Variational method of energy level calculation in pyramidal quantum dots

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Variational method of energy level calculation in pyramidal quantum dots. / Nenashev, A. V.; Dvurechenskii, A. V.

In: Journal of Applied Physics, Vol. 127, No. 15, 154301, 21.04.2020.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{fd9bf678bd9e407fa84fd25c062de860,

title = "Variational method of energy level calculation in pyramidal quantum dots",

abstract = "We suggest a variational method for finding the ground state energy in pyramidal quantum dots. The method is based on using a Gaussian trial wavefunction. We developed an analytical expression for the expectation value of the carrier energy in quantum dots with a constant confining potential (within a single-band model). The problem of finding the ground state energy was reduced to the minimization of an analytical function of three trial function parameters. The proposed variational approach is much faster than the direct approach when solving the three-dimensional Schr{\"o}dinger equation, does not demand any special software, and produces quite accurate values of the carrier ground state energy (an error does not exceed 2% of the potential well depth). Generalization of the method to multi-band models, spatially inhomogeneous potentials, effective mass discontinuity, and excited states is discussed. Applicability of the method to different quantum dot systems is considered.",

keywords = "ELECTRONIC-STRUCTURE, STRAIN, STATES, BAND, EXCITONS, SPACE, FIELD",

author = "Nenashev, {A. V.} and Dvurechenskii, {A. V.}",

year = "2020",

month = apr,

day = "21",

doi = "10.1063/1.5143822",

language = "English",

volume = "127",

journal = "Journal of Applied Physics",

issn = "0021-8979",

publisher = "AMER INST PHYSICS",

number = "15",

}

RIS

TY - JOUR

T1 - Variational method of energy level calculation in pyramidal quantum dots

AU - Nenashev, A. V.

AU - Dvurechenskii, A. V.

PY - 2020/4/21

Y1 - 2020/4/21

N2 - We suggest a variational method for finding the ground state energy in pyramidal quantum dots. The method is based on using a Gaussian trial wavefunction. We developed an analytical expression for the expectation value of the carrier energy in quantum dots with a constant confining potential (within a single-band model). The problem of finding the ground state energy was reduced to the minimization of an analytical function of three trial function parameters. The proposed variational approach is much faster than the direct approach when solving the three-dimensional Schrödinger equation, does not demand any special software, and produces quite accurate values of the carrier ground state energy (an error does not exceed 2% of the potential well depth). Generalization of the method to multi-band models, spatially inhomogeneous potentials, effective mass discontinuity, and excited states is discussed. Applicability of the method to different quantum dot systems is considered.

AB - We suggest a variational method for finding the ground state energy in pyramidal quantum dots. The method is based on using a Gaussian trial wavefunction. We developed an analytical expression for the expectation value of the carrier energy in quantum dots with a constant confining potential (within a single-band model). The problem of finding the ground state energy was reduced to the minimization of an analytical function of three trial function parameters. The proposed variational approach is much faster than the direct approach when solving the three-dimensional Schrödinger equation, does not demand any special software, and produces quite accurate values of the carrier ground state energy (an error does not exceed 2% of the potential well depth). Generalization of the method to multi-band models, spatially inhomogeneous potentials, effective mass discontinuity, and excited states is discussed. Applicability of the method to different quantum dot systems is considered.

KW - ELECTRONIC-STRUCTURE

KW - STRAIN

KW - STATES

KW - BAND

KW - EXCITONS

KW - SPACE

KW - FIELD

UR - http://www.scopus.com/inward/record.url?scp=85083572189&partnerID=8YFLogxK

U2 - 10.1063/1.5143822

DO - 10.1063/1.5143822

M3 - Article

AN - SCOPUS:85083572189

VL - 127

JO - Journal of Applied Physics

JF - Journal of Applied Physics

SN - 0021-8979

IS - 15

M1 - 154301

ER -

ID: 24076495