Matthias C. Krantz

Giant magnetoelectric effect in vacuum

Magnetoelectric (ME) thin film cantilever type sensors made of AlN and FeCoSiB are operated in vacuum, reducing air damping and thus increasing the ME coefficient and improving the limit of detection (LOD) for ac-magnetic fields. Depending on the sensor geometry, the response is increased by a factor of 5 resulting in a ME coefficient of 20 kV/cmOe at 152 Hz and by a factor of 11 with 12 kV/cmOe at 4.7 kHz and an improvement in LOD by an order of magnitude. Modelling these cantilevers reveals dominant contributions of viscoelastic and molecular damping above and intrinsic damping below 10−2 mbar, respectively.

Theory of magnetoelectric effect in multilayer nanocomposites on a substrate: Static bending-mode response

Magnetoelectric (ME) coefficients for bending excitation in static magnetic fields and the bending response of multilayer composites with alternating magnetostrictive (MS) and piezoelectric (PE) layers on a substrate are investigated systematically. Theory and closed-form analytic solutions for the static magnetoelectric and the bending response coefficients are presented. Results of systematic variation of layer numbers, layer sequences, PE volume fractions, substrate thicknesses, and four different material systems (employing FeCoBSi, Terfenol-D, AlN, PZT, and Si) are given for a fixed total composite thickness of 5μm. Among more than 105 structures investigated the greatest static ME coefficient of 62.3 V/cmOe is predicted for all odd layer number FeCoBSi-AlN multilayer composites on a Si substrate at vanishing substrate thickness and a PE material fraction of 38%. Varying the substrate thickness from 0μm to 20μm and the PE fraction from 0% to 100%, broad parameter regions of high ME coefficients are f...

Two-Dimensional Versus Three-Dimensional Finite-Element Method Simulations of Cantilever Magnetoelectric Sensors

This paper investigates the suitability of two-dimensional (2D) finite-element method (FEM) simulations to model the quasi-static bending-mode response of cantilever magnetoelectric (ME) sensors. We compute the deformation of the cantilever due to an applied magnetic field across the magnetostrictive (MS) layer as well as the generated voltage across the piezoelectric (PE) layer by solving a system of coupled linear elastostatic/elastodynamic and electrostatic/magnetostatic equations. In the 2D FEM formulation a plane-stress boundary condition is employed. Both 2D and 3D FEM results are compared for varying cantilever length and width. For cantilevers with length >> height >> width good agreement is obtained between 2D and 3D results. For cantilevers obeying the condition length >> width >> height, a systematic deviation occurs between 2D and 3D results as the plane-stress condition does not model the situation in the center of the cantilever. For a length:width:height ratio of 25:5:1, a difference in generated voltage of ~12% is obtained for the Terfenol-D-PZT-Si material system. Especially for cantilevers with high aspect ratios, we show that 2D FEM simulations are sufficient to investigate the ME properties.

Resonant magnetoelectric response of cantilevers with magnetostrictive and piezoelectric layers on opposite sides of the substrate

A theory is derived for the bending-mode magnetoelectric coefficients at resonance for magnetostrictive and piezoelectric layers on opposite sides of a substrate. Results are given for the transverse ME coefficient in the Metglas-Si-AlN system with magnetic field excitation parallel and electric polarization perpendicular to the cantilever. The center-substrate layer sequence is found to produce about 50 % enhancement of the magnetoelectric effect compared to magnetoelectric bilayers on one side of a substrate. Up to about 10 % additional enhancement of the ME effect is predicted if the magnetostrictive and piezoelectric layers are separated from the substrate by spacer layers with lower Youngs modulus. Lowest order bending mode resonance frequencies are given.

Tunable elastomer-based virtually imaged phased array

Virtually imaged phased arrays (VIPAs) offer a high potential for wafer-level integration and superior optical properties compared to conventional gratings. We introduce an elastomer-based tunable VIPA enabling fine tuning of the dispersion characteristics. It consists of a poly-dimethylsiloxane (PDMS) layer sandwiched between silver bottom and top coatings, which form the VIPAs high reflective and semi-transparent mirror, respectively. The latter also acts as an electrode for Joule heating, such that the optical PDMS resonator cavity tuning is carried out via a combination of thermal expansion and the thermo-optic effect. Analogous to the free spectral range (FSR), based on a VIPA specific dispersion law, we introduce a new characteristic VIPA performance measure, namely the free angular range (FAR). We report a tuning span of one FAR achieved by a 7.2K temperature increase of a 170μm PDMS VIPA. Both resonance quality and tunability are analyzed in numerical simulations and experiments.

