Coulomb Systems at Low Density: A Review

Results on the correlations of low-density classical and quantum Coulomb systems at equilibrium in three dimensions are reviewed. The exponential decay of particle correlations in the classical Coulomb system, Debye–Hückel screening, is compared and contrasted with the quantum case, where strong arguments are presented for the absence of exponential screening. Results and techniques for detailed calculations that determine the asymptotic decay of correlations for quantum systems are discussed. Theorems on the existence of molecules in the Saha regime are reviewed. Finally, new combinatoric formulas for the coefficients of Mayer expansions are presented and their role in proofs of results on Debye–Hückel screening is discussed.     

Screening of the electric field in covalent crystals containing point defects

An expression is derived within the framework of the Debye-Hückel approximation for the screening length of a field in a p-type semiconductor taking into account the energy spread of immobile acceptor levels and the density of states tail of the valence band. It is shown that the screening length depends additively on the product of the carrier density and their diffusion coefficient ratio (for free holes and holes hopping via acceptors).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 41–43, November, 1984.     

Saturation of Electrostatic Potential: Exactly Solvable 2D Coulomb Models

We test the concepts of renormalized charge and potential saturation, introduced within the framework of highly asymmetric Coulomb mixtures, on exactly solvable Coulomb models. The object of study is the average electrostatic potential induced by a unique “guest” charge immersed in a classical electrolyte, the whole system being in thermal equilibrium at some inverse temperature β. The guest charge is considered to be either an infinite hard wall carrying a uniform surface charge or a charged colloidal particle. The systems are treated as two-dimensional; the electrolyte is modelled by a symmetric two-component plasma (TCP) of point-like ±e charges with logarithmic Coulomb interactions. Two cases are solved exactly: the Debye–Hückel limit β e²→ 0 and the Thirring free-fermion point β e²=2. The results at the free-fermion point can be summarized as follows: (i) The induced electrostatic potential exhibits the asymptotic behavior, at large distances from the guest charge, whose form is different from that obtained in the Debye–Hückel (linear Poisson–Boltzmann) theory. This means that the concept of renormalized charge, developed within the nonlinear Poisson–Boltzmann (PB) theory to describe the screening effect of the electrolyte cloud, fails at the free-fermion point. (ii) In the limit of an infinite bare charge, the induced electrostatic potential saturates at a finite value in every point of the electrolyte region. This fact confirms the previously proposed hypothesis of potential saturation.     

Two-Dimensional Coulomb Systems on a Surface of Constant Negative Curvature

We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential created by one point charge exists and goes to zero at infinity. The pressure can be expanded as a series in integer powers of the density (the virial expansion). The correlation functions have a thermodynamic limit, and remarkably that limit is the same one for the Coulomb interaction and some other interaction law. However, special care is needed for defining a thermodynamic limit of the free energy density. There are sum rules expressing the property of perfect screening. These generic properties can be checked on the Debye–Hückel approximation, and on two exactly solvable models, the one-component plasma and the two-component plasma, at some special temperature.     

Consequences of an attractive force on collective modes and dust structures in a strongly coupled dusty plasma

We present investigations of the combined effects of Debye–Hückel repulsive and overlapping Debye spheres attractive interaction potentials around charged dust particles on collective modes, phase separation and ordered structures in a strongly coupled dusty plasma. We obtain static and dynamical information via Molecular Dynamics simulations in the liquid and crystallized phases and identify the onset of an instability in the transverse mode, by using lattice summation method. The results are useful for understanding the origin of coagulation/agglomeration of charged dust particles and the formation of ordered dust structures in low-temperature laboratory and space plasmas.     

Charge Correlations in a Coulomb System Along a Plane Wall: A Relation Between Asymptotic Behavior and Dipole Moment

Classical Coulomb systems at equilibrium, bounded by a plane dielectric wall, are studied. A general two-point charge correlation function is considered. Valid for any fixed position of one of the points, a new relation is found between the algebraic tail of the correlation function along the wall and the dipole moment of that function. The relation is tested first in the weak-coupling (Debye–Hückel) limit, and afterwards, for the special case of a plain hard wall, on the exactly solvable two-dimensional two-component plasma at coupling =2, and on the two-dimensional one-component plasma at an arbitrary even integer .     

Density Profiles in a Classical Coulomb Fluid Near a Dielectric Wall. II. Weak-Coupling Systematic Expansions

In the framework of the grand-canonical ensemble of statistical mechanics, we give an exact diagrammatic representation of the density profiles in a classical multicomponent plasma near a dielectric wall. By a reorganization of Mayer diagrams for the fugacity expansions of the densities, we exhibit how the long-range of both the self-energy and pair interaction are exponentially screened at large distances from the wall. However, the self-energy due to Coulomb interaction with images still diverges in the vicinity of the dielectric wall and the variation of the density is drastically different at short or large distances from the wall. This variation is involved in the inhomogeneous Debye–Hückel equation obeyed by the screened pair potential. Then the main difficulty lies in the determination of the latter potential at every distance. We solve this problem by devising a systematic expansion with respect to the ratio of the fundamental length scales involved in the two coulombic effects at stake. (The application of this method to a plasma confined between two ideally conducting plates and to a quantum plasma will be presented elsewhere). As a result we derive the exact analytical perturbative expressions for the density profiles up to first order in the coupling between charges. The mean-field approach displayed in Paper I is then justified.     

