Injected Electron Currents Through Insulators

Abstract

The previously presented unified theory of field and thermionic emission is extended to electron emission into dielectrics, including thin films between two metal electrodes. The current equations are derived under the assumption of a parabolic energy-momentum dependence and convenient barrier shape approximations for various thicknesses of the insulating layer, but the general method is used in the case of any arbitrary barrier shape. Both cases of equal and unequal effective electron masses in the insulator and the metals are considered. The current expressions obtained are applicable to the whole range of fields and temperatures between the limits of thermionic and field emission.Die friiher vorgelegte einheitliche Theorie der Feld-und Thermoemission wird auf die Elektronenemission in Dielektrika erweitert, einschliellich dunner Schichten zwischen zwei metallischen Elektroden. Die Stromgleichungen werden unter der Annahme einer parabolischen Energie-Impuls-AbhLngigkeit und geeigneter Niiherungen fiir die Barrierenform fur verschiedene Dicken der isolierenden Schicht abgeleitet, jedoch wird die allgemeine Methode fur den Fall einer beliebigen Barrierenform benutzt. Es werden sowohl der Fall gleicher wie ungleicher effektiver Elektronenmassen im Isolator und Metal1 berucksichtigt. Die erhaltenen Stromgleichungen sind fur den gesamten Feld-und Temperaturbereich zwischen den Grenzen der thermischen Emission und der Feldemission anwendbar.

Current-field and current-temperature dependences for AlAl2O3Al junctions in the regions of thermionic, field, and TF emission

“…As far as the effective electron mass and the metalinsulator work function were determined in the region of pure thermionic emission where no tunnelling occurs, the proof of the theory in the intermediate and the extended region of field emission, where tunnelling determines entirely the current, is carried out without any adjustment of parameters. Therefore, there is reason to consider the results of the present work as a rather satisfactory confirmation of the general theory of electron currents through dielectrics [4] with a large energy gap.…”

Electron currents across metal–semiconductor interfaces

“…On the basis of this theory one can calculate sufficiently accurately the energy distribution of the electrons transferred and the current flowing through a n arbitrary insulating region between two conductors under all possible emission conditions. Similar results on electron emission from metals [16] and semiconductors [17] in vacuum and dielectrics [18] are special cases of this more general treatment. These investigations were reviewed very recently [19].…”

“…may be used instead of the Fermi-Dirac function(18). For the energy range A, (0 < U < p') it is appropriate to make the expansion (1 1) for Ho( U ) about the Fermi level of the semiconductor ( U, = pI) or the metal (U,, = p,) when calculating jI and jII in (IS), respectively.…”

The values of the functions θ(y), t(y), and φ(y) in the unified theory of electron emission in the range 1 ≠ y ≠ 5

“…The unified theory has been recently extended by Christov (10) to include the injected electronic currents through dielectric layers between two metals. In the Short Notes In Table 1 the values of 8 (y), t(y), and (y) in the range 1 L y r 5 are presented.…”