An accelerated algorithm for full band electron-phonon scattering rate computation

a b s t r a c t Computing scattering rates of electrons and phonons stands at the core of studies of electron transport properties. In the high field regime, the interactions between all electron bands with all phonon bands need to be considered. This full band interaction implies a huge computational burden in calculating scattering rates. In this study, a new accelerated algorithm is presented for this task, which speeds up the computation by two orders of magnitude (100 times) and dramatically simplifies the coding. At the same time, it visually demonstrates the physical process of scattering more clearly. Computer: All. Program summary Operating system: All. RAM: Depends on problem, ∼kB to MB Classification: 16.5. Nature of problem: Electron-phonon scattering is a fundamental problem in studying electron transport in condensed matters. There are situations where the scattering rates need to be updated frequently during a simulation, e.g. when hot phonon effects are considered. The speed of scattering calculation is very important in such cases. Solution method: In searching for possible scattering events, we propose here a band-by-band method, instead of the traditional point by point method. The whole calculation is parallelized in this sense and dramatically accelerated. Moreover, we proposed a representation method for all scattering mechanisms, which greatly simplified the coding task. Also, the additional animation part of this program demonstrates many insights into the scattering process. Restrictions: To use the code directly, electron band and phonon band should have the same mesh size. In other words, for each phonon band and electron band, they should have the same number of data points. ✩ This paper and its associated computer program are available via the Computer Physics Communication homepage on ScienceDirec

Monte Carlo simulations of two-dimensional electron gasses in gallium nitride high electron mobility transistors via general-purpose computing on graphics processing units

The work in this thesis covers two main topics: successfully porting an Ensemble Monte Carlo (EMC) focused on bulk III-V semiconductors on to the graphics processing unit (GPU) and investigating carrier transport in a two-dimensional electron gas (2DEG) created at an Aluminium Gallium Nitride (AlGaN) and Gallium Nit ride (GaN) heterojunction, specifically the effect of introducing non-equilibrium phonons.The programming language used to be able to run on the GPU, NVIDIA CUDA, is introduced. The concept of highly parallel programming is explored, along with the challenges this poses to an EMC simulating semiconductor materials and devices. The changes made to the bulk EMC algorithm are explained, including architectural, memory strategies and execution optimisations. The performance increase related to each change is given, and it is found that the GPU algorithm has a run time that is approximately 30% of the original EMC algorithm. This is the first example of an EMC simulating electron transport in semiconductors on a GPU.A two-dimensional EMC is created to simulate the behaviour of electrons confined in the 2DEG created at an AlGaN/GaN heterojunction. Results are presented for the electron velocity, momentum and energy relaxation times and mobility, which are compared to experimental results from AlGaN/GaN High Electron Mobility Transistors (HEMTs), and agreement is good. No velocity overshoot is observed, in agreement with experiments.Finally, non-equilibrium phonons are introduced to the 2DEG simulation to study their effect on the electron transport. Non-equilibrium phonons are found to reduce the electron velocity due to diffusive heating. However, due to the confinement of electrons, the phonon distribution is only increased in a small volume of reciprocal space and the effects are shown to be weaker than in bulk. The consideration of electron confinement and a non-equilibrium phonon population has not been seen in the current literature

