  The resistance of a homogeneous semiconductor increases quadratically with
magnetic field at low fields and, except in very special cases, saturates at
fields much larger than the inverse of the carrier mobility, a number typically
of order 1 Tesla. Here, we argue that a macroscopically disordered and strongly
inhomogeneous semiconductor will instead show a non-saturating
magnetoresistance, with typically a quasi-linear behaviour up to very large
fields, and possibly also extending down to very low fields, depending on the
degree of inhomogeneity. We offer this as a possible explanation of the
observed anomalously large magnetoresistance in doped silver chalcogenides.
Furthermore, our model of an inhomogeneous semiconductor can be developed into
magnetoresistive devices that possess a large, controllable, linear response.
