An Analytical Theory of Piezoresistive Effects in Hall Plates with Large Contacts

Figure 13

Sensitivity of output voltage versus mechanical stress (normalized to supply voltage ) for a circular device of Figure 12. All other components of the stress tensor vanish, as well as . The plots are graphical representations of (26b), (28b), (28c), (18a)–(18i), and (19b) in the limit of small stress and with the piezoresistive coefficient for low p-doped silicon. Largest stress sensitivities are obtained for contact size with a flat maximum. The black curve denotes offset-free devices with at zero stress; they are the only ones, where at zero stress. The black curve goes through the maximum of the surface. The contours in (b) are for 48.25, 48, 47.5, 47, 46.5, 46, 45, 42.5, 40, …, 22.5, 20%/GPa. In (a) the steep slopes of the surface near and are only sketched due to numerical problems.

(a)

(b)