  We use laser-based spin- and angle-resolved photoemission spectroscopy
(laser-SARPES) with high-resolution, and experimentally determine, for the
first time, the Rashba-parameters of quantum well states (QWSs) systematically
changing with the film thickness and the quantum numbers, through the
observation of the Ag films grown on an Au(111) substrate. The data are very
well reproduced by the theoretical calculations based on the density functional
theory. Most importantly, we find a scaling law for the Rashba parameter
($\alpha_{\rm R}$) that the magnitude of $\alpha_{\rm R}$ is scaled by the
charge density at the interface and the spin-orbit coupling ratio between the
film and the substrate, and it is expressed by a single straight line
regardless of the film thickness and the quantum numbers. The new finding not
only is crucial to understand the Rashba effect in QWSs but also gives a
foundation of film growth engineering to fine-tune the spin splitting in 2D
heterostructure systems.
