Periodicity and thickness effects in the cross section of quantum well states

The photoemission cross section of quantum well states in very thin Cu films has been analyzed as a function of photon energy within a wide energy range. We show that this cross section is periodical in k space, peaking around vertical transitions of the respective Cu bulk band. The cross section peak width is analyzed in terms of final- and initial-state wave vector broadening. The latter can only be detected at low kinetic energies due to reduction of final state broadening. The initial state k(perpendicular to) broadening increases when the Cu film gets thinner, as simply expected from the uncertainty principle.