Lorentz-Force Magnetometers

The market for low-cost MEMS sensors is growing rapidly, particularity because of the exponential growth of smart phones and tablets. A compass, or magnetometer, is an essential component for providing navigation and location-based services in these devices. While magneto-resistive (MR) and Hall-effect magnetometers are dominant technologies in existing electronic compasses, Lorentz-force magnetometers have some notable advantages, including (1) no requirement of any specialized magnetic material, (2) no need of magnetic concentrators to sense fields parallel to the device, and (3) easy integration with MEMS gyroscopes and accelerometers currently used in consumer electronics.Because of these advantages, there are intensifying R&D efforts to develop practical Lorenz-force magnetometers, with efforts focused on reducing power consumption and noise [1] as well as integration with 9 degree-of-freedom monolithic inertial MEMS [2].

Design Challenges

Sensitivity, noise, hysteresis, linearity, dynamic range, reliability, and yield are all critical parameters for Lorentz-force magnetometers. Design engineers need to optimize the performance with respect to these criteria, while also reducing cost, form factor, and expediting time to market.

Magnetometers are multiphysics in nature. Device design typically includes analysis of resonant frequencies, Lorentz force, and capacitive output.The accompanying circuit design typically requires an accurate magnetometer model in order to design the AC current drive control, capacitance readout amplifier, ADC, and output signal processing. The system design aspects typically include noise analysis for the sensor and circuitry, and temperature stability.


Fig. 1: SEM image (left), with the white arrows indicating drive current in the y+ direction and sensing circuitry (right) of a Lorentz-force magnetometer from [1]. Reused with permission of the author.

Multiphysics Design Methodology

Sensing frequency and Lorentz force application
The magnetometer in [1], henceforth referred to as the UC Davis magnetometer, uses the single micro structure shown in Figure 2 to sense a two-axis B field. An AC drive current is sent through the structure in the y+ direction.

Diagram showing magnetic field and Lorentz force directions

Fig. 2: MEMS+ model of the UC Davis magnetometer (top), and Lorentz force due to interaction of the drive current and Bz (bottom left), and Bx (bottom right) fields.

To maximize sensitivity, the frequencies of the AC drive current are matched to the mechanical mode frequencies corresponding to x-direction, in-plane motion and z-direction, out-of-plane motion. Results of a modal analysis in MEMS+ are shown in Figure 3.

Mechanical mode shapes

Figure 3. MEMS+ modal analysis for the Bz sensing in-plane mode at 49.7kHz (left),
and Bx sensing out-of-plane mode at 112kHz (right).

Capacitive sensing of the Bz and Bx fields
Bz sensing is provided by differential capacitance between the x+ and x- electrostatic comb fingers, and Bx sensing is provided by capacitance to a single electrode beneath the micro structure, as shown in Figure 4.

capacitive sensing of Bz and Bx fields

Figure 4: MEMS+ model showing differential capacitance sensing for Bz (left, only x+ capacitor is highlighted), and single capacitance sensing for Bx via the electrode beneath the micro structure (right).

Sensing results for Bz and Bx fields are shown in Figure 5. Note that the frequency of the AC current for sensing each field is the same as the frequency predicted by the modal analysis for each sensing mode.

Capacitance output for Bz and Bx sensing

Figure 5. Capacitive sensing output for Bz (left) and Bx (right) predicted by MEMS+


[1] Area-Efficient Three Axis MEMS Lorentz Force Magnetometer, V. Rouf et al, IEEE Sensors Journal, Vol 13, 2013.

[2] A Monolithic 9 Degree of Freedom (DOF) Capacitive Inertial MEMS Platform, I. Ocak, et al, IEEE Electron Devices Meeting (IEDM), 2014.

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