Electronic Structure

Electronic Structure of Confined Devices with 8-band k.p

The carriers in the extrema of various energy bands govern the physics of semiconductors. The neighbourhood of these band extrema and the shape of the energy surfaces yield qualitative information about the dispersion relationship. The neighbourhood properties are obtainable through a perturbative approach while the shape of the energy surfaces manifests themselves through symmetry arguments. In this is contained the crux of the k.p theory.

Purpose of the simulator

To develop a full 3D discretized 8-band k.p model to calculate the band structures of quantum wells, wires, and dots.

Direct Comparison of continuum and atomistic methods of electronic structure calculation

Provide electronic dispersion to model hole transport

Capabilities of the current simulator

To capture the electronic properties of bulk, wells, wires, and dots we developed a k.p solver. The simulator has the following capabilities:

• 3D discretized and MPI parallelized C++ 8-band k.p solver
• Strain effects included by the following methods
  • Continuum Elastic Theory
  • Interpolation of strain field obtained through the Valence Force Field (VFF)
  • Scope to simulate arbitrarily directed external strain field
• Can handle Zinc Blende and Wurtzite crystals

Results achieved so far

A quantum dot heterostructure was simulated and eigen states obtained with the 8-band k.p simulator. Fig 1: Model Self-Assembled Quantum dot
Direct comparison to sp3d5s*  empirical tight binding Fig 2: Comparative chart of CB eigen states of QD hetero-structure Fig 3: Comparison of VB eigen states of QD hetero-structure
Demonstration of the influence of strain in the correct prediction of eigen states Fig 4: Optical transition wavelengths determined experimentally and computed with our band models. The simulation results are devoid of strain. The mismatch to experimental data is profound Fig 5: Optical transition wavelengths determined experimentally and computed with our band models. The simulation results have strain included. A VFF strain field was added to the continuum model by interpolation.
Proof of loss of anisotropy in the continuum model Fig 6: Anisotropy of wave functions for n = 2,3 state. Continuum k.p Assumes a higher C4v symmetry while atomistic TB captures the underlying C2v symmetry of the zinc-blende lattice correctly	Increased accuracy of anharmonic corrections to VFF model over a simple harmonic approximation Fig7: Optical transition wavelength with anharmonic corrections to the VFF model. Continuum model used an interpolation of the same strain field Fig 8: Optical transition wavelength with harmonic corrections to VFF model. The fit to experimental data is better with anharmonic approximations
Band structure of III-V alloys, useful for simulation of optoelectronic devices

Associated publications

Multiscale Modeling of Quantum Dot Heterostructures, Parijat Sengupta, Sebastian Steiger, Sunhee Lee, Hoon Ryu and Gerhard Klimeck. MRS Proceedings,Spring Meeting, 2011

Group member involved: