Application of coordinate transformation and finite differences method for electron and hole states calculations

• We are interested for GaAs/Ga1−xAlxAs V-groove quantum wires.
• We present an efficient and simple method for energy spectra and wave function calculations of carriers.
• The method is based on the coordinate transformation of the V-groove quantum wire structure.
• The influence of the parameters introduced, is studied on the energy levels as well as the oscillator strengths.

In this work we are particularly interested for GaAs/Ga1−xAlxAs V-groove quantum wires. The paper presents an efficient and simple method for energy spectra and wave function calculations of electrons and holes in V-groove quantum wires. The method is based on the coordinate transformation of the V-groove quantum wire structure and the computational domain using a function proposed by Inoshita. Then, the Hamiltonian followed by implementation of the FDM (Finite Difference Method) in the new computational space leads to an eigenvalues problem resolved using specialized LAPACK’s routines. The influence of the parameters introduced in the mathematical function, is studied on the energy levels of electrons and holes as well as the oscillator strengths.

We have used a simple method based on the coordinate transformation for the states calculations of electrons and holes in V-groove quantum wires.Figure optionsDownload as PowerPoint slide