Electrode position optimization in magnetoelectric sensors based on magnetostrictive-piezoelectric bilayers on cantilever substrates

Finite element method (FEM) simulations are performed to investigate the sensitivity to dc magnetic fields of magnetoelectric sensors on cantilever substrates with trenches or weights at different positions. For a simple layered cantilever, a 15% higher signal voltage across the piezoelectric layer is obtained for optimally positioned electrodes and an insulating magnetostrictive material. A further 25% increase in the signal voltage is achieved for a trenched cantilever design with a pick-up region.

Signal-to-Noise Ratio in Cantilever Magnetoelectric Sensors

The signal-to-noise ratio (SNR) is investigated for compound magnetoelectric (ME) sensors on cantilever substrates (SUBs) for the detection of low-level magnetic fields. Operated at the mechanical resonance, the magnetic field deforming the magnetostrictive (MS) layer causes a resonant bending-mode response in the ME cantilever. The deformation of the piezoelectric (PE) layer allows for the extraction of a voltage or charge signal. Here, the influence of the PE layer thickness and electrode length on the SNR is evaluated in a theoretical study. The signal levels are calculated using the finite-element method. Noise voltages are calculated including the intrinsic electric noise of the ME sensor and amplifier noise for the case of a voltage amplifier and a charge amplifier. AlN and PZT are considered as PE materials. For a cantilever geometry with 10 mm-length, 10 mm-width, and 300 μm-thick silicon SUB and a Metglas MS layer of 2 μm thickness, a limit of detection (LOD) in the pT-range is predicted for 2 μm-thick AlN layers, while the LOD of PZT ME sensors is approximately one order of magnitude worse. A doubling of the SNR is obtained for choosing an upper electrode covering only the fixed side of the cantilever. Operation with a charge amplifier shows at least ~50% better SNR values compared with PE voltage amplification.

Magnetic Flux Concentration Effects in Cantilever Magnetoelectric Sensors

This paper investigates the resonant bending-mode response of cantilever magnetoelectric (ME) sensors, with focus on the magnetic behavior in an external applied magnetic field, in a theoretical study. A system of coupled linear elastostatic/elastodynamic and electrostatic/magnetostatic equations is solved using 2-D and 3-D finite-element method simulations. The magnetic field is applied at the boundaries of an air-filled volume, surrounding the whole ME sensor, to consider the geometry-dependent deformation of the magnetic field in the presence of materials with high permeability. The deformation of the magnetostrictive (MS) material is calculated and generates an electric potential across a piezoelectric (PE) layer. Structuring the conductive MS layer is necessary to define a pickup region, if the MS layer is produced on top of the PE layer, to enhance the sensor output. For efficient excitation of the resonant bending mode, the tip of the cantilever also needs to be covered with an MS material. Thus, an air gap is necessary to electrically insulate both MS regions and has to be as small as possible to not decrease the magnetic field penetrating into the MS layer. The induced electric potential across the pickup region is optimized for a Metglas-AlN-Si thin-film ME sensor with an length:width:height ratio of 100:20:3. 2-D simulations are performed showing reasonable agreement in induced voltage with approximately 20% deviation compared with 3-D simulations, but with much lower computation times.

Resonant magnetoelectric response of composite cantilevers: Theory of short vs. open circuit operation and layer sequence effects

The magnetoelectric effect in layered composite cantilevers consisting of strain coupled layers of magnetostrictive (MS), piezoelectric (PE), and substrate materials is investigated for magnetic field excitation at bending resonance. Analytic theories are derived for the transverse magnetoelectric (ME) response in short and open circuit operation for three different layer sequences and results presented and discussed for the FeCoBSi-AlN-Si and the FeCoBSi-PZT-Si composite systems. Response optimized PE-MS layer thickness ratios are found to greatly change with operation mode shifting from near equal MS and PE layer thicknesses in the open circuit mode to near vanishing PE layer thicknesses in short circuit operation for all layer sequences. In addition the substrate layer thickness is found to differently affect the open and short circuit ME response producing shifts and reversal between ME response maxima depending on layer sequence. The observed rich ME response behavior for different layer thicknesses,...

Wavefront and polarization effects in actively tunable thin-film resonators for beam alignment in optical interconnects

Thin-film resonators operated at an oblique incidence angle produce significant spatial shifts of incident low divergence coherent beams based on the resonance-dependent effective group propagation angle. We investigate a single-layer resonator tuned by Joule heating and thermal expansion of the resonator cavity to allow for active beam position control. Operated in reflection on a right-angle glass prism, it is suitable for integration in optical interconnect networks and couplers to enable active beam alignment. The effects of polarization, beam divergence and wavefront aberrations are analyzed both in simulations and experiments.