Effect of electric field on diffusion in disordered materials

The effect of electric field on diffusion of charge carriers in disordered materials is studied by Monte Carlo computer simulations and analytical calculations. It is shown how an electric field enhances the diffusion coefficient in the hopping transport mode. The enhancement essentially depends on the temperature and on the energy scale of the disorder potential. It is shown that in one‐dimensional hopping the diffusion coefficient depends linearly on the electric field, while for hopping in three dimensions the dependence is quadratic.     

Effects of photoexcitation on the current transport mechanism in amorphous indium selenide thin films

The effect of photoexcitation on the current transport mechanism in amorphous indium selenide thin films was studied by means of dark and illuminated conductivity measurements as a function of temperature. Analysis of the dark electrical conductivity in the temperature range 110–320 K reveals behaviour characteristic of carriers excited to the conduction band and thermally assisted variable-range hopping (VRH) at the Fermi level above 280 K and below 220 K, respectively. In the temperature range 220–280 K, a mixed conduction mechanism was observed. A conductivity activation energy of ～300 meV (above 280 K), a density of localised states (evaluated assuming a localisation length of 5 Å) of 1.08 × 10²¹ cm^?3 eV^?1, an average hopping distance of 20.03 Å (at 120 K) and an average hopping energy of 27.64 meV have been determined from the dark electrical measurements. When the sample was exposed to illumination at a specific excitation flux and energy, the values of the conductivity activation energy, the average hopping energy and the average hopping range were significantly decreased. On the other hand, the density of localised states near the Fermi level increased when the light flux was increased. Such behaviour was attributed to a reversible Fermi level shift on photoexcitation.     

Equipartition of current in metallic armchair nanoribbon of graphene-based device

We numerically investigate the mesoscopic electronic transport properties of Bernal-stacked bilayer/trilayer graphene connected with four monolayer graphene terminals. In armchair-terminated metallic bilayer graphene, we show that the current from one incoming terminal can be equally partitioned into other three outgoing terminals near the charge-neutrality point, and the conductance periodically fluctuates, which is independent of the ribbon width but influenced by the interlayer hopping energy. This finding can be clearly understood by using the wave function matching method, in which a quantitative relationship between the periodicity, Fermi energy, and interlayer hopping energy can be reached. Interestingly, for the trilayer case, when the Fermi energy is located around the charge-neutrality point, the fractional quantized conductance 1/(4e²h) can be achieved when system exceeds a critical length.     

Theory of hopping and multiple-trapping transport in disordered systems

We present a general theory to describe equilibrium as well as nonequilibrium transport properties of systems in which the carriers perform an incoherent motion that can be described by means of a set of master equations. This includes hopping as well as trapping in the localized energy region of amorphous or perturbed crystalline semiconductors. Employing the mathematical analogy between the master equations and the tight binding problem we develop approximation schemes using methods of many-particle physics to derive expressions for the averaged propagator of the carriers and the conductivity tensor. The calculated conductivity and Hall conductivity of hopping systems compare extremely well to computer simulations over the whole range of frequency, density, and temperature. We are able to derive expressions for dispersive transport in hopping as well as trapping systems that contain the results of earlier theories of Scher, Montroll and Noolandi, Schmidlin as special cases and establish criteria for the occurrence of dispersive transport in such systems. We find that in principle hopping can lead to dispersive transport if the times and densities are very low, but actual experimental data are more easily explained in terms of multiple trapping.     

纳米硅薄膜的低温电输运机制

在很宽的温度范围(500—20K)研究了本征和不同掺磷浓度的纳米硅薄膜的电输运现象.发现 原先的异质结量子点隧穿(HQD)模型能很好地解释薄膜在高温下(500—200K)的电导曲线,但 明显偏离低温下的实验值.低温电导(100—20K)具有单一的激活能W,并与k_BT值 大小相当(W～1—3k_BT),呈现出Hopping电导的特征.对HQD模型做了修正,认为 纳米硅同时存在两种输运机制：热激发辅助的电子隧穿和费米能级附近定域态之间的Hoppin g电导.高温时(T 关键词： 纳米硅薄膜 低温电导 电输运     

Competition Between the SDW and CDW in Quasi-One-Dimensional Organic Polymer Ferromagnet

The next-nearest-neighbor hopping interactions of ρ-electrons in quasi-onedimensional organic polymer ferromagnet are considered by Peierls-Hubbard model, and a set of self-consistent equations are established to optimize the system. The competition between the SDW and CDW states, which is determined by the interplay between the electron-electron correlation and the next-nearest-neighbor hopping interaction, is studied. At the CDW state,the SDW along the main chain will be tuned by the CDW. Consequently the ferromagnetic state, in which all the spins of the unpaired electrons at side freeradicals are arranged parallelly,will be no longer a stable ground state of the system.     

