U - Index of

QUALITY and RELIABILITY
2.3 FUNDAMENTAL THEORY FOR ACCELERATED TESTING
Accelerated life testing is powerful because of its strong relation to failure physics. The Arrhenius model, which
is generally used for failure modelling, is explained below.
II
Arrhenius model
This model can be applied to accelerated Operating Life Tests and uses absolute (Kelvin) temperatures.
L=A+EalK·Tj
L : Lifetime
A : Constant
Ea : Activation Energy
K : Boltzman's constant
Tj : Absolute Junction temperature
If Lifetimes L 1 and L2 correspond to Temperatures T1 and T2,
L 1 = L2 exp [~a (T 1 1 -
T~ D
Lifetime(L)
L1
,/
T2
Temperature 11T (0 K -1)
Actual junction temperature should always be used, and can be computed using the following relationship.
Tj=Ta+(Px (jja)
Where Tj = Junction temperature
Ta = Ambient temperature
P = Actual power consumption
e ja=Junction to Ambient thermal resistance (typically 100 degrees celsius/watt for a 16·Pin DIP).
Activation Energy Estimate
Clearly the choice of an appropriate activation energy, Ea, is of paramount importance. The different mechanisms
which could lead to circuit failure are characterized by specific activation energies whose values are published
in the literature. The Arrhenius equation describes the rate of many processes responsible for the degradation
and failure of electronic components. It follows that the transition of an item from an initially stable condition to
a defined degraded state occurs by a thermally activated mechanism. The time for this transition is given by an
equation of the form:
MTBF = B EXP (EalKT)
MTBF = Mean time between failures
B = Temperature·independent constant
MTBF can be defined as the time to suffer a device degradation. The dramatic effect of the choice of the Ea value
can be seen by plotting the MTBF equation. The acceleration effect for a 125°C device junction stress with respect
to 70°C actual device junction operation is equal to 1000 for Ea= 1eV and 7 for Ea=0.3eV.
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