Introducing energy broadening in semiclassical Monte Carlo simulations

Combining an insight on the quantum transport given by the Wigner function formalism and the classical perturbation theory, an algorithm has been developed that allows the introduction of collisional broadening in semiclassical electron transport Monte Carlo (MC) simulations. In the proposed algorithm, electron energy and momentum are treated as independent variables; the laws of energy and momentum conservation are fulfilled at each scattering event, but the relationship between energy and momentum is not given by the traditional expression, since Bloch states are not eigenstates of the total Hamiltonian. The results obtained for a simple model semiconductor demonstrate that the non-physical instabilities observed in previous attempts to introduce collisional broadening in semiclassical MC simulations have been removed. The algorithm is suitable for application in MC simulations of realistic device models.     

Wigner Function-Based Simulation of Quantum Transport in Scaled DG-MOSFETs Using a Monte Carlo Method

Source-to-drain tunneling in deca-nanometer double-gate MOSFETs is studied using a Monte Carlo solver for the Wigner transport equation. This approach allows the effect of scattering to be included. The subband structure is calculated by means of post-processing results from the device simulator Minimos-NT, and the contribution of the lowest subband is determined by the quantum transport simulation. By separating the potential profile into a smooth classical component and a rapidly varying quantum component the numerical stability of the Monte Carlo method is improved. The results clearly show an increasing tunneling component of the drain current with decreasing gate length. For longer gate lengths the semi-classical result is approached.     

An improved Wigner Monte-Carlo technique for the self-consistent simulation of RTDs

We present an original approach to including quantum transport into classical Ensemble Monte Carlo (EMC) simulations. The method, based on the Wigner transport equation, is fully self-consistent, and includes impurity and phonon scattering according to the Fermi Golden rule. It is inspired by an approach suggested by Shifren et al. [IEEE Trans. Electron Dev. 50, 769 (2003)], with some major improvements that make possible successful comparison with other simulation techniques and experiments.     

A Wigner Function Based Ensemble Monte Carlo Approach for Accurate Incorporation of Quantum Effects in Device Simulation

We present results of both Gaussian wave-packet tunneling though a single barrier structure and RTD operation achieved from a particle-based Ensemble Monte Carlo (EMC) simulation that is based on the Wigner distribution function (WDF). Methods of including the Wigner potential into the EMC, to incorporate naturally quantum phenomena, via a particle property we call the affinity are discussed. Results showing tunneling and correlation build-up in both cases are presented.     

Monte Carlo simulation of double gate MOSFET including multi sub-band description

A new two-dimensional self-consistent Monte-Carlo simulator including the multi sub-band transport in a 2D electron gas is described and applied to an ultra-thin Double Gate MOSFET. This approach takes into account both out of equilibrium transport and quantization effects. This method improves significantly microscopic insight into the operation of deep sub-100 nm CMOS devices. We analyze the ballistic, quantization and roughness effects in a 12 nm-long DGMOS transistor. In particular, we focus on the link between non-stationary transport and the evolution of sub-band occupancy along the channel.     

Tetrahedral elements in self-consistent parallel 3D Monte Carlo simulations of MOSFETs

Novel thin-body architectures with complex geometry are becoming of large interest because they are expected to deliver the ITRS prescribed on-current when semiconductor transistors are scaled into nanometer dimensions. We report on the development of a 3D parallel Monte Carlo simulator coupled to a finite element solver for the Poisson equation in order to correctly describe the complex domains of advanced FinFET transistors. We study issues such as charge assignment, field calculation, treatment of contacts and parallelisation approach which have to be taken into account when using tetrahedral elements. The applicability of the simulator is demonstrated by modelling a 10 nm gate length double gate MOSFET with a body thickness of 6.1 nm.     

