Semiconductor nanowires (NWs) manifest unique physical properties due to their reduced dimensionality and represent a promising platform for a wide range of applications in nanotechnology and electronics. NWs can be reliably manufactured in single crystal structures, with precise control of crucial parameters such as chemical composition, dimensions, and doping, enabling to engineer a vast range of devices and integration techniques, including NW-based FETs, p-n junctions, light-harvesting and thermoelectric devices. Moreover, the demonstration of NWs with radial material modulation, also referred to as core-shell NWs (CSNWs), paved the way to devices with enhanced performance and new functionalities through wave-function engineering and quantum effects. Among the theoretical methods used to describe semiconductor nanostructures, the self-consistent k∙p method, combined with the envelope function approximation, stands out for computational efficiency and predictivity. Of relevance here is the ability to describe the interplay between spin-orbit coupling (SOC) in the underlying compounds, material modulations, and structural parameters. Within this thesis we developed and used an original state-of-the-art, object-oriented Python software where the coupled multiband Schrödinger and Poisson equations are solved by the finite element method (FEM); using unstructured and adaptive meshes in self-consistent k∙p keeps the numerical burden and precision under control also in strong confinement, high-doping, or low-symmetry regimes . The implemented 8-band k∙p Hamiltonian is suitable to describe type-I, type-II, and inverted band heterostructures discussed in this thesis. Modulation doping is a key functionalization technique for high-mobility devices, but relatively less under control in growth processes. Hence, we study a prototypical AlGaAs/GaAS radial heterostructure at different doping regimes. We show that high-doping brings about a strong carrier localization towards the core-shell interface, as well as mass inversions and non-trivial changes in the spinorial character of the low-energy valence states. We show by explicit calculations that indications of the band structure's evolution with doping can be exposed in the anisotropy patterns of linearly polarized optical absorption spectra. Full-shell hybrid NWs -semiconductor NWs embedded in a superconductor- have recently emerged as candidates in the search for Majorana zero modes, possible building-blocks for the implementation of fault-tolerant qubits thanks to their topological nature and ensuing robustness against local disorder. Up to now the primary issue has been the small SOC achieved in typical samples, hindering the possibility to attain a topological superconducting phase. Here, we propose to exploit the inherently strong SOC of the hole valence bands, exploring the potential of InP/GaSb CSNWs in full-shell geometries. Predictive self-consistent k∙p calculations foresee values of the intrinsic SOC as high as 20 meV·nm, regardless of the electric field or strain at the interface. InAs/GaSb CSNWs constitute a suitable system for applications in low-power electronics as well as core studies on electron-hole hybridization and topological insulating states. Using self-consistent k∙p simulations, we identify a new reentrant semimetal state with Weyl dispersion in the hybridization gap of slightly band-inverted NWs, which is triggered by a transverse electric field. Using an effective low-energy Bernevig-Hughes-Zhang model Hamiltonian we show that the semimetallic phase is due to an exact compensation of SOCs and electron-hole interactions. We further rationalize the closure of the indirect gap in terms of the appearance of localized states at both ends of the NW.
I nanofili (NFi) a semiconduttore manifestano proprietà fisiche uniche a causa della bassa dimensionalità e rappresentano una piattaforma promettente per una vasta gamma di applicazioni in nanotecnologia ed elettronica. I NFi possono essere cresciuti in strutture singolo-cristalline, controllando con precisione parametri cruciali come la composizione chimica, le dimensioni e il doping, permettendo così di ingegnerizzare una vasta gamma di dispositivi e tecniche di integrazione basati sui NFi, tra cui FET, giunzioni p-n, dispositivi di cattura della luce e dispositivi termoelettrici. Inoltre, la dimostrazione di NFi con modulazione radiale dei materiali, anche chiamati NFi core-shell (NFiCS), ha aperto la strada a dispositivi di maggiore efficienza e dotati di nuove funzionalità grazie effetti quantistici e tecniche come la wave-function engineering . Tra i metodi teorici utilizzati per descrivere le nanostrutture a semiconduttore, il metodo k∙p autoconsistente si distingue per efficienza computazionale e capacità predittive. Particolarmente rilevante è la capacità di descrivere l'interazione tra l’accoppiamento spin-orbita (ASO) e i parametri strutturali. In questa tesi, abbiamo sviluppato e utilizzato un software originale, allo stato dell’arte e orientato agli oggetti in Python, dove le equazioni di Schrödinger multibanda e di Poisson sono risolte mediante il metodo degli elementi finiti (FEM); L'uso di mesh non strutturate e adattative nel k∙p autoconsistente regola efficacemente il costo numerico e la precisione anche in condizioni di forte confinamento, doping elevato o bassa simmetria. Il modulation-doping è una tecnica chiave per la funzionalizzazione di dispositivi ad alta mobilità, ma relativamente meno sotto controllo nei processi di crescita. Pertanto, studiamo un’eterostruttura radiale AlGaAs/GaAS a diversi regimi di doping. Mostriamo che un doping elevato porta a una forte localizzazione dei portatori verso l'interfaccia fra il core e la shell, così come inversioni di massa e variazioni del carattere spinoriale degli stati di valenza a energia più bassa. Mostriamo che indicazioni