Space-charge anomalies in insulators caused by non-local impact ionisation

Abstract

The non-local nature of impact ionisation is modelled using lucky-drift theory with the assumption that the relevant electric field is the average field, but that the relevant drift velocity is that associated with the local field. The carrier density relevant for impact ionisation is also taken to be non-local. The model is applied to the case of a thin film insulator, with Fowler-Nordheim injections of electrons at the cathode. For clarity's sake, the authors avoid considering the excitation of holes and limit attention to the ionisation of a set of occupied deep-level states present in high concentration. Further simplifying assumptions include the neglect of diffusion, overshoot and non-parabolicity. The authors show that the non-local nature of the ionisation process reduces the local field markedly, resulting in a pile-up of free electrons to maintain current continuity in the rest of the film. This is contrasted with the prediction of local impact ionisation theory in which the field is reduced merely to that necessary to sustain a small level of ionisation. Under certain circumstances space-charge striations are produced-this is analogous to the situation in gas discharge-and for some film thicknesses a negative differential resistance occurs.

The electrical resistance of vacuum

“…'Large' means that the difference with E F , namely φ 0 + eU, is much larger than kT, which is the usual range, above E F , where conduction-band states of the metal are significantly populated in thermal equilibrium according to the Fermi-Dirac statistics (3). Upon entering the anodic plate, the hot electron releases its excess energy φ 0 + eU in scattering events with the lattice until its energy approaches E F ; the rate of energy loss is called the stopping power [15,16] and the relevant length of relaxation of energy is much longer than the mean free path associated with momentum relaxation [17,18]. This comes about because only a small fraction of the energy is relaxed in one scattering event.…”

Ionization Waves in ZNS

“…Non-local effect and dark space are incorporated in a straight forward manner ( Ridley and El-Ela, [9] ). The barrier height at the cathode is assumed to be 1.0 e.V and the deep-level trap is 3 e.V below the C.B while the shallow .…”

Impact of field-dependent electronic trapping across Coulomb repulsive potentials on low frequency charge oscillations

“…It must be emphasized, however, that the present work focuses only on the trapping process as a possible source of instabilities in semiinsulating semiconductors, but does not preclude the role of other mechanisms. For example, nonlocal impact ionization, 22 two-stream instabilities and optical phonon emission, 23 and detrapping within high-field domains 7 have also been shown to be potential sources for current oscillations and instabilities.…”