Stable finite element method of eight-band k·p model without spurious solutions and numerical study of interfaces in heterostructures

Ma, Xunpeng; Li, Kangwen; Zhang, Zuyin; Jiang, Yu; Xu, Ya‐Qiong; Song, Guofeng

doi:10.1063/1.4904845

Cited by 8 publications

(5 citation statements)

References 35 publications

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“…To solve these coupled differential equations we employ the plane wave expansion, 95,[100][101][102][103][104] that is, the Fourier transform of the real-space dependent parameters. In narrow gap semiconductors, real-space treatment of confined systems can lead to spurious solutions and special treatment 49,105,106 should be applied to eliminate them, while using Fourier transformation the spurious solutions are easily identifiable and controllable 102 . The plane wave expansion works by creating, effectively, periodically repeated systems of nanowires with vacuum in-between.…”

Section: Nanowire Modelingmentioning

confidence: 99%

Spin-orbit coupling effects in zinc-blende InSb and wurtzite InAs nanowires: Realistic calculations with multiband k·p method

et al. 2018

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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 [1010] or [1120] directions. Robust multiband k · p Hamiltonians are solved by using plane wave expansions of realspace 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 µeV scale, except for InAs wurtzite nanowires grown along [1010] or [1120], 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 [1120], 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. arXiv:1802.06734v2 [cond-mat.mes-hall] 30 Apr 2018Appendix A: Plane wave expansion and numerical details

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Section: Nanowire Modelingmentioning

confidence: 99%

Spin-orbit coupling effects in zinc-blende InSb and wurtzite InAs nanowires: Realistic calculations with multiband k·p method

et al. 2018

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“…The resulting problem is solved numerically, e.g., with finite element method (FEM). For the given approximation, stable FEM implementations, free from spurious solutions, have been developed [ 156 , 157 ]. As a result, the band structure and optical gain of low-dimensional nanostructures can be determined using the 8-band

model.…”

Section: Mathematical and Computational Models For Smart Materials An...mentioning

confidence: 99%

Coupled Multiphysics Modelling of Sensors for Chemical, Biomedical, and Environmental Applications with Focus on Smart Materials and Low-Dimensional Nanostructures

Singh

Melnik

2022

Chemosensors

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Low-dimensional nanostructures have many advantages when used in sensors compared to the traditional bulk materials, in particular in their sensitivity and specificity. In such nanostructures, the motion of carriers can be confined from one, two, or all three spatial dimensions, leading to their unique properties. New advancements in nanosensors, based on low-dimensional nanostructures, permit their functioning at scales comparable with biological processes and natural systems, allowing their efficient functionalization with chemical and biological molecules. In this article, we provide details of such sensors, focusing on their several important classes, as well as the issues of their designs based on mathematical and computational models covering a range of scales. Such multiscale models require state-of-the-art techniques for their solutions, and we provide an overview of the associated numerical methodologies and approaches in this context. We emphasize the importance of accounting for coupling between different physical fields such as thermal, electromechanical, and magnetic, as well as of additional nonlinear and nonlocal effects which can be salient features of new applications and sensor designs. Our special attention is given to nanowires and nanotubes which are well suited for nanosensor designs and applications, being able to carry a double functionality, as transducers and the media to transmit the signal. One of the key properties of these nanostructures is an enhancement in sensitivity resulting from their high surface-to-volume ratio, which leads to their geometry-dependant properties. This dependency requires careful consideration at the modelling stage, and we provide further details on this issue. Another important class of sensors analyzed here is pertinent to sensor and actuator technologies based on smart materials. The modelling of such materials in their dynamics-enabled applications represents a significant challenge as we have to deal with strongly nonlinear coupled problems, accounting for dynamic interactions between different physical fields and microstructure evolution. Among other classes, important in novel sensor applications, we have given our special attention to heterostructures and nucleic acid based nanostructures. In terms of the application areas, we have focused on chemical and biomedical fields, as well as on green energy and environmentally-friendly technologies where the efficient designs and opportune deployments of sensors are both urgent and compelling.

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“…These solutions can be removed by a proper ordering of differential operators [43,44]. Finally, the spurious solutions may also be triggered by the chosen discretization scheme and the mesh width, and it was found to be related to the ill-representation of the first-order derivative terms of the Hamiltonian [40,45].…”

Section: Parabolicmentioning

confidence: 99%

Modeling Energy Bands in Type II Superlattices

Bennecer

Sengouga

2019

Crystals

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We present a rigorous model for the overall band structure calculation using the perturbative k · p approach for arbitrary layered cubic zincblende semiconductor nanostructures. This approach, first pioneered by Kohn and Luttinger, is faster than atomistic ab initio approaches and provides sufficiently accurate information for optoelectronic processes near high symmetry points in semiconductor crystals. k · p Hamiltonians are discretized and diagonalized using a finite element method (FEM) with smoothed mesh near interface edges and different high order Lagrange/Hermite basis functions, hence enabling accurate determination of bound states and related quantities with a small number of elements. Such properties make the model more efficient than other numerical models that are usually used. Moreover, an energy-dependent effective mass non-parabolic model suitable for large gap materials is also included, which offers fast and reasonably accurate results without the need to solve the full multi-band Hamiltonian. Finally, the tools are validated on three semiconductor nanostructures: (1) the bound energies of a finite quantum well using the energy-dependent effective mass non-parabolic model; (2) the InAs bulk band structure; and (3) the electronic band structure for the absorber region of photodetectors based on a type-II InAs/GaSb superlattice at room temperature. The tools are shown to work on simple and sophisticated designs and the results show very good agreement with recently published experimental works.

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Stable finite element method of eight-band k·p model without spurious solutions and numerical study of interfaces in heterostructures

Cited by 8 publications

References 35 publications

Spin-orbit coupling effects in zinc-blende InSb and wurtzite InAs nanowires: Realistic calculations with multiband k·p method

Spin-orbit coupling effects in zinc-blende InSb and wurtzite InAs nanowires: Realistic calculations with multiband k·p method

Coupled Multiphysics Modelling of Sensors for Chemical, Biomedical, and Environmental Applications with Focus on Smart Materials and Low-Dimensional Nanostructures

Modeling Energy Bands in Type II Superlattices

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