Monte Carlo Particle Simulation Research Articles

Algorithm for forcing scattered radiation to arbitrary convex regions in neutral particle Monte Carlo simulation

A new algorithm is presented to improve the efficiency of neutral particle Monte Carlo radiation transport. When a radiation quantum is produced from a source or undergoes a scattering event, it is divided into two parts. One continues to undergo the normal analogue transport process. The other is deterministically transported to a randomly selected point on the surface of an arbitrary convex region, from where it continues normal transport. Application of this approach substantially improves efficiency in cases where particles must reach small geometric regions in order to make tally contributions. The algorithm is demonstrated in a simulation of X-ray scattering in a radiographic imaging application.

Test particle simulation of the role of ballistic electrons in hybrid dc/rf capacitively coupled CF4 plasmas

Hybrid dc/rf plasma sources are an emerging equipment technology in plasma etching for semiconductor manufacturing. In this type of plasma source, ballistic electrons originate as secondary electrons on a dc/rf (i.e., VHF, 60MHz) biased electrode and are then accelerated in the sheath toward an opposite non-dc biased lower electrode. For electropositive (argon) plasmas it has been shown that the primary contribution of ballistic electrons is ionization in the dc sheath and modulation of the discharge properties. Whether applied dc power net increases or decreases the plasma electron density depends on the rf power environment of the opposing substrate electrode. When rf power is applied to a substrate electrode, the rf self-bias creates a potential well that traps the ballistic electrons, the result being that the electron density increases with dc power. In most cases the fraction of high energy electrons that reach the electrode is small. In this article, the authors describe the use of test particle Monte Carlo simulations to describe the behavior of hybrid dc/rf electronegative (CF4) plasmas. In contrast to the behavior in argon, process experiments with electronegative gases such as CF4 indicate that the electron density is independent of dc bias power when no rf power is applied to the wafer. Test particle simulations show that CF4 provides for a “self-confinement” effect caused by large cross sections for vibrational excitation at intermediate to low electron energies, which results in weak dependence of electron density on dc bias voltage when low frequency bias is not applied to the wafer. This emphasizes the important role of gas composition and cross-section structure in the control of dc/rf plasmas. Consistent with experiment, test particle Monte Carlo simulations also show that when rf is applied to the substrate, overall the CF4 plasma’s macroscopic properties are similar manner to argon plasmas. Even so, differences between the argon and CF4 plasmas occur related to the scaling of the fraction of ballistic electrons that reach the wafer as a function of dc and rf power. A regime is identified in which CF4 and argon plasmas have the equivalent ratio of ballistic to thermal electron density adjacent to the surface. The authors explain that the differences are related to different thermalization and ionization mechanisms in these plasmas. In addition, they find the electron attachment constant is zero in the dc sheath and nearly constant value in the bulk as the transit time in the sheath is far less than the mean attachment time. The same simple function to express ionization rate constant as a function of electric field in the dc sheath, developed for argon, can be also applied to CF4.

Anomalous behavior of electronic noise related to the onset of current instabilities inn+nn+ diodes

We investigate the noise behavior in the presence of current instabilities induced by optical phononemission. Calculations are carried out by means of Monte Carlo particle simulations of InPn+nn+ diodes at lattice temperatures below about 80 K. A giant enhancement of the low-frequencynoise is observed in a narrow voltage region, which precedes the onset of currentself-oscillations caused by the instability. A possible origin of this enhancement is discussed.The impact of the non-linear effects on the anomalous low-frequency noise behavior isstressed.

On the Mean Free Path for Backscattering in $k_{B}T$ Layer of Bulk Nano-MOSFETs

We perform Monte Carlo particle simulations on a silicon conductor for the purposes of reexamining the channel backscattering in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bulk</i> nano-MOSFETs. The resulting mean free path lambda <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</i> for backscattering in a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">long</i> and near-equilibrium conductor is constant, regardless of the potential profile. However, the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">apparent</i> mean free path lambda <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> in a local quasi-ballistic <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kBT</i> layer depends on the curvature of the potential profile. In a linear potential profile, the lambda <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> extracted in a wide range of the conductor length (15 to 100 nm) and lattice temperature (150 to 300 K) is found to fall below lambda <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</i> . The carrier heating as the origin of reduced mean free path is inferred from the simulated carrier velocity distribution near the injection point. Strikingly, the mean free paths in a parabolic potential profile remain consistent: lambda <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> = lambda <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</i> . This indicates the absence or weakening of the carrier heating in the layer of interest, valid only for the parabolic potential barrier.

