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

Table 2

Mechanical stress sensitivity of a circular device from Figure 10(a): comparison of numerical finite element simulation (FEM) versus analytical theory. is the resistance between the -contacts in Figure 10(a) and is the resistance between the -contacts in Figure 10(a). The mesh of the FEM-simulation had 2.66 million elements and the model used Lagrange multiplier and the piezoresistivity matrix from (6a) to (6c) with , , and . The theory used (18d), (18e), (18g), (18h), (18i), (28b), (28c), and (26b) for . For we swapped with in (28b) and (28c) and with , and we replaced in (26b).

​; °	​; °	​	​			​; FEM	​; Difference FEM vs. theory	​; FEM	​; Difference FEM vs. theory
17	55			1.000000	1.00000	1.264527		0.796063
17	55			0.999976	1.006929	1.262001		0.800431
17	55			0.997613	1.071608	1.236262		0.838836
17	55			0.723332	2.337100	0.641383		1.068508
17	55			0.723332	0.427881	1.180510		0.280305
17	55			0.972803	1.073496	1.204879		0.819107
17	55			1.022421	1.069814	1.267640		0.858564
17	55			0.972803	0.931536	1.254778		0.731615
17	55			1.022421	0.934742	1.317534		0.771065
55	17			0.723332	2.337100	0.280305		1.180511