Machine learning approach for predicting the effect of statistical variability in Si junctionless nanowire transistors

This work investigates the possibility to replace numerical TCAD device simulations with a multi-layer neural network (NN). We explore if it is possible to train the NN with the required accuracy in order to predict device characteristics of thousands of transistors without executing TCAD simulations. In order to answer this question, here we present a hierarchical multi-scale simulation study of a silicon junctionless nanowire field-effect transistor (JL-NWT) with a gate length of 150 nm and diameter of an Si channel of 8 nm. All device simulations are based on the Drift-Diffusion (DD) formalism with activated density gradient (DG) quantum corrections. For the purpose of this work, we perform statistical numerical experiments of a set of 1380 automictically different JL-NWTs. Each device has a unique random distribution of discrete dopants (RDD) within the silicon body. From those statistical simulations, we extract important figures of merit (FoM), such as OFF-current (IOFF) and ONcurrent (ION), subthreshold slope (SS) and voltage threshold (VTH). Based on those statistical simulations, we train a multi-layer NN and we compare the obtained results with a general linear model (GLM). Our work shows the potential of using NN in the field of device modelling and simulation with a potential application to significantly reduce the computational cost

Random dopant-induced variability in Si-InAs nanowire tunnel FETs: a quantum transport simulation study

In this letter, we report a quantum transport simu- lation study of the impact of Random Discrete Dopants (RDD)s on Si-InAs nanowire p-type Tunnel FETs. The band-to-band tunneling is simulated using the non-equilibrium Green’s func- tion formalism in effective mass approximation, implementing a two-band model of the imaginary dispersion. We have found that RDDs induce strong variability not only in the OFF-state but also in the ON-state current of the TFETs. Contrary to the nearly normal distribution of the RDD induced ON-current variations in conventional CMOS transistors, the TFET’s ON- currents variations are described by a logarithmic distribution. The distributions of other Figures of Merit (FoM) such as threshold voltage and subthreshold swing are also reported. The variability in the FoM is analysed by studying the correlation between the number and the position of the dopants

Comprehensive study of cross-section dependent effective masses for silicon based gate-all-around transistors

The use of bulk effective masses in simulations of the modern-day ultra-scaled transistor is erroneous due to the strong dependence of the band structure on the cross-section dimensions and shape. This has to be accounted for in transport simulations due to the significant impact of the effective masses on quantum confinement effects and mobility. In this article, we present a methodology for the extraction of the electron effective masses, in both confinement and the transport directions, from the simulated electronic band structure of the nanowire channel. This methodology has been implemented in our in-house three-dimensional (3D) simulation engine, NESS (Nano-Electronic Simulation Software). We provide comprehensive data for the effective masses of the silicon-based nanowire transistors (NWTs) with technologically relevant cross-sectional area and transport orientations. We demonstrate the importance of the correct effective masses by showing its impact on mobility and transfer characteristics

An accurate analytical model for tunnel FET output characteristics

The analytical models for the output characteristics of tunnel FETs (TFETs) based on Maxwell–Boltzmann (MB) statistics have some accuracy issues, especially in linear region of operation, when compared with more sophisticated numerical approaches. In this letter, by exploiting the thermal injection method (TIM), an accurate analytical model for the TFET potential profile is proposed. Although the approach is initially envisaged for heterojunction TFETs (H-TFETs), it could be straightforwardly adopted for homojunction TFETs. After an accurate description of the potential profile is obtained, then, the current is computed by means of a Landauer-like expression. Comparison with the numerical simulations at different bias conditions show that the predicted output characteristics qualitatively improve, leading to a significant enhancement in accuracy at a much less-computational cost

Quantum Transport Investigation of Threshold Voltage Variability in Sub-10 nm JunctionlessSi Nanowire FETs

In this paper, we use the Non-Equilibrium Green's Function formalism to study the dependence of the threshold voltage variability on the cross-section shape and the gate length in Junction Less Field Effect Transistors. Each configuration, i.e. gate length and cross-section, was investigated using a statistical ensemble of 100 samples. We found that the variability in threshold voltage is increased independently of the cross-section shape when the gate length isshrunk down to 5 nm. We attribute this results to the higher wave function “randomization” in longer gate lengths

A Multi-Scale Simulation Study of the Strained Si Nanowire FETs

In this work, we study 2.1nm-diameter uniaxial strained Si gate-all-around nanowire field-effect transistors, focusing on the electron mobility and the variability due to random discrete dopants (RDDs). Firstly, we extract the electron effective masses under various strains from Density Functional Theory (DFT) simulations. Secondly, we present the impact of the strain on the electron mobility in the Si nanowire using the Kubo-Greenwood formalism with a set of multi-subband phonon, surface roughness, and ionized impurity scattering mechanisms. Finally, we perform quantum transport simulations to investigate the effect of RDD on the threshold voltage and ON-state current variation

Enhanced Capabilities of the Nano-Electronic Simulation Software (NESS)

The aim of this paper is to present a flexible TCAD platform called Nano-Electronic Simulation Software (NESS) which enables the modelling of contemporary future electronic devices combining different simulation paradigms (with different degrees of complexity) in a unified simulation domain. NESS considers confinement-aware band structures, generates the main sources of variability, and can study their impact using different transport models. In particular, this work focuses on the new modules implemented: Kubo-Greenwood solver, Kinetic Monte Carlo solver, Gate Leakage calculation, and a full-band quantum transport solver in the presence of hole-phonon interactions using a mode-space k⋅p approach in combination with the existing NEGF module

Schrödinger Equation Based Quantum Corrections in Drift-Diffusion: A Multiscale Approach

In this work, we report the development of a 3D drift-diffusion (DD) simulator for ultrascaled transistors with quantum corrections based on the solution of the Schrödinger equation. In a novel multi-scale simulation approach we use effective masses from tight-binding calculations, carrier mobility from the semi-classical Kubo-Greenwood formalism, and quantum corrections based on self-consistent Poisson-Schrödinger solution. This scheme has been implemented into the University of Glasgow TCAD tool called NESS (Nano Electronic Simulation Software). The approach is validated with respect to non-equilibrium Green's function (NEGF) simulations in the case of nanowire field effect transistors with different cross-sectional shapes

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

Quantum Enhancement of a S/D Tunneling Model in a 2D MS-EMC Nanodevice Simulator: NEGF Comparison and Impact of Effective Mass Variation

As complementary metal-oxide-semiconductor (CMOS) transistors approach the nanometer scale, it has become mandatory to incorporate suitable quantum formalism into electron transport simulators. In this work, we present the quantum enhancement of a 2D Multi-Subband Ensemble Monte Carlo (MS-EMC) simulator, which includes a novel module for the direct Source-to-Drain tunneling (S/D tunneling), and its verification in the simulation of Double-Gate Silicon-On-Insulator (DGSOI) transistors and FinFETs. Compared to ballistic Non-Equilibrium Green’s Function (NEGF) simulations, our results show accurate I D vs. V GS and subthreshold characteristics for both devices. Besides, we investigate the impact of the effective masses extracted Density Functional Theory (DFT) simulations, showing that they are the key of not only the general thermionic emission behavior of simulated devices, but also the electron probability of experiencing tunneling phenomena.This project has received funding from EPSRC UKRI Innovation Fellowship scheme under grant agreement No. EP/S001131/1 (QSEE) and No. EP/P009972/1 (QUANTDEVMOD)