Dynamics of Charge Flow in the Channel of a Thin-Film Field-Effect Transistor

The local conductivity in the channel of a thin-film field-effect transistor is proportional to the charge density induced by the local gate voltage. We show how this determines the frequency- and position-dependence of the charge induced in the channel for the case of "zero applied current": zero drain-source voltage with charge induced by a square-wave voltage applied to the gate, assuming constant mobility and negligible contact impedances. An approximate expression for the frequency dependence of the induced charge in the center of the channel can be conveniently used to determine the charge mobility. Fits of electro-optic measurements of the induced charge in organic transistors are used as examples.Comment: 9 pages including table + 3 figures; submitted to Jnl. Appl. Phy

Patterns of Striped order in the Classical Lattice Coulomb Gas

We obtain via Monte Carlo simulations the low temperature charge configurations in the lattice Coulomb gas on square lattices for charge filling ratio $f$ in the range $1/3 < f < 1/2$. We find a simple regularity in the low temperature charge configurations which consist of a suitable periodic combination of a few basic striped patterns characterized by the existence of partially filled diagonal channels. In general there exist two separate transitions where the lower temperature transition ($T_p$) corresponds to the freezing of charges within the partially filled channels. $T_p$ is found to be sensitively dependent on $f$ through the charge number density $\nu = p_{1}/q_{1}$ within the channels.Comment: 4 pages, 8 figure

Anisotropic generalization of Stinchcombe's solution for conductivity of random resistor network on a Bethe lattice

Our study is based on the work of Stinchcombe [1974 \emph{J. Phys. C} \textbf{7} 179] and is devoted to the calculations of average conductivity of random resistor networks placed on an anisotropic Bethe lattice. The structure of the Bethe lattice is assumed to represent the normal directions of the regular lattice. We calculate the anisotropic conductivity as an expansion in powers of inverse coordination number of the Bethe lattice. The expansion terms retained deliver an accurate approximation of the conductivity at resistor concentrations above the percolation threshold. We make a comparison of our analytical results with those of Bernasconi [1974 \emph{Phys. Rev. B} \textbf{9} 4575] for the regular lattice.Comment: 14 pages, 2 figure

Crossover from percolation to diffusion

A problem of the crossover from percolation to diffusion transport is considered. A general scaling theory is proposed. It introduces phenomenologically four critical exponents which are connected by two equations. One exponent is completely new. It describes the increase of the diffusion below percolation threshold. As an example, an exact solution of one dimensional lattice problem is given. In this case the new exponent $q=2$.Comment: 10 pages, 1 figur

The shape of invasion perclation clusters in random and correlated media

The shape of two-dimensional invasion percolation clusters are studied numerically for both non-trapping (NTIP) and trapping (TIP) invasion percolation processes. Two different anisotropy quantifiers, the anisotropy parameter and the asphericity are used for probing the degree of anisotropy of clusters. We observe that in spite of the difference in scaling properties of NTIP and TIP, there is no difference in the values of anisotropy quantifiers of these processes. Furthermore, we find that in completely random media, the invasion percolation clusters are on average slightly less isotropic than standard percolation clusters. Introducing isotropic long-range correlations into the media reduces the isotropy of the invasion percolation clusters. The effect is more pronounced for the case of persisting long-range correlations. The implication of boundary conditions on the shape of clusters is another subject of interest. Compared to the case of free boundary conditions, IP clusters of conventional rectangular geometry turn out to be more isotropic. Moreover, we see that in conventional rectangular geometry the NTIP clusters are more isotropic than TIP clusters

The grand canonical ABC model: a reflection asymmetric mean field Potts model

We investigate the phase diagram of a three-component system of particles on a one-dimensional filled lattice, or equivalently of a one-dimensional three-state Potts model, with reflection asymmetric mean field interactions. The three types of particles are designated as $A$, $B$, and $C$. The system is described by a grand canonical ensemble with temperature $T$ and chemical potentials $T\lambda_A$, $T\lambda_B$, and $T\lambda_C$. We find that for $\lambda_A=\lambda_B=\lambda_C$ the system undergoes a phase transition from a uniform density to a continuum of phases at a critical temperature $\hat T_c=(2\pi/\sqrt3)^{-1}$. For other values of the chemical potentials the system has a unique equilibrium state. As is the case for the canonical ensemble for this $ABC$ model, the grand canonical ensemble is the stationary measure satisfying detailed balance for a natural dynamics. We note that $\hat T_c=3T_c$, where $T_c$ is the critical temperature for a similar transition in the canonical ensemble at fixed equal densities $r_A=r_B=r_C=1/3$.Comment: 24 pages, 3 figure

Glassiness Vs. Order in Densely Frustrated Josephson Arrays

We carry out extensive Monte Carlo simulations on the Coulomb gas dual to the uniformly frustrated two dimensional XY model, for a sequence of frustrations f converging to the irraltional (3-sqrt 5)/2. We find in these systems a sharp first order equilibrium phase transition to an ordered vortex structure at a T_c which varies only slightly with f. This ordered vortex structure remains in general phase incoherent until a lower pinning transition T_p(f) that varies with f. We argue that the glassy behaviors reported for this model in earlier simulations are dynamic effects.Comment: 4 pages, 4 eps figure

Flux lattice melting and depinning in the weakly frustrated 2D XY model

Monte Carlo simulations of the frustrated 2D XY model were carried out at small commensurate values of the frustration $f$. For $f=1/30$ a single transition was observed at which phase coherence (finite helicity modulus) and vortex lattice orientational order vanish together. For $f=1/56$ a new phase in which phase coherence is absent but orientational order persists was observed. Where comparison is possible, the results are in detailed agreement with the behavior of the lattice Coulomb gas model of vortices. It is argued that the helicity modulus of the frustrated 2D XY model vanishes for any finite temperature in the limit of weak frustration $f$.Comment: 4 pages, RevTeX, 3 figures in separate uuencoded file The manuscript will appear in Phys. Rev.