Fourier-transform K∙P method for modeling electronic structures and optical properties of low dimensional heterostructures
Date of Issue2012
School of Electrical and Electronic Engineering
Photonics Research Centre
Low dimensional heterostructures are promising candidates for the applications of optoelectronic devices, therefore, they have drawn increasing research efforts. In order to bestow the development of related experimental applications, various numerical methods have been developed to explore the electronic structures and the optical properties of heterostructures. The Fourier-transform k∙p method (FTM) has opened an entirely new way to investigate the band structures of quantum wells (QWs). Consequently, the work contained in this thesis is directly towards the implementation of FTM to study the electronic structures and the optical properties of low dimensional heterostructures. In this thesis, an original meshless version of FTM for quantum dots (QDs) has been formulated and then been applied to calculate the electronic structures of isolated QDs successfully. The formulation of a simple and neat Hamiltonian matrix in the Fourier domain was fulfilled using the orthogonality of plane wave exponential functions and the truncation of higher Fourier harmonics. The geometric shape effect of QDs was introduced into the Hamiltonian matrix using the analytical Fourier transform of QD shape functions, and thus the formulation of the meshless programming. The critical factors related to computation accuracy were also discussed. In order to achieve enough computation accuracy in the calculation for isolated QD structures, the periodic length was employed as three times the largest dimension of the QD structure, and a higher order of Fourier truncation was selected for QDs with sharper geometric structures. Subsequently, the meshless FTM was adopted to investigate the electronic structures of QDs. This study shows that strain causes band mixing effect reduced. Strain also leads to variation in the shape and location of probability density functions (PDFs), and thus a weaker confinement to carriers. PDFs of HH and LH are more adapted to the variation of confining potential than that of CB due to heavier effective mass. Strain effect is more prominent for sharper pyramidal QDs due to stress concentration. This thesis shows that the wetting layer has to be considered in the calculation for very flat QDs. The wetting layer widens the potential well and, therefore, reduces the energy band-gap. The size of PDFs is magnified and the position of PDFs is driven towards the wetting layer. Both the band energies and the contour drawing of PDFs illustrate that the influence of the wetting layer on electronic structures is mainly from the region underneath the bottom of the dot region. Mechanism of redshift in InAs/InxGa(1-x)As QDs has also been studied. Increasing In composition reduces the compressive strain, and thus the emergence of the redshift. The influence of the thickness of the lower confining layer cannot be compared to that of In composition. 0≤ x ≤0.33 and a thicker lower confining layer can be adopted to avoid size fluctuations of QDs and weaken the thermal quenching due to the waning of band discontinuity. The Burt-Foreman (BF) operator ordering was then incorporated into FTM to resist spurious solutions, which is one of the main challenges of using the k∙p method. The BF operator ordering is effective to prevent spurious solutions in the six-band calculation, and spurious solutions in the CB met in the eight-band calculation can also be easily screened away in the inborn cut-off step (truncation of higher Fourier harmonics) in FTM. A wild-spreading spectrum of the Fourier series of the envelope function can be regarded as the signature of spurious solutions, which can be prevented by truncating the higher order of Fourier frequencies. Finally yet importantly, FTM results were employed to investigate optical properties of QWs successfully, further verifying the validity of the FTM calculation. Based on the band energy dispersions, the quasi-Fermi level and the interband transition momentum matrix elements were determined, and thus the optical gain spectrum. The interband transition matrix elements for both six-band and eight-band computation were given out by integrating the Fourier series of envelope functions conveniently.
DRNTU::Engineering::Electrical and electronic engineering::Optics, optoelectronics, photonics