Electrically Driven Quantum Dot Based Single-Photon Sources: Modeling and Simulation (Springer Theses)

✍ Scribed by Markus Kantner

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 190
• Category: Library

✦ Synopsis

Semiconductor quantum optics is on the verge of moving from the lab to real world applications. When stepping from basic research to new technologies, device engineers will need new simulation tools for the design and optimization of quantum light sources, which combine classical device physics with cavity quantum electrodynamics. This thesis aims to provide a holistic description of single-photon emitting diodes by bridging the gap between microscopic and macroscopic modeling approaches. The central result is a novel hybrid quantum-classical model system that self-consistently couples semi-classical carrier transport theory with open quantum many-body systems. This allows for a comprehensive description of quantum light emitting diodes on multiple scales: It enables the calculation of the quantum optical figures of merit together with the simulation of the spatially resolved current flow in complex, multi-dimensional semiconductor device geometries out of one box. The hybrid system isshown to be consistent with fundamental laws of (non-)equilibrium thermodynamics and is demonstrated by numerical simulations of realistic devices.

✦ Table of Contents

Supervisors’ Foreword
Abstract
Acknowledgements
Contents
Acronyms
1 Introduction
1.1 Semiconductor Quantum Dots
1.2 Single-Photon Sources and Applications
1.2.1 Requirements
1.2.2 Applications
1.3 Device Scale Simulation of Single-Photon Sources
1.4 Outline
References
2 Semi-classical Charge Transportpg in Semiconductor Devices
2.1 The van Roosbroeck System
2.1.1 Poisson's Equation
2.1.2 Charge Carrier Density
2.1.3 Current Density
2.1.4 Carrier Recombination and Generation
2.1.5 Boundary Conditions
2.2 Derivation from the Boltzmann Transport Equation
2.2.1 Continuity Equations
2.2.2 Drift-Diffusion Equations
2.3 Thermodynamics of the van Roosbroeck System
2.3.1 Thermodynamic Potentials
2.3.2 Consistency with (Non-)equilibrium Thermodynamics
References
3 Numerical Simulation of Carrier Transport at Cryogenic Temperatures
3.1 Finite Volume Method
3.1.1 Delaunay Triangulation and Voronoï Boxes
3.1.2 Discretization of Balance Equations
3.2 Discrete van Roosbroeck System
3.3 Scharfetter–Gummel Schemes for Fermi–Dirac Statistics
3.3.1 Classical Scharfetter–Gummel Scheme
3.3.2 Generalized Schemes for Fermi–Dirac Statistics
3.4 Structure Preserving Properties of the Discretization
3.5 Nonlinear Iteration Method
3.6 Temperature Embedding Method for Simulation at Cryogenic Temperatures
3.7 Simulation of Wide Band Gap Semiconductors Using the Temperature Embedding Method
3.8 Conclusions
References
4 Current Injection into Oxide-Confined Single-Photon Emitting Diodes
4.1 Introduction
4.2 Device Design and Site-Controlled Quantum Dot Nucleation
4.3 Electroluminescence of Parasitic Quantum Dots and Current Spreading
4.4 Numerical Simulation of the Carrier Injection
4.4.1 Stationary Injection in the Pin-Design
4.4.2 Impact of QDs on Free Carrier Densities
4.4.3 Current Confinement in the Ppn-Design
4.5 Conclusions
References
5 Hybrid Quantum-Classical Modeling of Electrically Driven Quantum Light Sources
5.1 Motivation
5.2 Lindblad Equation for Grand Canonical Reservoirs
5.2.1 Open Quantum Systems
5.2.2 Derivation of the Lindblad Master Equation in the Weak-Coupling Limit with Charge Conservation Constraint
5.2.3 Thermodynamic Properties
5.3 Hybrid Quantum-Classical Model for Electrically Driven Quantum Light Sources
5.3.1 Modeling of the Quantum System
5.3.2 Confined Charge Density and Charge Conservation
5.3.3 Energy, Charge and Entropy Balance
5.3.4 Thermodynamic Equilibrium
5.3.5 Macroscopic Scattering Rates
5.3.6 Microscopic Transition Rates
5.3.7 Entropy Production and the Second Law of Thermodynamics
5.4 Relation of the Hybrid Quantum-Classical Model to the GENERIC Formalism
5.5 Conclusions
References
6 Hybrid Simulation of an Electrically Driven Single-Photon Source
6.1 Device Structure
6.2 Model Specification
6.2.1 Hamiltonian
6.2.2 Dissipation Superoperators
6.2.3 Transition Rate Models
6.3 Numerical Method
6.4 Stationary Operation
6.5 Pulsed Electrical Excitation
6.6 Discussion and Outlook
6.7 Conclusions
References
7 Summary and Outlook
References
Appendix Appendix
A.1 Dopant Ionization at Cryogenic Temperatures
A.2 Recombination Rate Models
A.2.1 Direct Band-to-Band Recombination
A.2.2 Auger Recombination
A.2.3 Shockley–Read–Hall Recombination
A.3 Numerical Evaluation of Fermi–Dirac Integrals
A.4 Two-Time Correlation Functions and the Quantum Regression Theorem
A.5 Alternative Approach for the Macroscopic Scattering Rates
A.6 Wave Functions and Energy Levels of Lens Shaped InGaAs Quantum Dots
A.6.1 Single-Particle States
A.6.2 Coulomb Matrix Elements
References
Appendix About the Author
Index