Debye-Hückel limit of quantum coulomb systems

In this paper, we consider charge symmetric quantum Coulomb systems with Boltzmann statistics. We prove that the theory of screening of Debye and Hückel is a combined classical and mean field limit of these quantum Coulomb systems.Supported by the Swiss National Foundation for Scientific Research     

Debye–Hückel Theory for Charged Aligned Needles and for Polyelectrolyte Solutions

We consider a simple extension of the familiar Debye–Hückel theory of electrolyte solutions (in which the ions are represented by spheres with embedded point charges) to study the thermodynamic properties and the phase diagram of ionic solutions in which the ions of at least one of the species are deformed into parallel and rigid needle-like ellipsoidal objects that have a continuous line of charge distribution along their axis of revolution. We examine two specific cases: (a) solutions comprising both cationic and anionic needles that are identical in every respect except for the charge sign, and (b) solutions in which only one ionic species is made up of parallel rigid needles while the other species is made up of point ions. The first system is the analog, for ionic needles, of the familiar restricted primitive model of electrolytes, while the second one is a very simple model for a polyelectrolyte solution. For both systems we investigate how the phase diagram is affected by the extent of deformation of the ions, as measured by the spatial spread of their charge distribution.     

Certain properties of an electrically insulated Coulomb plasma. Numerical simulation of microfields and thermodynamic properties. the problem of ball lightning

Many-body dynamics is used to study the (quasi-)steady state of a classical Coulomb plasma. The shortest relaxation time in such a plasma, for both the Debye screening and the thermodynamic properties, is the electron transit time over the average distance between ions. The steady-state energy of the Coulomb interaction of the particles and the steady-state potential near a fixed charge can be described well by the Debye-Hückel theory, even if there is less than a single particle in a Debye sphere, on the average. Distributions of instantaneous values of the microfields in the plasma are derived. The results calculated for the electron turning distance are compared with the results of the quasibinary theory. An attempt is made to link the anomalously long lifetime of the plasma of ball lightning to a retardation of the recombination of a classical Coulomb plasma in the absence of a stochastic external agent.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 10–23, February, 1992.     

Large-Distance Behavior of Particle Correlations in the Two-Dimensional Two-Component Plasma

The model under consideration is a two-dimensional two-component plasma, i.e., a continuous system of two species of pointlike particles of opposite charges ±1, interacting through the logarithmic Coulomb interaction. Using the exact results for the form-factors of an equivalent Euclidean sine-Gordon theory, we derive the large-distance behavior of the pair correlation functions between charged particles. This asymptotic behavior is checked on a few lower orders of its -expansion ( is the inverse temperature) around the Debye–Hückel limit 0, and at the free-fermion point =2 at which the collapse of positive-negative pairs of charges occurs.     

Coherent electronic properties of coupled two-dimensional quantum dot arrays

In this paper we review our recent study of coherent electronic properties of coupled two-dimensional quantum dot arrays using numerical exact-diagonalization methods on a Mott–Hubbard type correlated tight-binding model. We predict the existence of a novel kind of persistent current in a two-dimensionalisolatedarray of quantum dots in a transverse magnetic field. We calculate the conductance spectrum for resonant tunneling transport through a coherent two-dimensional array of quantum dots in the Coulomb Blockade regime. We also calculate the effective two-terminal capacitance of an array coupled to bias leads.     

Hopping conductivity and weak localization in two-dimensional disordered systems

The low temperature dependence of hopping conductivity σ(T) in 2d-DS with weak localization of electron states is investigated. Hopping between neighbouring localized states is suggested and a power law for σ(T) is obtained. Coulomb effects are shown to be negligible for this process. The transition from the logarithmic T dependence and to the exponential Mott's law is discussed. The density distribution of localized electron states is proved to be exponential. The dielectric permeability ?′(ω) is found to be proportional to |ω|^?1 in the field of validity of the logarithmic corrections.     

Charge Fluctuations in Finite Coulomb Systems

When described in a grand canonical ensemble, a finite Coulomb system exhibits charge fluctuations. These fluctuations are studied in the case of a classical (i.e., non-quantum) system with no macroscopic average charge. Assuming the validity of macroscopic electrostatics gives, on a three-dimensional finite large conductor of volume V, a mean square charge Q ² which goes as V ^1/3. More generally, in a short-circuited capacitor of capacitance C, made of two conductors, the mean square charge on one conductor is Q ²=TC, where T is the temperature and C the capacitance of the capacitor. The case of only one conductor in a grand canonical ensemble is obtained by removing the other conductor to infinity. The general formula is checked in the weak-coupling (Debye–Hückel) limit for a spherical capacitor. For two-dimensional Coulomb systems (with logarithmic interactions), there are exactly solvable models which reveal that, in some cases, macroscopic electrostatics is not applicable even for large conductors. This is when the charge fluctuations involve only a small number of particles. The mean square charge on one two-dimensional system alone, in the grand canonical ensemble, is expected to be, at most, one squared elementary charge.     

