  The effect of silicon-oxide interface roughness on the weak-localization
magnetoconductance of a silicon MOSFET in a magnetic field, tilted with respect
to the interface, is studied. It is shown that an electron picks up a random
Berry's phase as it traverses a closed orbit. Effectively, due to roughness,
the electron sees an uniform field parallel to the interface as a random
perpendicular field. At zero parallel field the dependence of the conductance
on the perpendicular field has a well known form, the weak-localization
lineshape. Here the effect of applying a fixed parallel field on the lineshape
is analyzed. Many types of behavior are found including homogeneous broadening,
inhomogeneous broadening and a remarkable regime in which the change in
lineshape depends only on the magnetic field, the two length scales that
characterize the interface roughness and fundamental constants. Good agreement
is obtained with experiments that are in the homogeneous broadening limit. The
implications for using weak-localization magnetoconductance as a probe of
interface roughness, as proposed by Wheeler and coworkers, are discussed.
