Automated Parameter Extraction Of ScAlN MEMS Devices Using An Extended Euler–Bernoulli Beam Theory

Abstract

Magnetoelectric sensors provide the ability to measure magnetic fields down to the pico tesla range and are currently the subject of intense research. Such sensors usually combine a piezoelectric and a magnetostrictive material, so that magnetically induced stresses can be measured electrically. Scandium aluminium nitride gained a lot of attraction in the last few years due to its enhanced piezoelectric properties. Its usage as resonantly driven microelectromechanical system (MEMS) in such sensors is accompanied by a manifold of influences from crystal growth leading to impacts on the electrical and mechanical parameters. Usual investigations via nanoindentation allow a fast determination of mechanical properties with the disadvantage of lacking the access to the anisotropy of specific properties. Such anisotropy effects are investigated in this work in terms of the Young’s modulus and the strain on basis of a MEMS structures through a newly developed fully automated procedure of eigenfrequency fitting based on a new non-Lorentzian fit function and subsequent analysis using an extended Euler–Bernoulli theory. The introduced procedure is able to increase the resolution of the derived parameters compared to the common nanoindentation technique and hence allows detailed investigations of the behavior of magnetoelectric sensors, especially of the magnetic field dependent Young‘s modulus of the magnetostrictive layer.

Magnetoelastic Coupling and Delta-E Effect in Magnetoelectric Torsion Mode Resonators

“…The TMs were measured close to magnetic saturation at to reduce the influence of the delta-E effect. Slight deviations between the measurement and simulation might result from effectively different magnetoelectric coupling factors, e.g., due to the slightly different material parameters, geometric inaccuracies, or stress [ 62 ]. In conclusion, the model can estimate the electromechanical properties of the device and the effect of different electrode configurations well.…”

Anisotropy of the ΔE Effect in Ni-Based Magnetoelectric Cantilevers: A Finite Element Method Analysis

“…The simulated eigenfrequencies at t Ni = 100 nm are 20-30% higher than the respective experimental eigenfrequencies [26] of the structures in Figure 1a, on which the model is based. The main reason is the undercut that was neglected in the simulation, which can lead to a frequency shift in the range of 20% [25] or even higher, depending on the undercut depth. A second important influencing factor is the single crystal approximation of the individual layers in contrast to the experimental data.…”

“…As a consequence of the proposed (2D) model, the analysis of effects arising from the complex state of experimental (polycrystalline MEMS) structures is not possible, e.g., a non-rectangular cross-section with specific surface and interface roughness of the different layers affecting the shape anisotropy or contributions of other anisotropy types such as the uniaxial anisotropy. The complex stress distribution in such structures induced by the undercut thermal treatment or the growth-induced stress anisotropy, influences the eigenfrequency, especially at shorter cantilevers [25]. Within the single crystalline approximation, mechanical or magnetic effects arising from defects (vacancies, interstitial and substitution atoms, dislocations, grain boundaries) in (textured) polycrystalline layers cannot be reproduced.…”

“…The curvature of a cantilever has influence on its eigenfrequency behavior. This consideration is important for parameter extraction, where the Euler-Bernoulli theory is used [25]. Using Equation ( 8), the bending induced cantilever deflection allows an estimation of the shift of its eigenfrequency in magnetic saturation.…”

“…In recent studies, the properties of MEMS structures were investigated in regards to the implications of anisotropy of the elastic [25] and the magnetoelastic parameters [26]. The angle-dependent analysis of the ∆E effect sensors based on TiN/AlN/Nickel revealed a complex eigenfrequency behavior in the presence of a magnetic field (see Figure 1a,b).…”