Freescale Semiconductor, Inc.
The temperature acceleration factor for a particular failure
Where:
eA
TLS
THS
then;
AF
mechanism can be related by taking the ratio for the reaction
rate of the two different stress levels as expressed by the
Arrhenius type of equation. The mathematical derivation of
the first order chemical reaction rate computes to:
=
=
=
0.7eV/°K (assumed)
55°C + 273.16 = 328.16°K
125°C + 273.16 = 398.16°K
=
77.64
(RT)HS
(RT)LS
tHS
tLS
AF
Therefore, the equivalent cumulative device hours at the
customer’s use condition is:
tLS
or
=
AF x tHS = (32 500) 77.64
Ea
k
1
TLS
1
THS
AF
exp
tLS
=
1,242,172 device hours
Where:
AF
RT
t
T
Ea
=
=
=
=
=
Acceleration Factor
Reaction Rate
time
temperature [°K]
activation energy of expressed
in electron-volts [eV]
Boltzman’s constant, 8.6171 x 10 eV/°K
Low stress or nominal temperature
High stress or test temperature
Computing the lower one sided failure rate with a 90% confi-
dence level and no failures:
(
)
, d.f.
2
2t
or
or
λ
λ
=
=
1.853E–06 failures per hour
1,853 FITs
-5
k
LS
HS
=
=
=
The inverse of the failure, λ, or the Mean Time To Failure
(MTTF) is:
The activation energy is dependent on the failure mecha-
nism and typically varies from 0.3 to 1.8 electron-volts. The
activation energy is directly proportional to the degree of
influence that temperature has on the chemical reaction rate.
A listing of typical activation energies is included in reference
[6] and [7].
1
MTTF
or
MTTF = 540,000 device hours
An example using the Arrenhius equation will be demon-
strated. A 32 device HTB test for 500 hours total and no
failure was performed. The 125°C, 100% rated voltage test
resulted in no failures. If a customer’s actual usage
conditions was 55°C at full rated voltage, an estimate of the
lower one side confidence limit can be calculated. An
assumption is made that the failure rate is constant thus
implying the exponential distribution. The first step is to
calculate the equivalent device hours for the customer’s use
conditions by solving for the acceleration factor.
CONCLUSION
Reliability testing durations and acceptance numbers are
used as a baseline for achieving adequate performance in
the actual use condition that the silicon pressure sensor
might encounter. The baseline for reliability testing can be
related to the current record high jump bar height. Just as
athletes in time achieve a higher level of performance by
improvements in their level of physical and mental fitness,
silicon pressure sensors must also incorporate improve-
ments in the design, materials, and manufacturability to
achieve the reliability growth demands the future market
place will require. This philosophy of never ending improve-
ment will promote consistent conformance to the customer’s
expectation and production of a best in class product.
From the acceleration factor above, if eA is assumed equal
to 1,
Ea
k
1
TLS
1
THS
AF
exp
1–8
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