Excitonic States in Cylindrical Quantum Dots: A Variational Approach

Abstract

This work studies the exciton ground-state energy in a cylindrical quantum dot using a variational method. A trial wavefunction incorporating both in-plane and vertical confinement effects is employed to study the energy as a function of radius R and height H. The study also includes a detailed comparison between the 2D disk and 3D sphere geometries, using an identical trial wavefunction. Results show that quantum confinement dominates at small sizes, an optimal aspect ratio R/H ≈ 0.53 exists, and the correlation energy decreases with increasing system size.