Field electron emission through and from two-dimensional electron gas

Abstract

One of the most obvious trends i n microelectronics is the rapid decrease of the device sizes. In some technological areas, such as the new sub-100 nm electron beam lithography techniques [l] or the conshuction of miniaturized x-ray tubes [2, 31, there is a strong demand of intensive, narrow energy spectrum and miniaturized electron sources. It is already known that the field emission (FE) cathodes can be used as efficient sub-micrometer electron sources. In particular, sharp silicon tips which can be easily produced with the available microfabrication technology can be used as efficient electron emitters. It was also suggested that the energy spectrum of the emitted electrons could be significantly narrowed by coating the silicon tips with various kinds of wide-band-gap (WBG) materials [4]. To some extent the energy filtering of the emitted electrons performed by such coatings is similar to the wavelength-selective interferential devices used in optics. However, for the FE case, it turns out that the semiconductor interface layer (IL), where the carriers' behavior is affected by the penetrating electric field, plays a crucial role in the electron transport across the boundary.Usually, the IL electrons are said to form a two-dimensional (2D) gas. Despite of both its importance and the great deal of effort devoted to the subject [5, 61, it is still not clear to what extent IL electrons participate in the field emission current. The present paper aims to bring more insight to the subject by considering a simplified model of the semiconductor and vacuum interfaces. The potential energy of the electrons is taken as linear in all the significant regions ( Fig. 1) and its origin is assumed to be at the bulk value of the an ultra-thin layer of wide bandgap material used in the semiconductor conduction band minimum,The semiconductor is considered to be ncalculations.type doped. Such a simplified model of potential energy allows the exact description of the wave functions envelopes as linear combinations of Airy functions [7] (except for the bulk, where the envelopes are plane waves). The energy offset produced by the penetrating field in the direction transverse to the interfaces is actually splitting the electronic states in two main parts corresponding to the probability currents along the field. The states with positive energy carry non-zero transverse probability current and the related electrons can be therefore transmitted from the bulk semiconductor to the vacuum through the 2D and WBG regions. Since there is a finite probability that the electron can be reflected hack into the hulk region, such electron transport will be termed as scattering. On the contrary, no transverse current is associated to the states. with negative energy. The corresponding states appearing in IL may accordingly be designated as quasi-bound states. Electrons residing in such states may still decay into the vacuum, but the process is essentially different. The corresponding leakage current commences f.om the 2D region and is of a purely t...