On a simple and accurate quantum correction for Monte Carlo simulation

We investigate a quantum-correction method for Monte Carlo device simulation. The method consists of reproducing quantum mechanical density-gradient simulation by classical drift-diffusion simulation with modified effective oxide thickness and work function and using these modifications subsequently in Monte Carlo simulation. This approach is found to be highly accurate and can be used fully automatically in a technology computer-aided design (TCAD) workbench project. As an example, the methodology is applied to the Monte Carlo simulation of the on-current scaling in p- and n-type MOSFETs corresponding to a 65 nm node technology. In particular, it turns out that considering only the total threshold voltage shift still involves a significant difference to a Monte Carlo simulation based on the combined correction of oxide thickness and work function. Ultimately, this quantum correction permits to consider surface scattering as a combination of specular and diffusive scattering where the conservation of energy and parallel wave vector in the specular part takes stress-induced band structure modifications and hence the corresponding surface mobility changes on a physical basis into account.     

Monte Carlo simulation for evaluating retail wheeling effects

A Monte Carlo simulation method for evaluating retail-wheeling effects on power systems is formulated and solution methods are presented. The effects of wheeling on operating cost, transmission losses, and system security are considered. For a specific operating condition, the effects are quantified by the sensitivity of specific quantities of interest with respect to power wheeling level. Quantities of interest are total operating cost, transmission losses and security, which is quantified with several indices. This model is utilized within a Monte Carlo simulation to calculate probability distribution functions of the incremental effects of wheeling on operating cost, transmission losses, and system security. The model and solution methods are applied on an example power system and the results are presented.     

Monte Carlo simulation of resonant phonon THz quantum cascade lasers

We report on Monte Carlo (MC) simulations aimed at the design and optimization of GaAs-based THz quantum cascade lasers. Results are presented for a GaAs/Al_0.15Ga_0.85As quantum cascade laser design based on LO phonon scattering depopulation, which operates at 2.8 THz. The obtained electron distribution functions in the subbands and the photoluminescence spectra are compared to experimental results. Also the dependence of the inversion and current density on the applied field is investigated, and the parasitic channels are identified based on the intersubband lifetimes.     

Monte Carlo simulations of nanometric devices beyond the “mean-field” approximation

For nanoscale electron devices, the role of a single-electron (or a single-impurity) can have a large impact on their electrical characteristics. A new method for introducing the long-range and short-range Coulomb interaction in semiconductor semi-classical Monte Carlo simulations is presented. The method is based on directly dealing with a many-particle system by solving a different Poisson equation for each electron. The present work shows the numerical viability of this alternative approach for nanoscale devices with few (<100) electrons. The method is compared with the traditional “mean-field” Monte Carlo simulations. It is shown, numerically, that the “mean-field” approximation produces important errors for aggressively-scaled devices.     

Monte Carlo simulation of 2D TASER

A possibility to develop the so called TASER (Terahertz-Amplification-by-the-Stimulated-Emission-of- Radiation) by using two-dimensional (2D) electron transport in quantum well (QW) structures is investigated by Monte Carlo simulation of the optical-phonon-emission assisted transit-time resonance (OPTTR) of 2D electrons in momentum space under the low lattice temperature. A considerable extension of the frequency region for THz radiation generation (upto 5 times) when going from 3D- to 2D-case is predicted.     

A First Principles Alloy Scattering Approach for Monte Carlo Hole Mobility Calculations

We present an ab-inito band-structure approach that can be applied for holes in Monte Carlo simulations of strained SiGe channel devices in order to remove the uncertainties of alloy scattering parameters along with addressing the effects of strain.     

Boundary conditions with Pauli exclusion and charge neutrality: application to the Monte Carlo simulation of ballistic nanoscale devices

Electron transport becomes (quasi-) ballistic for nanoscale devices with active regions smaller than 20 nm. Under these conditions, the current and the noise are mainly determined by the electron injection process. Thus, the numerical simulation of these small devices can be very sensible to the boundary conditions (BC). In this work, we present a novel BC for (time-dependent) particle simulators that fulfill Fermi statistics and charge neutrality at the contacts. Monte Carlo simulations of a nanometric two-terminal device using a traditional injection model and the novel model presented in this work are compared.     

