Electron Dynamics in Surface States of NFE and Nobel Metals with Al and Cu
as First Examples
Robert Keyling, Wolf-Dieter Schöne, and Walter Ekardt
Energy and lifetimes of electrons in Surface states on various low index surface states are determined from first principles in the following way:
a) The electronic structure of the surface in the ground state is obtained by solving the KohnSham (KS) equations for a slab geometry. In this way we can use any first principle solid state
code available, e.g., the pseudopotential plane wave code fhi96md or the Full Potential Linearized Augmented Plane wave code (WIEN97).
b) The straightforward application of this procedure allows only relatively thin slabs to be considered (e.g., 9 layers of Cu plus 9 layers of vacuum). Whereas this is sufficient for the selfconsistent determination of the surface barrier it is not sufficient for the determination of the
surface states. The reason for this is that the two surface states formed on the two surfaces of
a slab overlap strongly to form two coupled states (an odd one and an even one) whose energetic mean value converges rapidly towards the position at a free surface.
c) As the lifetime of a state depends sensitively on the exact energetic position (relative to the
Fermi edge) it does not make sense to calculate the lifetimes for the two states and to calculate the corresponding mean value. For a reliable first principle determination of the lifetime
in surface states the two states have to be decoupled. To achieve this decoupling very thick
slabs (~ 40 layers) are to be considered. However, this is very time consuming and almost impossible with our available computing facilities.
d) We therefore apply a method known from car industry, namely a so-called stretching. In this
way, we are able to consider very thick slabs with fully converged surface state energies. The
remaining amount of splitting can be made arbitrarily small.
e) Finally after the energy and wave functions of the surface state are determined its lifetime is
calculated in the usual way.
In this way we are able to provide a benchmark for some approximate methods in use (e.g.,
Liebsch's two-phase model or Chulkov's model potential calculation). The decisive advantage of
the method is its transferability to the situation of recently observed lifetimes of electrons in
chemisorbed states – Cs on Cu (111) (Aeschlimann, Petek) – and to the determination of lifetimes
of electrons relevant for chemical reactions at surfaces as measured by DIMET experiments [see
M. Wolf's catalytic oxidation of CO on Ru(0001)].