variation of quadrupole oscillator strength versus confinement radius for the transitions ( ).

## Tables

Dipole oscillator strength (P_{D}) of various transitions in ZnO QD of radius 20 Å.

Dipole oscillator strength (P_{D}) of various transitions in ZnO QD of radius 20 Å.

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