Self-consistent Monte Carlo Simulations Research Articles

Gate length scaling for Al/sub 0.2/Ga/sub 0.8/N/GaN HJFETs: two-dimensional full band Monte Carlo simulation including polarization effect

Two-dimensional self-consistent full band Monte Carlo (FBMC) simulator was developed for electron transport in wurtzite phase AlGaN/GaN heterojunction (HJ) FET. Recessed gate Al/sub 0.2/Ga/sub 0.8/N/GaN HJFET structures with an undoped cap layer were simulated, where the spontaneous and piezoelectric polarization effects were taken into account. The polarization effect was shown to not only increase the current density, but also improve the carrier confinement, and hence improve the transconductance. An off-state drain breakdown voltage (BV/sub ds/) of 300 V and a maximum linear output power (P/sub max/) of 46 W/mm were predicted for a 0.9-/spl mu/m gate device. For a 0.1-/spl mu/m gate device, 60 V BV/sub ds/, 20 W/mm P/sub max/, and 160 GHz current-gain cutoff frequency were predicted. Although there is considerable uncertainty due to lack of information on the band structure, scattering rates, and surface conditions, the present results indicate a wide margin for improvements over current performance of AlGaN/GaN HJFETs in the future. To our knowledge, this is the first report on the FBMC simulation for AlGaN/GaN HJFETs.

Self-consistent Monte Carlo simulations of the positive column of gas discharges

Self-consistent Monte Carlo simulations of the positive column of gas discharges with a range of gas densities and currents are described. These simulations are performed using highly efficient Monte Carlo codes for electron transport in cylindrical geometry and using a realistic particle model of ion transport. No internal boundary conditions or assumptions about the plasma-sheath boundary are used in the simulations. Techniques to speed up the convergence are discussed. The self-consistent radial potential for each plasma is presented as a Taylor series expansion in radius squared terms. The 16 converged simulations presented here were checked using two independent codes, written by different authors, in different languages and executed on different computers. These positive column results are useful in comparisons with other types of fluid and kinetic theory simulations.

Symmetric diblock copolymers in thin films. I. Phase stability in self-consistent field calculations and Monte Carlo simulations

We investigate the phase behavior of symmetric AB diblock copolymers confined into a thin film. The film boundaries are parallel, impenetrable and attract the A component of the diblock copolymer. Using a self-consistent field technique [M. W. Matsen, J. Chem. Phys. 106, 7781 (1997)], we study the ordered phases as a function of incompatibility χ and film thickness in the framework of the Gaussian chain model. For large film thickness and small incompatibility, we find first order transitions between phases with different number of lamellae which are parallel oriented to the film boundaries. At high incompatibility or small film thickness, transitions between parallel oriented and perpendicular oriented lamellae occur. We compare the self-consistent field calculations to Monte Carlo simulations of the bond fluctuation model for chain length N=32. In the simulations we quench several systems from χN=0 to χN=30 and monitor the morphology into which the diblock copolymers assemble. Three film thicknesses are investigated, corresponding to parallel oriented lamellae with 2 and 4 interfaces and a perpendicular oriented morphology. Good agreement between self-consistent field calculations and Monte Carlo simulations is found.

Symmetric diblock copolymers in thin films. II. Comparison of profiles between self-consistent field calculations and Monte Carlo simulations

The structure of lamellar phases of symmetric AB diblock copolymers in a thin film is investigated. We quantitatively compare the composition profiles and profiles of individual segments in self-consistent field calculations with Monte Carlo simulations in the bond fluctuation model for chain length N=32 and χN=30. Three film thicknesses are investigated, corresponding to parallel oriented lamellae with 2 and 4 interfaces and a perpendicular oriented morphology. Taking account of capillary waves, we find good quantitative agreement between the Monte Carlo simulations and the self-consistent field calculations. However, the fluctuations of the local interfacial position are strongly suppressed by confinement and mutual interactions between lamellae.

Quantum Monte Carlo Simulation Studies of the Structures of the Liquid−Vapor Interfaces of Sn and Pb

We report the results of self-consistent quantum Monte Carlo simulations of the structure of the liquid−vapor interfaces of the tetravalent metals Sn and Pb.

Lattice-gas model driven by Hubbard electrons.