Polaronic transport in TiO2 thin films with increasing Nb content

The temperature dependence of the charge transport in TiO₂ films was investigated to establish the correlation between the Nb content and electrical properties. It was identified that temperature-dependent conductivity of the films is dominated by a phonon-assisted small polaron hopping model in the non-adiabatic regime. Applying the polaron hopping models of Mott, Schnakenberg and Emin to describe the observed behavior, temperature-dependent conductivity data of the films were analyzed. A detailed analysis in terms of small polaron hopping parameters in the investigated temperature regime was used to correlate electrical properties with the percentage of Nb.     

Phase separation and abnormal transport behaviours in La0.7-xGdxSr0.3MnO3 system

The magnetic and transport behaviours of the La_{0.7-x}Gd_xSr_{0.3}MnO_3 (0≤x≤0.70) system are investigated. The experimental results indicate that with increasing Gd doping content, the magnetism of the system changes from the long-range ferromagnetic order state to the cluster-spin glass state, then to the antiferromagnetic (AFM) state. It is interesting that the phase separation appears at x=0.30 and 0.40 and disappears for x≥0.50 where the AFM state occurs. At high doping content, the transport behaviours exhibit abnormality, e.g. there are two temperature ranges in which the ρ－T curves can be well fitted by a variable-range hopping (VRH) model. We suggest that the VRH does not come from the hopping of carriers between clusters, but from the different magnetic backgrounds in the clusters.     

Q有机聚合物材料中光生载流子传输的跳跃输运

本文描述了跳跃模型在有机聚合物光折变材料中空间电荷场理论上的应用.在Feinberg针对无机光折变晶体提出的电荷传输过程模型-跳跃模型(Hopping Model)基础上,根据有机聚合物光折变材料的特点,考虑了光生载流子产生过程中的电子空穴对的复合过程(对复合和双分子复合过程)和激发光场的频率(即激发光子的能量)对光生载流子产生的影响,给出了有机聚合物材料中光生载流子产生的量子效率和光生载流子的分布密度及其跳跃率的新表示,完成外加调制光场和静电场同时作用下有机聚合物材料中光生载流子传输的跳跃方程,得到空间电荷场建立的动态过程和稳态时的解析表达式及其数值计算结果.     

Modal decomposition of hopping states in cellular flames

We use Karhunen-Loeve (KL) decomposition of video images from an experiment to analyze a spatiotemporal dynamic state, unique to cellular flames, referred to as a "hopping state." Ordered states of cellular flames on a circular burner consist of one or two concentric rings of luminous cells. The hopping states correspond to the motions of individual cells in a ring sequentially executing abrupt changes in their angular position, while the other cells in the ring remain symmetric and at rest. KL decomposition separates the spatial and temporal characteristics of the hopping motion. The underlying symmetries of the experiment allow us to deduce a set of normal form equations that describe the formation of these states. We find that they result from secondary bifurcations connecting two primary branches of traveling waves. The solutions corresponding to hopping states exist as mixed-mode solutions away from the secondary bifurcations. (c) 1999 American Institute of Physics.     

STUDIES ON THE NEXT-NEAREST NEIGHBOR HOPPING INTERACTIONS OF π-ELECTRONS IN QUASI-ONE-DIMENSIONAL ORGANIC FERROMAGNETIC MODEL

Based on a theoretical model proposed for quasi-one-dimensional organic polymer fer-romagnets, the next-nearest neighbor hopping interactions of sr-electrons are considered. Allowing for full lattice relaxation, a set of self-consistent equations is established to study the system. The spin-density-wave (SDW) and the possible ferromagnetic ground state of the system are investigated in detail. It is found that the next-nearest neighbor hopping in-teractions will make the SDW stronger and consequently make the ferromagnetic state more stable as compared with the nonmagnetic reference state.     

Hopping Transport and Stochastic Dynamics of Electrons in Plasma Layers

We investigate the stochastic dynamics and the hopping transfer of electrons embedded into two‐dimensional atomic layers. First we formulate the quantum statistics of general atom ‐ electron systems based on the tight‐binding approximation and express ‐ following linear response transport theory ‐ the quantum‐mechanical time correlation functions and the conductivity by means of equilibrium time correlation functions. Within the relaxation time approach an expression for the effective collision frequency is derived in Born approximation, which takes into account quantum effects and dynamic effects of the atom motion through the dynamic structure factor of the lattice and the quantum dynamics of the electrons. In the last part we derive Pauli equations for the stochastic electron dynamics including nonlinear excitations of the atomic subsystem. We carry out Monte Carlo simulations and show that mean square displacements of electrons and transport properties are in a moderate to high temperature regime strongly influenced by by soliton‐type excitations and demonstrate the existence of percolation effects (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Breakdown of the resistor-network model for steady-state hopping conduction

Master equations are used to study steady-state hopping in a disordered solid. We express each site's occupancy in terms of its quasi-electrochemical potential (QECP); currents flow between sites whose QECP's differ. Coupled nonlinear circuit equations result from the steady-state condition and a boundary condition. When site-to-site QECP differences are much smaller than the thermal energyk _B T, the effect of current flow on occupancies is ignorable, and the equations reduce to those of a resistance network. But this resistor-network model fails: a) at low temperatures, b) with increasing disorder, and c) with increasing emf. We therefore study hopping conduction beyond this approximation. Exactly soluble examples show the importance of current-induced charge redistribution in non-ohmic steady-state flow.     

