Rate equations in the hopping transport

The rate equation formulation of the hopping transport problem is analyzed in detail. It is shown that the usual form of the rate equations for the system of electrons in localized states interacting with phonons is incorrect in the dc limit. A generalized form of the rate equations is derived. Both usual solution and that one corresponding to the result ofKasuya andKoide for the dc conductivity are shown to solve these equations. However, the former one is shown to be improper from the physical point of view as well as from the point of view of a (for a given model) exact asymptotic identity derived. For high frequencies, both forms of the rate equations are shown to be indistinguishable.     

Rate equations in the hopping transport III. A completely new interpretation of the dc phonon-assisted hopping in the mobility gap

A new interpretation of the low-frequency phonon-assisted hopping conduction in the mobility gap of disordered semiconductors which is inherently connected with the effect of broadening of electronic levels due to electron-phonon coupling is suggested. This interpretation is fully compatible with our previous reported mathematical theory of the hopping conduction. It is argued that the current understanding of the hopping transport is based on a dubious neglect of the above mentioned broadening which makes the usual theories of the dc phonon-assisted hopping conduction inconsistent.     

On thermopower in hopping transport

Certain general aspects of hopping transport in the context of thermopower are reinvestigated. Onsager symmetry of the macroscopic kinetic coefficients is derived from detailed balance of the microscopic coefficients of the kinetic equation by an expansion of the kinetic equation around local equilibrium in an external potential and temperature gradient. The resulting expression for the thermopower differs from expressions proposed in the literature. The difference however, seems to be small.     

Activation energies in hopping transport systems

A phenomenological theory of carrier transport under non-isothermal conditions has been developed to deduce the activation energies (δ) from thermally stimulated current measurements. This theory applies to hopping transport systems as well as band transport systems, but unlike existing theories, it is not limited to band transport systems. The determination of δ by the new method is intrinsically more accurate than existing heating-rate methods, making it possible to study small changes in δ such as field-dependence. The discussion is illustrated with data measured in amorphous PVK.     

Thermally assisted hopping transport in disordered systems

The response to an external field of localized electrons coupled to phonons is investigated. The low frequency (ω<T) linear response function is shown to obey a kinetic equation. The transition probabilities (including multiphonon contributions) can be expressed in terms of the dynamical correlation functions(k, ?) of the phonons. The low temperature d.c. conductivity in three dimensions obeys a law σ(0)=σ₀ · exp(? (T ₀/T)^1/4). By a combined variational and “nearest neighbor” approximation upper limits for the exponential as well as the pre-exponential factor are obtained. In two dimensions the 1/4 in the exponent has to be replaced by 1/3. The one-dimensional case requires separate considerations which do not simply lead to an exponent 1/2. An expression for the thermopower in the hopping regime is derived and evaluated.     

Non-ohmic variable-range hopping transport in one-dimensional conductors

We investigate theoretically the effect of a finite electric field on the resistivity of a disordered one-dimensional system in the variable-range hopping regime. We find that at low fields the transport is inhibited by rare fluctuations in the random distribution of localized states that create high-resistance breaks in the hopping network. As the field increases, the breaks become less resistive. In strong fields the breaks are overrun and the electron distribution function is driven far from equilibrium. The logarithm of the resistance initially shows a simple exponential drop with the field, followed by a logarithmic dependence, and finally, by an inverse square-root law.     

A stochastic approach to hopping transport in semiconductors

Generalized charge carrier equations for hopping transport in semiconductors are derived which include also the widely used Van Roosbroeck equations. The approach is based on a microscopic stochastic interacting particle system which models the hopping of electrons on a random set of states.     

Mechanism of hopping transport in disordered mott insulators

By using a combination of detailed experimental studies and simple theoretical arguments, we identify a novel mechanism characterizing the hopping transport in the Mott insulating phase of Ca2-xSrxRuO4 near the metal-insulator transition. The hopping exponent alpha shows a systematic evolution from a value of alpha=1/2 deeper in the insulator to the conventional Mott value alpha=1/3 closer to the transition. This behavior, which we argue to be a universal feature of disordered Mott systems close to the metal-insulator transition, is shown to reflect the gradual emergence of disorder-induced localized electronic states populating the Mott-Hubbard gap.     

Anomalous Hall effect in ferromagnetic semiconductors in the hopping transport regime

We present a theory of the anomalous Hall effect in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conductivity sigma(AH)(xy). We show that sigma(AH)(xy) is proportional to the first derivative of the density of states varrho(epsilon) and thus can be expected to change sign as a function of impurity band filling. We also show that sigma(AH)(xy) depends on temperature as the longitudinal conductivity sigma(xx) within logarithmic accuracy.     

