Title
Modelling the electron and hole states in semiconductor nanostructures by the multiband k.p theory
Creator
Čukarić, Nemanja A. 1985-
Copyright date
2015
Object Links
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Autorstvo-Nekomercijalno 3.0 Srbija (CC BY-NC 3.0)
License description
Dozvoljavate umnožavanje, distribuciju i javno saopštavanje dela, i prerade, ako se navede ime autora na način odredjen od strane autora ili davaoca licence. Ova licenca ne dozvoljava komercijalnu upotrebu dela. Osnovni opis Licence: http://creativecommons.org/licenses/by-nc/3.0/rs/deed.sr_LATN Sadržaj ugovora u celini: http://creativecommons.org/licenses/by-nc/3.0/rs/legalcode.sr-Latn
Language
English
Cobiss-ID
Theses Type
Doktorska disertacija
description
Datum odbrane: 25.05.2015.
Other responsibilities
mentor
Tadić, Milan Ž.
član komisije
Peeters, François M.
član komisije
Gvozdić, Dejan, 1964-
član komisije
Partoens, Bart.
član komisije
Arsoski, Vladimir, 1975-
Academic Expertise
Tehničko-tehnološke nauke
University
Univerzitet u Beogradu
Faculty
Elektrotehnički fakultet
Alternative title
Modelovanje elektronskih i šupljinskih stanja u poluprovodničkim nanaostrukturama pomoću višezonske k.p teorije
Publisher
[ N. A. Čukarić]
Format
XV, 153 lista
description
Electrical and Computer Engineering - Nanoelectronics and Photonics / Elektrotehnika i računarstvo - Nanoelektronika i fotonika
Abstract (en)
The dissertation presents a study of the electron and hole states in various
semiconductor nanostructures using the k p formalism. Si/SiO2 quantum wells, GaAs/
(Al,Ga)As quantum wells, GaAs/(Al,Ga)As ringlike quantum dots grown by droplet epitaxy,
and ringlike (In,Ga)As/GaAs quantum dots formed by epitaxy in the Stranski-Krastanov
mode are all considered. An overview of the techniques which are used to fabricate
the analyzed nanostructures is first given. The most basic properties of the electronic
structure of silicon and III-V compounds are briefly described.
The fundamentals of the k p theory are explained, and then applied to derive the
equations of the single-band effective-mass theory. The kp theory for degenerate energy
levels, which is the case in the valence band of diamond and zinc-blende semiconductors,
is then presented. By using the perturbation theory, the three-band Dresselhaus-Kip-
Kittel model of the valence-band states is derived for the case of absent spin-orbit interaction.
The spin-orbit interaction is taken into account in the 6-band Luttinger-Kohn model,
whose derivation is also briefly described. The conduction and valence band states of
wide band-gap direct semiconductors and their nanostructures are usually well described
by the single-band effective-mass theory and the 6-band Luttinger-Kohn model, respectively.
The mentioned k p models are well suited for low k states, whereas they cannot
be straightforwardly adopted to model states which are far away from the G point. Such
a situation arises in silicon, where low energy states in the conduction band have large
k. The model which has recently been proposed to handle such a situation is the 30-
band k p theory. It is the full-zone approach, which provides an accurate description of
the electronic structure of both direct and indirect semiconductors in the whole Brillouin
zone. The envelope function approximation, which is a way to apply the k p theory to
nanostructures, is also briefly discussed. Also, it is demonstrated how effects of magnetic...
Abstract (sr)
Rezime: Disertacija predstavlja analizu elektronskih i šupljinskih stanja u različitim
nanostrukturama korišćenjem k . p formalizma. Razmatrane su Si=SiO2 kvantne jame,
GaAs/(Al,Ga)As kvantne jame, prstenolike GaAs/(Al,Ga)As kvantne tačke formirane metodima
kapljične epitaksije i (In,Ga)As/GaAs kvantne tačke proizvedene epitaksijom u
Stranski-Krastanov modu. Dat je pregled tehnika fabrikacije koje se obično koriste za
proizvodnju razmatranih nanostruktura. Osnovna svojstva elektronske strukture silicijuma
i III-V jedinjenja su takođe ukratko razmatrana.
