This article demonstrates a vibration test for a resonant MEMS scanning system in operation to evaluate the vibration immunity for automotive lidar applications. The MEMS mirror has a reinforcement structure on the backside of the mirror, causing vibration coupling by a mismatch between the center of mass and the rotation axis. An analysis of energy variation is proposed, showing the direction dependency of vibration coupling. Vibration influences are evaluated by transient vibration response and vibration frequency sweep using a single tone vibration for translational y- and z- axis. The measurement results demonstrate standard deviation (STD) amplitude and frequency errors are up to 1.64% and 0.26%, respectively, for 2 $g_\text {rms}$ single tone vibrations on y axis. The simulation results also show a good agreement with both measurements, proving the proposed vibration coupling mechanism of the MEMS mirror. The phased locked loop (PLL) improves the STD amplitude and frequency errors to 0.91% and 0.15% for y axis vibration, corresponding to 44.4% and 43.0% reduction, respectively, showing the benefit of a controlled MEMS mirror for reliable automotive MEMS lidars.

This paper proposes a novel self-sensing control concept for resonant MEMS mirrors solely based on the comb-drive current generated by the mirror movement and simple circuitry. Phase errors are immediately compensated by asynchronous switching of the driving voltage using the precise zero crossing detection by the steep current gradient. The mirror amplitude is detected based on the time difference between a comparator threshold crossing of the current signal and the zero crossing of the mirror, while it is controlled by the duty cycle of the driving voltage signal. The proper threshold setting is analyzed regarding the obtained sensitivity and uncertainty of the amplitude detection and is verified by measurements. It is found that even for symmetric out-of-plane comb-drives the scanning direction can be determined utilizing the mode coupling phenomenon of a lightweight MEMS mirror design with reinforcement structure. Experiments show that the proposed control concept results in a low optical pointing uncertainty of 0.52mdeg, which allows 10000 pixels with a precision of 10 sigma at a scanning frequency of 2kHz. Thus a lightweight and simple design of a high performance MEMS mirror is precisely controlled in its oscillation without any additional sensors or complex circuitry.

This paper proposes an analytic model of a resonant MEMS mirror with electrostatic actuation based on a Fourier series approximation for both the comb drive torque and the input waveform and verifies the model by measurements using rectangular input waveforms with various duty cycles. The analytic model is derived by the perturbation method, results in slow flow evolution in amplitude and phase with dynamic influence matrices and vectors and also provides the local dynamics for each equilibrium described by a Jacobian matrix. An analysis of the dynamic influence matrices and vectors provides understanding of the mirror dynamics by frequency components of the input waveform and the comb drive capacitance. The asymptotic behavior at zero amplitude provides the transition curve in an extended dynamic model, which corresponds to the well-known Mathieu’s equation solely with the constant and fundamental frequency components of the input waveform. The measurement results verify the proposed model, showing less than ±0.06 % frequency error for large amplitudes and ±0.47 % for small amplitudes, which corresponds to ±1.2 Hz and ±9.6 Hz for the case of a mirror with 2 kHz natural frequency, respectively. Measurements of local dynamics and transition curves also show a good agreement with the proposed model, which can be used for a fast and accurate analysis of resonant MEMS mirrors for high precision applications. [2020-0387]

This chapter gives an overview on typical approaches in semiconductor industry to develop and manufacture a MEMS-based pressure sensor especially for high-volume applications. The sensor element is interpreted as mechanical transducer element focusing on the two most prominent readout principles, capacitive and piezoresistive. A capacitive sensor is analytically assessed for a first dimensioning, and the relevance of finite element method simulations is emphasized. An exemplary process integration scheme is presented, and the impact of chip–package interaction due to mechanical stress is discussed. Package-induced stress effects can be significantly reduced using reference elements in a differential bridge configuration. The capacitive sensor part concludes with a calibration flow to achieve the targeted sensor performance. Piezoresistive sensors are discussed in a similar approach. In addition, a discussion of scaling effects, a review of the piezoresistive effect, and specifics of piezoresistor positioning are given.

An accurate analytic model of a parametrically driven resonant MEMS mirror is proposed using a Fourier series based approximation for out-of-plane comb drive torque. The analytic model consists of slow evolution equations of the amplitude and phase derived by the averaging theorem of perturbation theory. Based on the model, analytic expressions of the primary frequencies and Jacobian are derived, which are computationally efficient and provide additional information on the steady state solutions and local dynamics. Measurement results of frequency response show less than ±0.04 % in frequency errors from the model for various input voltages, i.e. less than ±0.8 Hz for the case of a mirror with 2 kHz natural frequency. The eigenfrequency and damping of the Jacobian matrix show a good agreement with measured local dynamics as well. This verifies the high accuracy of the proposed model, which can be used for improvement of the MEMS mirror design parameters and control design for large amplitude operation.

Magnetic properties of two- and three-dimensional materials, id est large-area graphene and single crystals, respectively, of VB2 and MnB2, are studied at low temperatures and in high magnetic fields by torque magnetometry. Magnetic quantum oscillations are not observed for five differing graphene samples, consistent with sample quality available to date. Single crystals of VB2 and MnB2 of large size and unprecedented crystalline quality exhibit a pronounced de Haas-van Alphen effect. We report the angular and temperature dependencies of two de Haas-van Alphen frequencies for each crystal. They allow us to make a detailed comparison with band structure calculations and the isostructural compounds CrB2 and MgB2.

We report spin-wave (SW) propagation in a one-dimensional magnonic crystal (MC) explored by all electrical spectroscopy. The MC consists of a periodic array of 255 nm wide permalloy nanowires with a small edge-to-edge separation of 45 nm. Provoking antiparallel alignment of the magnetization of neighboring nanowires, we unexpectedly find reciprocal excitation of Damon-Eshbach type SWs. The characteristics are in contrast to ferromagnetic thin films and controlled via, both, the external magnetic field and magnetic states. The observed reciprocal excitation is a metamaterial property for SWs and attributed to the peculiar magnetic symmetry of the artificially tailored magnetic material. The findings offer great perspectives for nanoscale SW interference devices.

Defined magnetization states in magnetic nanotubes could be the basic building blocks for future memory elements. To date, it has been extremely challenging to measure the magnetic states at the single-nanotube level. We investigate the magnetization states of an individual Ni nanotube by measuring the anisotropic magnetoresistance effect at cryogenic temperature. Depending on the magnitude and direction of the magnetic field, we program the nanotube to be in a vortex- or onion-like state near remanence.

We describe a versatile and simple scheme for producing magnetically and optically trapped Rb-87 Bose-Einstein condensates, based on a moving-coil transporter apparatus. The apparatus features a TOP trap that incorporates the movable quadrupole coils used for magneto-optical trapping and long-distance magnetic transport of atomic clouds. As a stand-alone device, this trap allows for the stable production of condensates containing up to one million atoms. In combination with an optical dipole trap, the TOP trap acts as a funnel for efficient loading, after which the quadrupole coils can be retracted, thereby maximizing optical access. The robustness of this scheme is illustrated by realizing the superfluid-to-Mott insulator transition in a three-dimensional optical lattice.