Analysis of boundary conditions for the envelope functions of GaN/InGaN(0001) heterostructures

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Abstract

Within the framework of the method of envelope functions, various matching conditions on the GaN/InGaN(0001) heteroboundaries are considered. The conditions of matching the envelope functions at which functions are joined with functions and derivatives are joined with derivatives for states in the center of the flat Brillouin zone are conventionally used. In this case, the envelope functions are symmetric (antisymmetric) about the quantum well center. This should not be the case for the anisotropic nitride heterostructures. The matching conditions based on pseudopotential calculations are suggested. These conditions qualitatively differ from those used conventionally and lead to discontinuities of the envelope functions on the heteroboundaries and removal of the above-mentioned symmetry even disregarding embedded spontaneous and piezoelectric polarization fields. The electron envelope functions appear shifted from the quantum well center in the direction of the [0001] hexagonal axis, and the holes envelope functions are shifted in the opposite direction. Different matching conditions considered in the present work lead to the energy levels in the well that differ from each other by several millielectronvolts. The electron and hole envelope functions important for the optical characteristics differ insignificantly when different matching conditions are employed; however, some of them become nonzero due to removal of the artificial symmetry.

Original languageEnglish
Pages (from-to)764-771
Number of pages8
JournalRussian Physics Journal
Volume55
Issue number7
DOIs
Publication statusPublished - Dec 2012

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envelopes
boundary conditions
quantum wells
symmetry
Brillouin zones
pseudopotentials
nitrides
discontinuity
electrons
energy levels
polarization

Keywords

  • energy level
  • envelope functions
  • heterostructure
  • matching conditions
  • quantum well

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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title = "Analysis of boundary conditions for the envelope functions of GaN/InGaN(0001) heterostructures",
abstract = "Within the framework of the method of envelope functions, various matching conditions on the GaN/InGaN(0001) heteroboundaries are considered. The conditions of matching the envelope functions at which functions are joined with functions and derivatives are joined with derivatives for states in the center of the flat Brillouin zone are conventionally used. In this case, the envelope functions are symmetric (antisymmetric) about the quantum well center. This should not be the case for the anisotropic nitride heterostructures. The matching conditions based on pseudopotential calculations are suggested. These conditions qualitatively differ from those used conventionally and lead to discontinuities of the envelope functions on the heteroboundaries and removal of the above-mentioned symmetry even disregarding embedded spontaneous and piezoelectric polarization fields. The electron envelope functions appear shifted from the quantum well center in the direction of the [0001] hexagonal axis, and the holes envelope functions are shifted in the opposite direction. Different matching conditions considered in the present work lead to the energy levels in the well that differ from each other by several millielectronvolts. The electron and hole envelope functions important for the optical characteristics differ insignificantly when different matching conditions are employed; however, some of them become nonzero due to removal of the artificial symmetry.",
keywords = "energy level, envelope functions, heterostructure, matching conditions, quantum well",
author = "Karavaev, {G. F.} and Victor Nikolaevich Chernyshov and Razzhuvalov, {A. N.}",
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AU - Karavaev, G. F.

AU - Chernyshov, Victor Nikolaevich

AU - Razzhuvalov, A. N.

PY - 2012/12

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N2 - Within the framework of the method of envelope functions, various matching conditions on the GaN/InGaN(0001) heteroboundaries are considered. The conditions of matching the envelope functions at which functions are joined with functions and derivatives are joined with derivatives for states in the center of the flat Brillouin zone are conventionally used. In this case, the envelope functions are symmetric (antisymmetric) about the quantum well center. This should not be the case for the anisotropic nitride heterostructures. The matching conditions based on pseudopotential calculations are suggested. These conditions qualitatively differ from those used conventionally and lead to discontinuities of the envelope functions on the heteroboundaries and removal of the above-mentioned symmetry even disregarding embedded spontaneous and piezoelectric polarization fields. The electron envelope functions appear shifted from the quantum well center in the direction of the [0001] hexagonal axis, and the holes envelope functions are shifted in the opposite direction. Different matching conditions considered in the present work lead to the energy levels in the well that differ from each other by several millielectronvolts. The electron and hole envelope functions important for the optical characteristics differ insignificantly when different matching conditions are employed; however, some of them become nonzero due to removal of the artificial symmetry.

AB - Within the framework of the method of envelope functions, various matching conditions on the GaN/InGaN(0001) heteroboundaries are considered. The conditions of matching the envelope functions at which functions are joined with functions and derivatives are joined with derivatives for states in the center of the flat Brillouin zone are conventionally used. In this case, the envelope functions are symmetric (antisymmetric) about the quantum well center. This should not be the case for the anisotropic nitride heterostructures. The matching conditions based on pseudopotential calculations are suggested. These conditions qualitatively differ from those used conventionally and lead to discontinuities of the envelope functions on the heteroboundaries and removal of the above-mentioned symmetry even disregarding embedded spontaneous and piezoelectric polarization fields. The electron envelope functions appear shifted from the quantum well center in the direction of the [0001] hexagonal axis, and the holes envelope functions are shifted in the opposite direction. Different matching conditions considered in the present work lead to the energy levels in the well that differ from each other by several millielectronvolts. The electron and hole envelope functions important for the optical characteristics differ insignificantly when different matching conditions are employed; however, some of them become nonzero due to removal of the artificial symmetry.

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