Numerical modeling of silicon magnetic field sensors: Magnetoconcentration effects in split-metal-contact devices

The two-dimensional distributions of the electric potential, the electron concentration and the hole concentration in a silicon slab exposed to a magnetic field have been computed numerically. Generalizing the well-known Scharfetter-Gummel scheme to the case of two dimensions and nonzero magnetic field, we have employed a finite-difference technique. In case of Hall plates, where space charge is negligible, our results are in support of previous results obtained by analytical models or by conformal-mapping technique. In intrinsic or closely intrinsic silicon, our results show both magnetoconcentration and space-charge effects; these can be exploited in the design of split-metal-contact magnetic field sensors.