This is commonly justified because for many materials the piezoresistance effect dominates.
This shows a clear difference between Hall effect and piezoresistance effect: for the Hall effect we can transform devices onto the upper half plane with conformal transformation and preserve the Hall output voltage, whereas for the piezoresistance effect any direct conformal transformation onto the upper half plane would make the piezoresistive output voltage vanish.
Hence, the magnetic sensitivity of the Hall plate changes with mechanical stress due to the piezoresistance effect! Note that this is a different effect than the well-known piezo-Hall effect , which describes the change of a material property--the Hall coefficient [C.sub.H]--caused by mechanical stress.
If one uses an isotropic biaxial stress state [[sigma].sub.xx] = [[sigma].sub.yy] (e.g., in a wafer bow experiment ) to characterize the piezo-Hall effect, the current related magnetic sensitivity does not depend on the piezoresistance effect. In smart silicon Hall sensors with mechanical stress compensation the piezoresistance effect leads to a [[sigma].sub.xx] - [[sigma].sub.yy] dependence of the magnetic sensitivity, whereas the piezo-Hall effect has a [[sigma].sub.xx] + [[sigma].sub.yy] dependence: this leads to increased complexity of the compensation circuit as described in chapter 16.6.3 in .
This paper displayed similarities and differences between the reciprocal piezoresistance effect and the antireciprocal Hall effect.