Ionic solutions are mixtures of interacting anions and cations. They hardly resemble dilute gases of uncharged noninteracting point particles described in elementary textbooks. Biological and electrochemical solutions have many components that interact strongly as they flow in concentrated environments near electrodes, ion channels, or active sites of enzymes. Interactions in concentrated environments help determine the characteristic properties of electrodes, enzymes, and ion channels. Flows are driven by a combination of electrical and chemical potentials that depend on the charges, concentrations, and sizes of all ions, not just the same type of ion. We use a variational method EnVarA (energy variational analysis) that combines Hamilton’s least action and Rayleigh’s dissipation principles to create a variational field theory that includes flow, friction, and complex structure with physical boundary conditions. EnVarA optimizes both the action integral functional of classical mechanics and the dissipation functional. These functionals can include entropy and dissipation as well as potential energy. The stationary point of the action is determined with respect to the trajectory of particles. The stationary point of the dissipation is determined with respect to rate functions (such as velocity). Both variations are written in one Eulerian (laboratory) framework. In variational analysis, an “extra layer” of mathematics is used to derive partial differential equations. Energies and dissipations of different components are combined in EnVarA and Euler–Lagrange equations are then derived. These partial differential equations are the unique consequence of the contributions of individual components. The form and parameters of the partial differential equations are determined by algebra without additional physical content or assumptions. The partial differential equations of mixtures automatically combine physical properties of individual (unmixed) components. If a new component is added to the energy or dissipation, the Euler–Lagrange equations change form and interaction terms appear without additional adjustable parameters. EnVarA has previously been used to compute properties of liquid crystals, polymer fluids, and electrorheological fluids containing solid balls and charged oil droplets that fission and fuse. Here we apply EnVarA to the primitive model of electrolytes in which ions are spheres in a frictional dielectric. The resulting Euler–Lagrange equations include electrostatics and diffusion and friction. They are a time dependent generalization of the Poisson–Nernst–Planck equations of semiconductors, electrochemistry, and molecular biophysics. They include the finite diameter of ions. The EnVarA treatment is applied to ions next to a charged wall, where layering is observed. Applied to an ion channel, EnVarA calculates a quick transient pile-up of electric charge, transient and steady flow through the channel, stationary “binding” in the channel, and the eventual accumulation of salts in “unstirred layers” near channels. EnVarA treats electrolytes in a unified way as complex rather than simple fluids. Ad hoc descriptions of interactions and flow have been used in many areas of science to deal with the nonideal properties of electrolytes. It seems likely that the variational treatment can simplify, unify, and perhaps derive and improve those descriptions.

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Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids

Terahertz emission from InGaAs∕InAlAs lattice-matched high electron mobility transistors was observed. The emission appears in a threshold-like manner when the applied drain-to-source voltage UDS is larger than a threshold value UTH. The spectrum of the emitted signal consists of two maxima. The spectral position of the lower-frequency maximum (around 1 THz) is sensitive to UDS and UGS, while that of the higher frequency one (around 5 THz) is not. The lower-frequency maximum is interpreted as resulting from the Dyakonov–Shur instability of the gated two-dimensional electron fluid, while the higher frequency is supposed to result from current-driven plasma instability in the ungated part of the channel. The experimental results are confirmed by and discussed within Monte Carlo calculations of the high-frequency current noise spectra.

Voltage tuneable terahertz emission from a ballistic nanometer InGaAs∕InAlAs transistor

The performance enhancement associated with the scaling of pseudomorphic high electron mobility transistors (PHEMTs) to deep decanano dimensions is studied using Monte Carlo (MC) simulations. The full scaling of a standard 120 nm PHEMT to gate lengths of 90, 70, 50 and 30 nm in both lateral and vertical dimensions is compared with an approach where only the lateral dimensions are scaled. The study is based on an extended transport module integrated in the finite element MC simulator H2F and accurate up to an electric field of 200 kV/cm, and on the careful calibration of MC device simulations against I–V characteristics from the real 120-nm gate length PHEMT. The fully scaled devices exhibit a continuous improvement in transconductance as channel lengths reduce while performance deteriorates in devices scaled only laterally. The contact resistances become a limiting factor to the performance of the fully scaled devices at shorter channel lengths. The microwave performance of the scaled devices is studied using the transient MC analysis.

Scaling of pseudomorphic high electron mobility transistors to decanano dimensions

We present a generalized Ramo–Shockley theorem to evaluate particle currents and energy currents at device contacts, in classical drift‐diffusion or hydrodynamic simulation techniques as well as for semiclassical Monte Carlo and quantum mechanical transport simulation. In contrast to the Ramo–Shockley theorem, our technique (1) is derived for conditions of extreme time dependence in the charge carriers and forces (including particle‐induced radiation), (2) explicitly accounts for particle generation and recombination processes such as photoexcitation, forward and inverse Auger processes, or Shockley–Read–Hall recombination, and (3) distinguishes clearly between the contributions of electrons, holes, and the displacement current. The resulting simple new formalism reduces to the standard Ramo–Shockley theorem as a special case.

A generalized ramo-shockley theorem for classical to quantum transport at arbitrary frequencies

A comprehensive RF analysis technique based on ensemble Monte Carlo (EMC) simulation of compound FET's with realistic device geometry is presented. Y-parameters are obtained through Fourier transformation of the EMC transients in response to small changes in the terminal voltages. The terminal currents are statistically enhanced and filtered to allow for reliable y-parameters extraction. Improved analytic procedure for extracting the intrinsic device small-signal circuit components is described. As a result, stable y-parameters and reliable circuit components can he extracted for the whole range of device operation voltages. Parasitic components like contact and gate resistances are included in the y-parameters at a post processing stage to facilitate the forecast of the performance figures of merit of real devices. The developed RF technique has been applied in the EMC simulation of pseudomorphic HEMT's (pHEMT's) fabricated at the Glasgow Nanoelectronics Research Center. Good agreement has been achieved between the simulated and measured small-signal circuit components and performance figures of merit.

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Complete Monte Carlo RF analysis of "real" short-channel compound FET's

An introduction of a new functional form of Green's theorem for inhomogeneous media has enabled us to show that the Ramo-Shockley theorem derived for inhomogeneous media with electrodes maintained at constant potentials is still valid even when the electrode potentials are time-varying. Our proof, which is based on this modified Green's theorem, is an extension of Ramo's original proof and is different from the energy balance method which is the existing method of proof of the theorem for inhomogeneous media at constant electrode potentials. Our proof provides a basis for calculations of the instantaneous currents in semiconductor devices using particle simulations such as the Monte-Carlo method since it differentiates clearly the current induced in the electrodes due to the moving charges from the current caused by the time-varying potentials of the electrodes through capacitive couplings among the electrodes.

Hunsuk Kim

Papers

An extended proof of the Ramo-Shockley theorem