A one-dimensional system of Si(111)-(5 x 2)-Au is explored using scanning tunneling microscopy and spectroscopy. The chain of Si adatoms called bright protrusions (BP's) is found to be semiconducting with an evanescent state in the gap, which originates from adjoining metallic BP-free segments. A quantitative analysis shows that the evanescent state decays in inverse-Gaussian form, leading to an appearance of a parabolic BP chain, and scales to its chain length. Spatial decay of the state suggests a quadratic band bending and the existence of a Schottky-like potential barrier at the interface driven by charge transfer.