Micromechanical lab

Characterising MEMS sensors is much like trying to find out what is inside a black box without opening the lid. A behavioural model must be confirmed with a set of carefully chosen measurements. These measurements are usually not performed in the same environment as the sensor is supposed to operate in, which affects its behaviour. It is also hard to find unexpected phenomena that might distort the sensor signal since the verification measurements are not designed to reveal them. It is thus important to use several measurement set-ups, each one giving as much information as possible and together confirming the accuracy and correctness of each other. Such measurements also have an improved potential to reveal unexpected behaviour.

In the following paragraphs, we’ve outlined some of the equipment Imego has used to characterize a tri-axial accelerometer. The accelerometer characterisation is a good example since it requires several pieces of equipment in order to achieve a sound understanding and proper model verification. However, methodology and equipment are very much the same for measurements of other mechanical sensors and actuators such as gyroscopes, resonant beams and MEMS-switches.
 

The probe station, a "Karl Suss PA200-II semiconductor probe station", is a semi-automatic probe station enclosed in a dark electrically shielded box. The crosshair in the microscope can be used together with the position readout of the movable chuck to measure distances with micrometer accuracy.

The microscope can be replaced by two different optical confocal point sensors for measurement of vertical profiles or vibrations. The vibrometer is a "UBM NanoSwitch" with a resolution down to 10 nm and a measuring rate up to 50 kHz. The distance between the measuring head and the measured surface is 2 mm. The profilometer is a "UBM MicroFocus" with a resolution down to 6 nm. The stand off distance is 2 mm. LabView software for acquisition, display and export of 3D-profiles has been developed in-house.

With this equipment the probe station can be used for functionality verification of mechanical structures before bonding and packaging, or even at wafer level.
 

Vibrometer differs from the "UBM NanoSwitch" since it measures velocity instead of displacement. It also scans over a surface and thus has the potential of viewing the complete shape of the vibration modes.

The instrument is equipped with an internal signal source, data acquisition unit and software for FFT analysis of the response. The maximum resolution is 0.3.
 

The shaker is a "Bouché Labs Model 1000AD". The resonance frequency of the armature is 38 kHz. It has a stroke length of 12 mm and generates a maximum force of 9 N. The armature has a calibrated built-in reference accelerometer. A closed loop real-time system has been developed [1] allowing accurate reproduction of acceleration patterns containing frequencies up to about 5 kHz.

Reproduced acceleration pattern from the chassis of a car driving on a dirt road. The RMS value of the acceleration error is less than 4% of the acceleration's RMS value.

Acceleration steps, white noise, constant amplitude chirps and real world signals can thus be generated in the lab. Figure above shows a reproduced acceleration pattern from the chassis of a car driving on a dirt road and the signal error.
 

The rate table, an "Ideal Aerosmith Model 1601-4-TL", is mainly a horizontal spinning disc. It is accurately aligned with respect to the earth’s rotation axis allowing compensation for the earth rate. The rate of the disc can be adjusted up to 3000O/sec with a resolution down to 0.0002O/sec.

It is equipped with an automatic two-axis positioning fixture. The test object can thus be oriented with the angular rate in any direction. Further, the rate table is housed in a nitrogen cooled temperature chamber adjustable from
–65O C to 85OC.

In addition to angular rates, the table can be used to generate centripetal accelerations, or simply to accurately align objects with respect to the earth’s gravity. Therefore this system is a universal tool for characterization of most inertial sensors, not only gyroscopes.
 

The triple axis accelerometer consists of four seismic masses, each one suspended on a slanted [111] beam as illustrated in Figure 2. More information about this accelerometer topology is available in [2].

A triple axis accelerometer structure consisting of four seismic masses suspended on slanted [111] beams.

The x, y and z axis signals are obtained from the four output signals as

The fabricated prototype devices are built up from a single wet-etched silicon wafer anodically bonded to a glass substrate. The glass is patterned with capacitive readout electrodes underneath each seismic mass. A microscope photograph of a prototype device is shown below.

Photograph showing an accelerometer prototype. The silicon is electrically connected through an epoxy contact

When the prototype is characterized we want get the following questions answered.
• Does the performance agree with the models?
• What performance can we expect from devices in mass production?
• Does any phenomenon that we do not yet know affect the behaviour of the device?

To find the answer to the first question a modal analysis, measurement of the resonance modes, is helpful. However, the finite element model does not include air damping and is valid only in vacuum. Further on, the model requires an accurate measure of the beam widths. The probe station with the built in vibrometer is thus first used to find working prototypes, i.e. devices where all four masses vibrate when an AC signal is applied to the readout electrode. The beam widths were also measured in the probe station. The design goal was 80 mm to 75 mm.

The laser Doppler vibrometer is used to investigate the resonance frequencies and the damping of the spring-mass system. A voltage applied to the readout electrodes is used for electrostatic excitation of the masses. Figure 4 shows the amplitude of the mass displacement as a function of the frequency. From this measurement it is also possible to generate animations of the resonance modes. The measurements confirm that the intrinsic accelerometer structure behaves as predicted by the analytical model and the finite element models, but it does not tell us how the device acts as an accelerometer.
   

The displacement response of a seismic mass measured with the laser Doppler vibrometer at various pressures.

The next step in the accelerometer characterization is to measure the DC behaviour by applying the gravity vector in different directions as illustrated below. The automatic fixture of the rate table is suitable for this measurement since it can automatically measure a large number of inclinations. For this purpose dedicated readout electronics was built that converts capacitances into voltages. The electronics introduces an additional uncertainty since it is a link between the accelerometer and the output signal. It is impossible to distinguish between the sensor signal from parasitic signals or distortion generated by the electronics without other supporting measurements.

The inclination angles for DC characterization at the rate table. A large number of inclinations can be measured with the automatic two-axis fixture.

The DC characterization gives accurate values of the sensitivity as well as the important direction of the most sensitive axis assuming that the electronics does not distort the signal. Measurements further on prove this assumption. From the sensitivity and the beam widths it is now possible to determine the air-gap of the readout capacitors. The design goal was 3.1

Shaker results from all four sensing elements.

From the figure above we find that the accelerometer has strange behaviour below
70 Hz, which is explained by lateral vibration of the shaker's armature. The second interesting phenomenon is the difference in bandwidth. This can intuitively be explained by gas film damping since the element with the highest sensitivity, and thus smallest electrode gap, also has the lowest bandwidth. After these measurements a few questions remain:

• Does the laser Doppler vibrometer result correlate with acceleration sensitivity, i.e. does it agree with the shaker result?
• Does the electronics affect the acceleration signal?
• Are the calculated electrode gaps from the rate table measurements correct?
• Is it the gas film thickness differences that cause the difference in bandwidths?

The first two questions can be answered by plotting the shaker and the vibrometer measurements in the same graph. The last two questions can be answered by implementation of an analytical gas-film model that relates the frequency responses from the shaker and vibrometer measurements to the electrode gaps obtained from the rate table measurements. Since the gas film damping strongly depends on the film thickness an error will be revealed. Figure 7 shows all the data including the gas film model with the measured electrode gaps. The almost perfect agreement of the curves obtained by the three different methods together indicates that the results and conclusions are correct.