Research output: Contribution to journal › Article › peer-review
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
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TY - JOUR
T1 - Variational method of energy level calculation in pyramidal quantum dots
AU - Nenashev, A. V.
AU - Dvurechenskii, A. V.
N1 - Publisher Copyright: © 2020 Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
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