Galvanomagnetic phenomena and surface roughness in thin metallic films

We study the galvanomagnetic properties of an electron gas in quasibidimensional structures such as thin films, submitted to a magnetic induction perpendicular to their surfaces. The confinement generates electronic quantum states that are gathered in a subband scheme. We determine the electron distribution functions in the different subbands by solving the appropriate set of Boltzmann equations. Then we derive the general expressions of transport coefficients and discuss the variations of the Hall effect and magnetoresistance with film thickness in the special case in which electrons are scattered by impurities and surface roughness. In thin metallic films where the correlation length describing surface roughness is less than the electron Fermi wavelength, we find a Hall constant proportional to thickness d and a magnetoresistance that follows a ${\mathit{d}}^6$ law.