A Unified Axisymmetric BenDaniel–Duke Effective Mass Model for Investigating Strain-Engineered Optical Properties of Core–Shell Quantum Dots under Uniform External Electric Fields

A unified axisymmetric model based on the BenDaniel-Duke effective-mass approach is proposed to study the effect of lattice-mismatch induced strain on the electronic structure and optical properties of CdSe/CdS core-shell quantum dots. The formulation also permits the presence of a uniform external electric field. The model takes into account the continuum elastic strain, the shifts of the band edges due to the deformation potential, the position-dependent effective mass of the carriers, the quantum confinement, and the first-order direct Coulomb interaction between the electrons and holes, within a two-dimensional axisymmetric configuration. Numerical calculations were performed for a CdSe core of radius 4.0 nm and CdS shell of thickness 2.0 nm. The lattice mismatch was estimated to be 4.022%, giving rise to a compressive hydrostatic strain of - 2.298% in the core and a tensile strain of +0.817% in the shell, with a maximum elastic displacement of 0.130 nm. Thus, the strain-modified band gap of the CdSe core was 1.876 eV. The confinement energies for the ground state were found to be 0.0717 eV for electrons and 0.0390 eV for holes. The corresponding effective confinement potentials were about 0.081 and 0.420 eV, respectively. Accounting for the direct electron-hole Coulomb interaction leads to a binding-energy correction of 49.85 meV, and reduces the optical transition energy from the single-particle value of 1.986 eV to an excitonic value of 1.936 eV. This transition corresponds to an emission line at about 640.3 nm. The calculated ground-state wavefunction overlap of 0.904 and relative oscillator strength of 0.817 indicate a significant spatial overlap between the confined electron and hole states and a strong fundamental optical transition. The numerical implementation demonstrated good convergence in the ten lowest eigenstates, preservation of matrix symmetry within numerical precision, and errors in wavefunction normalisation of order ^(-16). Overall, the results demonstrate that the axisymmetric BenDaniel-Duke formulation is a numerically stable and physically consistent approach to describe strain-dependent carrier confinement and optical transitions in CdSe/CdS core-shell quantum dots. The developed framework also provides a basis for future investigations of electric-.field-induced modifications to their electronic and optical behavior