Ensemble Monte Carlo Approach Research Articles

Molecular modeling of CO2 affecting competitive adsorption within anthracite coal

This study aimed to investigate the adsorption properties of CO2, CH4, and N2 on anthracite. A molecular structural model of anthracite (C208H162O12N4) was established. Simulations were performed for the adsorption properties of single-component and multi-component gases at various temperatures, pressures, and gas ratios. The grand canonical ensemble Monte Carlo approach based on molecular mechanics and dynamics theories was used to perform the simulations. The results showed that the isotherms for the adsorption of single-component CO2, CH4, and N2 followed the Langmuir formula, and the CO2 adsorption isotherm growth gradient was negatively correlated with pressure but positively correlated with temperature. When the CO2 injection in the gas mixture was increased from 1 to 3% for the multi-component gas adsorption, the proportion of CO2 adsorption rose from 1/3 to 2/3, indicating that CO2 has a competing-adsorption advantage. The CO2 adsorption decreased faster with increasing temperature, indicating that the sensitivity of CO2 to temperature is stronger than that of CH4 and N2. The adsorbent potential energies of CO2, CH4, and N2 diminished with rising temperature in the following order: CO2 < CH4 < N2.

Ensemble Markov Chain Monte Carlo with Teleporting Walkers

We introduce an ensemble Markov chain Monte Carlo approach to sampling from a probability density with known likelihood. This method upgrades an underlying Markov chain by allowing an ensemble of such chains to interact via a process in which one chain's state is cloned as another's is deleted. This effective teleportation of states can overcome issues of metastability in the underlying chain, as the scheme enjoys rapid mixing once the modes of the target density have been populated. We derive a mean-field limit for the evolution of the ensemble. We analyze the global and local convergence of this mean-field limit, showing asymptotic convergence independent of the spectral gap of the underlying Markov chain, and moreover we interpret the limiting evolution as a gradient flow. We explain how interaction can be applied selectively to a subset of state variables in order to maintain advantage on very high-dimensional problems. Finally we present the application of our methodology to Bayesian hyperparameter estimation for Gaussian process regression.

Ensemble Monte Carlo modeling of quantum cascade detectors

We present a method to perform accurate and efficient simulations of photovoltaic quantum cascade detector (QCD) structures based on the ensemble Monte Carlo (EMC) approach. Since the photocurrent is typically orders of magnitude smaller than the pump current in a quantum cascade laser (QCL), a direct application of QCL simulation techniques is not sufficiently accurate. We demonstrate that by exploiting thermodynamic equilibrium relations for the electron populations and scattering rates, the EMC method can be adapted to yield reliable results for the essential QCD figures of merit, such as responsivity and specific detectivity. The modeling approach is validated against available experimental results for various mid-infrared and terahertz QCD designs and furthermore compared to simulations based on the non-equilibrium Green’s function method.

Ultrafast real-time tracing of surface electric field generated via hot electron transport in polar semiconductors

We trace an ultrafast real-space motion of photo-excited free carriers just near the surface of polar semiconductors GaAs and InAs by using the optical second-harmonic generation (SHG) technique. With a flat distribution of photo-carriers as an initial condition, ultrafast diffusion and drift motion followed by a rapid surface recombination develop a surface electric field which is efficiently probed by the electric-field-induced SHG. From the simulation based on the drift–diffusion equation combined with the ensemble Monte-Carlo approach, we could explain the experimental observation of the temporal evolution of the surface electric field, and extract time constants related to the hot electron cooling. Whereas the hot carrier cooling time is determined to be about 8 ps at room temperature for GaAs, it can be further extended to about 35 ps at 100 K due to the increase of the longitudinal optic phonon life time enhancing the hot phonon effect. Our work can be an important guide in designing optoelectronic nano-devices by providing a clear understanding of the ultrafast electron-hole separation near the surface of polar semiconductors in connection with the hot carrier cooling process.

