Limited accuracy of conduction band effective mass equations for semiconductor quantum dots

Abstract Effective mass equations are the simplest models of carrier states in a semiconductor structures that reduce the complexity of a solid-state system to Schrödinger- or Pauli-like equations resempling those well known from quantum mechanics textbooks. Here we present a systematic derivation o...

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Autores principales:	Adam Mielnik-Pyszczorski, Krzysztof Gawarecki, Paweł Machnikowski
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2018
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/db52853d41b247679ebfc2acbdcdf744
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spelling	oai:doaj.org-article:db52853d41b247679ebfc2acbdcdf7442021-12-02T15:07:44ZLimited accuracy of conduction band effective mass equations for semiconductor quantum dots10.1038/s41598-018-21043-32045-2322https://doaj.org/article/db52853d41b247679ebfc2acbdcdf7442018-02-01T00:00:00Zhttps://doi.org/10.1038/s41598-018-21043-3https://doaj.org/toc/2045-2322Abstract Effective mass equations are the simplest models of carrier states in a semiconductor structures that reduce the complexity of a solid-state system to Schrödinger- or Pauli-like equations resempling those well known from quantum mechanics textbooks. Here we present a systematic derivation of a conduction-band effective mass equation for a self-assembled semiconductor quantum dot in a magnetic field from the 8-band k · p theory. The derivation allows us to classify various forms of the effective mass equations in terms of a hierarchy of approximations. We assess the accuracy of the approximations in calculating selected spectral and spin-related characteristics. We indicate the importance of preserving the off-diagonal terms of the valence band Hamiltonian and argue that an effective mass theory cannot reach satisfactory accuracy without self-consistently including non-parabolicity corrections and renormalization of k · p parameters. Quantitative comparison with the 8-band k · p results supports the phenomenological Roth-Lax-Zwerdling formula for the g-factor in a nanostructure.Adam Mielnik-PyszczorskiKrzysztof GawareckiPaweł MachnikowskiNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 8, Iss 1, Pp 1-12 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Adam Mielnik-Pyszczorski Krzysztof Gawarecki Paweł Machnikowski Limited accuracy of conduction band effective mass equations for semiconductor quantum dots
description	Abstract Effective mass equations are the simplest models of carrier states in a semiconductor structures that reduce the complexity of a solid-state system to Schrödinger- or Pauli-like equations resempling those well known from quantum mechanics textbooks. Here we present a systematic derivation of a conduction-band effective mass equation for a self-assembled semiconductor quantum dot in a magnetic field from the 8-band k · p theory. The derivation allows us to classify various forms of the effective mass equations in terms of a hierarchy of approximations. We assess the accuracy of the approximations in calculating selected spectral and spin-related characteristics. We indicate the importance of preserving the off-diagonal terms of the valence band Hamiltonian and argue that an effective mass theory cannot reach satisfactory accuracy without self-consistently including non-parabolicity corrections and renormalization of k · p parameters. Quantitative comparison with the 8-band k · p results supports the phenomenological Roth-Lax-Zwerdling formula for the g-factor in a nanostructure.
format	article
author	Adam Mielnik-Pyszczorski Krzysztof Gawarecki Paweł Machnikowski
author_facet	Adam Mielnik-Pyszczorski Krzysztof Gawarecki Paweł Machnikowski
author_sort	Adam Mielnik-Pyszczorski
title	Limited accuracy of conduction band effective mass equations for semiconductor quantum dots
title_short	Limited accuracy of conduction band effective mass equations for semiconductor quantum dots
title_full	Limited accuracy of conduction band effective mass equations for semiconductor quantum dots
title_fullStr	Limited accuracy of conduction band effective mass equations for semiconductor quantum dots
title_full_unstemmed	Limited accuracy of conduction band effective mass equations for semiconductor quantum dots
title_sort	limited accuracy of conduction band effective mass equations for semiconductor quantum dots
publisher	Nature Portfolio
publishDate	2018
url	https://doaj.org/article/db52853d41b247679ebfc2acbdcdf744
work_keys_str_mv	AT adammielnikpyszczorski limitedaccuracyofconductionbandeffectivemassequationsforsemiconductorquantumdots AT krzysztofgawarecki limitedaccuracyofconductionbandeffectivemassequationsforsemiconductorquantumdots AT pawełmachnikowski limitedaccuracyofconductionbandeffectivemassequationsforsemiconductorquantumdots
_version_	1718388419986456576

Limited accuracy of conduction band effective mass equations for semiconductor quantum dots

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