In this application we present a study of the electronic and optical properties of a GaN nanocolumn p-i-n diode structure with an InGaN quantum disk (QD).

We use tiberCAD multiscale tools to apply both continuous and atomistic models in the simulations.

First, the strain maps and the electrostatic potential are calculated, respectively with the Elasticity and the Drift-diffusion modules. Then these results are projected onto the atomic positions in order to couple the atomistic calculation of electronic states with the continuous media model for particle transport.

Quantum properties are calculated for several values of column width and Indium concentration, by using an atomistic approach based on empirical tight binding (TB). In this method the electronic states are written as a linear combination of atomic orbitals (LCAO).

The tight-binding module is available from the release 2.5 of tiberCAD. See here for a Tutorial.

The atomistic structure, which is needed for TB calculations, is generated internally in tiberCAD according to the macroscopic device description and crystallographic orientation.

The generation algorithm allows for pseudomorphic heterostructures and it is able to deform the atomistic structure according to the strain obtained from the continuous media elasticity model by projecting the deformation field onto the atomic positions. In a similar way, the macroscopic electrostatic potential calculated with the Poisson/drift-diffusion model is projected onto the atomic positions in order to couple the atomistic calculation of electronic states with the continuous media model for particle transport.
The solution of the eigenvalue problems resulting from the TB model provides the energy spectrum, the particle densities and the probabilities of optical transitions. The particle densities can be fed back to the Poisson/drift-diffusion model for self-consistent Schroedinger-Poisson/drift-diffusion calculations. In the case of TB, the resulting density has to be projected onto the finite element mesh used for the continuous media models. This projection is done using an exponentially decaying function centered on each atomic site.

The simulated nanocolumn sample structures have a radius between 6.8 and 10.2 nm and the generated atomistic structures contain from 73000 to 160000 atoms. Indium concentration in the InGaN QD is varied between 10% and 30%.

Above are the calculated conduction and valence ground states confined in the QD.

TB results show that emission energies have a minor dependence on the nanocolumn dimension. In the figure below it can be seen that for 10% In content the emission energy increases by around 40 meV when column radius decreases form 10.2 to 6.8 nm. For higher In concentration, emission energy tends to increase slightly more.

M. Lopez et al., Opt. Quant. Electron. (2012) DOI 10.1007/s11082-012-9554-3