The exciton structure and optical properties of semiconductor nanodots and nanorings

Ova disertacija se bavi proračunom stanja neutralnog ekscitona u poluprovodničkim nanotačakama (kvantnim tačkama) i nanoprstenovima (kvantnim prstenovima) i modelovanjem njihovih optičkih osobina. Neutralni eksciton je kvazičestica koja predstavlja vezano stanje elektrona i šupljine izmeĎu kojih postoji privlačna Coulombova sila. Iako je električno neutralan, polarizacija ekscitona je konačna usled različitog konfiniranja elektrona i šupljine u nanotačkama. Ovo dovodi do povoljnih uslova za manifestaciju efekata kvantne interferencije, kakav je ekscitonski Aharonov-Bohmov (AB) efekat. Ovaj istaknuti efekat, koji otvara mogućnosti primene nanotačaka i nanoprstenova u nanoelektronici i fotonici, uslovljen je sastavom i morfologijom nanostrukture koji suštinski zavise od tehnologije koja se koristi za izradu nanotačaka i nanoprstenova. Stoga je u disertaciji dat sistematizovan prikaz novijih tehnika za formiranje nanotačaka i nanoprstenova. Prva prikazana tehnika je modifikovana kapljična epitaksija, koja se koristi za proizvodnju nenapregnutih GaAs/(Al,Ga)As nanotačaka, čiji se oblik moţe kontrolisati izborom odreĎenih tehnoloških parametara. Druga tehnika je Stranski-Krastanow (SK) mod narastanja, koji se koristi za proizvodnju napregnutih nanotačaka, kao što su one od (In,Ga)As u matrici od GaAs. Dimenzije ovih nanotačaka su reda nanometra, i paţljivom kontrolom parametara rasta ove nanotačke se mogu pretvoriti u strukture slične prstenovima, koje se nazivaju nanoprstenovi. MeĎutim, po rastu nanoprstena zaostaje tanak sloj unutar njegovog nominalnog otvora, tako da topologija ove strukture nije dvostruko povezana. Dat je sumarni pregled III-V poluprovodničkih jedinjenja i njihovih legura koje se koriste za proizvodnju analiziranih nanotačaka i nanoprstenova. Prikazane su i diskutovane formule koje se koriste za računanje parametara zonske strukture za datu temperaturu, molski udeo itd. Detaljno su opisani teorijski modeli analiziranih nanostruktura. Razmatrane su osobenosti aksijalno simetričnih nanotačaka i nanoprstenova. Korišćena su dva modela naprezanja koji su zasnovani na mehanici kontinuuma: kontinualno mehanički-model iv (CM) za slučaj kada je anizotropija elastičnih osobina prisutna u strukturi i jednostavni model izotropne elastičnosti (IE). Pokazano je da se rezultati dva modela malo meĎusobno razlikuju za analizirane aksijalno simetrične strukture. U slučaju idealizovane geometrije sa strmim granicama na mestu heterospoja postojeći IE model je sveden na numeričko rešavanje jednodimenzionih (1D) integrala...The main objective of the presented thesis is the calculation of the neutral exciton states in semiconductor nanodots (quantum dots) and nanorings (quantum rings) and the modelling of their optical properties. The neutral exciton is a quasiparticle that represents a bound state of the electron and hole which mutually interact by the attractive Coulomb force. Although the exciton is an electrically neutral object, the different confinement of the electron and hole in the nanodot brings about a finite exciton polarization. This in turn establishes a favorable condition for the manifestation of quantum interference effects, such as the excitonic Aharonov-Bohm (AB) effect. This quantum effect, which opens up venues for practical applications of nanorings and nanodots in nanoelectronics and photonics, is influenced by the composition and the morphology of the specific nanostructure, which essentially depends on the technology employed for the fabrication of those nanodots and nanorings. Therefore, recent techniques for the fabrication of nanodots and nanorings are systematically reviewed in the thesis. The first is the modified droplet epitaxy, which allows the fabrication of unstrained GaAs/(Al,Ga)As nanodots, whose shape could be easily controlled by varying certain technological parameters. The second technique is the Stranski-Krastanow (SK) mode of epitaxial growth, which is employed to produce strained nanodots, such as those made of (In,Ga)As in a matrix of GaAs. Their dimensions are of the order of a few nanometers, and by careful control of the growth parameters these nanodots can be turned into ring-like structures, which are called nanorings. However, after growth a thin layer remains inside the nominal ring opening, therefore they do not have double connected topology. The properties of III-V semiconductor compounds and their alloys which are employed to fabricate the analyzed nanodots and nanorings are reviewed. The formulas for computing various band structure parameters for a given temperature, mole fraction etc. are given and discussed. The theoretical models of the analyzed nanodots are described in detail. Peculiarities of the axially symmetric nanodots and nanorings are considered. I used two vii models of elasticity which are based on continuum mechanics: the continuummechanical model (CM) was applied to the case when anisotropic elasticity is present in the structure, and a simple model of isotropic elasticity (IE). I showed that the results of those two models negligibly deviate from each other for the analyzed axially symmetric structures. Furthermore, in the case of an idealized geometry with steep boundaries at the heterojunction the results of the IE model could be reduced to one-dimensional (1D) integrals that have to be calculated numerically..