Design optimization of flux concentrators for magnetic tunnel junctions-based sensors

Miniaturized, ultra-sensitive, and easily integrable magnetometers are needed for many applications, such as space exploration or health monitoring. Achieving this goal requires a magnetic sensor with high sensitivity and low noise. High sensitivity (>1000%/mT) can be obtained by integrating high gain Permalloy flux concentrators (FC), with the advantage of high field direction selectivity. Reducing the magnetic 1/f noise can be realized by increasing the number of magnetic tunnel junctions in the air-gap of the FC. However, this is obtained at the expense of a larger air-gap and consequently a decrease in the magnetic gain and thus in the sensitivity. In this paper, we explore a design optimization scheme in order to find the best trade-off between high FC gain and low magnetic noise. To model the gain of the flux concentrator, we propose two complementary approaches; one is based on finite-element simulations of the FC gain, where the influence of geometrical parameters of the air-gap is investigated. Then, in a second step, we propose an analytical formula consistent with all our simulation results and based on magnetic reluctance. Finally, we derive an analytical model of the sensor detectivity from which we can extract the optimal sensor design, which allows an improvement by three orders of magnitude in the performance compared to a single junction. Our research demonstrates that a multi-parameter approach outperforms single-parameter optimization, with peak performance surprisingly achieved at moderate parameter values.