Self-consistent Monte Carlo simulations are undertaken for a lattice-gas model which is driven by the free energy of electrons described by a Hubbard model with electronic hopping restricted to ions at nearest-neighbor sites. Our previous work, an independent-electron tight-binding lattice-gas model (bcc or fcc), is modified to introduce two effects: the disorder of the dense system and, more importantly, the role of the electronic correlation. The first effect is achieved using an fcc lattice, but restricted so an occupied site can have no more than eight, instead of twelve, occupied nearest-neighbor sites. To treat correlations, the electronic intra-atomic repulsion is, at first, included via the Gutzwiller approximation at finite temperature; this approach is simple enough to be solved for all cases in the large, disordered systems used in our Monte Carlo simulations but can still give a good qualitative representation of the main effects of the electronic correlations. Then, the exact treatment of the Hubbard model for clusters with up to six atoms is integrated into the calculation. We obtain vapor-liquid coexistence curves and then, approximations to the electronic conductivities and paramagnetic susceptibilities at coexistence conditions. This simple model is, in part, motivated by experiments on the alkali-metal fluids.

The structure of the liquid-vapor interface of a gallium-tin binary alloy

We report the results of self-consistent quantum Monte Carlo simulations of the structure of the liquid-vapor interface of the alloy Sn0.09Ga0.81. Our calculations are in very good agreement with the experimental results reported by Lei, Huang and Rice [J. Chem. Phys. 107, 4051 (1997)]. In particular, our calculations confirm the experimentally inferred existence of a partial second layer of Sn below the complete outermost layer of Sn in the stratified liquid-vapor interface of this alloy.

Gutzwiller approximation for a Hubbard lattice gas

We present a self-consistent Monte Carlo simulation for an ionic lattice gas coupled with electrons described by a Hubbard model with electronic hopping restricted to ions at nearest-neighbor sites. We treat a modification of our previous work, a tight-binding lattice gas model (bcc or fcc, uncorrelated electrons), to introduce two new effects: the disorder of the dense liquid metal at low temperature and, more importantly, the role of the electronic correlation. The lattice is taken to be fcc, but restricted so that an occupied site cannot have more than eight occupied nearest neighbors. The electronic intra-atomic repulsion is included via the Gutzwiller approximation; this approach is simple enough to be solved in the large, disordered systems used in our Monte Carlo simulations but can still give a good qualitative representation of the main effects of the electronic correlations.

Pyroelectronics: Novel device concepts based on nitride interfaces

A key property of nitrides is their large spontaneous and piezoelectric polarization fields that allow significant tailoring of the carrier dynamics and optical properties of nitride devices. In this article, based on first-principles calculations of structural and electronic properties of bulk nitrides and their heterostructures, we investigate the potential of this novel material class for modern device applications by performing self-consistent Monte Carlo simulations. We demonstrate that the internal electric fields have a significant and favorable influence on the transistor characteristics.

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory-Huggins theory becomes quantitatively correct in the long chain length limit, when the χ parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the χ parameter from small-angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like √χ/(ρb3) for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self-consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1/√N. Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non-additive monomer shapes, one has a large positive chain-length-independent entropic contribution to the χ parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the χ parameter of the order 10–3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non-entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End-functionalized homopolymers of different species react at the interface instantaneously and irreversibly to form diblock copolymers. The initial reaction rate for small reactant concentrations is time dependent and larger than expected from theory. At later times there is a depletion of the reactive chains at the interface and the reaction is determined by the flux of the chains to the interface. Pertinent off-lattice simulations and analytical theories are briefly discussed.

Monte Carlo simulations of capture into quantum well structures

The purpose of this paper is to simulate capture events into quantum well structures of the kinds studied in luminescence experiments in order to understand the carrier dynamics, to extract local electron and hole capture times and to relate microscopic carrier processes to the luminescence signal. To do this, a quantum mechanical model for charge capture by a quantum well has been incorporated into a self-consistent Monte Carlo simulation of carrier transport in quantum well laser diodes. The capture model makes use of the established technique of modifying Fermi's golden rule to calculate a dimensionless capture probability instead of a capture rate. This model has been used to simulate time-resolved photoluminescence experiments on a variety of InGaAsP-based structures which have unstrained quantum wells. Local electron and hole capture times have been extracted from the transport data for simulations performed at 300 K, and these times oscillate as a function of well width. Wells 85-90 Å wide permit fast electron capture into a second electronic subband (0.56 ps capture time) and hole capture into a second light hole band (0.44 ps). This may be contrasted with a 75 Å well for which electron capture into the single conduction subband exceeds 1.7 ps, and the peak hole capture time is 1.1 ps.

