Empty electronic states at the (100), (110), and (111) surfaces of nickel, copper, and silver

We have performed a systematic investigation of empty electronic surface states on the (100), (110), and (111) faces of nickel, copper, and silver using momentum-resolved inverse photoemission spectroscopy at ħω=9.7 eV. We present the measured two-dimensional energy-band dispersions E($k_{?}$) and discuss common trends. All the observed surface bands can be classified as being either crystal induced or image-potential induced. The former class of surface states is well known from ordinary photoemission and occurs in bulk band gaps as a consequence of the termination of the three-dimensional crystal periodicity. Image-potential states arise from the long-range forces which describe the screening of an electron approaching a metal surface by the conduction electrons and have no filled counterpart. The relationship between the two kinds of states can be qualitatively understood in terms of a one-dimensional model proposed by Echenique and Pendry. Numerical calculations are necessary for quantitative understanding. Comparison of the experimental data to such calculations is made where available. We conclude that the systematics of unoccupied sp-like surface states on fcc transition metals are now well established.