Effect of excitation mode on the magnetic field detection limit of magnetoelectric composite cantilevers

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.