Abstract
Magnetic field excitation of strain-coupled magnetoelectric composite cantilevers in different bending modes is investigated for magnetic field sensing, yielding the sensitivity, noise, and magnetic field detection limit. An analytic theory covering the resonant magnetoelectric response and thermal vibration noise of arbitrary bending modes and the Johnson–Nyquist noise from the composite and electronics is presented, and detection limit results of thin film FeCoBSi–Si–AlN composite cantilevers are calculated for the first three bound–free and free–free bending modes over a wide range of dimensions. We use size-scaling to yield the same 1 kHz resonance frequency for all modes and dimensions, constant quality factors Qf = 1000, and thickness-independent experimental material parameters. Magnetic field detection limits in the 1 pT/Hz1/2 to 100 fT/Hz1/2 range are predicted for practical cantilever dimensions, whereby higher modes are found to yield lower detection limits at similar functional layer thicknesses but a greater cantilever size. All detection limits are found to be thermal vibration noise limited and for different modes to display the same 1/size2 scaling behavior but require different FeCoBSi–Si–AlN layer thickness ratios.
Highlights
Large magnetoelectric (ME) effects have been observed in composites by the strain-coupling of different functional materials
The sensitivity of magnetoelectric cantilevers, noise, and the resulting magnetic field detection limit are affected by many parameters including the resonance frequency, cantilever dimensions and layer thicknesses, modes, and materials
We have presented a theory of the magnetic field detection limit (LOD) of ME composite cantilevers for arbitrary bound–free and free–free bending modes resulting from the resonant ME response and thermal vibration, Johnson–Nyquist, and amplifier-intrinsic noise
Summary
Large magnetoelectric (ME) effects have been observed in composites by the strain-coupling of different functional materials. Excitation of different bending modes affects essentially all contributions to the detection limit, e.g., the ME response due to different strain distributions along the cantilever, loss mechanisms and resonance enhancement, thermal vibration amplitudes and the corresponding strain-induced noise, as well as the associated cantilever size and frequency effects. We present a theory of the resonant magnetoelectric response and the noise density from thermal vibration, Johnson–Nyquist, and electronics noise yielding the magnetic field detection limit of ME cantilevers excited to arbitrary bound–free and free–free bending modes. As opposed to the theory for the ME-response for the first bound–free mode given earlier,[17] arbitrary higher bending modes, the differing solutions for free–free modes, mode-dependent thermal vibration noise, and the above noise sources are included here, predicting the detection limit parameterized to cantilever and layer dimensions and permitting the investigation of scaling behavior. A systematic comparison of the results of the thermal vibration noise limited magnetic field detection limit of the first three bound–free and free–free modes is given, whereby cantilever size scaling to a constant resonance frequency is used
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