무한한 상관길이를 가지는 위스너 수송 방정식의 결정론적 해

학위논문(박사) -- 서울대학교대학원 : 공과대학 전기·정보공학부, 2022. 8. 최우영.We propose a new discrete formulation of the Wigner transport equation (WTE) with infinite correlation length of potentials. Since the maximum correlation length is not limited to a finite value, there is no uncertainty in the simulation results, and Wigner-Weyl transformation is unitary in our expression. For general and efficient simulation, the WTE is solved self-consistently with the Poisson equation through the finite volume method and the fully coupled Newton-Raphson scheme. By applying the proposed model to resonant tunneling diodes and double gate MOSFET, transient and steady-state simulation results including scattering effects are shown.본 연구에서는 무한한 상관 길이를 가지는 위그너 수송 방정식의 새로운 수치해석적 풀이법을 제시하였다. 최대 상관 길이가 한정된 값으로 제한되지 않기 때문에, 시뮬레이션 결과에 불확실성이 발생하지 않으며, 제안된 표현법에서는 Wigner-Weyl 변환이 unitary하다. 일반적이고 효율적인 시뮬레이션을 위해, 위그너 수송 방정식을 푸아송 방정식과 유한 체적법과 뉴턴-랩슨 방식을 통해 self-consistent하게 풀었다. 제안된 모델을 resonant tunneling diode와 double gate MOSFET에 적용하여, 산란효과를 고려한 동적 그리고 정적 시뮬레이션 결과를 보여주었다.Chapter 1 Introduction 1 1-1 Various models for device simulation 1 1-2 Numerical problems in solving WTE 5 Chapter 2 Simulation methods 10 2-1 WTE with infinite correlation length 10 2-2 Numerical Methods 13 2-3 Multi-dimensional Simulation Methods 23 Chapter 3 Simulation methods 26 2-1 Simulation results according to the correlation length 26 2-2 Simulation for resonant tunneling diode 30 2-3 Simulation for double gate MOSFET 51 Chapter 4 Conclusion 70 Appendix 72 A-1 Numerical integration method of the nonlocal potential terms 72 A-2 2D electron density and electric potential results 75 A-3 Wigner function for each subband 78 References 85 Abstract 92박

Microscopic modeling of energy dissipation and decoherence in nanoscale materials and devices

Primary goal of this thesis work is to develop and implement microscopic modeling strategies able to describe semiconductor-based nanomaterials and nanodevices, overcoming both the intrinsic limits of the semiclassical transport theory and the huge computational costs of non Markovian approaches. The progressive reduction of modern optoelectronic devices space-scales, triggered by the evolution on semiconductor heterostructures at the nanoscale, together with the decrease of the typical time-scales involved, pushes device miniaturization toward limits where the application of the traditional Boltzmann transport theory becomes questionable, and a comparison with more rigorous quantum transport approaches is imperative. In spite of the quantum-mechanical nature of electron and photon dynamics in the core region of typical solid-state nanodevices, the overall behavior of such quantum systems is often governed by a highly non-trivial interplay between phase coherence and dissipation/dephasing. To this aim, the crucial step is to adopt a quantum mechanical description of the carrier subsystem; this can be performed at different levels, ranging from phenomenological dissipation/decoherence models to quantum-kinetic treatments. However, due to their high computational cost, non-Markovian Green’ s-function as well as density-matrix approaches like quantum Monte Carlo techniques or quantum-kinetics are currently unsuitable for the design and optimization of new-generation nanodevices. On the other end, the Wigner-function technique is a widely used approach which, in principle, is well suited to describe an interplay between coherence and dissipation: in fact it can be regarded both as a phase space formulation of the electronic density matrix and a quantum equivalent of the classical distribution function. The evolution of this quasi-distribution function is governed by the Wigner-equation, which is usually solved by applying local spatial boundary conditions. However, such a scheme has recently shown some intrinsic limits. In this thesis work we analyze both the reasons for these unphysical features –pointing out the needing of different and purely quantum approaches– and the limits in which they should not appear, thus justifying why these problems had not been encountered in numerous quantum-transport simulations based on this procedure. For these reasons here we present a novel single-particle simulation strategy able to describe the interplay between coherence and dissipation/dephasing. In the presence of one- as well as two-body scattering mechanisms, we apply the mean-field approximation to the many-body Lindblad-type (hence, positive-definite) scattering superoperators provided by a recently proposed Markov approach, and we derive a closed equation of motion for the electronic single-particle density matrix. Although the resulting scattering superoperator turns out to be, at finite or high carrier densities, nonlinear and non-Lindblad, we prove that it is able to guarantee the positivity of the evolution (in striking contrast with conventional Markov approaches) independently of the scattering mechanisms, an essential prerequisite of any reliable kinetic treatment of semiconductor quantum devices; furthermore, it may be extended to the cases of quantum systems with open spatial boundaries (in this regard, it provides a formal derivation of a recently proposed Lindblad-like device-reservoir scattering superoperator). The proposed theoretical scheme is able, one the one hand, to recover the space-dependent Boltzmann equation and, on the other, to point out the regimes where a relevant role may be played by scattering-nonlocality effects, e.g. scattering-induced variations of the spatial charge-density which may not be provided by semiclassical treatments. Supplementing our analytical investigation with a number of simulated experiments in homogeneous as well as inhomogeneous GaN-based systems, we provide a rigorous treatment of scattering nonlocality in semiconductor nanostructures: in particular, we show how the scattering-nonlocality effects (i) are particularly significant in the presence of a carrier localization on the nanometric space scale, (ii) cause a speedup of the diffusion and (iii) in superlattice structures induce, with respect to scattering-free evolutions, a suppression of coherent oscillations between adjacent wells. These genuine quantum effects may be predicted also by other simplified treatments of the dissipation/decoherence like, e.g., the Relaxation Time Approximation: the latter however turns out to be, contrary to the proposed microscopic theoretical scheme, totally nonlocal, e.g. it is unable to recover the local character of the Boltzmann collision term in the semiclassical limit and it leads, especially for the case of quasielastic dissipation processes, to a significant overestimation of the diffusion speedup

