AC Hopping Conductivity Research Articles

Crossover between transport mechanisms in the region of the transition from sublinearity to superlinearity of the AC-conductivity frequency dependence for disordered semiconductors

The transition of the frequency dependence of AC conductivity of disordered semiconductors from sublinear to superlinear behavior with an increase in frequency, which is observed for many disordered systems, is investigated. It is shown that the standard approach to calculating the superlinearity of the frequency dependence of the AC hopping conductivity in the form Reσ(ω) ∼ \(\frac{\omega } {{\ln \left( {\omega _{c,ph} /\omega } \right)}}\) (ωc, ph is the characteristic frequency), based on the single-particle density of states with a Coulomb gap, generally cannot be used to calculate high-frequency conductivity. The superlinearity of the experimentally observed frequency dependences of the conductivity Reσ(ω) in the crossover region indicates that the optimal hop length is frequency-independent and that the resonance mechanism of conductivity plays a key role. The resonance mechanism causes abnormally large measured values cot(γ) = Ims/Reσ (γ is the dissipation factor) in the crossover region.

Capacitance analyses of hydrogenated nanocrystalline silicon based thin film transistor

The capacitance–voltage (C–V) measurements within 106–10−2Hz frequency range were performed on the hydrogenated nanocrystalline silicon (nc-Si:H) bottom-gate thin film transistor (TFT) and metal-insulator-amorphous silicon (MIAS) structure, mechanically isolated from the same TFT. It was found that the conducting thin layer in nc-Si:H film expands the effective capacitor area beyond the electrode in the TFT structure, which complicates its C–V curves. Considering the TFT capacitance-frequency (C–F) curves, the equivalent circuit of the TFT structure was proposed and mechanism for this area expansion was discussed. On the other hand, the MIAS C–F curves were fitted by the equivalent circuit models to deduce its electrical properties. nc-Si:H neutral bulk effect was revealed by the dependence of the MIAS capacitance on frequency within 106–103Hz at both accumulation and depletion regimes. The inversion in MIAS was detected at 102–10−2Hz for relatively low negative gate bias without any external activation source. The presence of the ac hopping conductivity in the nc-Si:H film was inferred from the fitting. In addition, the density of the interface traps and its energy distribution were determined.

Study of ac hopping conductivity on one-dimensional nanometre systems

In this paper, we establish a one-dimensional random nanocrystalline chain model, we derive a new formula of ac electron-phonon-field conductance for electron tunnelling transfer in one-dimensional nanometre systems. By calculating the ac conductivity, the relationship between the electric field, temperature and conductivity is analysed and the effect of crystalline grain size and distortion of interfacial atoms on the ac conductance is discussed. A characteristic of negative differential dependence of resistance and temperature in the low-temperature region for a nanometre system is found. The ac conductivity increases linearly with rising frequency of the electric field and it tends to increase as the crystalline grain size increases and to decrease as the distorted degree of interfacial atoms increases.

Bipolaron ac conductivity in amorphous semiconductors and dielectrics.

We have developed a theory of the alternating-current (ac) relaxation-type conductivity due to small bipolaron (SB) hopping in amorphous semiconductors and insulators that possess deep centers of the dangling-bond type (D centers) with a negative two-electron correlation energy ${\mathit{U}}_{\mathrm{eff}}$. Unlike small po- larons, SB's were treated as essentially three-level systems in the framework of a two-site approximation. To calculate, both numerically and analytically, the real part ${\mathrm{\ensuremath{\sigma}}}_{1}$\ensuremath{\propto}${\mathrm{\ensuremath{\omega}}}^{\mathit{s}}$${\mathit{T}}^{\mathit{n}}$ of the ac hopping conductivity for different temperatures T in a wide range of audio and low radio frequencies \ensuremath{\omega}, the dynamic polariz- ability, and the SB hopping rates for dangling bond pairs have been determined. When the electron tunneling integral corresponding to the smallest intersite separations is greater than the doubled polaron shift, both the polarizability and the hopping rate strongly depend upon the shape and parameters of the ground-state adiabatic potential of a small-size pair of strongly interacting D centers. This intimate pair can be viewed as a stretched or weakened bond. A classification of possible regimes of relaxation-type SB hopping (adiabatic and nonadiabatic, as well as tunnel and activation) has been proposed. Each of these corresponds to a specific temperature dependence of the exponents s and n. A comparison to experimental data on ac losses in chalcogenide glasses and a-${\mathrm{SiO}}_{2}$ has been made.

