Non-equilibrium Green's function predictions of band tails and band gap narrowing in III-V semiconductors and nanodevices

High-doping induced Urbach tails and band gap narrowing play a significant role in determining the performance of tunneling devices and optoelectronic devices such as tunnel field-effect transistors (TFETs), Esaki diodes and light-emitting diodes. In this work, Urbach tails and band gap narrowing values are calculated explicitly for GaAs, InAs, GaSb and GaN as well as ultra-thin bodies and nanowires of the same. Electrons are solved in the non-equilibrium Green's function method in multi-band atomistic tight binding. Scattering on polar optical phonons and charged impurities is solved in the self-consistent Born approximation. The corresponding nonlocal scattering self-energies as well as their numerically efficient formulations are introduced for ultra-thin bodies and nanowires. Predicted Urbach band tails and conduction band gap narrowing agree well with experimental literature for a range of temperatures and doping concentrations. Polynomial fits of the Urbach tail and band gap narrowing as a function of doping are tabulated for quick reference

An Enhanced Statistical Phonon Transport Model for Nanoscale Thermal Transport and Design

Managing thermal energy generation and transfer within the nanoscale devices (transistors) of modern microelectronics is important as it limits speed, carrier mobility, and affects reliability. Application of Fourier’s Law of Heat Conduction to the small length and times scales associated with transistor geometries and switching frequencies doesn’t give accurate results due to the breakdown of the continuum assumption and the assumption of local thermodynamic equilibrium. Heat conduction at these length and time scales occurs via phonon transport, including both classical and quantum effects. Traditional methods for phonon transport modeling are lacking in the combination of computational efficiency, physical accuracy, and flexibility. The Statistical Phonon Transport Model (SPTM) is an engineering design tool for predicting non-equilibrium phonon transport. The goal of this work has been to enhance the models and computational algorithms of the SPTM to elevate it to have a high combination of accuracy and flexibility. Four physical models of the SPTM were enhanced. The lattice dynamics calculation of phonon dispersion relations was extended to use first and second nearest neighbor interactions, based on published interatomic force constants computed with first principles Density Functional Theory (DFT). The computation of three phonon scattering partners (that explicitly conserve energy and momentum) with the inclusion of the three optical phonon branches was applied using scattering rates computed from Fermi’s Golden Rule. The prediction of phonon drift was extended to three dimensions within the framework of the previously established methods of the SPTM. Joule heating as a result of electron-phonon scattering in nanoscale electronic devices was represented using a modal specific phonon source that can be varied in space and time. Results indicate the use of first and second nearest neighbor lattice dynamics better predicted dispersion when compared to experimental results and resulted in a higher fidelity representation of phonon group velocities and three phonon scattering partners in an anisotropic manner. Three phonon scattering improvements resulted in enhanced fidelity in the prediction of phonon modal decay rates across the wavevector space and thus better representation of non-equilibrium behavior. Comparisons to the range of phonon transport modeling approaches from literature verify that the SPTM has higher phonon fidelity than Boltzmann Transport Equation and Monte Carlo and higher length scale and time scale fidelity than Direct Atomic Simulation. Additional application of the SPTM to both a 1-d silicon nanowire transistor and a 3-d FinFET array transistor in a transient manner illustrate the design capabilities. Thus, the SPTM has been elevated to fill the gap between lower phonon fidelity Monte Carol (MC) models and high fidelity, inflexible direct quantum simulations (or Direct Atomic Simulations (DAS)) within the field of phonon transport modeling for nanoscale electronic devices. The SPTM has produced high fidelity device level non-equilibrium phonon information in a 3-d, transient manner where Joule heating occurs. This information is required due to the fact that effective lattice temperatures are not adequate to describe the local thermal conditions. Knowledge of local phonon distributions, which can’t be determined from application of Fourier’s law, is important because of effects on electron mobility, device speed, leakage, and reliability

Nano-electronic Simulation Software (NESS): a flexible nano-device simulation platform

The aim of this paper is to present a flexible and open-source multi-scale simulation software which has been developed by the Device Modelling Group at the University of Glasgow to study the charge transport in contemporary ultra-scaled Nano-CMOS devices. The name of this new simulation environment is Nano-electronic Simulation Software (NESS). Overall NESS is designed to be flexible, easy to use and extendable. Its main two modules are the structure generator and the numerical solvers module. The structure generator creates the geometry of the devices, defines the materials in each region of the simulation domain and includes eventually sources of statistical variability. The charge transport models and corresponding equations are implemented within the numerical solvers module and solved self-consistently with Poisson equation. Currently, NESS contains a drift–diffusion, Kubo–Greenwood, and non-equilibrium Green’s function (NEGF) solvers. The NEGF solver is the most important transport solver in the current version of NESS. Therefore, this paper is primarily focused on the description of the NEGF methodology and theory. It also provides comparison with the rest of the transport solvers implemented in NESS. The NEGF module in NESS can solve transport problems in the ballistic limit or including electron–phonon scattering. It also contains the Flietner model to compute the band-to-band tunneling current in heterostructures with a direct band gap. Both the structure generator and solvers are linked in NESS to supporting modules such as effective mass extractor and materials database. Simulation results are outputted in text or vtk format in order to be easily visualized and analyzed using 2D and 3D plots. The ultimate goal is for NESS to become open-source, flexible and easy to use TCAD simulation environment which can be used by researchers in both academia and industry and will facilitate collaborative software development