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The Ben Daniel-Duke model in general nanowire structures

Willatzen, M. and Lassen, Benny LU (2007) In Journal of Physics: Condensed Matter 19(13).
Abstract
A simple computationally effective method is developed for solving the Ben Daniel - Duke equations for nanowire semiconductor heterostructures. The method allows eigenstates and associated energy levels of nanowires with varying cross- sectional shape and/ or varying composition to be obtained, and is based on expanding the envelope function eigenstates on local eigenstates of the corresponding cross- sectional problem. In this way, the original partial differential equation problem is reduced to a set of coupled ordinary differential equations ( this set can to a good approximation be limited to a small number of coupled equations). In the first part of the paper, the model equation framework is derived; it can be easily modified to... (More)
A simple computationally effective method is developed for solving the Ben Daniel - Duke equations for nanowire semiconductor heterostructures. The method allows eigenstates and associated energy levels of nanowires with varying cross- sectional shape and/ or varying composition to be obtained, and is based on expanding the envelope function eigenstates on local eigenstates of the corresponding cross- sectional problem. In this way, the original partial differential equation problem is reduced to a set of coupled ordinary differential equations ( this set can to a good approximation be limited to a small number of coupled equations). In the first part of the paper, the model equation framework is derived; it can be easily modified to account for a more general set of partial differential equations. In the second part of the paper, three different cases of axisymmetrical nanowire problems are analysed in terms of eigenstates and energy eigenvalues. The cases considered are ( a) conical nanowires, ( b) a nanowire with a step in radius, and ( c) a conical GaAs/ GaAlAs nanowire. Comparison with computationally more expensive finite- element results on a two- dimensional domain is made, and good agreement is found. (Less)
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organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Physics: Condensed Matter
volume
19
issue
13
publisher
IOP Publishing
external identifiers
  • wos:000245653500023
  • scopus:33947607551
ISSN
1361-648X
DOI
10.1088/0953-8984/19/13/136217
language
English
LU publication?
yes
id
a3d92d16-8422-410f-95d1-06f60be396e3 (old id 665934)
date added to LUP
2008-01-03 10:28:45
date last changed
2017-01-01 07:28:41
@article{a3d92d16-8422-410f-95d1-06f60be396e3,
  abstract     = {A simple computationally effective method is developed for solving the Ben Daniel - Duke equations for nanowire semiconductor heterostructures. The method allows eigenstates and associated energy levels of nanowires with varying cross- sectional shape and/ or varying composition to be obtained, and is based on expanding the envelope function eigenstates on local eigenstates of the corresponding cross- sectional problem. In this way, the original partial differential equation problem is reduced to a set of coupled ordinary differential equations ( this set can to a good approximation be limited to a small number of coupled equations). In the first part of the paper, the model equation framework is derived; it can be easily modified to account for a more general set of partial differential equations. In the second part of the paper, three different cases of axisymmetrical nanowire problems are analysed in terms of eigenstates and energy eigenvalues. The cases considered are ( a) conical nanowires, ( b) a nanowire with a step in radius, and ( c) a conical GaAs/ GaAlAs nanowire. Comparison with computationally more expensive finite- element results on a two- dimensional domain is made, and good agreement is found.},
  author       = {Willatzen, M. and Lassen, Benny},
  issn         = {1361-648X},
  language     = {eng},
  number       = {13},
  publisher    = {IOP Publishing},
  series       = {Journal of Physics: Condensed Matter},
  title        = {The Ben Daniel-Duke model in general nanowire structures},
  url          = {http://dx.doi.org/10.1088/0953-8984/19/13/136217},
  volume       = {19},
  year         = {2007},
}