Proper orthogonal decomposition methods for noise reduction in particle-based transport calculations

Proper orthogonal decomposition techniques to reduce noise in the reconstruction of the distribution function in particle-based transport calculations are explored. For two-dimensional steady-state problems, the method is based on low rank truncations of the singular value decomposition of a coarse-grained representation of the particle distribution function. For time-dependent two-dimensional problems or three-dimensional time-independent problems, the use of a generalized low-rank approximation of matrices technique is proposed. The methods are illustrated and tested with Monte Carlo particle simulation data of plasma collisional relaxation and guiding-center transport with collisions in a magnetically confined plasma in toroidal geometry. It is observed that the proposed noise reduction methods achieve high levels of smoothness in the particle distribution function by using significantly fewer particles in the computations.

Analysis of Conditions for Free-Carrier Grating Formation in InP n+nn+Structures using Monte Carlo Technique

Electron transport in 5 μm long InP nnn structure with the n-region doping of 10 cm−3 is theoretically investigated by the Monte Carlo particle technique at low lattice temperature (T = 10 K), when dominating scattering mechanism is the optical phonon emission. It is shown that at the constant bias a free-carrier grating can be formed inside the n-region. The free-carrier grating formation conditions are analysed by Monte Carlo particle simulation of electric field profiles and noise in the considered InP structure.

3D Monte Carlo simulation of current trends and performance in scaled trigate MOSFET

Silicon nanowires with multiple-gates provide better source drain isolation and are thought to be the most promising candidate to replace bulk Si MOSFETs as we downscale deep into the nanometer regime. In this study we utilize a 3D full-band particle Monte Carlo (MOCA3D) simulator to investigate the performance and current trends of fully-depleted Trigate MOSFETs with different cross-sections. Results indicate that as we reduce the cross-section, the increased coupling between the top and lateral gates reduces the channel potential in different axes. In addition, device current normalized with respect to the Trigate perimeter alleviates as we scale the cross-section.

Techniques for computational study of plasma–solid interaction at higher pressures

Several techniques of computational physics used in low-temperature plasma simulations at higher pressures are presented in our contribution. The first approach is called fluid modelling, the second one hybrid modelling and the third technique—particle modelling presented here is realized as a part of hybrid model. There are several techniques applicable in computational plasma physics but some of these methods have explicit limitation. For example, time consumption of standard particle-in-cell Monte Carlo (PIC-MC) particle simulation is increased profoundly with increasing pressure of plasma. Hence, we have used the fluid and hybrid modelling. Hybrid model consists of two parts—particle model, simulating fast electrons while fluid model simulates slow electrons and positive argon ions. In particle model, the positions and velocities of fast electrons are calculated by means of deterministic Verlet algorithm while the collision processes are treated by the stochastic way. For solution of fluid equations, the Scharfetter–Gummel exponential scheme was used. Typical results of our calculations are electric field distribution, fluxes and collision rates of charged particles near the planar probe.

Temperature-Oriented Experiment and Simulation as Corroborating Evidence of MOSFET Backscattering Theory

The MOSFET backscattering theory relies on a so-called kB T layer. In this letter, we adopt two different approaches to examine the temperature dependencies of the width spanned by this critical zone. First of all, a 55-nm channel length n-MOSFET is extensively characterized at three temperatures of 233 K, 263 K, and 298 K while undergoing a parameter decoupling/transformation process. A unique relationship is straightforwardly created and is comparable with that in the literature: The width of the kBT layer is proportional to the square root of temperature. The case of 77 K is also projected. Other corroborating evidence is a Monte Carlo particle simulation conducted on an 80-nm-long silicon conductor with the kBT layer's width proportional to the temperature in the high field region. Without adjusting any parameters, the backscattering theory is shown to work well for the demonstrated temperatures down to 77 K

Free-carrier grating due to the optical phonon emission in InP n + nn + structures

Electron transport in 5 μm long InP n+nn+ structure with the n-region doping of 1015cm−3 is theoretically investigated by the Monte Carlo Particle (MCP) technique at low lattice temperature (T = 10 K), when dominating scattering mechanism is the optical phonon emission. It is shown that at the constant bias a free-carrier grating (FCG) can be formed inside the n-region. The simple model of FCG formation is proposed and verified by MCP simulation of electron transport and noise in the considered InP structure.