Single-Chain Conformations in Symmetric Binary Polymer Blends: Quantitative Comparison between Self-Consistent Field Calculations and Monte Carlo Simulations

Single-chain properties in a symmetric binary polymer blend are studied by self-consistent field calculations and Monte Carlo simulations. Within the self-consistent field scheme, the statistical mechanics of a cluster of neighboring polymers is solved. Interactions among the polymers of a cluster and composition fluctuations within a cluster are incorporated exactly, a mean field approximation is invoked for intercluster interactions and long-range fluctuations. The results are compared to large scale Monte Carlo simulations for a broad range of chain lengths. While we find nearly quantitative agreement for single chain propertiese.g., the reduction of the chain dimensions of the minority componentonly qualitative agreement is achieved for thermodynamic quantitiese.g., the critical temperature. The temperature and composition dependence of the chain conformations are attributed to a balance between the entropy loss upon contraction and the exchange of intermolecular and intramolecular contacts. The calculations suggest that the relative reduction of the spatial extension of the minority chains depends on the parameter χ for not too large incompatibilities χ. The scaling limit is, however, approached only for very long chain lengths N.

Mutual Hot-Phonon Effects in Coupled GaAs Quantum Wires

Hot phonon effects on electron transport in coupled GaAs quantum wires embedded in AlAs have been investigated by a self-consistent Monte Carlo simulation. These results take into account optical phonon confinement within the GaAs region and localization at its boundaries which is caused by the presence of GaAs/AlAs heterointerfaces. Electrical confinement of electrons in several spatially separated quantum wire channels inside the GaAs region with common optical phonons (confined within the whole GaAs bar) is assumed. We have investigated numerically mutual interaction of electrons and phonons over a wide range of electric fields (0 < E < 1000 V/cm) and lattice temperatures (30 K ≤ T ≤ 300 K). We demonstrate that in a system of two quantum wires coupled through the common confined optical phonons, electron transport in one wire significantly affects electron transport in the second wire due to the presence of the strong mutual hot-phonon drag between these electron channels. This leads to a sufficient modification of the carrier velocity–field characteristics in the structures investigated.

Comparison of the structures of the liquid-vapor interfaces of Al, Ga, In, and Tl

We report the results of self-consistent quantum Monte Carlo simulations of the liquid-vapor interfaces of the members of the family of trivalent metals Al, Ga, In, and Tl. In each case the single particle density distribution along the normal to the liquid-vapor interface is stratified and the pair correlation function in the plane of the interface is essentially the same as that in the bulk liquid. We have examined the results of the calculations for structural similarities that hint at the existence of a corresponding states representation valid for a family of metals, such as has been shown for the family of alkali metals. The effective pair potentials of Al, Ga, In, and Tl are rather different from each other. Consequently, characterization of the interface structure using a corresponding states representation in two variables (reduced density and reduced diameter) is not accurate, unlike the case of the alkali metals for which such a characterization is accurate. Experimental data concerning the structure of the liquid-vapor interface exist for only one member of this family of metals, namely Ga. Good agreement between theory and experiment in that case argues for the validity of the results reported for all of the metals of this family, and the inferences drawn therefrom.

Structure of the liquid–vapor interface of a metal from a simple model potential: Corresponding states of the alkali metals

We present the results of self-consistent quantum Monte Carlo simulations of the structures of the liquid-vapor interfaces of alkali metals (Na, K, Rb, Cs) using a modified semiempirical empty-core model potential. The purpose of this investigation is to simplify the analysis of inhomogeneous metals sufficiently to permit qualitative inferences to be drawn about the properties of families of metals. Both electronic and ion density profiles along the normal to the surface show oscillations in the liquid–vapor transition zone. These oscillations closely resemble those found in previous simulation studies of the liquid–vapor interfaces of alkalis, based on sophisticated nonlocal model potentials. Because of its semianalytical representation, the model potential used in this paper allows considerable simplification in the computational scheme relative to the effort involved in the previously published simulations. We find liquid Na, K, Rb, and Cs to exhibit similar surface layering. Moreover, our results suggest the existence of a corresponding states representation of the properties of this class of metals. We expect this new analysis will be useful in predicting the qualitative properties of the surface structures of a broad range of pure liquid metals.

Calculation of hole mobilities in relaxed and strained SiGe by Monte Carlo simulation

Hole mobilities in relaxed and strained undoped SiGe layers have been calculated with a one-dimensional self-consistent bipolar Monte Carlo simulation code. We have adopted a novel bandstructure model that incorporates strain effects in the alloy valence band. Both alloying and strain enhance the hole mobility compared with bulk Si and we find that alloy scattering is the dominant scattering mechanism. An alloy potential of 1.4 eV was obtained by matching our Monte Carlo data on drift mobilities to experimental Hall mobility measurements. Uncertainties in this value arise from scatter in the experimental data and a lack of detailed knowledge of the Hall factor.

