In another tiberCAD application (see Selfconsistent EFA - Drift-diffusion 3D calculation for a GaAs quantum well in a nanocolumn), we show the results of fully Self-Consistent Schroedinger (EFA) - Drift-diffusion calculations for a 3D nanostructure made of an AlGaAs rectangular nanocolumn p-i-n diode structure with an embedded GaAs quantum well.

AlGaAs/GaAs nanocolumn

Here, we present selfconsistent TB/EFA/drift-diffusion calculations performed on the same AlGaAs/GaAs nanocolumn, demonstrating the ability of tiberCAD to calculate electronic and optical properties of such systems selfconsistently, using different quantum mechanical approaches coupled to a classical transport model.

We begin by devising an atomistic model of the device, whose electronic properties are then calculated with a tigh-binding (TB) approach. Then the TB atomistic model will be coupled to Drift-diffusion for a real multi-scale concurrent simulation of the nanocolumn structure.

The Empirical Tight-Binding Module is now available with the new release 2.5 of tiberCAD. See here for a Tutorial.

Based on the FEM mesh used to discretize PDEs for continuous models, tiberCAD atomistic generator tool is able to create an atomistic structure of the quantum region, as it was defined for the continuous case. It comprises the active region of the device, that is the GaAs QW, and two portions of the AlGaAs barrier regions. It is worthwile to note that the atomistic structure is associated to the finite element representation, thus allowing for a coupled atomistic-continuous calculation.

The resulting atomistic structure generated by tiberCAD contains 50.945 atoms, including the hydrogen passivation atoms, which are placed to saturate the dangling bonds on the free surfaces in order to allow a correct calculation of the quantum states of the system.

electrostatic potential

The atomistic structure used for the ETB calculations is shown above, together with the FEM mesh, where the electrostatic potential is plotted.

The atomistic calculations are performed in the following way.
The Hamiltonian of the system is build up based on a sp3d5s* TB parametrization and then solved for the eigenvectors and eigenvalues of the system.

Below, the probability density for the calculated ground electron state shows the confinement in the GaAs QW.

probability density for the calculated ground electron state

Now, we perform a selfconsistent calculation using ETB for the electron states only. Due to the fact that for the considered structure there are many dense hole states in the GaAs quantum disk, it is computationally unfeasible to use ETB for the hole states.

For this reason we use ETB for the electrons only, calculating two states (due to spin degeneracy), and EFA for the holes such that we can include enough hole states to obtain an approximately convergent hole density.

Below are the selfconsistent band profiles (left) and particle densities (right) along the z-axis, obtained from the simulation; the results are compared with the classical result.

selfconsistent band profile (left) and particle densities (right)

Next, we compute the ETB optical emission spectra, including the first electron and the first three hole states (each twofold degenerate).

ETB optical emission spectra