A percolation treatment of the ac hopping conductivity at low frequencies and dimensionalities

A theory for the low frequency conductivity, σ(ω), in strongly disordered insulators is applied to systems of limited dimensionality. The dominant relaxation times of impedance clusters are determined, and σ(ω) is calculated by a summation over cluster contributions. As ω approaches 0, the size of the most important clusters diverges. In one dimension, known results for σ(ω are recovered for two classes of systems.For thin films σ(ω) is calculated both parallel, σ ∥( ω), and perpendicular, σ ⊥( ω), to the film. The two cases differ markedly; σ ⊥( ω) − σ ⊥(0) ∝ ω 0.5 + ω 0.9 while σ ∥( ω) − σ ∥(0) ∝ ω 2.

AC hopping conductivity and DLTS studies on electron-irradiated boron-doped silicon

AC hopping conductivity and DLTS measurements have been performed on boron-doped electron-irradiated silicon at <or approximately=18 K. Isochronal anneals of the AC hopping conductivity revealed defect annealing stages correlating with the known behaviour of the vacancy and the boron-substitutional-vacancy pair. A reverse annealing stage between 240-260 K was tentatively attributed to a boron-vacancy-related complex. In one particular material, recovery stages between 40 and 60 K and between 220 and 300 K were attributed to electron emission from electron traps present in the as-grown material. Both of these disappeared with electron irradiation. DLTS carried out on specimens that had been warmed to room temperature after electron irradiation at approximately 18 K revealed a number of previously unreported defects.

The temperature dependence of the AC hopping conductivity of lightly compensated semiconductors

AbstractThe temperature dependence of the ac hopping conductivity of lightly compensated semiconductors is explained by taking into account the transitions of a hole within three donor clusters. The effect of the defect wave function anisotropy is discussed. The anisotropy does not change the temperature and frequency dependence of the conductivity. The results are compared with experimental data on Si:P and Ge:P.

Universal behaviour of AC hopping conductivity in disordered systems

A scaling law of the form σ( ω)/ σ(0) = f[A ω/ ω(0)] is apparent in theoretical conductivities calculated in the EPA and experimental conductivities for a variety of disordered semiconductors. It follows that the behaviour of σ(ω) is primarily generic and that and the pair approximation is an incomplete explanation of ω s.

A simple model of ac hopping conductivity in disordered solids

Using the CTRW approximation the simplest possible nontrivial model of ac hopping conductivity in disordered solids, is constructed. The model predicts universality of the frequency-dependent conductivity, independent of temperature, chemical composition, and conductivity mechanism, in resonably good agreement with experiments. It is shown that all qualitative features of experimental ac hopping conductivity can be understood within the model.

Hopping conductivity of a one-dimensional bond-percolation model in a constant field: Exact solution

The recent work of Odagaki and Lax on the ac hopping conductivity in a one-dimensional bond-percolation model is generalized to include a constant applied field. The corresponding biased random-walk problem on a finite chain of arbitrary length and with properly terminated ends is solved analytically. The solution is extended to include all continuous-time random walks. (It is thus directly applicable, for instance, to spectral diffusion with asymmetric transfer rates and memory effects.) The diffusivity (and thence the conductivity and relative permittivity) on a chain of $N$ sites is obtained exactly, in closed form. A configuration averaging over $N$ yields the diffusivity and relative permittivity for the randomly interrupted infinite chain. Our analytic results are valid at all frequencies, and are in a form amenable to extensive numerical computation. This is done, and the noteworthy features of the results are displayed graphically. All the known results in the field-free case are recovered as special cases of the expressions presented here.

Analysis of AC and DC hopping conductivity in impurity bands and amorphous semiconductors

The extended pair approximation is used to compare the predictions of the Miller-Abrahams rate equation theory (1960) for AC and DC hopping conductivity with experiment. For an analysis of impurity conduction the authors consider data for n-type silicon and gallium arsenide. In both cases the theory accurately predicts the DC conductivity when reasonable assumptions concerning the density of states are made. In the AC regime the theory provides a good description of the data on silicon but in the case of the gallium arsenide data the theory predicts an onset of AC behaviour at a frequency about six orders of magnitude higher than that observed. Data for amorphous germanium are also analysed. The theory fits the DC conductivity which follows a T-1/4 law, with a characteristic frequency R0, of 1021 Hz. The AC conductivity is qualitatively in agreement but the onset of AC behaviour is two orders of magnitude higher in frequency than is observed.

