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.     

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.     

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.     

Microscopic theory of dispersive transport in disordered semiconductors

A theory of dispersive transport based on the microscopic master equation is presented. The theory agrees with previous approaches and unifies them but is much more general. By means of the two-site effective medium approximation of Movaghar et al. we derive a generalised master equation for the averaged propagator of the carriers the kernel of which can be calculated directly from the microscopic transfer rates and distribution functions. We give analytic expressions for the transient current i(t) including the conditions for the transition from dispersive to Gaussian transport for three relevant hopping models. The influence of multiple trapping is treated by means of the coherent potential approximation. We find the same results for trapping with an exponentiak trap depth distribution and fixed-range hopping over energy barriers with an exponential barrier height distribution.     

Charge-carrier and polaron hopping mobility in disordered organic solids: Carrier-concentration and electric-field effects

The effective-medium approximation (EMA) analytical theory is advanced further to describe charge transport at arbitrary charge-carrier concentration in a disordered organic material with superimposed polaron effects. A key point of this model compared to the previous treatment [Phys. Rev. B 76 (2007) 045210] is that it is formulated for arbitrary electric fields and is able to describe consistently both the carrier-concentration and field dependences of charge mobility. The mobilities of both bare charge carriers and polarons were calculated using the Miller–Abrahams and polaron jump rate models, respectively. An excellent quantitative agreement was obtained between the theoretical calculations and the recent numerical simulations of the field- and carrier-density dependences of the mobility for bare charge carriers using the same parameters. The polaronic carrier density effect was also calculated using the complete Marcus jump rate equation and straightforward EMA configurational averaging, and the results compared to that obtained with the use of the symmetrical jump rate model and the effective transport energy concept. This study confirms that a strong dependence of carrier mobility upon increasing carrier density and electric field, which has conventionally been observed in experiment for numerous organic semiconducting materials, is incompatible with the notion of large polaron binding energy in these materials, implying that the energetic disorder plays a dominant role.     

Multiphonon hopping in disordered semiconductors

Equations of motion for the nonequilibrium single-frequency density matrix are used to obtain a balance equation describing the kinetics of electron hopping between localized states in disordered semiconductors. Conclusions are drawn about the applicability of the theory of multiphonon processes to systems with a small nonadiabaticity. The decoupling used is a generalization of one used earlier to the multiphonon case. The balance equation found in the Markov approximation for the average number of sites occupied in an electric field contains the field dependence of the multiphonon-transition probability, tending to the well-known weak-field limit.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No.2, pp.35–42, February, 1976.In conclusion the author is grateful to V. L. Bonch-Bruevich and A. G. Mironov for discussing this work.     

The calculation of transport properties and density of states of disordered solids

A computational method is presented for the calculation of the conductivity tensor and the density of states of disordered solids. This is a more general and detailed discussion of an algorithm which has been applied to d.c. and a.c. conductivity, Hall effect and density of states of various systems.     

Temperature dependence of elastic constants for ionic solids

In this paper the thermal variation of volume for NaCl, KCl, MgO and CaO has been investigated on the basis of Anderson model. We have evaluated the values of elastic constants C₁₁, C₄₄ and K_T at different temperature on the basis of Murnaghan and Tallon models. Tallon's model with second approximation presents slightly better agreement with experimental results which shows that the Anderson–Grüneisen parameter is directly proportional to the volume ratio. Tallon's model can be used to evaluate the values of elastic constants for solids at different temperatures.     

Phonons in disordered solids

The effects of crystalline disorder on the frequency distribution and lifetimes of phonons are investigated. As the disorder parameter g characterizing the scattering of normal modes is increased to g>g_c, the normal mode spectrum becomes unstable against arbitrarily small nonlinearities while the ground state (if any) becomes increasingly degenerate. The bandwidth of the acoustic phonon spectrum increases with g, from a value ω_Dat g = 0 to 1.24ω_D at g_c. The speed of sound at long wavelengths decreases with increasing g; at threshold (g_c) it has decreased by some 29.3% from its value at g = 0. For g < g_c the scattering lifetime of long-wavelength normal modes satisfies Rayleigh's law (1/τ = A(_g)ω⁴). At g_c the damping satisfies a different law: 1/τ = Bω². Similar effects are obtained for the optic mode phonons. For these reasons, it appears that g_c marks the threshold of amorphous behavior, although the regime g >g_c is beyond the scope of our model.     

The temperature dependence of the conductivity and thermal emf due to multiphonon hopping in disordered semiconductors

Using transport theory, we studied the temperature dependence of the static conductivity and of the thermal emf due to multiphonon hopping in disordered semiconductors. In the low-temperature region when T < _m ( _m is the maximum phonon frequency), the temperature dependences of the conductivity and the thermal emf are the same as when single-phonon hopping is dominant. At higher temperatures (T _m), the hopping conductivity and thermal emf are characterized by a slower dependence on reciprocal temperature than in the low-temperature region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No.2, pp.42–47, February, 1976.The author is to V. L. Bonch-Bruevich and A. G. Mironov for discussing this work.     

Theory of hopping conductivity in disordered semiconductors

The bond percolation method is used to investigate the conditions under which a linear (and not exponential) temperature dependence of hopping conductivity can be observed.Translated from Izvestiya Vysshikh Uchbenykh Zavedenii, Fizika, No.2, pp. 52–62, February, 1976.     

Theory of hopping transfer in disordered systems

The problem of hopping conduction in a system with randomly distributed impurity centers at low temperatures has been considered in terms of the linearized balance equation. The Gochanour-Andersen-Fayer diagram technique has been used to obtain a self-consistent expression for the configuration-averaged Green’s function, which describes the charge transfer in a disordered system with inclusion of Fermi correlations. In the framework of the developed formalism, a relationship has been derived for hopping conductivity as a function of the temperature with a power law of the density of states. The results obtained agree well with the percolation approach and, in the static limit, lead to the Mott’s law.     

The effect of electron state hybridization on the frequency dependence of hopping conductivity in disordered systems

The effect of electron state hybridization on phononless hopping conductivity in a disordered system of point localization centers in the intermediate frequency range corresponding to electron transitions to distant centers is discussed. When the basis of the atom-type localized functions is applied, with the hybridization of the wave functions of the distant centers not being taken into account, the frequency dependence of phononless conductivity is shown to be superlinear and monotonic in a wide frequency range. In this case, the kink in the vicinity of a crossover from a linear to a quadratic frequency dependence of the conductivity turns out to be sharper as distinct from the standard theory.     

Temperature and pressure dependence of self diffusion in nonassociating liquids

Recent results of self diffusion studies on a series of halomethanes and alkanes at elevated pressure are reviewed. The data are evaluated with the rough hard sphere model and the interacting sphere model. The parameters obtained from both treatments are critically discussed. The least-squares fits are of very good quality except for the highly unsymmetric alkanes with carbon numbers between 4 to 7. For these liquids, significant and systematic deviations are ascribed to the strong departure from spherical symmetry of the molecules.     

Temperature dependence of high field transport in ZnS

High field transport process in ZnS in the temperature range of (10–500) K was simulated by help of Monte Carlo method. The band structure of ZnS is described by analytical fitting of real band structure. Phonon scattering, spatial charge scattering, and impact ionization process are included in the simulation. The phonon scattering rates at different temperatures are calculated and compared. The transient acceleration time of electrons in ZnS is found to be temperature-independent. We attribute this result to the compensation of two opposite factors in ZnS. Average energy of electrons decreases with temperature.