Size effects on the Hall constant in thin gold films

We report the Hall constant R H , drift mobility μ D , and Hall mobility μ H measured at 4 K in thin gold films deposited on mica substrates, where the dominant electron scattering mechanism is electron-surface scattering. R H increases with increasing film thickness and decreases with increasing magnetic field. For high magnetic fields B ≥ 6 T , R H turns out to be approximately independent of magnetic field, and its value is close to that of the free electron model. We use the high magnetic field values of R H to determine film thickness. This nondestructive method leads to a determination of film thickness that agrees to within 10% with the thickness measured by other techniques. The theoretical predictions, based upon the theory of Fuchs-Sondheimer and the theory of Calecki, are at variance with experimental observations.