Self-sustained current oscillations in the kinetic theory of semiconductor superlattices

We present the first numerical solutions of a kinetic theory description of self-sustained current oscillations in n-doped semiconductor superlattices. The governing equation is a single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term. Appropriate boundary conditions for the distribution function describe electron injection in the contact regions. These conditions seamlessly become Ohm's law at the injecting contact and the zero charge boundary condition at the receiving contact when integrated over the wave vector. The time-dependent model is numerically solved for the distribution function by using the deterministic Weighted Particle Method. Numerical simulations are used to ascertain the convergence of the method. The numerical results confirm the validity of the Chapman-Enskog perturbation method used previously to derive generalized drift-diffusion equations for high electric fields because they agree very well with numerical solutions thereof.Comment: 26 pages, 16 figures, to appear in J. Comput. Phy

Wigner-function formalism applied to semiconductor quantum devices: Need for nonlocal scattering models

In designing and optimizing new-generation nanomaterials and related quantum devices, dissipation versus decoherence phenomena are often accounted for via local scattering models, such as relaxation-time and Boltzmann-like schemes. Here we show that the use of such local scattering approaches within the Wigner-function formalism may lead to unphysical results, namely anomalous suppression of intersubband relaxation, incorrect thermalization dynamics, and violation of probability-density positivity. Furthermore, we propose a quantum-mechanical generalization of relaxation-time and Boltzmann-like models, resulting in nonlocal scattering superoperators that enable one to overcome such limitations.Comment: 12 pages, 7 figure

Charge transport and mobility in monolayer graphene

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Noise enhanced spontaneous chaos in semiconductor superlattices at room temperature

Physical systems exhibiting fast spontaneous chaotic oscillations are used to generate high-quality true random sequences in random number generators. The concept of using fast practical entropy sources to produce true random sequences is crucial to make storage and transfer of data more secure at very high speeds. While the first high-speed devices were chaotic semiconductor lasers, the discovery of spontaneous chaos in semiconductor superlattices at room temperature provides a valuable nanotechnology alternative. Spontaneous chaos was observed in 1996 experiments at temperatures below liquid nitrogen. Here we show spontaneous chaos at room temperature appears in idealized superlattices for voltage ranges where sharp transitions between different oscillation modes occur. Internal and external noises broaden these voltage ranges and enhance the sensitivity to initial conditions in the superlattice snail-shaped chaotic attractor thereby rendering spontaneous chaos more robust.Comment: 6 pages, 4 figures, revte

Chaos-based true random number generators

Random number (bit) generators are crucial to secure communications, data transfer and storage, and electronic transactions, to carry out stochastic simulations and to many other applications. As software generated random sequences are not truly random, fast entropy sources such as quantum systems or classically chaotic systems can be viable alternatives provided they generate high-quality random sequences sufficiently fast. The discovery of spontaneous chaos in semiconductor superlattices at room temperature has produced a valuable nanotechnology option. Here we explain a mathematical model to describe spontaneous chaos in semiconductor superlattices at room temperature, solve it numerically to reveal the origin and characteristics of chaotic oscillations, and discuss the limitations of the model in view of known experiments. We also explain how to extract verified random bits from the analog chaotic signal produced by the superlattice.This work has been supported by the Spanish Ministerio de Economía y Competitividad grants FIS2011-28838-C02-01 and MTM2014-56948-C2-2-P

Quantum Hydrodynamic Model by Moment Closure of Wigner Equation

In this paper, we derive the quantum hydrodynamics models based on the moment closure of the Wigner equation. The moment expansion adopted is of the Grad type firstly proposed in \cite{Grad}. The Grad's moment method was originally developed for the Boltzmann equation. In \cite{Fan_new}, a regularization method for the Grad's moment system of the Boltzmann equation was proposed to achieve the globally hyperbolicity so that the local well-posedness of the moment system is attained. With the moment expansion of the Wigner function, the drift term in the Wigner equation has exactly the same moment representation as in the Boltzmann equation, thus the regularization in \cite{Fan_new} applies. The moment expansion of the nonlocal Wigner potential term in the Wigner equation is turned to be a linear source term, which can only induce very mild growth of the solution. As the result, the local well-posedness of the regularized moment system for the Wigner equation remains as for the Boltzmann equation

Efficient GPU implementation of a Boltzmann‑Schrödinger‑Poisson solver for the simulation of nanoscale DG MOSFETs

81–102, 2019) describes an efficient and accurate solver for nanoscale DG MOSFETs through a deterministic Boltzmann-Schrödinger-Poisson model with seven electron–phonon scattering mechanisms on a hybrid parallel CPU/GPU platform. The transport computational phase, i.e. the time integration of the Boltzmann equations, was ported to the GPU using CUDA extensions, but the computation of the system’s eigenstates, i.e. the solution of the Schrödinger-Poisson block, was parallelized only using OpenMP due to its complexity. This work fills the gap by describing a port to GPU for the solver of the Schrödinger-Poisson block. This new proposal implements on GPU a Scheduled Relaxation Jacobi method to solve the sparse linear systems which arise in the 2D Poisson equation. The 1D Schrödinger equation is solved on GPU by adapting a multi-section iteration and the Newton-Raphson algorithm to approximate the energy levels, and the Inverse Power Iterative Method is used to approximate the wave vectors. We want to stress that this solver for the Schrödinger-Poisson block can be thought as a module independent of the transport phase (Boltzmann) and can be used for solvers using different levels of description for the electrons; therefore, it is of particular interest because it can be adapted to other macroscopic, hence faster, solvers for confined devices exploited at industrial level.Project PID2020-117846GB-I00 funded by the Spanish Ministerio de Ciencia e InnovaciónProject A-TIC-344-UGR20 funded by European Regional Development Fund

Optical and transport properties of GaN and its lattice matched alloys

The study of carrier dynamics in wide band gap semiconductors is of great importance for UV detectors and emitters which are expected to be the building blocks for optoelectronic applications and high voltage electronics. On the experimental side, the progress made in the past two decades in generating subpicosecond laser pulses, resulted in numerous experiments that gave insight into the carrier dynamics in semiconductors. From the theoretical standpoint, the study of carrier interactions together with robust simulation methods, such as Monte-Carlo, provided great progress toward explaining the experimental results. These studies immensely improve our understanding of time scales of carrier recombination, relaxation and transport in semiconductor materials and devices which lead to optimizing the operation of optoelectronic devices, more specifically, emitters and detectors. Wide band gap materials having high breakdown field, wide band gap energy and high saturation velocity are among the most important semiconductors employed in the active layer of LEDs and lasers. GaN , its alloys, and ZnO are among the most important materials in semiconductor devices. Moreover, the use of lattice matched layers based on InAlN or InAlGaN is an alternative design approach which could mitigate the effect of polarization and enable growing thicker layers due to the higher structural quality. We first perform the study of carrier dynamics generated by ultrafast laser pulses in bulk GaN and ZnO materials to investigate the temperature dependent luminescence rise time. The obtained results are compared to the experimental results which show an excellent agreement. In this work, we use Monte Carlo method to evaluate the distribution of carriers considering the interaction of carriers with other carriers and also with polar optical phonons in the system. Considering the ongoing research about the advantages of lattice matched nitride based material systems, we also studied the properties of GaN layers lattice matched to InAlN and InAlGaN. As an application, we utilized the GaN/InAlGaN material system to study the carrier dynamics in Quantum Cascade Lasers. Furthermore, due to the superior properties of GaN which makes it an excellent candidate in power electronic applications, we also design and simulate an advanced vertical trench power MOSFET using drift diffusion and Monte Carlo models and characterize the performance of the device