Pearson versus gaussian effective potentials for quantum-corrected Monte-Carlo simulation

We propose a new effective potential for includ- ing quantization effects in nanometer scaled nMOSFET. It is calculated as the convolution of a Pearson IV distribu- tion by the Poisson potential resulting from the 2D Poisson equation. Compared to the usual Gaussian distribution, the Pearson IV distribution, calibrated to fit the squared mod- ulus of the ground sub-band Schrodinger's wave function, drastically improves the wave-packet description close to the oxide barrier. This approach has been implemented into a semi-classical Monte-Carlo particle simulator and tested in DGMOS capacitors. We find that the new Pearson Effective Potential gives a very good representation of the electron density profile inside the silicon film, which overcomes the well-known weakness of the Gaussian Effective Potential.

Self-consistent ion transport simulation in carbon nanotube channels

We propose a method to self-consistently deal with polarisation effects in Monte Carlo particle simulations of charge transport. The systems of interest were membrane structures with a narrow (4–8 A) carbon nanotube (CNT) channel in an aqueous environment. Due to computational limitations for Molecular Dynamics (MD) simulations, we extended the Transport Monte Carlo known from semiconductor simulations to ionic transport in water as a background medium.

Particle Simulation Study of Transition of Spatial Structure in a Plane-Parallel Hollow Cathode Discharge

A self-consistent Monte Carlo particle simulation is carried out to study a transition process of macroscopic spatial structure in a plane-parallel hollow cathode discharge filled with argon. The fine subslab technique and the weight probability method are introduced here. The photoelectric emission is considered. The simulation results show that the luminous structure of the discharge is rapidly changed after a step-increase in applied voltage, and eventually the discharge plasma seems to be sustained dominantly by secondary electrons (i.e., the γ effect) as judged from the potential profile. In the non-equilibrium transition phase, the electron energy distribution is found to consist of two components that are thermal electrons and the high-energy tail electrons.

A ZnS–Si isotype heterojunction avalanche photodiode structure for scintillation light detection

We have developed a zinc sulfide–silicon (ZnS–Si) isotype heterojunction avalanche photodiode (APD) structure that has high quantum efficiency and low excess noise factor for photons of wavelength in the region from 340 to 800 nm. The dependence of quantum efficiency, mean signal and its fluctuation on incident photons wavelength are calculated in a well-defined device geometry by a Single Particle Monte Carlo simulation technique. Based on this work, we offer a new APD structure for scintillation light detection.

Lyman radiative transfer in a multiphase medium

Hydrogen Lyman a (Lya) is our primary emission-line window into high-redshift galaxies. Despite an extensive literature, Lya radiative transfer in the most realistic case of a dusty, multiphase medium has received surprisingly little detailed theoretical attention. We investigate Lya resonant scattering through an ensemble of dusty, moving, optically thick gas clumps. We treat each clump as a scattering particle and use Monte Carlo simulations of surface scattering to quantify continuum and Lya surface scattering angles, absorption probabilities, and frequency redistribution, as a function of the gas dust content. This atomistic approach speeds up the simulations by many orders of magnitude, making possible calculations which are otherwise intractable. Our fitting formulae can be readily adapted for fast radiative transfer in numerical simulations. With these surface scattering results, we develop an analytic framework for estimating escape fractions and line widths as a function of gas geometry, motion, and dust content. Our simple analytic model shows good agreement with full Monte Carlo simulations. We show that the key geometric parameter is the average number of surface scatters for escape in the absence of absorption, N 0 , and we provide fitting formulae for several geometries of astrophysical interest. We consider the following two interesting applications. (i) Equivalent widths (EWs). Lya can preferentially escape from a dusty multiphase interstellar medium if most of the dust lies in cold neutral clouds, which Lya photons cannot penetrate. This might explain the anomalously high EWs sometimes seen in high-redshift/submillimetre sources. (ii) Multiphase galactic outflows. We show the characteristic profile is asymmetric with a broad red tail, and relate the profile features to the outflow speed and gas geometry. Many future applications are envisaged.

