Miniaturized Delta-E Effect Magnetic Field Sensors

Magnetoelectric delta-E effect sensors utilize the change in the elastic modulus of the magnetostrictive material upon applying a magnetic field, resulting in a shift in the resonance frequency. Such sensors have demonstrated the potential to detect small-amplitude and low-frequency magnetic fields. It was also shown that the limit of detection can be improved by using sensor arrays including a large number of sensor elements [1]. However, building compact arrays and achieving high spatial resolutions using mm-sized sensors is challenging. Moreover, the reproducibility of the sensors is significantly impacted by the anisotropic stress developing in the magnetic layer upon releasing the resonator during the fabrication process [2]. Additionally, sensors with a cantilever design suffer from inhomogeneous magnetic properties caused by different stress relaxation at the clamping region affecting their performance [3]. Here, we present an experimental and theoretical investigation of µm-sized delta-E effect sensors employing a free-free beam design that overcomes the limitations and challenges encountered in previous approaches. To control and minimize the residual stress in the magnetic layer, we use a shadow-mask deposition technique where the magnetic layer is deposited on the released resonators. The spatial stress distribution can be accurately determined by combining displacement measurements with a magneto-mechanical model. Different resonance modes are identified, and the dependency of the resonance frequency shift and the sensitivities on these modes are established. The influence of the anchors and the stiffness tensor components on the resonance frequency shift are analyzed by combining a magnetoelastic macrospin model and an electromechanical finite element model. Noise performance and the limit of detection of different sensor geometries are investigated to gain general insight into the relationship between geometry, resonance mode, and sensor performance. We demonstrate extreme stress control with a minimal change of smaller than 8 MPa in the normal stress components (σ₁₁ and σ₂₂) and smaller than 2 MPa in the shear stress component (σ₁₂) following the deposition of the magnetic layer. We find that the delta-E effect and sensitivities exhibit strong dependence on resonance modes, attributed to distinct variations in local magnetic and mechanical properties specific to each mode. We identify the optimum mode shape and achieve detection limits below 300 pT/Hz^1/2 at 10 Hz, comparable to macroscopic sensors [4,5]. Overall, we demonstrate the successful production and miniaturization of delta-E effect sensors with high reproducibility and similar performance to the macroscopic sensors using the proposed manufacturing process and sensor design. The achieved miniaturization and reproducibility represent a significant step toward developing fully integrated sensor arrays and emphasize the potential for high spatial resolution and improved detection limits with large sensor arrays or using flux concentrators.<br/><br/>[1] B. Spetzler, P. Wiegand, P. Durdaut, M. Höft, A. Bahr, R. Rieger, F. Faupel, <i>Sensors</i> <b>2021</b>, <i>21</i>, 7594<br/>[2] A. D. Matyushov, B. Spetzler, M. Zaeimbashi, J. Zhou, Z. Qian, E. V. Golubeva, C. Tu, Y. Guo, B. F. Chen, D. Wang, A. Will-Cole, H. Chen, M. Rinaldi, J. McCord, F. Faupel, N. X. Sun, <i>Adv. Mater. Technol. </i><b>2021</b>, <i>6</i>, 2100294.<br/>[3] B. Spetzler, E. V. Golubeva, R. M. Friedrich, S. Zabel, C. Kirchhof, D. Meyners, J. McCord, F. Faupel, <i>Sensors </i><b>2021</b>, <i>21</i>, 2022.<br/>[4] S. Zabel, C. Kirchhof, E. Yarar, D. Meyners, E. Quandt, F. Faupel, <i>Appl. Phys. Lett.</i> <b>2015</b>, <i>107</i>, 152402.<br/>[5] P. Durdaut, J. Reermann, S. Zabel, C. Kirchhof, E. Quandt, G. Schmidt, R. Knöchel, F. Faupel, M. Höft, <i>IEEE Trans. Instrum. Meas.</i> <b>2017</b>, <i>66</i>, 2771.