Image resonances at the Schottky barrier

Abstract

A density of barrier-image resonance states and the corresponding charge distributions are calculated -outside the metal -when an external negative electric field is applied to a free-electron-like tungsten surface. A possibility of detection of such resonances in the photofield emission experiment is discussed.The aim of this Brief Report is to discuss properties of the barrier-image resonance states (BIRS) in an external "negative" electric field using densities of such states calculated outside the metal, that is, in a surface region of the Schottky barrier.The idea of BIRS has been recently introduced in Refs. 1 -3. Such resonances form, in fact, a special class of the well-known image states ' -they are always localized outside the metal. However, in contrast, to the image states, their existence does not need any gap in the band structure of a metal, i.e. , the electron may freely propagate in it.In Ref. 6, these resonances were studied in the presence of an external "positive" electric field and their role in the field-ionization process was discussed. On the other hand, it has been suggested that the image states at Ni(111) might be involved in the field emission phenomena. However, the most typical material for such experiments is tungsten. Remembering that BIRS (like image states) lie close to the vacuum level, it is justified to treat tungsten within the free-electron approximation. This creates a possibility to calculate analytically properties of BIRS at tungsten surfaces under the field emission conditions (i.e. , in the presence of an external negative electric field).In this Brief Report we present our preliminary calculations for the tungsten surface with the cutoff approximation of the Schottky barrier near the metal surface [the more realistic, so-called JJJ model, seems to smooth over the barrier resonance peaks, as shown in Refs. 1 and 2 for the free-electron Al(111) -nevertheless, a detailed comparison of both approximations for tungsten will be presented in a forthcoming paper].The Schottky barrier V(x) is assumed to have the following form (in the Hartree atomic units):Vo -