Query:  k⋅p method for strained wurtzite semiconductors

Candidate papers:

abstract: We derive the effective mass Hamiltonian for wurtzite semiconductors, including the strain effects. This Hamiltonian provides a theoretical groundwork for calculating the electronic band structures and optical constants of bulk and quantum well wurtzite semiconductors. We apply Kane's model to derive the band edge energies and the optical momentum matrix elements for strained wurtzite semiconductors. We then use the k\ensuremath{\cdot}p perturbation method to derive the effective mass Hamiltonian, which is then checked with that derived using an invariant method based on the Pikus Bir model. We obtain the band structure \mathit{A}}_{\mathit{i} parameters in the group theoretical model explicitly in terms of the momentum matrix elements. We also find the proper definitions of the important physical quantities used in both models and present analytical expressions for the valence band dispersions, the effective masses, and the interband optical transition momentum matrix elements near the band edges, taking into account the strain effects. \textcopyright{ 1996 The American Physical Society.
author_names: Shun Lien Chuang

C S Chang
title: k.p method for strained wurtzite semiconductors
year: 1996

abstract: Calculations of the electronic properties of AIN, GaN, InN and their alloys are presented. Initial calculations are performed using the first principles pseudopotenial method to obtain accurate lattice constants. Further calculations then investigate bonding in the nitrides through population analysis and density of state calculations, the empirical pseudopotential method is also used in this work. Pseudopotentials 'or each of the nitrides are constructed using a functional form that allows strained material and alloys to be studied. The conventional k,p valence band parameters for both zincblende and wurtzite are obtained from the empirical band structure using two different methods. A Monte Carlo fitting of the k.p band structure to the pseudopotential data (or an effective mass method for the zincblende structure) is used to produce one set. Another set is obtained directly from the momentum matrix elements and energy eigenvalues at the centre of the Brillouin zone. Both methods of calculating k.p parameters produce band structure in excellent agreement with the original empirical band calculations near the centre of the Brillouin zone. The advantage of the direct method is that it produces consistent sets of parameters, and can be used in studies involving a series of alloy compositions. Further empirical pseudopotential method calculations are then performed for alloys of the nitrides. In particular, the variation of the band gap with alloy composition is investigated, and good agreement with theory and experiment is found. The direct method is used to obtain k.p parameters for the alloys, and is contrasted with the fitting approach. The behaviour of the nitrides under strain is also studied. In particular, valence band offsets for nitride heterojunctions are calculated, and a strong forward backward asymmetry in the band offset is found, in good agreement with other results in the literature.
author_names: D J David
title: Electronic structure calculations on nitride semiconductors and their alloys
year: 2000

abstract: The full zone kp method of band structure calculation is extended to crystals of wurtzite structure, point group C6v. The form of the momentum matrix elements as allowed by symmetry is deduced and used to model the dispersion relations throughout the Brillouin zone for AlN, GaN, and InN. By means of a fitting procedure that refers to an empirical pseudopotential calculation of the eigenvalues at selected high symmetry points, a truncated basis set of 23 states is derived that enables realistic representation of the first ten states, with the remainder serving to encompass all of the deleted remote band interactions. The result is a relatively small dimension effective Hamiltonian suitable for full zone envelope function applications.
author_names: Roderic Beresford
title: Full zone kp method of band structure calculation for wurtzite semiconductors
year: 2004

abstract: We present a theoretical model for calculating the band structures of strained quantum well wurtzite semiconductors. The theory is based on the Hamiltonian for wurtzite semiconductors and includes the strain effects on the shifts of the band edges. We show new results that include the matrix elements of the Hamiltonian using the finite difference method for the calculations of the valence electronic band structures of quantum well wurtzite semiconductors based on the effective mass theory.
author_names: Shun Lien Chuang

C S Chang
title: A band structure model of strained quantum well wurtzite semiconductors
year: 1997

abstract: A simple theoretical method for deducing the effective bond orbital model (EBOM) of III nitride wurtzite (WZ) semiconductors is presented. In this model, the interaction parameters for zinc blende (ZB) structures are used as an initial guess for WZ structure based on the two center approximation. The electronic band structure of III nitride WZ semiconductors can hence be produced by utilizing this set of parameters modified to include effects due to three center integrals and fitting with first principles calculations. Details of the semi empirical fitting procedure for constructing the EBOM Hamiltonian for bulk III nitride WZ semiconductors are presented. The electronic band structure of bulk AlN, GaN, and InN with WZ structure calculated by EBOM with modified interaction parameters are shown and compared to the results obtained from density functional (DFT) theory with meta generalized gradient approximation (mGGA) The set of parameters are further optimized by using a genetic algorithm. In the end, electronic band structures and electron (hole) effective masses near the zone center calculated by the proposed model with best fitting parameters are analyzed and compared with the \mathbf{k}\cdot \mathbf{p} model.
author_names: Fu Chen Hsiao