A unified equivalent-circuit approach to the theory of AC and DC hopping conductivity in disordered systems

The Miller-Abrahams equivalent circuit is used to motivate an extension of the pair approximation to the AC hopping conductivity sigma ( omega ) of a random system, which embraces the DC limit sigma (0). The theory is simple to develop and readily yields both analytical and numerical results. The formulae obtained reproduce the pair approximation in the low-density limit and give known exact asymptotic results at high densities and high frequencies. The numerical predictions of the theory are compared with data obtained by direct numerical solution of Kirchhoff's equations for random networks. Excellent agreement is obtained for sigma (0) for energy-independent and energy-dependent hopping in 2D and 3D, and for sigma ( omega ) for energy-independent hopping in 3D.

Reply to "Effect of periodic boundary conditions in the calculation of ac conductivity for a one-dimensional percolation model"

The ac hopping conductivity of a one-dimensional bond-percolation model is shown to be given by a weighted average of the conductivity associated with finite clusters over the probability distribution of a site belonging to a finite cluster.

A simple extension of the pair approximation to AC hopping conductivity in disordered systems to embrace the DC limit

The Miller-Abrahams equivalent circuit is used to motivate a simple modification of the pair approximation to AC hopping conductivity which yields transparent analytical formulae showing the correct behaviour at all frequencies including zero.

Random walks on bond percolation clusters: ac hopping conductivity below the threshold

The frequency dependence of the ac hopping conductivity in two and three dimensional lattices with random interruptions is calculated by Monte Carlo simulation of random walks on bond percolation clusters. At low frequencies the real and imaginary parts of the ac conductivity vanish linearly and quadratically with the frequency, respectively. The critical behaviour of the imaginary part of the ac conductivity below the percolation threshold is shown to depend on the long time limit of the mean square displacement of random walksR ∞ 2 , while the real part depends on the time constant of the system as well.R ∞ 2 is found to diverge with an exponentu=2ν-β according to the conjecture of Stauffer.

Ac Hopping Conductivity of a One-Dimensional Bond-Percolation Model

The exact frequency dependence of the ac hopping conductivity of a one-dimensional chain with random interruptions is obtained. The real and imaginary parts of the ac conductivity are shown to vanish quadratically and linearly, respectively, with frequency at the static limit. Critical behavior of the ac conductivity in the limit of no interruptions is discussed.

Random walks and AC conductivity of disordered systems

The controversy about the precise form of the waiting time distribution for the first observed hop in the Scher and Lax description (1973) of AC hopping conductivity of disordered systems by a continuous time random walk (CTRW) on a lattice is resolved. Starting from an exact general definition of the above waiting time distribution for random walks in the actual disordered medium, the corresponding first hop waiting time distribution for the CTRW on a lattice is shown to coincide with the distribution of waiting times between consecutive hops, as assumed originally by Scher and Lax. The authors' analysis thus supports the correctness of the Scher and Lax theory of AC conductivity of disordered systems. The relation between the random walk equation for hopping in a random medium proposed by Scher and Lax and the more familiar rate equations for site-occupancy probabilities is also established.

Cluster approximation in the theory of the AC hopping conductivity in disordered systems. II. The three-dimensional case

For pt.I see ibid., vol.12, p.2797 (1979). AC hopping conductivity calculations are performed using a method analogous to the one used in percolation theory for frequencies lower than those described by two-site models. An expression was obtained for sigma ( omega ) approximately omega f( omega tau c), f being a slowly decreasing function of omega tau c( tau c is a few orders of magnitude larger than the characteristic time in two-site models, tau 0 approximately 1/ nu ph). Over a wide frequency range sigma ( omega ) approximately omega s, with s<1, and s may depend on omega , temperature and concentration of localisation centres. Agreement between the theory and the available experimental data is discussed.

Cluster approximation in the theory of the AC hopping conductivity in disordered systems. I. One-dimensional systems

A theory is developed for the low-frequency AC hopping conductivity in disordered systems which accounts for multiple hops. The ideas of percolation theory are used to reduce the problem to a study of sigma ( omega ) (the frequency-dependent conductivity) in a cluster model. It is found that the size of the clusters increases with decreasing frequency and that sigma ( omega ) approximately omega s,s<1. An expression is obtained for the exponents. At low temperatures sigma depends weakly on temperature, but at higher temperatures it exhibits activated behaviour. Results are obtained for a one-dimensional system and compared with numerical results given in the literature.

Evidence for power law localization in disordered systems

Various lines of evidence are presented to show that for electrons in three-dimensional ordered systems there may be a regime intermediate between the extended states characteristic of weak disorder and the exponentially localized states characteristic of strong disorder. It is suggested that in the intermediate regime the wavefunctions may fall off from its maximum amplitude with a power law. A detailed study of the eigenstates of a system of 216 atoms arranged on a diamond lattice supports this suggestion. Consequences of this power law behaviour for the AC conductivity at zero temperature, the DC conductivity at low temperatures, and the AC hopping conductivity are derived.