Accurate quantum transport modelling and epitaxial structure design of high-speed and high-power In0.53Ga0.47As/AlAs double-barrier resonant tunnelling diodes for 300-GHz oscillator sources

Terahertz (THz) wave technology is envisioned as an appealing and conceivable solution in the context of several potential high-impact applications, including sixth generation (6G) and beyond consumer-oriented ultra-broadband multi-gigabit wireless data-links, as well as highresolution imaging, radar, and spectroscopy apparatuses employable in biomedicine, industrial processes, security/defence, and material science. Despite the technological challenges posed by the THz gap, recent scientific advancements suggest the practical viability of THz systems. However, the development of transmitters (Tx) and receivers (Rx) based on compact semiconductor devices operating at THz frequencies is urgently demanded to meet the performance requirements calling from emerging THz applications. Although several are the promising candidates, including high-speed III-V transistors and photo-diodes, resonant tunnelling diode (RTD) technology offers a compact and high performance option in many practical scenarios. However, the main weakness of the technology is currently represented by the low output power capability of RTD THz Tx, which is mainly caused by the underdeveloped and non-optimal device, as well as circuit, design implementation approaches. Indeed, indium phosphide (InP) RTD devices can nowadays deliver only up to around 1 mW of radio-frequency (RF) power at around 300 GHz. In the context of THz wireless data-links, this severely impacts the Tx performance, limiting communication distance and data transfer capabilities which, at the current time, are of the order of few tens of gigabit per second below around 1 m. However, recent research studies suggest that several milliwatt of output power are required to achieve bit-rate capabilities of several tens of gigabits per second and beyond, and to reach several metres of communication distance in common operating conditions. Currently, the shortterm target is set to 5−10 mW of output power at around 300 GHz carrier waves, which would allow bit-rates in excess of 100 Gb/s, as well as wireless communications well above 5 m distance, in first-stage short-range scenarios. In order to reach it, maximisation of the RTD highfrequency RF power capability is of utmost importance. Despite that, reliable epitaxial structure design approaches, as well as accurate physical-based numerical simulation tools, aimed at RF power maximisation in the 300 GHz-band are lacking at the current time. This work aims at proposing practical solutions to address the aforementioned issues. First, a physical-based simulation methodology was developed to accurately and reliably simulate the static current-voltage (IV ) characteristic of indium gallium arsenide/aluminium arsenide (In-GaAs/AlAs) double-barrier RTD devices. The approach relies on the non-equilibrium Green’s function (NEGF) formalism implemented in Silvaco Atlas technology computer-aided design (TCAD) simulation package, requires low computational budget, and allows to correctly model In0.53Ga0.47As/AlAs RTD devices, which are pseudomorphically-grown on lattice-matched to InP substrates, and are commonly employed in oscillators working at around 300 GHz. By selecting the appropriate physical models, and by retrieving the correct materials parameters, together with a suitable discretisation of the associated heterostructure spatial domain through finite-elements, it is shown, by comparing simulation data with experimental results, that the developed numerical approach can reliably compute several quantities of interest that characterise the DC IV curve negative differential resistance (NDR) region, including peak current, peak voltage, and voltage swing, all of which are key parameters in RTD oscillator design. The demonstrated simulation approach was then used to study the impact of epitaxial structure design parameters, including those characterising the double-barrier quantum well, as well as emitter and collector regions, on the electrical properties of the RTD device. In particular, a comprehensive simulation analysis was conducted, and the retrieved output trends discussed based on the heterostructure band diagram, transmission coefficient energy spectrum, charge distribution, and DC current-density voltage (JV) curve. General design guidelines aimed at enhancing the RTD device maximum RF power gain capability are then deduced and discussed. To validate the proposed epitaxial design approach, an In0.53Ga0.47As/AlAs double-barrier RTD epitaxial structure providing several milliwatt of RF power was designed by employing the developed simulation methodology, and experimentally-investigated through the microfabrication of RTD devices and subsequent high-frequency characterisation up to 110 GHz. The analysis, which included fabrication optimisation, reveals an expected RF power performance of up to around 5 mW and 10 mW at 300 GHz for 25 μm2 and 49 μm2-large RTD devices, respectively, which is up to five times higher compared to the current state-of-the-art. Finally, in order to prove the practical employability of the proposed RTDs in oscillator circuits realised employing low-cost photo-lithography, both coplanar waveguide and microstrip inductive stubs are designed through a full three-dimensional electromagnetic simulation analysis. In summary, this work makes and important contribution to the rapidly evolving field of THz RTD technology, and demonstrates the practical feasibility of 300-GHz high-power RTD devices realisation, which will underpin the future development of Tx systems capable of the power levels required in the forthcoming THz applications

