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

Figure 7

Sensitivity of output voltage versus mechanical stress (normalized to supply voltage ) for a device of Figure 6 operated in the same way as in Figure 6. All other components of the stress tensor vanish, as well as . (a) is a 3D-plot and (b) shows the contour lines thereof. In (a) the steep slopes of the surface near and and are only sketched due to numerical problems. The plots are graphical representations of (18a)–(18m) in the limit of small stress and with the piezoresistive coefficient for low p-doped silicon. Largest stress sensitivities are obtained for aspect ratios . The dependence on contact size is small, but tends to be best. The black curve denotes offset-free devices with , where at zero stress. The maximum of the surface does not lie on this curve. The contours in (b) are for 46.75, 46.5, 46, 45, 44, 42.5, 40, …, 22.5, 20%/GPa.

(a)

(b)