A NUMERICAL FRAMEWORK FOR CONFINEMENT ELECTRON AND HOLE STATES OF SPHERICAL CDSE/CDS CORE–SHELL QUANTUM DOTS USING THE BENDANIEL–DUKE EFFECTIVE-MASS APPROXIMATION

Ahmed Mohammed Khudhur

Авторы

Ahmed Mohammed Khudhur Department of Sciences- Faculty of Basic Education Basic- Al-Shirqat – Tikrit University, Iraq

Ключевые слова:

CdSe/CdS core-shell quantum dots, Effective Mass Approximation, BenDaniel-Duke Hamiltonian, Position dependent effective mass, Schrodinger equation, Quantum confinement, Carrier localization, Semiconductor heterostructures, Numerical simulation

Аннотация

Semiconductor core-shell quantum dots have drawn much attention because of their tunable electronic characteristics and anticipated uses in optoelectronic and quantum devices. In this work we develop a numerical framework to analysis the confined electron and hole states in spherical CdSe/CdS core-shell quantum dots under the Effective Mass Approximation (EMA). The electronic states are characterized by the BenDaniel-Duke Hamiltonian with position-dependent effective masses. The radial time-independent Schrodinger equation is translated into a one-dimensional formulation and discretized by means of a conservative second-order finite-difference technique. The resulting sparse Hermitian eigenvalue problem is easily solved in MATLAB to produce the restricted energy levels and the related wavefunctions.
The numerical results show discrete spectra of electron and hole energies typical for quantum-confined semiconductor nanostructures. The estimated radial wavefunctions are continuous at the CdSe/CdS heterointerface and show finite penetration into the shell region because of finite confinement potentials and quantum tunneling. The resultant probability-density distributions show a stronger localization of holes in the CdSe core while electrons exhibit a higher degree of spatial delocalization due to their lower effective mass. The computed energy spectra show sharp bound states with monotonically increasing eigenvalues, which is a signature of the expected quantum-confinement behavior of spherical core-shell quantum dots. The numerical framework developed here provides a physically consistent and computationally efficient approach for carrier confinement modelling and offers a flexible platform for future investigations of exciton effects, external electromagnetic fields, and more advanced semiconductor nanostructure models.

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