Dispersive effects in quantum kinetic equations:The Wigner-Poisson-Fokker-Planck system

Durch seine kinetische Beschreibung der Quantenmechanik hat der Wigner-Formalismus beträchtliche Aufmerksamkeit auf sich gezogen und die Bildung von anwendbaren Modellen für Simulationen von Halbleiterbauelementen, der Quanten-Brownschen Bewegung und der Quantenoptik ermöglicht. Diese Arbeit behandelt das Wigner-Poisson-Fokker-Planck (WPFP) System, eine kinetische Evolutionsgleichung eines offenen Quantensystems mit einem nicht linearen Hartree Potential. Es werden Existenz, Eindeutigkeit und Regularität einer zeitglobalen Lösung in 3D gezeigt. Das Ausschlaggebende dieser rein kinetischen Analysis ist die Verwendung der dispersiven Effekte des freien Transportes und der parabolischen Regularisierung, um die Wohldefiniertheit der Partikeldichte zu umgehen, was ein zentrales Problem in der quantenkinetischen Theorie ist. Zur numerischen Approximation des 1D-WPFP Systems mit periodischen Randbedingungen wird eine Zeitdiskretisierung mit einem Operator-Splitting Verfahren verwendet.Providing a kinetic description of quantum mechanics the Wigner formalism has attracted considerable attention of physicists for constituting valuable models for simulations in semiconductor devices, for quantum Brownian motion and quantum optics. This work is concerned with the Wigner-Poisson-Fokker-Planck (WPFP) system, a kinetic evolution equation for an open quantum system with a non-linear Hartree potential. Existence, uniqueness and regularity of global-in-time solutions to the Cauchy problem in 3D are established. The crucial novel tool of this purely kinetic analysis is to exploit the dispersive effects of the free transport equation and the parabolic regularization to circumvent the lacking of definition of the particle density, which is a central problem in the quantum kinetic context. Considering the 1D-WPFP system with periodic boundary conditions, a first-order approximation in time through an operator splitting method is studied and illustrated by numerical simulations

Nanoscale structure and transport : from atoms to devices

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.Includes bibliographical references (p. 145-159).Nanoscale structures present both unique physics and unique theoretical challenges. Atomic-scale simulations can find novel nanostructures with desirable properties, but the search can be difficult if the wide range of possible structures is not well understood. Electrical response and other non-equilibrium transport phenomena are measured experimentally, but not always simulated accurately. This thesis presents four diverse applications that demonstrate how first-principles calculations can address these challenges. Novel boron nanotube structures with unusual elastic properties are presented. Internal degrees of freedom are identified that allow longitudinal stress to be dissipated without changing the tube's diameter, leading to high lateral stiffness. Self-trapped hole structures in amorphous silicon dioxide are investigated in order to connect the behavior of hole currents to atomic-scale structures. Calculations on a paired-oxygen analogue to the ... center show that such a configuration does not result in a metastable trapped-hole state. A novel method to enable first-principles mobility calculations in ultrathin silicon-on-insulator (UTSOI) structures is presented and applied to interface roughness scattering in transistor channels. Self-consistent potentials and accurate wavefunctions and band structures allow for a direct link between measured electrical response and atomic structure. Atomic-scale interface roughness is shown to be an important limit on mobility at high carrier densities. At low carrier densities, such short-wavelength roughness results in qualitatively different mobility behavior than gradual UTSOI channel thickness fluctuations.(cont.) An effective Hamiltonian technique to calculate short-time, non-equilibrium fluctuations in quantum devices is developed. Applications to quantum dots and resonant tunneling diodes show that temporal fluctuations are reproduced well.by Matthew Hiram Evans.Ph.D