# Quantum Confinement Induced Shift in Energy Band Edges and Band Gap of Spherical Quantum Dot

## TL;DR

This paper presents a theoretical model using an effective potential ansatz to analyze quantum confinement effects on energy band edges and band gap in spherical quantum dots, validated by experimental data.

## Contribution

The study introduces a new ansatz combining harmonic oscillator and Coulomb interactions for confining particles in spherical quantum dots, validated against experimental results.

## Key findings

- Energy band edge shifts depend on quantum dot size.
- Quantum confinement causes a measurable increase in band gap energy.
- Theoretical results align well with experimental data for CdSe quantum dots.

## Abstract

We have proposed and validated an ansatz as effective potential for confining electron/hole within spherical quantum dot in order to understand quantum confinement and its consequences associated with energy states and band gap of Spherical Quantum Dot. Within effective mass approximation formalism, considering an ansatz incorporating a conjoined harmonic oscillator and coulomb interaction as the effective potential for confining an electron or a hole within a spherical quantum dot and by employing appropriate boundary conditions we have calculated the shifts in energy of minimum of conduction band(CBM) and maximum of valence band(VBM) with respect to size of spherical quantum dot. We have also determined the quantum confinement induced shift in band gap energy of spherical quantum dot. In order to verify our theoretical predictions as well as to validate our ansatz, we have performed phenomenological analysis in comparison with available experimental results for quantum dots made of CdSe and observe a very good agreement in this regard. Our experimentally consistent theoretical results also help in mapping the probability density of electron and hole inside spherical quantum dot. The consistency of our results with available experimental data signifies the capability as well as applicability of the ansatz for the effective confining potential to have reasonable information in the study of real nano-structured spherical systems.