ELECTROSTATIC AND ELECTRICAL TRANSPORT ANALYSIS OF NANOMATERIALS AND NUMERICAL METHODS DEVELOPMENT

The nanotechnology today is continuously boosting the application of nanostructured materials in the development and innovation of electronic devices, such as Nano &ndash Electromechanical Systems (NEMS), electrical transistors, thermoelectric devices, and solar cells. Due to the size miniaturization, quantum mechanical effects play important roles in the performance of such devices. To correctly capture the quantum mechanical effects and understand how these effects influence the electrostatic and electrical transport properties of nanomaterials, efficient and accurate computational models are highly desirable. Currently, the commonly used model for electrostatic analysis of nanoscale devices is based on self &ndash consistent solution of the effective &ndash mass Schroedinger equation coupled with the Poisson equation. However, a major drawback of this model is its inefficiency to simulate systems with large Degrees of Freedom (DOFs). To reduce the computational cost, in this thesis, two Component Mode Synthesis (CMS) approaches, namely the fixed &ndash interface CMS and the free &ndash interface CMS, are incorporated into the Schroedinger &ndash Poisson model to speed up the electrostatic analysis in nanostructures. The new model is employed to analyze the quantum electrostatics in both nanowires and FinFETs. Numerical results demonstrate the superior computational performance in terms of efficiency and accuracy. In addition to the electrostatic analysis, carrier transport in nanostructures with perturbation from quantum effects also merits careful consideration. Among the computational models developed for quantum mechanical carrier transport analysis, the Non &ndash Equilibrium Green &rsquo s Function (NEGF) coupled with Poisson equation has gained vast application in both ballistic and diffusive transport analysis of nanodevices. In this thesis, the NEGF model is expanded to include mechanical strain and carrier scattering effects. Two important multiphysics systems are investigated in this work. We first study the effect of mechanical strain on the electrical conductivity of Si/Si 1 &minus x Ge x nanocomposite thin films. The strain effect on the bandstructures of nano &ndash thin films is modeled by a degenerate two &ndash band k · p theory. The strain induced bandstructure variation is then incorporated in the NEGF &ndash Poisson model. The results introduce new perspectives on electrical transport in strained nano &ndash thin films, which provides useful guidance in the design of flexible electronics. Secondly, nanoporous Si as an efficient thermoelectric material is studied. The Seebeck coefficient and electrical conductivity of nanoporous Si are computed by using the NEGF &ndash Poisson model with scatterings modeled by Buttiker probes. The phonon thermal conductivity is obtained by using a Boltzmann Transport Equation (BTE) model while the electron thermal conductivity is captured by the Wiedemann &ndash Franz law. The thermoelectric figure of merit of nanoporous Si is computed for different doping density, porosities, temperature and pore size. An optimal combination of the material design parameters is explored and the result proves that nanoporous Si has better thermoelectric properties than its bulk counterpart. In the electrical transport analysis of nanomaterials, we found that the standard NEGF &ndash Poisson model using the Finite Difference (FD) method has a high computational cost, and is inapplicable to devices with irregular geometries. To overcome these difficulties, an accelerated Finite Element Contact Block Reduction (FECBR) method is developed in this thesis. The performance of the accelerated FECBR is evaluated through the simulation of two types of electronic devices: taper &ndash shaped DG &ndash MOSFETs and DG &ndash MOSFETs with Si/SiO 2 interface roughness. Numerical results show that the accelerated FECBR can be applied to model ballistic carrier transport in devices with multiple leads, arbitrary geometry and complex potential profile. The accelerated FECBR significantly improves the flexibility and efficiency of electrical transport analysis of nanomaterials and nanodevices

Linear-scaling algorithm for rapid computation of inelastic transitions in the presence of multiple electron scattering

Strong multiple scattering of the probe in scanning transmission electron microscopy (STEM) means image simulations are usually required for quantitative interpretation and analysis of elemental maps produced by electron energy-loss spectroscopy (EELS). These simulations require a full quantum-mechanical treatment of multiple scattering of the electron beam, both before and after a core-level inelastic transition. Current algorithms scale quadratically and can take up to a week to calculate on desktop machines even for simple crystal unit cells and do not scale well to the nanoscale heterogeneous systems that are often of interest to materials science researchers. We introduce an algorithm with linear scaling that typically results in an order of magnitude reduction in computation time for these calculations without introducing additional error and discuss approximations that further improve computational scaling for larger-scale objects with modest penalties in calculation error. We demonstrate these speedups by calculating the atomic resolution STEM-EELS map using the L-edge transition of Fe, for a nanoparticle 80 Å in diameter, in 16 hours, a calculation that would have taken at least 80 days using a conventional multislice approach

Modeling techniques for quantum cascade lasers

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation of quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schr\"odinger equation and Schr\"odinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function (NEGF) formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures

Automated computation of materials properties

Materials informatics offers a promising pathway towards rational materials design, replacing the current trial-and-error approach and accelerating the development of new functional materials. Through the use of sophisticated data analysis techniques, underlying property trends can be identified, facilitating the formulation of new design rules. Such methods require large sets of consistently generated, programmatically accessible materials data. Computational materials design frameworks using standardized parameter sets are the ideal tools for producing such data. This work reviews the state-of-the-art in computational materials design, with a focus on these automated $\textit{ab-initio}$ frameworks. Features such as structural prototyping and automated error correction that enable rapid generation of large datasets are discussed, and the way in which integrated workflows can simplify the calculation of complex properties, such as thermal conductivity and mechanical stability, is demonstrated. The organization of large datasets composed of $\textit{ab-initio}$ calculations, and the tools that render them programmatically accessible for use in statistical learning applications, are also described. Finally, recent advances in leveraging existing data to predict novel functional materials, such as entropy stabilized ceramics, bulk metallic glasses, thermoelectrics, superalloys, and magnets, are surveyed.Comment: 25 pages, 7 figures, chapter in a boo