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334 MEMS and Microstructures in Aerospace Applications

N ¼ C=(DT) g (15:2)

where
N is the number of cycles to failure
C is a constant, characteristic of the metal
g is another constant, also characteristic of the metal
and
DT is the temperature range of the thermal cycle.

This model is basically the inverse power law relationship, where instead of the
stress, V, the range DV is substituted to give

L(V) ¼ 1=KV n (15:3)
where
L represents a quantifiable life measure, such as mean life, characteristic life,
median life, B(x) life, etc.
V represents the stress level
K is one of the model parameters to be determined (K > 0)
and
n is another model parameter to be determined.

This is an attempt to simplify the analysis of a time-varying stress test by using
a constant stress model. It is a very commonly used methodology for thermal
cycling and mechanical fatigue tests. However, by performing such a simplifica-
tion, the following assumptions and shortcomings are inevitable. First the acceler-
ation effects due to the stress rate of change are ignored. In other words, it is
assumed that the failures are accelerated by the stress difference and not by how
rapidly this difference occurs. Secondly, the acceleration effects due to stress
relaxation and creep are ignored.

15.4.4.1 Fracture
Fracturing occurs when the load on the device is greater than the strength of the
material. Clearly good design with proper margins or alternately, less brittle ma-
terials is the solution. In addition, debris can form, leading to additional failure
modes. In the space environment applications, this is particularly a concern as
conductive particles could induce numerous failures. Additional failure mechan-
isms such as radiation degradation and thermally induced reliability concerns are
handled in other sections of this book.

15.5 ENVIRONMENTAL FACTORS AND DEVICE RELIABILITY

Environmental factors that strongly influence MEMS reliability are included in
Table 15.1, which provides a checklist for typical environmental factors to be
considered. Specific components may need to take extra factors into account or

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