Abstract
In this paper, we present one simple model of quantum dot to describe the potential. Based on the boundary continuity of wave function and its derivative, using the Chebyshev polynomial of the second kind and matrix theory, we deduced one eigen-equation of electronic energy which can clearly describe the relationship between the energy level and the surface potential in quantum dot. The further study shows that the eigen-equation of electronic energy is different when the material of quantum dot is different.
Highlights
Semiconductor quantum dot is composed of a small number of atoms
Our aim is to deduce an eigen-equation theoretical for describing the relationship of electronic energy with the surface potential, the internal periodic potential and structure parameters, which will be used to calculate the electronic energy in quantum dot
Eq(16), (20)and (23) are defined as the eigen equation of electronic energy in quantum dot, which can clearly describe the relationship of electronic energy with the surface potential, the internal periodic potential and structure parameters
Summary
Semiconductor quantum dot is composed of a small number of atoms. The number of atoms is usually about a few to hundreds of atoms, and the size of the three dimensions is less than 100 nm. A large number of studies have been reported on the energy level of the quantum dot [1,2,3,4,5,6,7,8,9,10,11,12,13]. K G Dvoyan[16] used perturbation theory and limiting potential to study the energy states of electron in ellipsoidal quantum dot. We try to study the dependence of the electronic energy on the quantum surface potential and other structure parameters. Our aim is to deduce an eigen-equation theoretical for describing the relationship of electronic energy with the surface potential, the internal periodic potential and structure parameters, which will be used to calculate the electronic energy in quantum dot
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