Solution of the 1D Schrödinger equation in semiconductor heterostructures using the immersed interface method

Momox, Ernesto; Zakhleniuk, N. A.; Balkan, N.

doi:10.1016/j.jcp.2012.05.017

Cited by 5 publications

(3 citation statements)

References 21 publications

(21 reference statements)

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“…The propagation of mechanical wave with audible frequency range is not permitted in phononic crystals of periodicities ranging from meters to centimeters. To find the band gap in a phononic crystals, we need to understand the energy band structure of a solid for electrons in a crystalline solid by using following Schrödinger equation [16]:…”

Section: Band Gapmentioning

confidence: 99%

Phononic Crystal Resonators

Bao¹,

Khan²,

Bao³

2018

Phonons in Low Dimensional Structures

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In this chapter we present the theory of phononic crystal, classification of PnC according to its physical nature, and phononic crystal (PnC) phenomena in locally resonant materials with 2D, and 3D crystals structure. In this chapter, phononic crystal (PnC) micro-electro mechanical system (MEMS) resonators with different transduction schemes such as electrostatically, piezoresistively, piezoelectrically transduced MEMS resonators are explained. In this chapter, we employed phononic crystal strip in MEMS resonators is explained to reduce anchor loss, and analysis of eigen frequency mode of the resonators. The phononic crystal strip with supporting tethers is designed to see the formation of band gap by introducing square holes, and improvement of quality factor and harmonic response. We show that holes can help to reduce the static mass of PnC strip tether without affecting on band gaps.

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Section: Band Gapmentioning

confidence: 99%

Phononic Crystal Resonators

Bao¹,

Khan²,

Bao³

2018

Phonons in Low Dimensional Structures

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“…The rapid advancement of semiconductor technology has led to the development of novel heterostructures, such as quantum wells, wires, and dots, which have garnered significant interest due to their unique properties and potential applications in cutting-edge optoelectronic devices [1][2][3][4]. Among these heterostructures, the InP/ InAs/InP system has emerged as a promising candidate for various applications, including lasers, light-emitting diodes, field-effect transistors, photodetectors, and solar cells [5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…Determining the energy levels of charge carriers in semiconductor heterostructures is a fundamental problem in quantum mechanics. The confinement of electrons and holes in potential wells results in the quantization of energy levels, which can be obtained by solving the Schrödinger equation [1][2][3]. Several approaches have been employed to solve this equation, including graphical methods [15][16][17], and various approximate techniques [18][19][20][21][22][23][24][25][26][27][28][29] numerical solutions [30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Unraveling the effects of non-parabolicity on electron energy levels in InP/InAs/InP heterostructures

Davlatov,

Gulyamov,

Nabiyev

et al. 2024

Phys. Scr.

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In this research, electron energy levels were calculated analytically using Nelson's formula, the shooting method, and Garrett's formula for effective mass. These calculations were performed for a rectangular finite deep potential well, focusing on the InP/InAs/InP heterostructure, which is a narrow-bandgap semiconductor system. Our results demonstrate that the nonparabolicity of the dispersion has a more significant effect on higher energy levels compared to lower ones, with deviations of up to 15% for the third energy level. An equation estimating the number of observable energy levels in the potential well is suggested, revealing that considering nonparabolicity leads to a 20% increase in the number of levels compared to the parabolic dispersion case. The relationship between the widths of infinite and finite potential wells for equivalent energy levels follows a linear behaviour, with bonding coefficients ranging from 95,93% to 97,49% and a maximum difference of 1.5% between parabolic and non-parabolic cases. The transcendental equation for the energy levels is linearized, yielding a fourth-order equation that provides results within 98% accuracy compared to the original equation. These findings contribute to the understanding of the energy distribution in InP/InAs/InP heterostructures with a view to their application in optoelectronic devices such as lasers, light-emitting diodes

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EJIIM for the stationary Schrödinger equations with delta potential wells

Bai

Wang

2015

Applied Mathematics and Computation

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Solution of the 1D Schrödinger equation in semiconductor heterostructures using the immersed interface method

Cited by 5 publications

References 21 publications

Phononic Crystal Resonators

Phononic Crystal Resonators

Unraveling the effects of non-parabolicity on electron energy levels in InP/InAs/InP heterostructures

EJIIM for the stationary Schrödinger equations with delta potential wells

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