DESIGN OF NANOSTRUCTURED ENTANGLED PHOTON PAIR GENERATOR FOR QKD APPLICATIONS

Author

Md Rezaul Karim Nishat, Southern Illinois University CarbondaleFollow

Date of Award

8-1-2018

Degree Name

Doctor of Philosophy

Department

Electrical and Computer Engineering

First Advisor

Ahmed, Shaikh

Abstract

Finite structure splitting (FSS) is a bottleneck for quantum dot (QD) based solid state entangled photon pair generator (EPPG) for Quantum Key Distribution (QKD) application. In QD, entangle photon pairs are generated through a cascaded emission process—biexciton to exciton to ground state. The FSS of the excitonic state destroys the entanglement of the photon pairs, hence needs to be eliminated. FSS can be tuned by engineering the crystal growth direction, varying dot shape or size, changing the material composition and/or applying external strain. Numerical investigation of FSS and designing of realistically-sized QD based EPPG demands multiscale-multiphysics many-body simulation efforts. To this end, in this work, we report the coupling of full configuration integration (FCI) method with the atomistic empirical tight-binding (TB) models (10-band sp3s* and 20-band sp3d5s*) to calculate the excitonic energetics and FSS in recently reported multimillion-atom III-V dot-in-nanowire structures. The core of the computational framework comprises two parts: i) NEMO3D, which, using the TB models, can compute single-electron energetics of multimillion-atom structures, and ii) An FCI kernel, which computes the many-particle energetics and wavefunctions using the single-electron outputs as derived from NEMO3D. NEMO3D is a broad platform that handles geometry construction, calculation of strain distributions and built-in potential fields, solving the Schrodinger’s equation and computing optical matrix elements. Three output files from NEMO3D are of particular importance for the FCI toolkit: i) Single-electron energy values, ii) Eigen functions, and iii) Relaxed atom positions of the device. FCI calculates the Coulomb and Exchange matrix elements associated with multi-particles and forms the many-body Hamiltonian. The excitonic states (electron-hole pair) are calculated by solving the many-body Hamiltonian and the value of FSS, if exists, is determined. Recently, nitride-based nanostructured devices have been found to be a promising candidate for single and entangled multi-photon emitter applications. The principal goal of this dissertation is to facilitate the numerical design of InGaN/GaN based dot-in-nanowire EPPG units. To this end, a number of kernels in NEMO3D and FCI packages were augmented. The geometry constructor in NEMO3D was extended for two non-polar planes of wurtzite crystal: m-plane and a-plane. It is found that these two non-polar planes, with much smaller built-in piezoelectric fields, exhibit improved optical transition probabilities than the polar c-plane counterpart. As test cases, light-emitters in dot-in-wire and multiple quantum well (MQW) configurations were simulated and compared in all three (c-plane, m-plane, and a-plane) growth directions. TCAD toolkits are used to simulate the terminal optical characteristics such as internal quantum efficiency (IQE) and spontaneous emission rate. Hexagonal-base truncated-pyramid shaped QD was also added to the NEMO3D geometry constructor as pyramid shaped dots offer directionality and better extraction efficiency of emitted photons, which is important for single or entangled photon generators. The FCI simulator was modified for calculating the excitonic states that involve an electron-hole pair. As for EPPG design, four device structures are considered: i) Disk-in-nanowire on the polar c-plane, ii) pyramid shaped dot-in-nanowire on polar c-plane, iii) Disk-in-nanowire on non-polar m-plane, and iv) Disk-in-nanowire on non-polar a-plane. Simulations are done for different disk thicknesses, material compositions, quantum dot shapes and crystal directions. Results and in-depth analysis are presented on the effects of these design parameters on many-body energetics e.g. binding energy, excitonic bandgaps and FSS. The derivation of excitonic transition probability from single-electron momentum matrix is discussed in detail. Finally, an EPPG design is proposed employing the entangled polarization profiles from two excitonic emissions.