Monte Carlo modeling of spin-polarized photoemission from p-doped bulk GaAs

The anticorrelation between quantum efficiency (QE) and electron spin polarization (ESP) from a p-doped GaAs activated to negative electron affinity is studied in detail using an ensemble Monte Carlo approach. The photoabsorption, momentum and spin relaxation during transport, and tunneling of electrons through the surface potential barrier are modeled to identify fundamental mechanisms, which limit the efficiency of GaAs spin-polarized electron sources. In particular, we study the response of QE and ESP to various parameters, such as the photoexcitation energy, doping density, and electron affinity level. Our modeling results for various transport and emission characteristics are in good agreement with available experimental data. Our findings show that the behavior of both QE and ESP at room temperature can be fully explained by the bulk relaxation mechanisms and the time that electrons spend in the material before being emitted.

Simulation of nonequilibrium effects in quantum cascade lasers

AbstractQuantum cascade lasers exploit optical transitions between quantized electronic energy levels in multi‐quantum‐well structures for light generation and detection. This design principle enables the realization of compact, semiconductor‐based lasers in the mid‐infrared and terahertz spectral regions. In this contribution, the modeling of such devices is discussed based on an ensemble Monte Carlo approach, enhanced by modifications obtained from the density matrix formalism. A special emphasis is put on the inclusion of nonequilibrium electron and phonon effects. The simulations are validated against available experimental data for a terahertz quantum cascade laser.

Gibbs Ensemble Monte Carlo for Reactive Force Fields to Determine the Vapor-Liquid Equilibrium of CO2 and H2O.

Absorption and reactive properties of fluids in porous media are key to the design and improvement of numerous energy related applications. Molecular simulations of these systems require accurate force fields that capture the involved chemical reactions and have the ability to describe the vapor–liquid equilibrium (VLE). Two new reactive force fields (ReaxFF) for CO2 and H2O are developed, which are capable of not only modeling bond breaking and formation in reactive environments but also predicting their VLEs at saturation conditions. These new force fields include extra terms (ReaxFF-lg) to improve the long-range interactions between the molecules. For validation, we have developed a new Gibbs ensemble Monte Carlo (GEMC–ReaxFF) approach to predict the VLE. Computed VLE data show good agreement with National Institute of Standards and Technology reference data as well as existing nonreactive force fields. This validation proves the applicability of the GEMC–ReaxFF method to test new reactive force fields, and simultaneously it proves the applicability to extend newly developed ReaxFF force fields to other more complex reactive systems.

A Comprehensive Analysis of the 2-DEG Transport Properties in In x Al1 – x N/AlN/GaN Heterostructure: Experiments and Numerical Simulations

A comprehensive investigation on the low-field 2-DEG mobility in In <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-N</sub> /AlN/GaN heterostructure has been made through Hall experimental and numerical calculation based on an ensemble Monte Carlo (MC) approach. Hall measurement on a lattice-matched (LM) In <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.18</sub> Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.82</sub> N/AlN/GaN heterostructure grown by metal-organic chemical vapor deposition (MOCVD) has been carried out as a function of temperature ranging from 77 to 405 K. A more rigorous model is presented taking both inter- and intra-subband scattering into account. The scattering rates are derived from the results of the electron density, the quantized energy levels, and the corresponding wave functions based on the self-consistent solutions of Poisson's and Schrödinger's equation given in our previous work. We confirm that the interface scattering process dominates the mobility within the low temperature (77-130 K), as increasing of the temperature, the highly inelastic scattering caused by partial occupation of the higher subband is responsible for the rapid degradation of the 2-DEG mobility. The role of surface morphology and indium fraction of the heterostructure on the dependence of the 2-DEG mobility have been clarified qualitatively in detail. The calculated results are widely compared with the published literature and our experimental finding. A reasonable agreement is achieved.

