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.     

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.     

Control of hopping conductivity by structural modification of amorphous silicon

By re-irradiation of ion-bombarded amorphous silicon at elevated temperatures structural modifications of the state of disorder can be achieved which allow a wide-ranging control of variable range hopping conductivity. In this way the conductivity of a-Si films can be increased by many orders of magnitude until metal-like conduction is obtained.     

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

The usual kinetic equations for the site occupation probabilities in an external field are solved exactly in a simple one-dimensional periodic model with two kinds of atoms using a) free boundary conditions and order of limitsN, 0 needed for a proper treatment of the dc conductivity here b) boundary conditions with metallic contacts and order of limitsN, 0 and c) the same boundary conditions but reversed order of limiting processes 0,N typical of e.g. numerical and percolation treatments. (N and are the number of sites and frequency.) It is demonstrated that though the bulk dc conductivity is the same in all three cases, local bulk properties of the material are strongly dependent on the régime used. The role of the order of all three limiting processes 0,N+ andn+ (N–n+) for local shifts of the chemical potential _n in the dc limit is examined (n is the number of the relevant site calculated from a boundary of the chain). It is shown especially that the rate equation treatment (régime a) on the one hand and numerical or percolation treatments (régime c) on the other hand never yield the same bulk values of _r.     

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.     

Theory of thermally assisted electron hopping in amorphous solids

The reaction¹⁶O(n, α)¹³C was studied with 13.9 MeV neutrons using two different counter telescopes. Absolute differential cross sections were measured for the transitions to the ground state and to the 3.08 and 3.68+3.85 MeV levels of¹³C. The results are interpreted in terms of a direct reaction mechanism.     

Phononless hopping in the mobility gap of amorphous semiconductors

Two different theories are analyzed and shown to yield the same result for the phononless contribution to the dc hopping conductivity due to electrons in localized states (with single-electron energies broadened by the electron-phonon interaction) in the mobility gap of amorphous semiconductors. Numerical estimate is then used to show that this mechanism cannot explain experimental data on elemental covalent amorphous semiconductors.     

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.     

The hopping variable range conduction in amorphous InAs thin films

This paper studies the influence of temperature on electrical resistivity in α-InAs thin films between 30 K-2K based on the analysis of Mott VRH model and ES VRH model. The effect of the interactions between electrons at lower temperature must be considered, therefore, ES VRH conduction will dominate mechanism, and the crossover from Mott to ES VRH conduction is observed about 7 K. Based on available experiment data and VRH conduction model, the parameters of VRH conduction are determined. And the calculated values of T_C are consistent with the experimental results. In addition, R_M/ξ, Δ_M/kT, R_ES/ξ and Δ_ES/kT are satisfied with the validity of Mott and ES models. Furthermore, the temperature dependence of resistivity at low temperature obeys a universal scaling law, which well describes the overall temperature range of VRH conduction. However, the values of T^’_M from the universal function are two order of magnitudes lower than T_M deduced from fitting experiment.     

Single-phonon contribution to the hopping conductivity of amorphous solids

The electronic d.c. hopping conductivity of amorphous materials is calculated exactly up to the second power of the coupling constant of electrons and acoustic phonons. Its temperature dependence is discussed.Ke Karlovu 3, Praha 2, Czechoslovakia.     

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.     

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.     

Electron transport in amorphous metals

Electron transport measurements—resistivity, thermopower, magnetoresistivity and Hall effect—in non-magnetic amorphous metals are surveyed and compared with predictions from several theoretical models proposed to describe electron scattering in highly disordered metals.     

Polaron effect and the dc phonon-assisted hopping conductivity in amorphous semiconductors

A new small parameterW of off-diagonal electron-phonon matrix elements with respect to diagonal ones is introduced. Limiting ourselves to terms of the second order inW, the dc phonon assisted hopping conductivity is calculated to the infinite order in the electron-phonon coupling constant. Result clearly exhibits the polaron effect which is discussed in detail.