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Appendix C
—
Acoustic Resonances and other
factors Affecting Acceleration Measurements
Any mechanical system has acoustic resonances that can be excited by either sinusoidal acceleration or repeated
impulses. Traditional accelerometers are usually mounted into metal blocks that have thicknesses comparable to
their lateral dimensions. This is done so that the resonance frequency of the mechanical system is driven to high
frequencies and therefore does not interfere with the acceleration measurement. However, in trying to measure
accelerations in systems that handle semiconductor wafers, the thin flat shape of the wafer and the relatively low
resonant frequencies makes comparative acceleration measurements difficult.
Semiconductor wafers can have “drumhead” resonances at relatively low frequencies. As the name suggests,
these resonances occur in the direction normal to the flat surface of the wafer. Because of the large diameter to
thickness ratio, the resonant frequencies can be quite low. A typical illustration of one of the lower order
drumhead mode patterns (0,1) is shown below. Depending on the excitation frequency, multiple modes, such as
(0,0), (0,1), (2,1), etc. can be excited.
In the same way, Wafersense units that measure vibration, such as AVS and AMS, also have these modes, as well
as other smaller resonances caused by the housing structures. The resonance frequency is primarily determined
by the thickness, area and material density. So, an AMS unit will have different resonances from an AVS unit which
will have different resonances from a silicon wafer.
The method of clamping, whether uniformly clamped at the edge, clamped in a few places at the edge, or
supported in the middle, will also change the resonant frequencies in both Wafersense units as well as silicon
wafers.
The amplitude of the driving force, i.e. the acceleration, will not affect the resonant frequencies, but will
determine which resonances show up in the measurement.
One common question is whether two AVS units or two AMS units will show the same waveform if vibrated or
translated in the same manner. The answer is that two units of the same type will show the same acceleration if a
resonance is not excited. Even an AVS and an AMS unit will show almost the same waveform off resonance.
Below in figure 1 is a comparison of an AVS unit (top) and an AMS unit (bottom) that were clamped together and
simultaneously shaken in the z direction. As you can see, their waveforms are very similar but not identical. One
would not expect them to be identical since the housing construction of the two are different. The AMS housing is
much thinner and the electronics enclosure is smaller in diameter than the AVS housing.
