Comparison of Double-Gate MOSFETs and FinFETs with Monte Carlo Simulation

A full-band Monte Carlo simulator has been used to analyze and compare the performance of n-channel double-gate MOSFETs and FinFETs. Size quantization effects were accounted for by using a quantum correction based on Schrödinger equation. FinFETs are a variation of typical double-gate devices with the gate surrounding the channel on three sides. From our simulations, we observed that the quantization effects in double-gate devices are less significant as compared to bulk MOSFETs. The total sheet charge density drops only slightly as the depletion of charge at the interface is counterbalanced by the increased volume inversion effect. We also observed an appreciable drop in average velocity distribution when quantum corrections were applied. For FinFETs, the fin extension lengths on either side of the gate affect the device performance significantly. These underlap regions have low carrier concentration and behave as large resistors. The current drops non-linearly with increasing fin extension lengths.     

3-D self-consistent Schrödinger-Poisson solver: the spectral element method

In this paper, we developed an efficient three-dimensional (3-D) nanoelectronic device simulator based on a self-consistent Schrödinger-Poisson solver to simulate quantum transport. An efficient and fast algorithm, the spectral element method (SEM), is developed in this simulator to achieve spectral accuracy where the error decreases exponentially with the increase in the sampling density and the order of the polynomial basis functions, thus significantly reducing the CPU time and memory usage. Perfectly matched layer (PML) boundary method, as an alternative to the open-boundary conditions in NEGF, is applied in this solver to simplify the numerical implementation. The validity of the Schrödinger and Poisson solvers are illustrated by a multiple-terminal device and a spherical charge example, respectively. The utility of the self-consistent Schrödinger-Poisson solver is illustrated by a nanotube example.     

Calibration of the Density-Gradient model by using the multidimensional effective-mass Schrödinger equation

A calibration method is developed for the electron effective mass in the Density-Gradient model. This method uses the two- and three-dimensional effective-mass Schrödinger equations, which are solved for bounded quantum systems. The electron effective mass is computed by fitting the electron concentration computed by using the Density-Gradient model to the electron concentration computed by using the Schrödinger equation. Results for strongly confined silicon system with (100), (110), and (111) crystallographic orientations are presented. It is shown that the effective mass varies with the shape and dimensions of the quantum box. In device simulations, one should use the value of m_n that corresponds to the right shape and dimensions of the confinement region in the device.     

Schrödinger-equation-based quantum corrections addressing degeneracy-breaking and confinement-enhanced scattering

We review extensions of Schrödinger-equation-based quantum corrections that have been implemented within the semiclassical Monte Carlo simulator Monte Carlo of The University of Texas (MCUT) to address quantum-confinement-induced redistribution of carriers in momentum as well as real space, and confinement-enhanced scattering in n-channel MOSFETs. The significance of these quantum confinement effects and of these corrections has been illustrated via calculation of channel mobility and short-channel MOSFET drive currents for strained and unstrained devices.     

“Atomistic”, Quantum and Ballistic Effects in Nanoscale MOSFETs

In this paper we describe the effects of quantum confinement and ballistic transport in the channel on the dispersion of threshold voltage due to the discrete distribution of dopants. To this aim, a recently developed 3D Poisson-Schrödinger solver is used, along with a 2D solver of ballistic transport. The Schrödinger equation is solved with density functional theory, in the local density approximation. Results on statistically meaningful ensembles of devices show that both ballistic transport and quantum confinement lead to an increase of threshold voltage dispersion.     

New schemes for creating large optical Schrödinger cat states using strong laser fields

Recently, using conditioning approaches on the high-harmonic generation process induced by intense laser-atom interactions, we have developed a new method for the generation of optical Schrödinger cat states (Lewenstein et al. in Nat Phys, 17 1104–1108, 2021. https://doi/10.1038/s41567-021-01317-w). These quantum optical states have been proven to be very manageable as, by modifying the conditions under which harmonics are generated, one can interplay between kitten and genuine cat states. Here, we demonstrate that this method can also be used for the development of new schemes towards the creation of optical Schrödinger cat states, consisting of the superposition of three distinct coherent states. Apart from the interest these kind of states have on their own, we additionally propose a scheme for using them towards the generation of large cat states involving the sum of two different coherent states. The quantum properties of the obtained superpositions aim to significantly increase the applicability of optical Schrödinger cat states for quantum technology and quantum information processing.