A model of hopping and band DC photoconduction in doped crystals

Expressions for the screening length and the ambipolar diffusion length are derived, for the first time, for the case where hopping conduction and band conduction coexist in semiconductors with hydrogen-like impurities. A method is proposed for calculating the diffusion coefficient of electrons (holes) hopping between impurity atoms from data on the Hall effect, in the case where the hopping and band conductivities are equal. An interpretation is given of available experimental data on hopping photoconduction between acceptors (Ga) and donors (As) in p-Ge at T=4.2 K doped by a transmutation method. It is shown that the relative magnitude of the mobilities of electrons hopping between donors and holes hopping between acceptors can be found from the hopping photoconductivity measured as a function of the intensity of band-to-band optical carrier excitation.     

The study of electronic conduction in amorphous thin films of Al-In<Subscript>2</Subscript>O<Subscript>3</Subscript>-Al structure deposited by thermal evaporation

A discussion of electronic conduction in amorphous thin films of Al-In₂O₃-Al structure is presented. Particular attention is given to the question of film thickness, substrate temperature during deposition and post-deposition annealing, since these conditions are known to have a profound effect on the structure and electrical properties of the films. The effects of temperature on the V-I characteristics and effects of frequency on conductivity and capacitance of the Al-In₂O₃-Al structure are also reported. Activation energies for conduction processes are estimated and the results are discussed in terms of the hopping model. The conduction at higher temperature is seemingly a contact-limited, i.e. Schottky type process, so a transition from hopping to free-band conduction takes place. The capacitance decreases with the rise of frequency and the lowering of temperature. The values of dielectric constants are estimated and the results are discussed in terms of Schottky type of conduction. The increase in conductivity with the increase in temperature during measurements of electrical properties, film thickness, substrate temperature and post deposition annealing is reported and results are discussed in terms of current theory.     

Design,fabrication and characterization of a Schottky diode on an AlGaAs/GaAs HEMT structure for on-chip RF power detection

A Schottky diode was designed and fabricated on an n-AlGaAs/GaAs high electron mobility transistor (HEMT) structure for RF power detection. The processing steps used in the fabrication were the conventional steps used in standard GaAs processing. Current–voltage measurements showed that the devices had rectifying properties with a barrier height of 0.5289–0.5468 eV. The fabricated Schottky diodes detected RF signals well and their cut-off frequencies up to 20 GHz were estimated in direct injection experiments. To achieve a high cut-off frequency, a smaller Schottky contact area is required. The feasibility of direct integration with the planar dipole antenna via a coplanar waveguide transmission line without insertion of matching circuits was discussed. A higher cut-off frequency can also be achieved by reducing the length of the coplanar waveguide transmission line. These preliminary results represent a breakthrough as regards direct on-chip integration technology, towards the realization of a ubiquitous network society.     

Design and fabrication of 0.5 micron GaAs Schottky barrier diodes for low-noise terahertz receiver applications

Recent technological advances have made possible the development of heterodyne receivers with high sensitivity and high spectral resolution for frequencies in the range 1,000–3,000 GHz (1–3 THz). These receivers rely on GaAs Schottky barrier mixer diodes to translate the high-frequency signal to a lower frequency where amplification and signal processing are possible. At these frequencies, the diode quality is a major limitation to the performance of the receiver. The design, fabrication and DC evaluation of a diode for this frequency range is presented. A figure-of-merit cut-off frequency of over 10 THz is achieved with a record low zero biased capacitance of 0.5 fF. Results from RF tests are also given.This work has been supported in part by the National Science Foundation under contract ECS-8720850 and the US Army.     

Effect of Schottky-diode barrier capacitance on low-frequency noise of microwave detector

It is shown experimentally and theoretically that low-frquency-noise sources localized in the transition region and in the base resistance of a Schottky diode change their contribution to the retified-current noise by an order of magnitude or more under the influence of the barrier capacitance: the more the barrier capacitance shunts the junction at the high frequency, the higher the detector's noise level. Fluctuations of the barrier capacitance caused by fluctuations of the electron-trap occupation in the space-charge region do not manifest themselves in the noise of the studied detectors.St. Petersburg State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 5, pp. 407–420, May, 1992.     

Capacitance of Organic Schottky Diodes Based on Copper Phthalocyanine （CuPc）

The capacitance of an organic Schottky diode based on copper phthalocyanine （CuPc） is investigated. Based on the organic small-signal equivalent model established, we calculate the reverse capacitance CMetal Of the organic Schottky diode with different kinds of metal cathodes （Mg, Al, Au）. It is found that the reverse capacitance of the organic Schottky diode shows behavior as CMg 〉 CAl 〉 CAu at the same frequency, and according to our analysis, the reverse Schottky junction capacitance Cj is expected to have little effect on the reverse capacitance of the organic Schottky diode, and the space-charge limited current capacitance Us is considered to dominate the reverse capacitance, which limits the improvement of frequency characteristics of organic Schottky diodes.