# Tuning The Properties of Quantum Dots Via The Effective Mass

## Abstract

In the present work we revisit effective mass theory (EMT) for a semiconductor quantum dot (QD) and employ the BenDaniel-Duke (BDD) boundary condition. In effective mass theory mass m{sub i} inside the dot of radius R is different from the mass m{sub o} outside the dot. That gives us a crucial factor in determining the electronic spectrum namely {beta} = m{sub i}/m{sub 0}. We show both by numerical calculations and asymptotic analysis that the ground state energy and the surface charge density, {rho}(r) can be large. We also show that the dependence of the ground state energy on the radius of the well is infraquadratic. We demonstrate that the significance of BDD condition is pronounced at large R. We also study the dependence of excited state on the radius as well as the difference between energy states. Both exhibit an infra quadratic behavior with radius. The energy difference is important in study of absorption and emission spectra. We find that the BDD condition substantially alters the energy difference. Hence the interpretation of experimental result may need to be reexamined.

- Authors:

- Dr. H. S. Gour University, Sagar (M.P.), India 470 002 (India)
- Electrical Engineering Department, IIT Bombay, Mumbai, India 400076 (India)
- Homi Bhabha Centre for Science Education (TIFR), V.N. Purav Marg, Mankhurd, Mumbai, India 400088 (India)

- Publication Date:

- OSTI Identifier:
- 21608153

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1349; Journal Issue: 1; Conference: 55. DAE solid state physics symposium 2010, Manipal (India), 26-30 Dec 2010; Other Information: DOI: 10.1063/1.3605925; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 77 NANOSCIENCE AND NANOTECHNOLOGY; ABSORPTION; ASYMPTOTIC SOLUTIONS; BOUNDARY CONDITIONS; CHARGE DENSITY; CHARGE EXCHANGE; EFFECTIVE MASS; EMISSION SPECTRA; EXCITED STATES; GROUND STATES; HALL EFFECT; QUANTUM DOTS; QUANTUM WELLS; SEMICONDUCTOR MATERIALS; ENERGY LEVELS; MASS; MATERIALS; MATHEMATICAL SOLUTIONS; NANOSTRUCTURES; SORPTION; SPECTRA

### Citation Formats

```
Singh, R. A., Sinha, Abhinav, and Pathak, Praveen.
```*Tuning The Properties of Quantum Dots Via The Effective Mass*. United States: N. p., 2011.
Web. doi:10.1063/1.3605925.

```
Singh, R. A., Sinha, Abhinav, & Pathak, Praveen.
```*Tuning The Properties of Quantum Dots Via The Effective Mass*. United States. doi:10.1063/1.3605925.

```
Singh, R. A., Sinha, Abhinav, and Pathak, Praveen. Fri .
"Tuning The Properties of Quantum Dots Via The Effective Mass". United States. doi:10.1063/1.3605925.
```

```
@article{osti_21608153,
```

title = {Tuning The Properties of Quantum Dots Via The Effective Mass},

author = {Singh, R. A. and Sinha, Abhinav and Pathak, Praveen},

abstractNote = {In the present work we revisit effective mass theory (EMT) for a semiconductor quantum dot (QD) and employ the BenDaniel-Duke (BDD) boundary condition. In effective mass theory mass m{sub i} inside the dot of radius R is different from the mass m{sub o} outside the dot. That gives us a crucial factor in determining the electronic spectrum namely {beta} = m{sub i}/m{sub 0}. We show both by numerical calculations and asymptotic analysis that the ground state energy and the surface charge density, {rho}(r) can be large. We also show that the dependence of the ground state energy on the radius of the well is infraquadratic. We demonstrate that the significance of BDD condition is pronounced at large R. We also study the dependence of excited state on the radius as well as the difference between energy states. Both exhibit an infra quadratic behavior with radius. The energy difference is important in study of absorption and emission spectra. We find that the BDD condition substantially alters the energy difference. Hence the interpretation of experimental result may need to be reexamined.},

doi = {10.1063/1.3605925},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1349,

place = {United States},

year = {2011},

month = {7}

}