     

A study of envelope functions in FD-SOI devices for non-parabolic bands

In this study we analyzed the envelope functions obtained by solving the effective-mass Schrödinger equation including the non-parabolicity of the valence band in p-type FD-SOI devices. In order to carry out this task, we used two different algorithms to solve the effective-mass Schrödinger equation in barriers, and calculated the envelope functions and eigenenergies yielded by these methods for several states along the subbands. This study enabled us to propose a method for selecting the most appropriate envelope functions for each subband. Finally, we quantified the differences in phonon and interface-roughness scattering rates resulting from using the envelope function proposed rather than that obtained by simpler approaches in barriers.     

Fully Numerical Monte Carlo Simulator for Noncubic Symmetry Semiconductors

In this paper, we present the workings of a fully numerical Monte Carlo simulator that can be employed to study transport in materials with noncubic symmetry. All of the principal ingredients of the Monte Carlo model, i.e., the energy band structure, phonon scattering rates, and impact ionization transition rate are used in numerical form. Various considerations such as k-space mesh size, numerical integration convergence, etc. that impact numerical accuracy will be discussed. The workings of the simulator are illustrated using example calculations of the bulk transport properties of GaAs and GaN. The simulation of bulk GaAs in particular challenges the numerics since the low electron effective mass within the gamma valley requires a high degree of numerical refinement to correctly capture the dynamics in this region. We calculate the steady-state drift velocity, impact ionization coefficients, valley occupations, and average carrier energy in bulk GaAs and GaN.     

A many-particle quantum-trajectory approach for modeling electron transport and its correlations in nanoscale devices

Electron transport in mesoscopic systems is analyzed in terms of quantum (Bohm) trajectories associated to wave-function solutions of a many-particle (effective-mass) Schrödinger equation. Many-particle Bohm trajectories can be computed from single-particle Schrödinger equations. As an example, electron correlations for a triple-barrier tunneling system with electron-electron interactions are computed. Simulated noise results for interacting electrons that tunnels through triple barriers are presented. The approach opens a new path for studying electron transport and quantum noise in nanoscale systems, beyond the “Fermi liquid” paradigm.     

Quantum Monte Carlo Device Simulation of Nano-Scaled SOI-MOSFETs

Quantum transport properties of nano-scaled SOI-MOSFETs are investigated based on a quantum Monte Carlo (MC) device simulation. The quantum mechanical effects are incorporated in terms of a quantum correction of potential in the well-developed particle MC computational techniques. The ellipsoidal multi-valleys of silicon conduction band are also considered in the simulation. First, the validity of the quantum MC technique is verified by comparing the simulated results with a self-consistent Schrödinger-Poisson solution at thermal equilibrium. Then, we apply the technique to non-equilibrium and quasi-ballistic quantum transport in nano-scaled SOI-MOSFETs.     

Influence of Carrier Mobility and Interface Trap States on the Transfer and Output Characteristics of Organic Thin Film Transistors

We have used two dimensional drift diffusion simulations to calculate the electrical properties of bottom contact pentacene based organic thin film transistor, taking into account field-dependent mobility and interface or bulk trap states. In order to derive from basic principles the transport properties of the organic semiconductor we have developed a Monte Carlo simulator to calculate the field dependent mobility. We analyzed the presence of trap states at the interface between organic material and gate insulator and we show the influence of trap states combined with the effect of field-dependent mobility on the transfer characteristic. Numerical calculations are also reported for the output characteristics of the device showing a very good agreement with the available experimental results.     

