

nextnano^{3}  Tutorialnext generation 3D nano device simulator2D TutorialElectron wave functions in a cylindrical well (2D Quantum Corral)Author: Stefan Birner If you want to obtain the input files that are used within this tutorial, please contact stefan.birner@nextnano.de. Electron wave functions in a cylindrical well (2D Quantum Corral)A cylindrical InAs
quantum well (diameter 80 nm) is
surrounded by a cylindrical GaAs barrier (20 nm) which
is surrounded by air.
We assume infinite GaAs barriers. This can be achieved by a circular quantum cluster with Dirichlet boundary conditions, i.e. the wave function is forced to be zero in the GaAs barrier. The electron mass of InAs is assumed to be isotropic and parabolic (m_{e} = 0.026 m_{0}). Strain is not taken into account.
Electron wave functionsThe size of the quantum cluster is a circle of diameter 80 nm. The following figures shows the square of the electron
wave functions (i.e. psi²) of the corresponding eigenstates. They were calculated
within the effectivemass approximation (singleband) on a rectangular
finitedifferences grid.
The following figure shows the energy spectrum of the quantum corral. (The
zero of energy corresponds to the InAs conduction band edge.)
The parameters of the quantum corral are the following:
The energies are: E_{nl} = h_{bar}^{2} / (2m_{e}
a^{2}) * j_{l,n}^{2}
Further details about the analytical solution of the cylindrical quantum well
with infinite barriers can be found in:

