Three-Dimensional S-Matrix Simulation of Single-Electron Resonant Tunnelling Through Random Ionised Donor States

This paper presents a numerical study of single-electron resonant tunnelling (RT) assisted by a few ionised donors in a laterally-confined resonant tunnelling diode (LCRTD). The 3D multi-mode S-matrix simulation is performed newly introducing the scattering potential of discrete impurities. With a few ionised donors being placed, the calculated energy-dependence of the total transmission rate shows new resonances which are donor-configuration dependent. Visualised electron probability density reveals that these resonances originate in RT via single-donor-induced localised states. The I-V characteristics show current steps of order 0.1 nA per donor before the main current peak, which is quantitatively in good agreement with the experimental results.Peer Reviewe

Entangling electrons and nuclei in a four-qubit, two-atom device in silicon.

The nuclear spins of ion-implanted donor spins in silicon have demonstrated record-breaking coherence times of over 30-seconds, along with high fidelity (>99%) single and two-qubit operations, approaching the fidelity required to perform fault-tolerant quantum computation. The considerable coherence times observed for the nuclei are owing to the fact that the nuclear spin interacts very weakly with its environment. This property of the nucleus, although a highly desirable advantage from the perspective of noise resilience, results in nuclear qubits only weakly coupling to one another, presenting a challenge for performing scalable, multi-qubit operations. Fortunately, donor atoms have the additional resource of the donor-bound electron, which can be utilised as a means of coupling nuclei over larger distance scales. In this thesis, we focus on a system of two 31P nuclei, each possessing their own bound electron. These electrons are exchange-coupled to one another with a strength of 12 MHz. We begin by experimentally demonstrating high fidelity operation of the electrons in this always-on exchange coupled system. In the regime of weak exchange coupling, defined as the regime for which the qubit coupling is much weaker than the detuning, every native operation on the electrons represents either a conditional rotation (CROT) or zero-conditional rotation (zCROT) gate; rotating one electron conditional on the state of the other electron. We benchmark these native gates using gate set tomography (GST), obtaining single-qubit fidelities of >99.63% for both electrons. Additionally, we benchmark the electron two-qubit gate fidelity using phase reversal tomography, obtaining a Bell state fidelity of 90.3%. Moreover, we assess the coherence times of the electrons both with and without the presence of the exchange interaction and find that the presence of the weak exchange interaction has no discernible impact on the electron’s coherence. We then proceed to utilise these electron operations to perform a two-qubit nuclear geometric controlled-Z (CZ) gate between the two nuclei in the system. Using this gate, we are able to demonstrate entanglement between two nuclei, over the larger distance afforded by the exchange interaction, compared to the previously used hyperfine coupling. Lastly, we use this nuclear geometric CZ gate to entangle the two nuclei with the electrons, thus completing the toolbox for constructing a scalable spin-based quantum processor in silicon

Impact of precisely positioned dopants on the performance of an ultimate silicon nanowire transistor: a full three-dimensional NEGF simulation study

In this paper, we report the first systematic study of quantum transport simulation of the impact of precisely positioned dopants on the performance of ultimately scaled gate-all-around silicon nanowire transistors (NWTs) designed for digital circuit applications. Due to strong inhomogeneity of the selfconsistent electrostatic potential, a full 3-D real-space nonequilibrium Green function formalism is used. The simulations are carried out for an n-channel NWT with 2.2 × 2.2 nm2 cross section and 6-nm channel length, where the locations of the precisely arranged dopants in the source-drain extensions and in the channel region have been varied. The individual dopants act as localized scatters, and hence, impact of the electron transport is directly correlated to the position of the single dopants. As a result, a large variation in the ON-current and a modest variation of the subthreshold slope are observed in the ID-VG characteristics when comparing devices with microscopically different discrete dopant configurations. The variations of the current-voltage characteristics are analyzed with reference to the behavior of the transmission coefficients

Modelling the optical and electronic transport properties of AlGaAs and AlGaN intersubband devices and optimisation of quantum cascade laser active regions

Terahertz quantum cascade lasers (THz QCLs) have many potential applications such as medical and security screening. While their output power has recently exceeded 1 W, their highest operating temperature is currently limited to approximately 200K due to mechanisms such as thermal backfilling and non-radiative phonon emission between lasing states. To achieve higher operating temperatures, theoretical models are key to suppressing these degradation mechanisms either through further design optimisation or new material systems. This work investigates the opto-electronic properties of state-of-the-art intersubband devices in AlGaAs/GaAs and AlGaN/GaN material systems as well as the applications of QCLs. A density matrix model is investigated and used to predict the electron distribution, gain and current density in an arbitrary QCL active region. This model is validated with a comparison to rate equation, non-equilibrium Green’s function, and experimental data for AlGaAs/GaAs QCLs. Novel designs using tall AlAs barriers to suppress leakage current are modelled, and the effect of long and short range interface roughness is investigated. An increased sensitivity to roughness is shown for tall barrier structures which have a larger conduction band offset discontinuity and thinner epitaxial layers. The model is then used to optimise both AlGaAs and AlGaN QCL structures to propose new designs for a desired emission wavelength. The use of the density matrix approach to model possible applications is demonstrated by modelling the origin of the self-mixing (optical feedback) interferometry terminal voltage variations. It is shown that the self-mixing voltage amplitude is highly dependent on the differential resistance of the QCL, and the increased sensitivity of a particular QCL is explained. The feasibility of nitride QCLs is shown by comparing the calculated and experimental absorption linewidth of near-infrared and THz AlGaN/GaN quantum wells grown by molecular beam epitaxy. Finally, a novel adaptation of the density matrix approach is used to investigate the transport properties of nitride resonant tunnelling diodes alongside sequential tunnelling devices. This allows the extent of transport due to bound defect states and interface roughness values to be estimated

Hydrostatic pressure studies of semiconductor heterostructures and Schottky diodes

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN004148 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Experiments on quantum knowledge and reality with spins in silicon

Electron and nuclear spins are highly controllable and coherent quantum objects. They are therefore an excellent platform to study both fundamental physics and quantum information. Semiconductor quantum devices leverage the vast infrastructure that currently exists to produce our everyday electronics. With spins integrated into semiconductor devices, coherent control of individual electrons and nuclei has been demonstrated. Further development of these devices is essential to propel novel quantum technologies, such as quantum computers, beyond the lab. This thesis focuses on three themes: spin physics, quantum information processing and the foundations of quantum theory. We explore these topics with donors in silicon, phosphorus (31 P) and antimony (123 Sb). With a ‘Maxwell’s demon’ observing a single electron spin, its knowledge of the spin state heralds high-fidelity electron spin initialisation without requiring additional quantum resources. We benchmark the electron initialisation with high-fidelity nuclear spin readout by first mapping the electron state to the nucleus. We then motivate further improvements to the measurement apparatus to further enhance electron spin initialisation and readout. Recent advances have demonstrated embryonic two-qubit gates between donor-bound electrons. Alongside the high-fidelity readout afforded by nuclear spins, we are rapidly approaching the fault-tolerant threshold for some error-correcting codes, e.g. the surface code. We also discuss an electrical technique to coherently control quadrupolar nuclei, which we discovered for the first time in silicon with 123 Sb. With electrical control of donor electrons, this discovery could pave the way to an all-electrical donor spin quantum computer. Finally, with the highly-coherent ionised nuclear spin 123 Sb, we explore a foundational question in quantum mechanics. Originating from the Einstein-Podolsky-Rosen paradox, we discuss the reality of the quantum state. The quantum state is an incredibly accurate predictive tool, however the predictions are inherently probabilistic. The key question we seek to answer: is the probabilistic nature of the quantum state a representation of our (lack of) knowledge of the true state of reality? We propose an experimental test with 123 Sb that constrains the degree to which the quantum state can only represent knowledge

Quantum computation and simulation in silicon donors: from optically-controlled entangling gates to the Hubbard model