An effective algorithm for numerical Schrödinger solver of quantum well structures

An effective algorithm for a one dimensional Schrödinger solver is proposed. The algorithm is derived from Bohm’s form of Schrödinger equation, and can be interpreted as a generalization of the Numerov process for the computational solution to the Schrödinger equation with quantum well structures. The proposed algorithm averages the probability slope’s discontinuity to converge the given energy to the nearest eigenstate, and generate complete eigenstates in a general heterojunction potential well. The new algorithm is applied to double-well III–V nanoscale MOSFET and generates each of the quantized levels.     

Physical modeling of hole mobility in silicon inversion layers under uniaxial stress

A physical model for hole mobility under either biaxial or uniaxial stress has been developed. The six-band k ? p theory is used to obtain the bandstructure through stress-dependent Hamiltonian. The hole mobility in the silicon inversion layer is studied in details using Monte Carlo method. A numerically robust method has been applied to achieve self-consistent solution of Poisson’s and Schrödinger equations.     

A Quantum Correction Model for Nanoscale Double-Gate MOS Devices Under Inversion Conditions

A quantum correction model for nanoscale double-gate MOSFETs under inversion conditions is proposed. Based on the solution of Schrödinger-Poisson equations, the developed quantum correction model is optimized with respect to (i) the left and right positions of the charge concentration peak, (ii) the maximum of the charge concentration, (iii) the total inversion charge sheet density, and (iv) the average inversion charge depth, respectively. This model can predict inversion layer electron density for various oxide thicknesses, silicon film thicknesses, and applied voltages. Compared to the Schrödinger-Poisson results, our model prediction is within 3.0% of accuracy. This quantum correction model has continuous derivatives and is therefore amenable to a device simulator.     

Electro-thermal simulation based on coupled Boltzmann transport equations for electrons and phonons

To study the thermal effect in nano-transistors, a simulator solving self-consistently the Boltzmann transport equations for both electrons and phonons has been developed. It has been used to investigate the self-heating effects in a 20 nm-long double-gate MOSFET (Fig. 1). A Monte Carlo solver for electrons is coupled with a direct solver for the steady-state phonon transport. The latter is based on the relaxation time approximation. This method is particularly efficient to provide a deep insight of the out-of-equilibrium thermal dissipation occurring at the nanometer scale when the device length is smaller than the mean free path of both charge and thermal carriers. It allows us to evaluate accurately the phonon emission and absorption spectra in both real and energy spaces.     

Numerical simulation of ballistic surface transport in cylindrical nanosystems

We study, by numerical simulations, the effect of topology on coherent electron transport through cylindrical junctions and bent cylindrical surfaces. The dynamics of a particle bound to a curved surface is described by a modified Schrödinger equation depending on two curvilinear coordinates. The modeling approach based on a finite-difference discretization of the latter equation is described, and a comparison with the standard solution of Schrödinger equation for flat surfaces is given. The effect of the geometrical parameters of the structures is reported.     

Analysis of saturation velocity and energy relaxation time of electrons in Si using full-band Monte Carlo simulation

In this paper, we have investigated the influence of optical phonon energy on electron saturation velocity and energy relaxation time by using a full band Monte Carlo simulator. The energy band structure is obtained using the first principle calculation. The scattering probability is calculated so as to conserve the energy and momentum in the full band structure. It is found that the range of optical phonon energy from 56.2 to 63.9 meV allows experimental saturation velocity and energy relaxation time. Electron saturation velocity is more sensitive than relaxation time to the optical phonon energy.     

A deterministic study of hot phonon effects in a 2D electron gas channel formed at an AlGaN/GaN heterointerface

We investigate the hot phonon effects on the transport properties of a two-dimensional electron gas formed in an AlGaN/GaN heterostructure. For this purpose, we use a deterministic numerical scheme to solve the coupled system of Boltzmann transport equations. The envelope wave functions of the confined carriers are self-consistently calculated from the Schrödinger-Poisson system. The simulation results show that the electron drift velocity is reduced by hot phonons for moderate and high electric fields, but become enhanced for low fields. This interesting behavior is elucidated by virtue of the energy balance equation using an analytic electron temperature model. We find good agreement to experimental data when hot phonon and degeneracy effects are taken into account.