ΔE-Effect Magnetic Field Sensors

Abstract

In recent years, magnetoelectric ΔE-effect sensors have been investigated for the detection of small amplitude and low-frequency magnetic fields that typically occur in many biomedical and diagnostic applications. Such sensors are based on magnetoelectric composite resonators, which consist of mechanically coupled magnetostrictive and piezoelectric materials. They can be processed on a large scale by microelectromechanical system (MEMS) technology with dimensions of a few millimeters down to a few micrometers and are compatible with complementary metal-oxide-semiconductor (CMOS) electronics. Furthermore, they can be operated at room temperature with a broad-bandwidth and a large dynamic range and are robust against microphony and mechanical noise. Such sensors utilize the ΔE-effect of the magnetostrictive material, i.e. the change of the mechanical stiffness tensor with magnetization and hence, with an applied magnetic field.Since our first publication of this sensor concept in 2011 [1], much progress has been made in understanding the complex interplay of magnetic, mechanical, and electrical properties and their influence on signal and noise of the sensor system. This holds for different designs of magnetoelectric MEMS cantilevers, but also for surface acoustic wave devices [2]. Here, we present recent experimental and theoretical results on the ΔE-effect, the sensitivity, and the noise of magnetoelectric ΔE-effect sensors. The sensors consist of magnetoelectric MEMS resonators with sputter-deposited AlN or Al73Sc27N as a piezoelectric material and soft-magnetic (Fe90Co10)78Si12B10-based single or multilayers.A magnetoelastic macrospin model of the ΔE-effect in all stiffness tensor components is presented and combined with a finite element electro-mechanical model of the resonator. First and higher order torsion (Fig. 1) and bending modes are compared and analyzed regarding the sensitivity and the ΔE-effect [3]. Measurements and simulations reveal the dependency of the sensitivity on the mode number, caused by the geometry, mode shape, and the ΔE-effect in different stiffness tensor components. Specific rules for the resonator design are derived as a result.Besides the geometric and magnetic material properties, we find that the resonator loss and the piezoelectric material have a decisive impact on signal and noise. The influence of the quality factor Q [4] and the piezoelectric material [5] on signal and noise are investigated experimentally and explained by combining the previous model with a signal-and-noise equivalent circuit model (Fig. 2). Both quantities, Q and the piezoelectric material show the promising potential of significantly increasing the sensitivity and improving the limit of detection (LOD). Yet, an improvement in the LOD is currently limited by magnetic noise that becomes dominant at large operating voltage amplitudes [6]. Hence, understanding the specific origins of magnetic noise in such magnetostrictive resonant structures is crucial for sensor improvement in the future.A physical magnetic noise model is presented to identify the origin of stress-amplified, thermal-magnetic noise. It combines large scale finite differences micromagnetism with the mechanical equations of motion to capture magnetostrictive self-energy and frequency effects. Including the piezoelectric constitutive relation and the operating electronics the sensor’s output voltage noise density can be estimated. With the model, we evaluate and discuss experimental results and explain the dependency of magnetic noise on the excitation amplitude and the magnetic bias field. The model provides detailed insights into general noise limits, which arise from using the ΔE-effect as the sensing principle.Finally, we briefly present first applications in cell imaging [7] and show that small signal measurements with simultaneous localization are enabled by a dual-mode operation scheme with compact self-biased ΔE-effect sensors [8]. This is of particular interest for typical biomedical inverse solution problems where the precise knowledge of the sensor’s position and orientation is essential. Such applications could benefit from sensor arrays that provide many measurements with a high spatial resolution. The noise equivalent model is extended to arrays of parallel sensor elements and compared with measurements. Implications and prospects for sensor developments in the future are discussed in a conclusion. **