Quantum computing holds the promise to solve classically intractable problems. While some beyond-classical computations have been demonstrated, a useful application has yet to be shown. The biggest challenge is to scale up the number of quantum bits and simultaneously increase the accuracy of elementary operations in order to enable correction of errors. Silicon-based implementations promise to enable compatibility with complementary metal–oxide–semiconductor technology and hence a rapid scaling up. For the main part, this thesis is focussed on one particular quantum computing implementation in which the qubit is represented by the spin of the electron of a phosphorous atom in a silicon lattice. This implementation holds the record for the longest coherence times, of the order of days. So far, scalability with such donor-based computers is challenging because of the requirement to precisely position donors in the silicon lattice in architectures currently proposed. In this thesis, two architectures which do not require precise placement of donors are presented: an implementation of a quantum computer in a completely randomly doped sample and a scheme based on the electric dipolar long-range interactions between donors using a translation of ideas from implementations with laser-cooled atoms. Furthermore, we discuss the simulation of quantum materials with dopant atom arrays, in particular making precise predictions for feasible small-scale proof of principle experiments. Lastly, a condensed matter model which is known to be a symmetry protected topological state is implemented into a quantum software library originally written for qubits which is being expanded for use in continuous-variable systems. Our results work towards enabling the implementation of large-scale quantum computation in silicon

Gate leakage variability in nano-CMOS transistors

Gate leakage variability in nano-scale CMOS devices is investigated through advanced modelling and simulations of planar, bulk-type MOSFETs. The motivation for the work stems from the two of the most challenging issues in front of the semiconductor industry - excessive leakage power, and device variability - both being brought about with the aggressive downscaling of device dimensions to the nanometer scale. The aim is to deliver a comprehensive tool for the assessment of gate leakage variability in realistic nano-scale CMOS transistors. We adopt a 3D drift-diffusion device simulation approach with density-gradient quantum corrections, as the most established framework for the study of device variability. The simulator is first extended to model the direct tunnelling of electrons through the gate dielectric, by means of an improved WKB approximation. A study of a 25 nm square gate n-type MOSFET demonstrates that combined effect of discrete random dopants and oxide thickness variation lead to starndard deviation of up to 50% (10%) of the mean gate leakage current in OFF(ON)-state of the transistor. There is also a 5 to 6 times increase of the magnitude of the gate current, compared to that simulated of a uniform device. A significant part of the research is dedicated to the analysis of the non-abrupt bandgap and permittivity transition at the Si/SiO2 interface. One dimensional simulation of a MOS inversion layer with a 1nm SiO2 insulator and realistic band-gap transition reveals a strong impact on subband quantisation (over 50mV reduction in the delta-valley splitting and over 20% redistribution of carriers from the delta-2 to the delta-4 valleys), and enhancement of capacitance (over 10%) and leakage (about 10 times), relative to simulations with an abrupt band-edge transition at the interface

Gate-based sensing of silicon quantum dot devices towards 2D scaling

This thesis focuses on using the radio-frequency reflectometry technique for dispersive gate sensing of foundry fabricated silicon nanowire quantum dot devices. I will attempt to answer three questions relating to the scalability of these devices. How do electron and hole spin qubits perform in silicon quantum dots? How do we implement and distribute the placement of dispersive gate sensors in scaled-up quantum dot arrays? And how does a single dopant in the silicon channel affect the gate-defined quantum dot? First, I investigate the difference between electron and hole quantum dots in an ambipolar nanowire device which successfully demonstrated reconfigurable single and double electron and hole quantum dots in the same crystalline environment. I further investigate the effective bath temperature of two-dimensional electron gas and two-dimensional hole gas by performing the thermometry experiment on the same type of device. Secondly, I demonstrate a two-dimensional quantum dot array enabled by a floating gate architecture between silicon nanowires. An analytical model is developed to study the capacitive coupling between remote quantum dots over different distances. Coupling strength under different qubit encodings is also discussed to show the best implementation for neighbour silicon nanowires. Finally, the in-situ dispersive gate sensing allows the measurement of the inter-dot transition between the bismuth donor-dot system. The novel implementation with bismuth donor can open up the possibility of a hybrid singlet-triplet qubit or transferring a coherent spin state between the quantum dot and the donor