Quantum Ensemble Monte Carlo simulation of silicon-based nanodevices

A Quantum Ensemble Monte Carlo (QEMC) simulator is used to calculate electrical characteristics and transient response of actual nanotransistors: both sub-50 nm CMOS N-MOSFETs and ultrathin double gate SOI transistors have been deeply studied. Doping profiles and oxide thickness have been selected to cope with the available specifications of the ITRS Roadmap. The Quantum corrected Ensemble Monte Carlo simulator (QEMC) has been used to self-consistently solve the Boltzmann Transport and Poisson equations in actual devices. Quantum effects are included through the Multi-Valley Effective Conduction Band Edge (MV-ECBE) technique, and adequate approaches for phonon and surface roughness scattering have been developed to include the effects of carrier quantization in pseudo-2DEG simulations.     

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.     

Monte Carlo simulation of terahertz quantum cascade lasers: The influence of the modelling of carrier-carrier scattering

A theoretical investigation of electron-electron scattering in quantum cascade lasers is presented. The devices are studied by means of an ensemble Monte Carlo simulation that includes all relevant scattering mechanisms. The energy levels and wave functions are determined by a self-consistent resolution of the Schrödinger and Poisson equations. The influence of the modelling of carrier-carrier scattering is discussed on the example of a resonant-phonon structure operating at 3.4 THz. To demonstrate the usefulness of such a model for optimization purpose, an alternative design operating at a lower frequency is proposed. Our model predicts that a significant population inversion can be achieved at about 1 THz.     

蒙特卡罗方法在网损分摊中的应用

研究了计算网损分摊的方法,针对在实际生产运行中,特定时段的计算网损分摊电量的通常方法,提出采用蒙特卡罗方法计算得到的用户在一段时间的分摊电量的一种方法,通过在负荷功率概率模型基础上抽取负荷样本,并而根据该抽样数据计算出的结果,在一定程度弥补了计算量大、计算时间长的问题.     

A three‐dimensional Monte Carlo model for the simulation of nanoelectronic devices

We present a three‐dimensional (3D) semi‐classical ensemble Monte Carlo model newly developed to simulate a variety of nanoelectronic devices. The characteristics of the 3D model are compared with the widely used two‐dimensional (2D) models. The advantages of our model, in terms of accuracy in modelling the physics behind the operation of nanodevices, are presented by applying it to T‐branch junctions based on InGaAs/InAlAs heterostructures. Simulation of a T‐branch junction with a Schottky gate terminal is presented, using both 2D and 3D models, demonstrating the necessity of using 3D simulation models to study the physics of complex‐geometry nanostructures. Copyright © 2009 John Wiley & Sons, Ltd.     

Monte Carlo simulation of low-field mobility in strained double gate SOI transistors

Electron transport in strained double gate silicon on insulator transistors has been studied by Monte Carlo method. Poisson and Schroedinger equations have been self-consistently solved in these devices for different silicon layer thicknesses both for unstrained and strained silicon channels. The results show that the strain of the silicon layer leads to a larger population of the no-primed subbands, thus decreasing the average conduction effective mass. However, strain also contributes to a larger confinement of the charge close to the two Si/SiO₂ interfaces, thus weakening the volume inversion effect, and limiting the potential increase of the phonon limited mobility.     

Study of Electron Transport in SOI MOSFETs Using Monte Carlo Technique with Full-Band Modeling

Effects of conduction-band non-parabolicity on electron transport properties in silicon-on-insulator (SOI) metal-oxide-semiconductor field effect transistors (MOSFETs) are studied by performing Monte Carlo simulation with a full-band modeling. An empirical pseudo-potential method is adopted for evaluating the two-dimensional electronic states in SOI MOSFETs. SOI-film thickness dependence of phonon-limited mobility, drift-velocity and subband occupancy is calculated and the results are compared with those of a simple effective mass approximation. The non-parabolicity effects are found to play an important role in 4-fold valleys under higher applied electric fields or at higher temperatures.