(a) Schematic of investigated magnetoelectric sensor structure based on an insulating magnetostrictive (MS) layer and a piezoelectric (PE) layer on a cantilever substrate (Sub) with a weight at the tip. The position of electrode 2 is optimized. (b) Schematic of sensor with conductive MS layer structured with trenches for electric insulation. 

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... shown schematically in Fig. 1(a), the cantilever sen- sor is assumed to consist of a silicon cantilever substrate that is clamped rigidly on the bottom left and has two bending regions of lengths L 1 and L 2 and heights h 1 and h 2 . The silicon substrate is assumed to be conductive and serves as the bottom electrode for the piezoelectric layer (alternatively, a ...

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... electrode design concept may be transferred to conductive magnetostrictive materials by electrically sepa- rating different regions of the magnetostrictive material with small trenches, as depicted in Fig. 1(b). The conduc- tivity of the magnetostrictive material forces a constant electric potential at the interface between the piezoelectric layer and the respective area of the magnetostrictive ma- terial. In the following, we calculate the electric potential distribution in the cantilever beam using FEM. From the Manuscript received ...

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... we consider the case of cantilever substrates with- out a weight at the tip (h 1 = h 2 in Fig. 1) and compare the induced electric potential at the surface for conductive and insulating magnetostrictive materials. The geometric parameters of the cantilever are chosen as depicted in Fig. 1(a) with a total cantilever length of 2.5 mm. an h-field of 400 a/m is applied along the cantilever by setting the magnetic potential on the ...

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... we consider the case of cantilever substrates with- out a weight at the tip (h 1 = h 2 in Fig. 1) and compare the induced electric potential at the surface for conductive and insulating magnetostrictive materials. The geometric parameters of the cantilever are chosen as depicted in Fig. 1(a) with a total cantilever length of 2.5 mm. an h-field of 400 a/m is applied along the cantilever by setting the magnetic potential on the surfaces at x = 0 to V m = 0 and at the surfaces at x = 2.5 mm to V m = 1 a. The bottom electrode 1 is set to an electric potential of 0 V. Fig. 2 plots the resulting electric potential ...

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... optimal value of h 1 = h 2 = 100 µm derived here is valid for the geometric parameters defined in Fig. 1. For other ratios of geometric parameters, the solution must be recomputed to determine the optimal substrate thickness and electrode position. Table I lists the optimal cantilever substrate thickness h 1 = h 2 = h opt for other active layer thicknesses h PE = h Ms with other parameters identical to the ones given in Fig. 1. For ...

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... parameters defined in Fig. 1. For other ratios of geometric parameters, the solution must be recomputed to determine the optimal substrate thickness and electrode position. Table I lists the optimal cantilever substrate thickness h 1 = h 2 = h opt for other active layer thicknesses h PE = h Ms with other parameters identical to the ones given in Fig. 1. For thinner active layers, the optimal substrate thickness is thinner as well and (within the 10 µm simulation step resolution) identical to the ac- tive layer thickness. Fig. 5(a) plots the electric potential on the surface of an insulating magnetostrictive layer for each of the five optimal cases of Table I. It is observed that the ...

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... com- plete width of the cantilever, as depicted in Fig. 6(b), a reduced voltage is observed, as seen in Fig. 6(c). These results demonstrate that the optimal electrode positioning depends on the cantilever aspect ratios. Because of the linear constitutive laws, a scaling of all cantilever dimen- With other Parameters Identical to Those Given in Fig. 1(a). simulations were carried out in steps of 10 µm for h 1 = h 2 . V max is the maximum voltage from Fig. 5 along the center line shown dashed in Fig. 2(b). V avg is the average voltage along the center line. allowing for a drop in voltage by 5% from the maximum in Fig. 5, the optimal electrode 2 should extend from x 1 (95%) to x 2 (95%) ...

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... a constant silicon substrate thickness of h 1 = 100 µm is assumed for the trench with the other param- eters given in Fig. 1. The length L 2 of the weight and the thickness h 2 are varied. Figs. 7(a) and 7(b) show an example of the induced voltage on the surface for a trench length of L 1 = 300 µm, a weight length of L 2 = 1700 µm and a weight height h 2 = 300 µm. above the trench, a significantly higher induced voltage of 0.042 V is observed compared with ...

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... region is positioned at the tip of the cantilever, with a maximum voltage value of 0.041 V. In Fig. 8(c), the resulting maxi- mum induced voltage for a systematic variation of h 1 and h 2 is given (L 1 = 1500 µm and L 2 = 500 µm in all cases). Fig. 2(b) for five different layer thicknesses h PE = h Ms = h 1 = h 2 with other parameters the same as Fig. 1(a). (b) optimal placement of electrode 2, allowing for a 5% drop from the maximum voltage V max for the case of h PE = h Ms = h 1 = h 2 = 100 µm and length L = 2.5 mm. The electrode extends from x 1 (95% V max ) = 20.8% L = 0.52 mm to x 2 (95% V max ) = 80.4% L = 2.01 mm. optimal voltage values are obtained if either h 1 or h 2 has a ...