Ching-Tarng Liang

Yia-Chung Chang

John M Dallesasse
title: Effective bond orbital model of III nitride wurtzite structures based on modified interaction parameters of zinc blende structures
venue: Comput. Phys. Commun.
year: 2020

abstract: A systematic numerical investigation of spin orbit fields in the conduction bands of III V semiconductor nanowires is performed. Zinc blende InSb nanowires are considered along [001] [011] and [111] directions, while wurtzite InAs nanowires are studied along [0001] and [10$\overline{1}$0] or [11$\overline{2}$0] directions. Realistic multiband \vec{k} \cdot \vec{p} Hamiltonians are solved by using plane wave expansions of real space parameters. In all cases the linear and cubic spin orbit coupling parameters are extracted for nanowire widths from 30 to 100 nm. Typical spin orbit energies are on the \mu$eV scale, except for InAs wurtzite nanowires grown along [10$\overline{1}$0] or [11$\overline{2}$0] in which the spin orbit energy is about meV, largely independent of the wire diameter. Significant spin orbit coupling is obtained by applying a transverse electric field, causing the Rashba effect. For an electric field of about 4 mV/nm the obtained spin orbit energies are about 1 meV for both materials in all investigated growth directions. The most favorable system, in which the spin orbit effects are maximal, are InAs WZ nanowires grown along [1010] or [11$\overline{2}$0] since here spin orbit energies are giant (meV) already in the absence of electric field. The least favorable are InAs WZ nanowires grown along [0001] since here even the electric field does not increase the spin orbit energies beyond 0.1 meV. The presented results should be useful for investigations of optical orientation, spin transport, weak localization, and superconducting proximity effects in semiconductor nanowires.
author_names: Tiago de Campos

Paulo E Faria Junior

Martin Gmitra

Guilherme Matos Sipahi

Jaroslav Fabian
title: Spin orbit coupling effects in zinc blende InSb and wurtzite InAs nanowires: realistic calculations with multiband \vec{k} \cdot \vec{p} method
year: 2018

abstract: Using the effective mass Hamiltonian for an arbitrary direction wurtzite semiconductor on the basis of kp theory, we investigate the strain effects on the optical anisotropy in semi polar and nonpolar GaN planes. The optical matrix elements are formulated for an arbitrary direction and calculated for the A and R planes. It is found that giant optical anisotropy appears in the A and R planes and the biaxial strain significantly changes the polarization properties.
author_names: Guo-Dong Hao

Ying-fei Chen
title: IN PLANE OPTICAL ANISOTROPY OF STRAINED WURTZITE GaN IN THE A AND R PLANES
year: 2010

abstract: The problem of spin manipulation via the spin orbit interaction in nonmagnetic semiconductors in the absence of magnetic fields is investigated in this work. We begin with a review of the literature on spin dynamics in semiconductors, then discuss the semi empirical k p method of calculating direct gap semiconductor properties, which we use to estimate material parameters significant for manipulation of spin even in the absence of a magnetic field. The total effective magnetic fields and precession lengths are calculated for a variety of quantum well orientations, and a class of devices are proposed that will allow for all electric arbitrary manipulation of spin orientations. The strainand momentum dependent spin splitting coefficient C3 has been calculated using a fourteen band Kane k *p model for a variety of III V semiconductors as well as ZnSe and CdSe. It is observed that the spin splitting parameters C3 and g, corresponding to the strain induced spin orbit interaction and Dresselhaus coefficient, are sensitive to the value of the inter band spin orbit coupling between the p valence and p second conduction band in all cases. The value of has therefore been recalculated in these materials using a tight binding model and modern experimental values of the valence and second conduction band spin orbit splittings. The total effective magnetic field and precession length of spins in strained quantum wells in the (001) (110) and (111) planes are derived with consideration for all known effective magnetic fields except those due to interface effects in noncommon atom heterostructures (native inversion asymmetry) The orientation of the k linear Dresselhaus field and the strain dependent fields vary strongly with the growth axis of the quantum well. The precession length in the (110) and (001) cases can achieve infinite anisotropy, while the precession length of (111) quantum wells is
author_names: B J Moehlmann
title: Spin transport in strained non magnetic zinc blende semiconductors
year: 2012

abstract: Abstract The electronic band structure of wurtzite semiconductor heterostructures is investigated theoretically using the envelope function k P formalism. We use a Lagrangian formulation for the valence bands so that the order of the derivatives appearing in the multiband description is explicitly specified when Schrodinger's equations for the envelope functions are generated through the application of the principle of least action. The issues of derivative operator ordering and boundary conditions at material interfaces are examined in detail. The theoretical results are presented for arbitrary growth directions and the spin orbit interaction is taken into account. This is of interest, for example, in treating A plane wurtzite heterostructures such as GaN/AlGaN quantum wells grown on R plane sapphire. Strain effects are included using a general rotation method that diagonalizes strain and is appropriate for pseudomorphic wurtzite structures in any allowed orientation. It is shown that inversion asymmetry in the valence band leads to shifts in the band edge energies in the 11 2 0 grown quantum wells. The finite element method is used with the Lagrangian for the composite layered semiconductor structure in order to obtain the energy eigenvalues for multi quantum well systems. Calculations for quantum wells and superlattices are presented.
author_names: L R Ram-Mohan

A Girgis

John D Albrecht

Cole W Litton
title: Wavefunction engineering of layered wurtzite semiconductors grown along arbitrary crystallographic directions
year: 2006

abstract: Abstract The bond orbital Hamiltonian for wurtzite semiconductors is developed. This method contains no fitting parameters, and all interaction parameters involved are directly related to the k p parameters for describing bulk bands near the Brillouin zone center. A comparative study of wurtzite GaN band structures between the bond orbital model and the k p method is also made.
author_names: Chun-Nan Chen
title: Bond orbital model for wurtzite semiconductors
year: 2004