Investigation of Cu and Ni Band Structure above the Vacuum Level Using Low Energy Electron Reflection

Abstract

Incidence angle dependent elastic electron reflection curves in the 0 to 30 eV range are measured on Cu(ll1) and Ni(ll1) using target current regime. They are compared with the calculated ones. Computations are made very fast using a simple approximation. The extrema of the reflection energy derivative are shown to correspond unambigiously to definite critical points of bands. These points are mapped when the energies of the experimental extrema are compared with the calculated ones. Varying the incidence angle, in this way bands in the variety of Brillouin 7one directions may be investigated.

E(k) above the Vacuum Level from Low Energy Electron Reflection. ΓK Line of Cu and Ni

“…This masking may be understood analysing the Fourier expansion of wave functions. Near any of these points the Bloch function is the sum of plane waves exp (i(k + C ) v) that did not contain any "conducting" component [6] associated with the primary plane wave exp ( X v ) (this component is discriminated by its k l l + Gll being equal Kll). In this case matching of wave functions on the surface [2] gives no excitation of this Bloch function and the associated CP cannot manifest itself.…”

“…The data on Ni are similar to the data on Cu because of the similarity of their upper states. Calculated dRldE curves were obtained applying the conducting Fourier approximation [6]. This approximation reduces the calculations to primitive band structure calculations with a sufficiently close mesh of k, along k , , = KlI + g rods of BZ and this enables very fast computations within a wide range of incident Kll.…”

“…The basis for band mapping above the vacuum level using LEED is delivered by the matching approach [2 to 41: every feature of the elastic reflection coefficient R is associated with a definite feature of the band structure [5,6]. But direct band mapping is usually hindered by inelastic smoothing of experimental R(E) curves [7].…”

“…An algorithm to overcome these difficulties is proposed in [6,7]. Briefly, each extremum of the dR/dE curve is caused by the rapid change of Bloch functions, taking place in a definite critical point (CP) of the band or in its immediate proximity.…”

Mapping the excited-state bands above the vacuum level with VLEED: principles, results for Cu, and the connection to photoemission

“…The theoretical foundation for VLEED investigations is the matching approach [12,13,14], which links the elastic reflectivity R(E) to the properties of the Bloch waves excited in a crystal, including their dispersion. However, detailed band mapping from VLEED data was demonstrated only recently [15,16,17], using the no-absorption approximation. It has been found that an incident beam of energy E and parallel wave-vector component K significantly excites only so-called coupling bands.…”