Page 270 - An Introduction to Microelectromechanical Systems Engineering

Quality Control, Reliability, and Failure Analysis 249

parameters, including temperature, humidity, and voltage [32]. The Arrhenius
equation, a special case of the Eyring equation, is a well-known example of a rate
process where the stress parameter is only temperature. If the failure rate is constant
in time and the exponential distribution function is applicable, then the degrading
life characteristic is time to failure (lifetime) and the corresponding acceleration fac-
tor is proportional to exp(−E /kT) where E is the activation energy, k is the Boltz-
a a
mann constant, and T is temperature [33]. Should there be an indication that the
failure rate is not constant in time, then a more appropriate probability distribution
function must be used, resulting in a different degrading life characteristic and a dif-
ferent expression for the Arrhenius acceleration factor [33, 34]. The Arrhenius
equation is very useful to model failures that depend on chemical reactions, diffu-
sion processes, and migration processes. This includes failure modes in die attach,
epoxies, solder, metal interconnects, thin films, and semiconductor junctions. The
Arrhenius model has a limitation specific to micromachined components and
MEMS: it is not suitable to analyze accelerated failures resulting from mechanical
fatigue, a phenomenon that has been observed in polycrystalline and amorphous
materials used in the fabrication of MEMS. This limitation is of most significance to
surface-micromachined actuators made of polysilicon or metal alloys.
To find the activation energy, the time to failure is measured at a few elevated
temperatures. It is advantageous to make the measurements at the highest possible
temperatures in order to shorten the observation time, provided that the applied
temperatures do not alter the nature of the failure or damage the device under test.
For example, it is not possible to apply a temperature that exceeds the flow tempera-
ture of epoxies or solder because the physics of the failure modes will certainly
change and the accelerated life model will fail. An exponential curve fit is then
applied to the measured data. The slope of the logarithm of the time to failure plot-
ted against the inverse of absolute temperature (in Kelvins) is equal to the activation
energy. The MTTF or lifetime at the normal operating temperature (often room
temperature) is extrapolated using the Arrhenius equation (see Figure 8.18).

Major Failure Modes
It is evident from the diversity of materials, fabrication processes, and products
introduced in the earlier chapters that the possible failure modes would be numer-
ous and equally diverse. The purpose of this section is not to replace standard failure
mode and effect analysis (FMEA) methodology to unravel the details of a failure,
but rather to point to a few common failure modes that the industry has learned to
address.
Decades of development and millions of deployed units have provided plenty of
insight and knowledge into the reliability of micromachined electromechanical
sensors, in particular pressure sensors and accelerometers. These products have
evolved through multiple generations and can now operate and survive under
extreme environmental conditions. Over the years, engineers incorporated many
design and manufacturing improvements, each addressing one or more possible fail-
ure modes. In some instances, these details have become public knowledge. For
example, rounding of the corners is now a common practice to reduce stress concen-
tration in micromechanical structures. But in many other instances, manufacturers
consider these details as trade secrets, especially when utility patents cannot be