sull'evoluzione della struttura a bande con il doping possono essere evidenziate nei pattern di anisotropia degli spettri di assorbimento ottico di luce linearmente polarizzata. I NFi ibridi full-shell - NFi a semiconduttore incorporati in un superconduttore - sono recentemente emersi come candidati nella ricerca dei Majorana zero modes, potenzialmente essenziali per i qubits fault-tolerant grazie alla loro natura topologica e robustezza contro il disordine locale. Fino ad ora, il basso valore di ASO ottenuto in campioni tipici ha ostacolato la possibilità di raggiungere una fase superconduttiva topologica. Qui, proponiamo di sfruttare l’ASO intrinseco delle bande di valenza, esplorando il potenziale di NFiCS di InP/GaSb nelle geometrie full-shell. Calcoli autoconsistenti k∙p prevendono valori dell’ASO intrinseco fino a 20 meV·nm, indipendentemente dal campo elettrico o dallo strain presente all'interfaccia. I NFiCS di InAs/GaSb costituiscono un sistema adatto per applicazioni in elettronica a basso consumo energetico, nonché per studi fondamentali sull'ibridazione elettrone-buca e stati isolanti topologici. Tramite simulazioni k∙p autoconsistenti, identifichiamo un nuovo stato semimetallico rientrante con dispersione di Weyl nel gap di ibridazione di NFi con una lieve inversione di bande, innescato da un campo elettrico trasversale. Utilizzando una Hamiltoniana modello di tipo Bernevig-Hughes-Zhang, mostriamo che la fase semimetallica è dovuta a una compensazione esatta di ASO e interazioni elettrone-buca. Razionalizziamo ulteriormente la chiusura del gap indiretto nei termini dell'apparizione di stati localizzati su entrambi gli estremi del NF.
Calcolo di stati spin-orbitali in nanofili a semiconduttore core-shell di tipo I, II e broken gap, con un approccio k∙p autoconsistente / Andrea Vezzosi , 2024 Apr 15. 36. ciclo, Anno Accademico 2022/2023.
Calcolo di stati spin-orbitali in nanofili a semiconduttore core-shell di tipo I, II e broken gap, con un approccio k∙p autoconsistente
VEZZOSI, ANDREA
2024
Abstract
Semiconductor nanowires (NWs) manifest unique physical properties due to their reduced dimensionality and represent a promising platform for a wide range of applications in nanotechnology and electronics. NWs can be reliably manufactured in single crystal structures, with precise control of crucial parameters such as chemical composition, dimensions, and doping, enabling to engineer a vast range of devices and integration techniques, including NW-based FETs, p-n junctions, light-harvesting and thermoelectric devices. Moreover, the demonstration of NWs with radial material modulation, also referred to as core-shell NWs (CSNWs), paved the way to devices with enhanced performance and new functionalities through wave-function engineering and quantum effects. Among the theoretical methods used to describe semiconductor nanostructures, the self-consistent k∙p method, combined with the envelope function approximation, stands out for computational efficiency and predictivity. Of relevance here is the ability to describe the interplay between spin-orbit coupling (SOC) in the underlying compounds, material modulations, and structural parameters. Within this thesis we developed and used an original state-of-the-art, object-oriented Python software where the coupled multiband Schrödinger and Poisson equations are solved by the finite element method (FEM); using unstructured and adaptive meshes in self-consistent k∙p keeps the numerical burden and precision under control also in strong confinement, high-doping, or low-symmetry regimes . The implemented 8-band k∙p Hamiltonian is suitable to describe type-I, type-II, and inverted band heterostructures discussed in this thesis. Modulation doping is a key functionalization technique for high-mobility devices, but relatively less under control in growth processes. Hence, we study a prototypical AlGaAs/GaAS radial heterostructure at different doping regimes. We show that high-doping brings about a strong carrier localization towards the core-shell interface, as well as mass inversions and non-trivial changes in the spinorial character of the low-energy valence states. We show by explicit calculations that indications of the band structure's evolution with doping can be exposed in the anisotropy patterns of linearly polarized optical absorption spectra. Full-shell hybrid NWs -semiconductor NWs embedded in a superconductor- have recently emerged as candidates in the search for Majorana zero modes, possible building-blocks for the implementation of fault-tolerant qubits thanks to their topological nature and ensuing robustness against local disorder. Up to now the primary issue has been the small SOC achieved in typical samples, hindering the possibility to attain a topological superconducting phase. Here, we propose to exploit the inherently strong SOC of the hole valence bands, exploring the potential of InP/GaSb CSNWs in full-shell geometries. Predictive self-consistent k∙p calculations foresee values of the intrinsic SOC as high as 20 meV·nm, regardless of the electric field or strain at the interface. InAs/GaSb CSNWs constitute a suitable system for applications in low-power electronics as well as core studies on electron-hole hybridization and topological insulating states. Using self-consistent k∙p simulations, we identify a new reentrant semimetal state with Weyl dispersion in the hybridization gap of slightly band-inverted NWs, which is triggered by a transverse electric field. Using an effective low-energy Bernevig-Hughes-Zhang model Hamiltonian we show that the semimetallic phase is due to an exact compensation of SOCs and electron-hole interactions. We further rationalize the closure of the indirect gap in terms of the appearance of localized states at both ends of the NW.File | Dimensione | Formato | |
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