Zatim su predstavljeni osnovi k . p teorije. Prvo je prikazan koncept ove teorije, a zatim
je k . p formalizam primenjen na izvođenje jednozonske jednačine efektivnih masa. Zatim
je predstavljena k . p teorija degenerisanih energetskih nivoa, što je slučaj u valentnoj
zoni poluprovodnika sa dijamantskom i sfaleritnom rešetkom. Izveden je Dresselhaus-
Kip-Kittelov model stanja u valentnoj zoni u odsustvu spin-orbitne interakcije korišćenjem
vremenski nezavisne teorije perturbacija za degenerisana stanja.Potom je uzeta u
obzir spin-orbitna interakcija u okviru šestozonskog Latindžer-Konovog modela. Stanja u
provodnoj i valentnoj zoni u poluprovodnicima sa širokim energetskim procepom obično
se mogu dobro opisati jednozonskom teorijom efektivnih masa i šestozonskim Latindžer-
Konovim modelom, respektivno. Međutim, primena ovih modela je ograničena na stanja
sa malim vrednostima talasnog vektora elektrona k, dok se ne mogu primeniti za opis
elektronske strukture daleko od G tačke. Potreba za dobrim opisom disperzije elektronskih
zona daleko od centra Briluenove zone postoji u silicijumu, gde niskoenergetska elektronska
stanja imaju veliku vrednost k. Pogodna teorija za ovaj slučaj je 30-zonski k . p
model. Ovaj metod omogućuje računanje elektronske strukture u celoj prvoj Briluenoj
zoni, stoga se može koristiti kako za direktne, tako i za indirektne poluprovodnike. Zatim
je ukratko izložena aproksimacija anvelopnih funkcija, koja predstavlja metod za...
Authors Key words
silicon, III-V compounds, quantum well, quantum dot, quantum ring, k . p
theory, multiband, 30-band Hamiltonian, optical absorption, Aharonov-Bohm effect
Authors Key words
silicijum, III-V jedinjenja, kvantna jama, kvantna tačka, kvantni prsten,
k . p teorija, višezonski, 30-zonski hamiltonijan, optička apsorpcija, Aharonov-Bohmov
efekat
Classification
621.3
Type
Tekst
Abstract (en)
The dissertation presents a study of the electron and hole states in various
semiconductor nanostructures using the k p formalism. Si/SiO2 quantum wells, GaAs/
(Al,Ga)As quantum wells, GaAs/(Al,Ga)As ringlike quantum dots grown by droplet epitaxy,
and ringlike (In,Ga)As/GaAs quantum dots formed by epitaxy in the Stranski-Krastanov
mode are all considered. An overview of the techniques which are used to fabricate
the analyzed nanostructures is first given. The most basic properties of the electronic
structure of silicon and III-V compounds are briefly described.
The fundamentals of the k p theory are explained, and then applied to derive the
equations of the single-band effective-mass theory. The kp theory for degenerate energy
levels, which is the case in the valence band of diamond and zinc-blende semiconductors,
is then presented. By using the perturbation theory, the three-band Dresselhaus-Kip-
Kittel model of the valence-band states is derived for the case of absent spin-orbit interaction.
The spin-orbit interaction is taken into account in the 6-band Luttinger-Kohn model,
whose derivation is also briefly described. The conduction and valence band states of
wide band-gap direct semiconductors and their nanostructures are usually well described
by the single-band effective-mass theory and the 6-band Luttinger-Kohn model, respectively.
The mentioned k p models are well suited for low k states, whereas they cannot
be straightforwardly adopted to model states which are far away from the G point. Such
a situation arises in silicon, where low energy states in the conduction band have large
k. The model which has recently been proposed to handle such a situation is the 30-
band k p theory. It is the full-zone approach, which provides an accurate description of
the electronic structure of both direct and indirect semiconductors in the whole Brillouin
zone. The envelope function approximation, which is a way to apply the k p theory to
nanostructures, is also briefly discussed. Also, it is demonstrated how effects of magnetic...
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