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

Table 1

Mechanical stress sensitivity of rectangular device from Figure 9: comparison of numerical simulation (FEM) versus analytical theory. , , . The small residual output voltage of the FEM in the first line is probably due to insufficiently fine mesh. In the last line the stress difference is so large that gets nearly zero. Then gets large (~48.9), gets small (~0.13), gets small (~0.0017), and the output voltage approaches the supply voltage. For even larger stress difference the first-order piezoresistive theories (6a) and (6b) break down and also the numerical simulation gives meaningless results.

			FEM	theory	FEM	theory
0	0	1.00000	−0.000229		1.27104	1.27140
10	0	1.00025	0.004341	0.004570	1.26859	1.26895
0	10	1.00025	−0.004792	−0.004563	1.27416	1.27453
10	10	1.00055	−0.000229		1.27174	1.27210
1000	900	1.04998	0.043525	0.043750	1.30872	1.30910
−1000	−900	0.94523	−0.048074	−0.047841	1.23156	1.23190
856	−600	0.05801	0.994747	0.994751	0.45175	0.45216