Generalized Poole Frenkel (PF) effect with donors distributed in energy

Abstract

2014 Une étape supplémentaire est franchie dans la généralisation de l'effet PF, en considérant l'effet d'une répartition des donneurs, en énergie, dans la bande interdite. Différentes lois de répartition sont étudiées. Les distributions uniformes sont d'abord traitées d'une manière extensive. Les simulations numériques ont révélé des similarités évidentes avec le cas d'un seul niveau donneur. L'ionisation par le champ est ensuite déterminée pour des distributions exponentielles. Au passage, une loi exponentielle, rencontrée quelquefois dans la littérature, est analysée. Les conditions de résolvabilité de l'équation différentielle de base sont indiquées. Le calcul et la simulation sont, en outre, étendus à un système à deux bandes uniformes. Finalement, une méthode de résolution approchée est proposée, lorsque les distributions ont des formes quelconques.

Failure of Arrhenius plots for investigation of localized levels

“…TO FORMER WORKS. -As far as we know it, the essential of calculations made in [9] and [10] are original, even if some authors, like Connell et al,…”

“…-It is now necessary to investigate the reasons why the splittability principle generally fails. We believe that this comes essentially from the fact that, in equations (12), (16) and (17), as when integrating equation (3) of [10], the total density nr of conduction electrons is present in each term of the discrete sums, as well as in the infinitesimal summation leading to equations (4) therein. The respective contribution to these sums, of either of the terms, is therefore dependent on the overall contribution of all the levels involved.…”

“…This brief recall gives an idea of the upsetting, any challenge of the validity of Arrhenius plots, as a proof of the actual existence of some kind of level distribution in the gap of materials, would introduce into the practice of experimental, as well as theoretical, analyses. Now, we have developed, in two preceeding papers [9,10], an exact formulation of models with one donor level only, or with donors distributed in energy. With the help of computer simulation, we have been able to compare curves obtained in either case, when F is varied.…”

“…Developments in [9] and [10] were devoted to the analysis of curves obtained, at constant temperature under the influence of a field, either when one level only exists, or when donors are distributed in energy. The related behaviours, in terms of temperature variations, can then be deduced readily.…”

“…However, it introduces one more parameter, the band-width 03B403A6. Moreover, the saturation ratio is now necessarily defined as 039403A6p/03A62, 03A62 being the maximum donor depth (see [10], Fig. 1).…”