Nanoscale surface optical constants of copper determined by angle-resolved photoemission

Abstract

We study angle-resolved photoemission peak intensities I( ψ) on Cu(1 1 0) and Cu(1 1 1) surfaces varying the light incidence angle ψ of p-polarized light with photon energies between ℏω=8.44 eV and ℏ ω=21.22 eV. Transitions out of several initial states are probed, including the well-known surface states at the Γ - and Y -point, bulk bands of sp- and d-like orbital character, as well as an oxygen-derived adsorbate state on Cu(1 1 0)(2×1)O. All data can well be explained within the dipole approximation I(ψ)=| A → (ψ,ε)· P → fi | 2 , where A → is the vector potential of the photon field and P → fi the momentum matrix element. Especially it is not necessary to include “surface photoemission” via a 〈 f| div A → | i〉 term in the photoemission matrix elements. However, quantitative agreement with experimental data is obtained if and only if A → is calculated using Fresnel's equations with a modified surface optical constant ε s, which differs drastically from the bulk parameters ε b. Surprisingly independent of ℏ ω all results can be explained using ε s=(1.0±0.1)+i(0.1±0.1), which is much closer to the vacuum value than to ε b.