A comparison of quasi-harmonic lattice dynamics and Monte Carlo simulation of polymeric crystals using orthorhombic polyethylene

The temperature dependence of lattice parameters, elastic constants and other physical properties of crystalline polyethylene at zero pressure in the orthorhombic phase is discussed. Two complementary approaches, self-consistent quasi-harmonic lattice dynamics and Monte Carlo simulation, both of which are predicated on the use of empirical force fields to describe the interatomic potentials, are critically compared. Both techniques are studied in their classical and quantum mechanical versions, to assess the accuracy and limitations of each method. Particular attention is paid to the classical approximation, the onset of anharmonicities in dynamical behavior which are not captured by the quasi-harmonic approximation, and finite size effects. It is shown that quantum effects are important throughout the range of temperatures 0⩽T⩽300 K. At temperatures below about 23 of the melting temperature (i.e., 250 K for polyethylene) the two approaches yield consistent results in both classical and quantum mechanical cases for a given empirical force field, provided that finite size effects are avoided. Above 300 K, anharmonic effects become quite pronounced. The combined treatment of these effects in the framework of path integral Monte Carlo (PIMC) pushes the limits of current computational feasibility, due to simulation sizes required. Guidelines are offered for choosing between classical simulations, quasi-harmonic methods, and full path integral Monte Carlo simulation.

Self-consistent quantum Monte Carlo simulations of the structure of the liquid-vapor interface of a eutectic indium-gallium alloy

We report the results of self-consistent quantum Monte Carlo simulations of the density distribution along the normal to the liquid-vapor interface, and the in-plane structure function, of the liquid-vapor interface of a eutectic binary alloy of indium and gallium (16.5% In) at 86 \ifmmode^\circ\else\textdegree\fi{}C. The density distribution along the normal to the interface exhibits layering, with a sensibly complete monolayer of In outermost in the interface. Our results are in good agreement with the experimental data of Regan et al. [Phys. Rev. B 55, 15874 (1997)]. We also report the results of self-consistent quantum Monte Carlo simulations of the structure of the liquid-vapor interfaces of In:Ga alloys with In concentrations greater than and less than the eutectic concentration. The In atoms segregate in the outermost layer of the interface as a sensibly complete monolayer when the bulk In concentration is 25% and as a partial monolayer when the bulk In concentration is 11%. In these cases, as well as for the eutectic alloy, there is some Ga well mixed with the In in the outermost layer of the stratified liquid-vapor interface. And for all alloy compositions studied the layer of the interface beneath the monolayer of segregated In is deficient in In relative to the bulk concentration; the bulk concentration of In is reached in the third layer of the liquid-vapor interface.

Modelling the influence of high currents on the cutoff frequency in Si/SiGe/Si heterojunction transistors

A one-dimensional self-consistent bipolar Monte Carlo simulation code has been used to model carrier mobilities in strained doped SiGe and the base-collector region of Si/SiGe/Si and SiC/Si heterojunction bipolar transistors (HBTs) with wide collectors, to study the variation of the cutoff frequency with collector current density . Our results show that while the presence of strain enhances the electron mobility, the scattering from alloy disorder and from ionized impurities reduces the electron mobility so much that it is less than that of Si at the same doping level, leading to larger base transit times and hence poorer performance for large for an Si/SiGe/Si HBT than for an SiC/Si HBT. At high values of , we demonstrate the formation of a parasitic electron barrier at the base-collector interface which causes a sharp increase in and hence a dramatic reduction in . Based on a comparison of the height of this parasitic barrier with estimates from an analytical model, we suggest a physical mechanism for base pushout after barrier formation that differs somewhat from that given for the analytical model.

Quantum Monte Carlo simulations of the structure in the liquid–vapor interface of BiGa binary alloys

We report the results of self-consistent quantum Monte Carlo simulations of the structure of the liquid–vapor interface of a dilute alloy of Bi in Ga. The results of the simulations are shown to be in good agreement with the results of experimental studies of the structure of the liquid–vapor interface of such an alloy reported by Lei, Huang, and Rice [J. Chem. Phys. 104, 4802 (1996), who determined the longitudinal density distribution] and by Flom et al. [Science 260, 332 (1993), who determined the transverse pair structure function].