Simulating the electronic properties of semiconductor nanostructures using multiband <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si16.svg"><mml:mrow><mml:mi mathvariant="bold">k</mml:mi><mml:mo>·</mml:mo><mml:mi mathvariant="bold">p</mml:mi></mml:mrow></mml:math> models

Marquardt, Oliver

doi:10.1016/j.commatsci.2021.110318

“…More specifically, this method assumes that all states of U n = (0, r) (potential function) and the energy E n (0) of the crystal electrons at k = 0 are known, and as a result, the expression and wave function of E n (k) near k = 0 are obtained using the perturbation method according to the crystal symmetry. The band structures of special points in the k space can be determined by the band parameters, such as the band gap width, the electron effective mass, and the hole effective mass obtained experimentally, so the band structures of other points in the k space can be determined according to the k•p perturbation method [176]. Owing to the narrow band gap width, strong electron interactions, and strong electron spin-orbit interactions, these effects can be handled well by the perturbation method (Figure 10).…”

Section: Definition Of the K•p Perturbation Methodsmentioning

confidence: 99%

“…Furthermore, the application of strain was found to easily shift the energy band of the pyramidal InAs/GaAs QD heterostruc-Figure 10. Calculation of the electronic band structure using the k•p perturbation method with bulk GaAs as an example [176]: (a) zinc-blende (ZB), (b) wurtzite (WZ).…”

Section: Iii-v Pyramidal Semiconductor Quantum Dotsmentioning

confidence: 99%

Role of Pyramidal Low-Dimensional Semiconductors in Advancing the Field of Optoelectronics

Jiang,

Xing,

Lin

et al. 2024

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Numerous optoelectronic devices based on low-dimensional nanostructures have been developed in recent years. Among these, pyramidal low-dimensional semiconductors (zero- and one-dimensional nanomaterials) have been favored in the field of optoelectronics. In this review, we discuss in detail the structures, preparation methods, band structures, electronic properties, and optoelectronic applications (photocatalysis, photoelectric detection, solar cells, light-emitting diodes, lasers, and optical quantum information processing) of pyramidal low-dimensional semiconductors and demonstrate their excellent photoelectric performances. More specifically, pyramidal semiconductor quantum dots (PSQDs) possess higher mobilities and longer lifetimes, which would be more suitable for photovoltaic devices requiring fast carrier transport. In addition, the linear polarization direction of exciton emission is easily controlled via the direction of magnetic field in PSQDs with C3v symmetry, so that all-optical multi-qubit gates based on electron spin as a quantum bit could be realized. Therefore, the use of PSQDs (e.g., InAs, GaN, InGaAs, and InGaN) as effective candidates for constructing optical quantum devices is examined due to the growing interest in optical quantum information processing. Pyramidal semiconductor nanorods (PSNRs) and pyramidal semiconductor nanowires (PSNWRs) also exhibit the more efficient separation of electron-hole pairs and strong light absorption effects, which are expected to be widely utilized in light-receiving devices. Finally, this review concludes with a summary of the current problems and suggestions for potential future research directions in the context of pyramidal low-dimensional semiconductors.

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“…The first term in 𝐹 𝑎 𝜇𝜁,𝜇 ′ 𝜁 ′ gives the contribution from the all-electron wavefunction in the augmentation sphere, and the second term cancels the contribution from the pseudo wavefunction in the augmentation sphere that is counted in the first term of Eq. (25).…”

Section: ∑︀mentioning

confidence: 99%

“…Therefore, to calculate the matrix of the local operator F , we need to calculate ⟨ ̃︀ 𝑚(𝑘0)| F |̃︀ 𝑛(𝑘0)⟩ and 𝐹 𝑎 𝜇𝜁,𝜈𝜁 ′ in Eq. (25).…”

Section: ∑︀mentioning

confidence: 99%

“…There are some arbitrary parameters in 𝑘•𝑝 models, which could be determined by fitting to the corresponding experimental data or the DFT calculation data such as band structures. The 𝑘 •𝑝 method has been successfully applied to many condensed-matter systems, including metals, [15,16] semiconductors, [17,18] topological insulators and superconductors, [19][20][21][22] spin-lasers, [23,24] nanostructured solids, [25] two-dimensional van der Waals materials, [26,27] and so on. [28][29][30][31] When a magnetic field is applied to a condensed matter system, we can use effective Zeeman's coupling Hamiltonian to describe the effects of the magnetic field.…”

mentioning

confidence: 99%

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VASP2KP: k⋅p Models and Landé g-Factors from ab initio Calculations

Zhang 章,

Sheng 盛,

Song 宋

et al. 2023

Chinese Phys. Lett.

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The k⋅p method is significant in condensed matter physics for the compact and analytical Hamiltonian. In the presence of magnetic field, it is described by the effective Zeeman’s coupling Hamiltonian with Landé g-factors. Here, we develop an open-source package VASP2KP (including two parts: vasp2mat and mat2kp) to compute k⋅p parameters and Landé g-factors directly from the wavefunctions provided by the density functional theory (DFT) as implemented in Vienna ab initio Simulation Package (VASP). First, we develop a VASP patch vasp2mat to compute matrix representations of the generalized momentum operator π ^ = p ^ + 1 2 m c 2 [ s ^ × ∇ V ( r ) ] , spin operator s ^ , time reversal operator T ^ , and crystalline symmetry operators R ^ on the DFT wavefunctions. Second, we develop a python code mat2kp to obtain the unitary transformation U that rotates the degenerate DFT basis towards the standard basis, and then automatically compute the k⋅p parameters and g-factors. The theory and the methodology behind VASP2KP are described in detail. The matrix elements of the operators are derived comprehensively and computed correctly within the projector augmented wave method. We apply this package to some materials, e.g., Bi2Se3, Na3Bi, Te, InAs and 1H-TMD monolayers. The obtained effective model’s dispersions are in good agreement with the DFT data around the specific wave vector, and the g-factors are consistent with experimental data. The VASP2KP package is available at https://github.com/zjwang11/VASP2KP.

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Band parameters of group III–V semiconductors in wurtzite structure

Ziembicki

¹

,

Scharoch

²

,

Polak

³

et al. 2022

Journal of Applied Physics

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The properties of most III–V semiconductor materials in the wurtzite structure are not known because of their metastable character. However, recent advances in the growth of III–V wurtzite nanorods open new perspectives for applications. In this work, we present a systematic computational study of bulk wurtzite III–V semiconductors, using predictive ab initio methods, to provide a necessary base knowledge for studying the nanostructures. The most important physical properties of bulk systems, i.e., lattice constants, elasticity, spontaneous polarization, piezoelectricity, band structures, deformation potentials, and band offsets, have been studied. Comparison with the available experimental and theoretical data shows the high credibility of our results. Moreover, we provide a complete set of parameters for a six-band [Formula: see text] model, which is widely used for simulating devices based on semiconductor heterostructures.

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Simulating the electronic properties of semiconductor nanostructures using multiband k·p models

Cited by 5 publications

References 89 publications

Role of Pyramidal Low-Dimensional Semiconductors in Advancing the Field of Optoelectronics

Role of Pyramidal Low-Dimensional Semiconductors in Advancing the Field of Optoelectronics

VASP2KP: k⋅p Models and Landé g-Factors from ab initio Calculations

Band parameters of group III–V semiconductors in wurtzite structure

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