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The ratio of the imaginary and real parts of the a.c. hopping conductivity is evaluated numerically in the pair approximation for some simple models. The results confirm the analytical formula 0·293 log (ωτ0)-1 where τ0 is a time constant. The application of this formula to experimental data is discussed.

Applying the Monte Carlo technique, we have simulated the time decay of a reservoir of geminate electron - hole pairs for one- and three-dimensional lattices where the site energies are subject to a Gaussian distribution of width σ. As a result of disorder the recombination spectra shift towards longer times, broaden, and lose their power-law decay pattern. The average recombination time [τr] scales with exp (σ/T)2. This behaviour reflects dispersive motion of the carriers within their mutual Coulombic well. A relationship is proposed that allows one to predict [τr] once the dispersive parameter α for the transport process is known, independent of the type of distribution of hopping sites. Comparison is made with experimental data for a-Si: H and a-As2S3.

Decay of donor phosphorescence is used as a sensor for time-dependent diffusion of triplet excitons in an amorphous organic solid (benzophenone) where diagonal disorder of the hopping sites prevails. The exciton jump rate is found to follow a tα-1 law. Between 4·2 K and 100 K the dispersion parameter α increases from 0·25 to 0·55. The results are compared with computer simulations based on experimental data for the density-of-states distribution.

Field- and temperature-assisted dissociation of carrier pairs produced by the absorption of radiation has been simulated for perfectly isotropic (3D) and perfectly linear (1D) systems composed of a discrete array of hopping sites, as well as for systems with anisotropic hopping rates parallel and perpendicular to a preferred direction. For the 3D and 1D systems the exact solutions of the Onsager formalism are recovered. In neither case is Poole - Frenkel behaviour observed. The dissociation yield increases with increasing separation a of the hopping sites. The governing parameter is ΔU/kT, where ΔU, which is a function of a, is the difference in potential energy between the sites at which a carrier starts its random walk and the nearest-neighbour site in the direction of the field. Agreement with experimental data for organic solids indicates that the assumption of field-independent hopping rates implicitly contained in both simulations and analytic theory is justified. Anisotropy of the carrier transport coefficient has a marked effect on the zero-field dissociation yield. On the basis of the computer results, an analytical expression is proposed that relates φ(E = 0) and μ|/μ⊥. The effect of finite sample size on the zero-field yield is also treated quantitatively.

The resonant and non-resonant luminescence changes in a-silicon are considered. It is suggested, that the effect is closely related to the anomalous spin-dependent magnetoresistance and photoconductivity changes observed in evaporated and glow-discharge-deposited silicon. The novel feature here is the existence of stable quenching lines. This considerably reduces the choice of recombination models to either a geminate radiative process with singlet-spin memory or to the usual localized-localized recombination process with a spin-dependent, non-radiative transition. The steady-state and time-dependent features of the latter model are analysed. The results are in good agreement with experiment if the exchange interaction between the spins is assumed to be negligibly small. Some interesting and novel time-dependent effects are found and related to recent observations. In particular, it is found that microwave chopping can turn a quenching line into an enhancing one. The problems associated with exchange-coupled spins are discussed. It is concluded that anomalous spin effects in pair models can only be expected for the recombination of distant electron-hole pairs.

The resonant and non-resonant photoconductivity changes due to a magnetic field and an additional microwave field are ocnsidered. The effect is shown to bear a close relationship to the anomalous spin-dependent magnetoresistance observed in amorphous semiconductors. It is suggested that a spin-dependent, non-radiative recombination process is responsible for the resonant and non-resonant photo-conductivity changes. Interesting time-dependent effects are found; in particular microwave chopping can turn a quenching line into an enhancing one. The problems associated with exchange-coupled spins are discussed. We compare our results with our recent luminescence results and conclude that the same model can account for both experiments.

Using the Monte Carlo technique, the time dependence of the dissociation of a Coulombically bound electron-hole pair has been simulated for both a regular cubic lattice and a one-dimensional linear chain as a function of applied electric field. In contrast to pair recombination, the dissociation kinetics turn out to be strongly affected by the stochastic character of carrier diffusion in the vicinity of the maximum potential. The results are compared with the predictions of an analytical treatment and discussed in terms of experimental realization.

The time dependence of recombining geminate pairs in a hopping system has been simulated as a function of the initial pair separation r0, the anisotropy of the diffusion constant, the dimensionality, the concentration of hopping sites and the final-step recombination velocity. It is found that the decay of the recombination rate R follows a power law, R ∼ t-x, with x ≥ 3/2. Both the exponent x and the initial onset of the recombination rate depend on r0 and the dimensionality. In the time domain of experimental relevance, significant deviations from the asymptotic form of the analytic solution of Hong and Noolandi are found. The introduction of anisotropy in the carrier mobility yields a multiplicity of decay rates. On the other hand, if the final recombination step is hindered by an energy barrier, the recombination kinetics ultimately become exponential.

Motivated by the recent work of Santos Lemus and Hirsch and of Pai, Yanus and Stolka on the concentration dependence of hole transport in selected molecularly doped polymers, a Monte Carlo computer study has been conducted. It predicts that transport should in principle exhibit percolative features without, however, showing a well-defined percolation threshold ("pseudo-percolation"). A threshold concentration c0 for pseudo-percolation will be defined. In a van der Waals solid with exponential wavefunction overlap it decreases with decreasing wavefunction localization because of non-nearest-neighbour jumps. A relation between c0 and the effective coordination number of the lattice, defined via overlap, is established. For c < c0 the carrier mobility remains finite and follows approximately a power law, μ∝cm, in accord with experiment. The exponent m increases with increasing localization of the wavefunction which depends on the energetic separation between the transport levels of dopant and host.