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Title: Applicability of the {bold k}{center_dot}{bold p} method to the electronic structure of quantum dots

Abstract

The {bold k}{center_dot}{bold p} method has become the {open_quotes}standard model{close_quotes} for describing the electronic structure of nanometer-size quantum dots. In this paper we perform parallel {bold k}{center_dot}{bold p} (6{times}6 and 8{times}8) and direct-diagonalization pseudopotential studies on spherical quantum dots of an ionic material{emdash}CdSe, and a covalent material{emdash}InP. By using an equivalent input in both approaches, i.e., starting from a given atomic pseudopotential and deriving from it the Luttinger parameters in {bold k}{center_dot}{bold p} calculation, we investigate the effect of the different underlying wave-function representations used in {bold k}{center_dot}{bold p} and in the more exact pseudopotential direct diagonalization. We find that (i) the 6{times}6{bold k}{center_dot}{bold p} envelope function has a distinct (odd or even) parity, while atomistic wave function is parity-mixed. The 6{times}6{bold k}{center_dot}{bold p} approach produces an incorrect order of the highest valence states for both InP and CdSe dots: the p-like level is above the s-like level. (ii) It fails to reveal that the second conduction state in small InP dots is folded from the L point in the Brillouin zone. Instead, all states in {bold k}{center_dot}{bold p} are described as {Gamma}-like. (iii) The {bold k}{center_dot}{bold p} overestimates the confinement energies of both valence states and conduction states. Amore » wave-function projection analysis shows that the principal reasons for these {bold k}{center_dot}{bold p} errors in dots are (a) use of restricted basis set, and (b) incorrect {ital bulk} dispersion relation. Error (a) can be reduced only by increasing the number of basis functions. Error (b) can be reduced by altering the {bold k}{center_dot}{bold p} implementation so as to bend upwards the second lowest bulk band, and to couple the conduction band into the s-like dot valence state. Our direct diagonalization approach provides an accurate and practical replacement to the standard model in that it is rather general, and can be performed simply on a standard workstation. {copyright} {ital 1998} {ital The American Physical Society}« less

Authors:
; ;  [1]
  1. National Renewable Energy Laboratory, Golden, Colorado 80401 (United States)
Publication Date:
OSTI Identifier:
600990
Resource Type:
Journal Article
Journal Name:
Physical Review, B: Condensed Matter
Additional Journal Information:
Journal Volume: 57; Journal Issue: 16; Other Information: PBD: Apr 1998
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; ELECTRONIC STRUCTURE; SEMICONDUCTOR MATERIALS; CADMIUM SELENIDES; INDIUM PHOSPHIDES; WAVE FUNCTIONS; BRILLOUIN ZONES; DISPERSION RELATIONS; BAND THEORY; INTERFACES

Citation Formats

Fu, H, Wang, L, and Zunger, A. Applicability of the {bold k}{center_dot}{bold p} method to the electronic structure of quantum dots. United States: N. p., 1998. Web. doi:10.1103/PhysRevB.57.9971.
Fu, H, Wang, L, & Zunger, A. Applicability of the {bold k}{center_dot}{bold p} method to the electronic structure of quantum dots. United States. https://doi.org/10.1103/PhysRevB.57.9971
Fu, H, Wang, L, and Zunger, A. 1998. "Applicability of the {bold k}{center_dot}{bold p} method to the electronic structure of quantum dots". United States. https://doi.org/10.1103/PhysRevB.57.9971.
@article{osti_600990,
title = {Applicability of the {bold k}{center_dot}{bold p} method to the electronic structure of quantum dots},
author = {Fu, H and Wang, L and Zunger, A},
abstractNote = {The {bold k}{center_dot}{bold p} method has become the {open_quotes}standard model{close_quotes} for describing the electronic structure of nanometer-size quantum dots. In this paper we perform parallel {bold k}{center_dot}{bold p} (6{times}6 and 8{times}8) and direct-diagonalization pseudopotential studies on spherical quantum dots of an ionic material{emdash}CdSe, and a covalent material{emdash}InP. By using an equivalent input in both approaches, i.e., starting from a given atomic pseudopotential and deriving from it the Luttinger parameters in {bold k}{center_dot}{bold p} calculation, we investigate the effect of the different underlying wave-function representations used in {bold k}{center_dot}{bold p} and in the more exact pseudopotential direct diagonalization. We find that (i) the 6{times}6{bold k}{center_dot}{bold p} envelope function has a distinct (odd or even) parity, while atomistic wave function is parity-mixed. The 6{times}6{bold k}{center_dot}{bold p} approach produces an incorrect order of the highest valence states for both InP and CdSe dots: the p-like level is above the s-like level. (ii) It fails to reveal that the second conduction state in small InP dots is folded from the L point in the Brillouin zone. Instead, all states in {bold k}{center_dot}{bold p} are described as {Gamma}-like. (iii) The {bold k}{center_dot}{bold p} overestimates the confinement energies of both valence states and conduction states. A wave-function projection analysis shows that the principal reasons for these {bold k}{center_dot}{bold p} errors in dots are (a) use of restricted basis set, and (b) incorrect {ital bulk} dispersion relation. Error (a) can be reduced only by increasing the number of basis functions. Error (b) can be reduced by altering the {bold k}{center_dot}{bold p} implementation so as to bend upwards the second lowest bulk band, and to couple the conduction band into the s-like dot valence state. Our direct diagonalization approach provides an accurate and practical replacement to the standard model in that it is rather general, and can be performed simply on a standard workstation. {copyright} {ital 1998} {ital The American Physical Society}},
doi = {10.1103/PhysRevB.57.9971},
url = {https://www.osti.gov/biblio/600990}, journal = {Physical Review, B: Condensed Matter},
number = 16,
volume = 57,
place = {United States},
year = {Wed Apr 01 00:00:00 EST 1998},
month = {Wed Apr 01 00:00:00 EST 1998}
}