Enhanced acceleration of electrons populations by crossing electron cyclotron waves in an ambient magnetic field, Resonant Moments method

A mechanism for enhancing the acceleration of electrons by considering the effect of a low amplitude electron cyclotron waves crossing a primary wave in an ambient magnetic field is investigated. The underlying idea is that a low amplitude secondary wave may improve the transfer of parallel momentum from the high amplitude primary wave to charged particles. An analytical approximation, referred to as the Resonant Moments (RM) method, is proposed to estimate the efficiency of the wave configuration. Based on the RM method, optimal configurations are proposed for the two-wave scheme in which the secondary wave should be launched perpendicularly to the external magnetic field. Direct statistical (particle Monte Carlo) simulations confirm that such a configuration can yield an increase of the mean electron velocity of one order of magnitude when compared to the one-wave configuration. It is a quite promising result because the amplitude of the secondary wave is 10 times lower than the one of the first wave. The parameters used are related to electron acceleration in planetary magnetospheres, ionospheres as well in magnetic plasma fusion experiments.

Avalanche photodiode for measurement of low-energy electrons

We report on the performance of an Avalanche Photodiode (APD) produced by Hamamatsu Photonics Co. Ltd. (Type Z7966-20) for measurements of low energy electrons. We have set up an electron gun, which can generate a 1–20 keV electron beam impinging onto the APD in a vacuum chamber. The result shows that the pulse height distribution (PHD) of the APD signal exhibits a significant peak for electrons with energies above 8 keV, and the variation of the PHD peak shows a good linearity with the energy of incident electrons. The energy resolution is quite good, though it slightly depends on the electron energy. In the case of low-energies (lower than 10 keV), the pulse height distribution has a characteristic tail on the low energy side, and the energy resolution becomes a little worse. The position of the peak appears on a slightly lower channel than is expected from data at higher energies (near 20 keV). Qualitatively, the low-energy tail is caused by the dead-layer on the surface of the device. The nonlinearity and the worse resolution of the peaks for higher energy electrons may have resulted from a space-charge effect due to created e–h pairs. For a quantitative understanding, we have made a Monte Carlo particle simulation of charge transport and collection inside the APD.

Separation of Channel Backscattering Coefficients in Nanoscale MOSFETs

Channel backscattering coefficients in the k/sub B/T layer (near the source) of 1.65-nm-thick gate oxide, 68-nm gate length bulk n-channel MOSFETs are systematically separated into two distinct components: the quasithermal-equilibrium mean-free-path for backscattering and the width of the k/sub B/T layer. Evidence to confirm the validity of the separation procedure is further produced: 1) the near-source channel conduction-band profile; 2) the existing value of k/sub B/T layer width from the sophisticated device simulation; and 3) an analytic temperature-dependent drain current model for the channel backscattering coefficients. The findings are also consistent with each other and therefore corroborate channel backscattering as the origin of the coefficients. Other interpretations and clarifications are determined with respect to the very recently released Monte Carlo particle simulation. Consequently, it can be reasonably claimed that the separated components, as well as their dependencies on temperature and bias, are adequate while being used to describe the operation of the devices undertaken within the framework of the channel backscattering theory.

Effect of discrete impurities on electron transport in ultrashort MOSFET using 3D MC simulation

This paper discusses the influence of the channel impurity distribution on the transport and the drive current in short-gate MOSFET. In this purpose, a careful description of electron-ion interaction suitable for the case of discrete impurities has been implemented in a 3D particle Monte Carlo simulator. This transport model is applied to the investigation of 50 nm MOSFET operation. The results show that a small change in the number of doping impurities or in the position of a single discrete impurity in the inversion layer may significantly influence the drain current. This effect is not only related to threshold voltage fluctuations but also to variations in transport properties in the inversion layer, especially at high drain voltage. The results are analyzed in terms of local fluctuations of electron velocity and current density. In a set of fifteen simulated devices the drive current Ion, determined at VGS = VDS = 0.6 V, is found to vary in a range of 23% according to the position of channel impurities.

Influence of discrete impurity position in the channel of an ultra-small MOSFET

This paper discusses the influence of the channel impurity distribution on the transport and the drive current in a short-gate MOSFET. For this purpose, a careful description of electron–ion interaction suitable for the case of discrete impurities has been implemented in a 3D (three-dimensional) particle Monte Carlo simulator. This transport model is applied to the investigation of a 50 nm MOSFET operation. The paper shows that a small change in the position of a single discrete impurity may significantly influence the drain current. This effect is not only related to threshold voltage fluctuations but rather to variations in transport properties in the inversion layer.