Statistical properties of Lyapunov exponents and of quantum conductance of random systems in the regime of hopping transport

The statistics of the zero-temperature conductance and the Lyapunov exponents of one-, two- and three-dimensional disordered systems in the regime of strong localization is studied numerically. In one dimension, the origin of the universality of the moments of the conductance is explained. The relation between the most probable value of the conductance and its configurational average is discussed. The relative fluctuations of the conductance (and of the resistance) are shown to grow exponentially with the system length. In higher dimensions the conductance is almost entirely determined by the smallest of the Lyapunov exponents. The statistics of the conductance is therefore the same as in the one dimensional case. A model is proposed for the treatment of the fluctuations in hopping transport at finite temperatures. An exponential dependence of the relative fluctuations of the conductance/resistance on the temperature is predicted, log (δg/g) ∞ T^?a with α = 1/(d+1). It is concluded that the presently available experimental data on the temperature dependence of the conductance fluctuations in the hopping regime can be understood by replacing the system size in the zerotemperature result for the fluctuations of the conductance by the hopping length.     

Scaling approach to the theory of frequency dependent hopping conductivity of disordered systems

By studying the change of the probability distribution function for the hopping propagation of carriers under differential changes of the temperature and density of sites partial differential equations are derived which couple the frequency, temperature, and density dependence of the conductivity. In certain special cases the conductivity can be calculated explicitly for zero frequency as well as in regions where the frequency dependence is known from experiment or some other theory. This leads to results which are well suited for experimental tests. Approximations used in this treatment are discussed and related to other types of theories for hopping conductivity.     

Disorder and localization of electrons in bilayer graphene

We investigate localization behavior of electron states in bilayer graphene formed with the Bernal stacking in the presence of various types of disorder (site-energy, in-plane hopping and inter-plane hopping) by the use of the transfer matrix method. It is found that all the states are localized at various kinds of disorder (site-energy, in-plane hopping and inter-plane hopping) except that in the case of inter-plane-hopping disorder the states at the zero energy are critical. The implications of the results are discussed.     

Alternative generalized master equation approach to the dc phonon-assisted hopping

As the momentum operator has no diagonal elements between localized states, the hopping conduction theory should be formulated in terms of the linear response of the site-off-diagonal elements of the single-electron density matrix to an external field. A theory of this kind, starting from generalized master equations and yielding the dc phonon-assisted hopping conductivity and thermopower is formulated. This is an alternative to the usual approach treating the current conduction via a time-derivative of the electric dipole momentum.Stimulating discussions with Dr. B. Velický turning the present author's attention to his own old ideas about the hopping conduction via off-diagonal elements of the single-electron density matrix are appreciated.     

Difference equation solutions for non-steady-state diffusion of charged particles in solids

The hopping transport of charged particles through a solid is described by means of difference equations based on the concept of classical thermal motion over discrete energy barriers. Homogeneous electric fields and concentration gradients are considered to be the driving forces for transport. Transient and steady-state currents are derived, and the concentration profiles are obtained for the mobile charged defect species. For the case of a slab geometry the discreteness of the potential barriers leads to a nonlinear dependence of current on voltage in the high electric field limit, with a more rapid increase of current with voltage than would be expected from an extrapolation of the low field linear dependence. The field-dependent relaxation of a non-steady-state defect concentration profile to the corresponding steady-state profile can be nearly exponential in the limit of large fields. Tracer distributions for the cases of semi-infinite and unbounded diffusion mediums are likewise affected appreciably in the high field limit. The velocity of the peak is increased over that obtained by linear extrapolation from the low field limit. It is concluded that the combination of high electric fields with the natural microscopic discreteness of a solid-state diffusion medium can result in readily observable nonlinear electric field effects which increase approximately exponentially with the atomic separation distances of the discrete barriers in hopping transport. Some of this nonlinear behavior can be retained in differential equations derived from the difference equations by means of Taylor series expansions of the carrier concentration with respect to position.     

Universal spin-dependent variable range hopping in wide-band-gap oxide ferromagnetic semiconductors

This paper proposes a universal spin-dependent variable range hopping theoretical model to describe various experimental transport phenomena observed in wide-band-gap oxide ferromagnetic semiconductors with high transition metal concentration. The contributions of the `hard gap' energy, Coulomb interaction, correlation energy, and exchange interaction to the electrical transport are considered in the universal variable range hopping theoretical model. By fitting the temperature and magnetic field dependence of the experimental sheet resistance to the theoretical model, the spin polarization ratio of electrical carriers near the Fermi level and interactions between electrical carriers can be obtained.