Hot-Carrier Degradation in GaN HEMTs Due to Substitutional Iron and Its Complexes

We report the experimental data, quantum-mechanical calculations, and engineering-level modeling that provide insight into the atomic-scale processes that underlie the hot-electron degradation of AlGaN/GaN high-electron-mobility transistors during electrical stress at moderate drain bias. There is relatively large degradation (up to 20%) of the peak transconductance ( $g_{m}$ ) in the semi-ON state, along with a small shift of the threshold voltage ( $V_{T}$ ). The $V_{T}$ shift and $g_{m}$ degradation increase with temperature. A model of the degradation is presented, based on the hot-carrier-induced defect generation. The model considers carrier energy distributions for different temperatures obtained using an ensemble Monte Carlo (EMC) approach. The Ensemble Monte-Carlo results show that the concentration of energetic carriers is maximum at the end of the gate on the gate–drain access side in the semi-ON state of operation. The degradation is directly related to the number of carriers with sufficient energy to generate defects, and the carrier energy distribution depends strongly on the device temperature. The first-principles density functional theory calculations and the analysis suggest that the dehydrogenation of substitutional iron and its complexes is the dominant cause of the observed degradation in these devices.

Orientational ordering and phase behaviour of binary mixtures of hard spheres and hard spherocylinders.

We study the structure and fluid-phase behaviour of binary mixtures of hard spheres (HSs) and hard spherocylinders (HSCs) in isotropic and nematic states using the NPnAT ensemble Monte Carlo (MC) approach in which the normal component of the pressure tensor is fixed in a system confined between two hard walls. The method allows one to estimate the location of the isotropic-nematic phase transition and to observe the asymmetry in the composition between the coexisting phases, with the expected enhancement of the HSC concentration in the nematic phase. This is in stark contrast with the previously reported MC simulations where a conventional isotropic NPT ensemble was used. We further compare the simulation results with the theoretical predictions of two analytic theories that extend the original Parsons-Lee theory using the one-fluid and the many-fluid approximations [Malijevský et al., J. Chem. Phys. 129, 144504 (2008)]. In the one-fluid version of the theory, the properties of the mixture are related to an effective one-component HS system, while in the many-fluid theory, the components of the mixtures are represented as separate effective HS particles. The comparison reveals that both the one- and the many-fluid approaches provide a reasonably accurate quantitative description of the mixture including the predictions of the isotropic-nematic phase boundary and degree of orientational order of the HSC-HS mixture.

Monte Carlo study of terahertz difference frequency generation in quantum cascade lasers

We present an extended ensemble Monte Carlo approach, allowing for the self-consistent modeling of terahertz difference frequency generation in quantum cascade lasers. Our simulations are validated against available experimental data for a current room temperature design. Tera-hertz output powers in the mW range are predicted for ideal light extraction.

Multi-Subband Ensemble Monte Carlo simulation of bulk MOSFETs for the 32 nm-node and beyond

With the 32nm node in mass production, simulation tools have to include quantum effects to correctly describe the behavior of the devices. The Multi-Subband Ensemble Monte Carlo (MSB-EMC) approach constitutes today’s most accurate method for the study of nanodevices with important applications to SOI devices. However, the study of bulk devices with MSB-EMC codes presents practical limitations arising from the device geometry and the existence of a semi-infinite quantum well. This work presents a in-depth study of such issues to properly apply the Multi-Subband approach to bulk devices. The developed simulator has been used to study bulk-nMOSFETs for the 32nm technological node and beyond which still constitutes the mainstream technology in commercial ICs and to compare them to their SOI counterparts.

Monte Carlo Study of Temperature and Bias dependence of Spin Transport in GaAs

An ensemble Monte Carlo approach has been used to simulate spin relaxation in GaAs devices. Effect of varying temperature and applied bias on spin relaxation time has been studied in n-type bulk GaAs. Our results show that the spin relaxation times are longer at low temperatures and that increasing the applied bias yields enhancement of the spin polarization in the system.

Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs

Resonant phonon depopulation terahertz quantum cascade lasers based on vertical and diagonal lasing transitions are systematically compared using a well established ensemble Monte Carlo approach. The analysis shows that for operating temperatures below 200 K, diagonal designs may offer superior temperature performance at lasing frequencies of about 3.5 THz and above; however, vertical structures are more advantageous for good temperature performance at lower frequencies.

Fin shape fluctuations in FinFET: Correlation to electrical variability and impact on 6-T SRAM noise margins

Threshold voltage ( V T ) and drive current ( I ON ) variability of low stand-by power (LSTP)-32 nm FinFETs subject to fin line-edge roughness (LER) is investigated through Technology Computer-Aided Design (TCAD) simulations featuring quantum-corrected hydrodynamic transport. Statistical results provided by an ensemble Monte Carlo (MC) approach highlight an increase in the average V T and a decrease in the average I ON with respect to sensitivity analysis based predictions. Correlations of fin shape fluctuations to electrical performance are investigated, thus assessing further limitations of sensitivity analysis and proposing better alternatives to the expensive MC approach. An equivalent fin width is calculated, which allows reducing the spread in I ON scatter plots and highlights relative importance of LER in different fin regions. Simplified device instances with linearly varying fin width are simulated to better assess the impact of local thinning/thickening in the channel, source and drain extensions. Asymmetries in the device behavior are observed upon swapping the taper direction and the critical role of extensions is identified. Moreover, the impact of LER on noise margins of FinFET-based Static Random Access Memories (SRAMs) is investigated, considering the hold, read and write operating modes. Results are compared to published data on fabricated cells with similar device features. “ μ - 6 σ ” statistics extracted from 1000 mixed-mode simulations helps with assessing variability concerns for mainstream integration of aggressively scaled of FinFET-SRAMs.

Phase behavior and far-from-equilibrium gelation in charged attractive colloids

In this Rapid Communication we demonstrate the applicability of an augmented Gibbs ensemble Monte Carlo approach for the phase behavior determination of model colloidal systems with short-ranged depletion attraction and long-ranged repulsion. This technique allows for a quantitative determination of the phase boundaries and ground states in such systems. We demonstrate that gelation may occur in systems of this type as the result of arrested microphase separation, even when the equilibrium state of the system is characterized by compact microphase structures.

Path integral method in quantum statistics problems: generalized ensemble Monte Carlo and density functional approach

Path integral method in quantum statistics problems: generalized ensemble Monte Carlo and density functional approach

Monte Carlo simulation of the hole transport properties for wurtzite GaN

The simulation of the hole transport properties of wurtzite phase GaN are performed by the full band ensemble Monte Carlo approach. The band structure data of GaN used in the simulation are obtained by the empirical pseudopotential method. The scattering mechanisms included in the simulation are acoustic phonon scattering, optical phonon scattering, polar optical phonon scattering, piezoelectronic scattering, ionized impurity scattering, as well as the intervalley scattering. The dependence of the hole average drift velocity and average energy in three main symmetry directions for wurtzite GaN on the electric field are obtained. At room temperature, the velocity-field relation shows the non-saturated characteristics. The maximum drift velocity is about 6×106 cm s-1, and the maximum average energy is 0.12 eV in the range of the field of this work. These values are much smaller than the corresponding parameters of the electrons in GaN. Furthermore, the dependence of the diffusion mobility on the impurity density is reported.

Extended ensemble Monte Carlo approach to hardly relaxing problems

A set of methods based on an idea of extended ensemble has been proposed for simulating hardly relaxing systems such as spin glasses. The multicanonical method, simulated tempering and exchange Monte Carlo are typical examples of this family. We briefly review extended ensemble Monte Carlo methods, particularly focusing on the exchange Monte Carlo method. Using the method, we study the number of solutions of the N queens problem which is a kind of constraint-satisfaction problem. This problem is a typical example of hardly relaxing problems because there exist numerous solutions and energy barriers between them. Our numerical result supports the conjecture that the number of solutions is proportional to N N in the large N limit. We also discuss the thermodynamic properties of the N queens problem at finite temperatures introduced artificially.

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.