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.     

On the variation of hopping transport in amorphous silicon with preparation conditions

Thedc conductivity of amorphous silicon prepared by two successive ion bombardments at different temperatures has been measured as a function of temperature. The results may be expressed in terms of a generalized hopping formula =₀ exp [–(T ₀/T) ⁿ where the parameter set {n,T ₀, ₀} varies with the irradiation conditions. In particular, the hopping exponent has been found to assume the limiting values ofn1/4 at irradiation temperatures ofT _i100 K and ofn1/2 atT _i500 K, whereas intermediate values ofn have been observed for temperatures inbetween. It is concluded that thermally activated redistribution processes of radiation defects control the final state of disorder in the irradiated samples, which in turn determines the particular hopping characteristics. Within the framework of existing theories the two limiting cases can be explained to be due to a disordered solid of homogeneous and granular structure, respectively.     

Many-electron Coulomb correlations in hopping transport along layers of quantum dots

Experimental data are analyzed on the hopping transport of holes in two-dimensional layers of Ge/Si(001) quantum dots (QDs) under conditions of the long-range Coulomb interaction of charge carriers localized in QDs, when the temperature dependence of the conductivity obeys the Efros-Shklovskii law. It is found that the parameters of hopping conduction significantly deviate from the predictions of the model of one-electron excitations in “Coulomb glasses.” Many-particle Coulomb correlations associated with the motion of holes localized in QDs play a decisive role in the processes of hopping charge transfer between QDs. These correlations lead to a substantial decrease in the Coulomb barriers for the tunneling of charge carriers.     

Coupling of tunneling and hopping transport interactions in neutron scattering lineshapes

The results of a recently presented formalism for neutron scattering lineshape calculations are used to characterize the observable consequences of the coupling of tunneling and hopping interactions of atoms moving in solids and are compared with those of another development, which treats the two interactions but neglects the coupling.     

Temperature dependence of dispersive hopping transport and diffusion in disordered solids

The time- and temperature-dependent drift mobility μ_d for dispersive transients in disordered solids is $\text{μ}{}_{\mathrm{d}}\text{(T,t) =}\text{L}\text{Et}{}_{\mathrm{T}}$ in terms of distance L, field E and transit time t_T. Since current I ∝ tsu?(1?α) for t <_Tand 0<α<1 by Scher-Montroll theory for hopping among localized states, it follows that $\text{μ}{}_{\mathrm{d}}\text{(T) = α[μ}{}_{\mathrm{d}}\text{(T,t)]}{}^{\mathrm{\alpha }}\text{(}\text{L}\text{Eτ}\text{)}{}^{\mathrm{1?\alpha }}$ where τ≈ 10^?13s is estimated. Further $\text{μ}{}_{\mathrm{d}}\text{(T) ∝ exp (}\text{?Δ}{}_0\text{KT}\text{)}$ and the activation energy Δ₀ is time independent. On this basis Δ for the carbazole polymers is ca. zero, that for a-Se is ca. 0.05 eV, and that for a-As₂Se₃ is 0.35 eV rather than 0.5, 0.3 and 0.6 eV respectively on a phenomenological basis for μ_d(T,t). Trap-controlled hopping transport may be excluded. Time-resolved optical studies of excess carrier recombination supplement mobility measurements in a-Si:H and a-As₂Se₃ as well as other systems. Combined results suggest a dielectric response mechanism in which the time-dependent hopping frequency of localized carriers ν ∝ t^α?1 arises from distortion of the medium at localization sites. This is satisfied by Δ(T,t) = Δ₀+(1?α)KTT ln(t/τ) where τ is the mean initial localization time of the carrier, 10^?13?10^?12s, Δio is the height of the barrier at T, and 0<α<l. Consequently ν = ν₀(t/τ)^α?1 exp(frsol|?Δ₀/KT) which applies also to bimolecular recombination.     

次近邻跃迁对石墨烯纳米带输运性质的影响

根据紧束缚模型,利用格林函数的方法,将次近邻跃迁考虑在内,研究了扶手椅型石墨烯纳米带的输运性质.通过数值计算,给出了不同尺寸和不同次近邻跃迁能下系统的能量-电导和电流-电压特征曲线.结果表明,次近邻跃迁对扶手椅型石墨烯纳米带的输运性质有显著的影响.它破坏了电导共振峰关于能量的对称分布,增强了系统的导电性,减小了电子导电偏压阈值,加速了系统输运性能由半导体向导体转变. 次近邻跃迁能和石墨烯纳米带的尺寸越大,这种影响越明显