Semiconductor devices are described that have a metal interconnect extending vertically through a portion of the device to the back side of a semiconductor substrate. A selected ferrimagnetic constituent is associated with the sample portion, by molecular or biological attachment or by some other means, so that the sample portion is distinguished from other adjacent portions of the sample that do not have the selected ferrimagnetic constituent associated therewith. A magnetic field distribution calculating unit generates a first magnetic field equation, generates a second magnetic field equation, and solves the simultaneous equations thereof.