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We present two-dimensional numerical simulations of two types of integrated silicon magnetic-field sensors realized recently in standard CMOS technology, viz. the split-drain MOSFET and the vertical Hall-effect device sensitive to magnetic fields perpendicular and parallel to the chip surface, respectively. Our results include potential, current, and surface charge distributions as well as sensitivity, linearity, and noise. Improved device geometries are suggested. Both the finite-difference method and a novel Greens function approach are used for solving the differential equations governing the carrier transport in the presence of a magnetic field.