4. ANÁLISIS Y DISCUSIÓN DE RESULTADOS
4.1 Presentación de resultados de los instrumentos para establecer las necesidades de los
Accelerated life tests are performed to accelerate a physical failure mechanism without inducing new failure mechanisms that do not exist in the use environment. Acceleration factors use time-to-fail at a particular accelerated stress level for a particular failure mechanism to predict the equivalent time to fail at a use or field stress level. Under linear acceleration we define acceleration factor (AF) as:
( )
( )
whereStress2 Stress1fail to TimeTime to fail
( (
AF = 1 (26)
Acceleration models are usually based on the science underlying a particular failure mechanism. Successful empirical models are close approximations of a number of complicated physics or kinetics models as to determine when the theory of the failure mechanism is eventually
under-Weibull, Exponential, etc) and the slope parameters do not change but the location parameters change.
Let’s discuss some of the acceleration models for failure mechanisms accelerated by temperature, humidity, voltage and temperature cycling.
4.1 Arrhenius Relationship
The Arrhenius model has been used successfully for many chemical and physical failure mechanisms (chemical reactions, diffusion processes or migration processes) accelerated by temperature stress. This empirically based model takes up the following form:
( ) 'exp R( )) § Q ·
exp¨§§ QQ ¸··
©− kT¹
¨ ¸
¨ kT¸ (27)
where
R(T) = reaction rate A = constant
Q = activation energy (eV)
k = Boltzmann’s constant (8.617 x 10–5 eV/K) T = Temperature inoK (oC + 273.16)
'
to-fail at for the use environment, the type of life distribution (Lognormal, stood. Note that in the case of linear acceleration, while predicting
time-Typical activation energy (Q) values are in the range of 0.2 to 2.0 eV depending on the failure mechanism. The acceleration factor between accelerated stress and use environment is given by:
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=
stress env
use T
T k ¨
©¨¨
s env use
AF Q 1 1
exp (28)
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Note that the only parameter unknown in the above equation is the activation energy. By running multiple stress conditions, the activation energy for a specific failure mechanism can be calculated.
4.2 Peck’s Model
Corrosion induced by the moisture in the environment is one of the commonly seen failure mechanisms in electronics packaging. Humidity also is responsible for causing some of the interfacial delamination failures induced by hygro-thermal stresses. The acceleration model widely used to model the effect of relative humidity on failures is Peck’s model.
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=
−
stress env
use c
stress env use
T T
k ¨
©¨¨
s env use
Q RH
AF RH 1 1
exp (29)
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where
RH = Relative Humidity (%)
c = RH inverse power law coefficient Q = Activation energy (eV)
k = Boltzmann’s constant (8.617 x 10–5 eV/K) T = Temperature inoK (oC + 273.16)
4.3 Temperature-Voltage-Relative Humidity model (Eyring model)
Sometimes in addition to high temperature and relative humidity, voltage is also influential in driving failures. In such cases, the failure are modeled using:
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=
−
−
stress env
use c
stress env use n
stress env use
T T
k ¨
©¨¨
s env use
Q RH
RH Vs
Vu
AF 1 1
exp (30)
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where
A’ = constant V = Voltage (V)
n = Voltage inverse power law coefficient RH = Relative Humidity (%)
c = RH inverse power law coefficient Q = Activation energy (eV)
k = Boltzmann’s constant (8.617 x 100–55eV/K) T = Temperature inoK (oC + 273.16)
4.4 Coffin-Manson Model
A popular model used for thermo-mechanical fatigue effects is the
“Coffin-Manson” model. This model was originally used to model metal fatigue subjected to thermal cycling.
( )
f cf
(
p
(((
2 ε'
ε =
∆ c (31)
where
∆εp = Plastic strain
εf’ = fatigue ductility coefficient Nf = cycles to failure
c = a material dependent constant
Plastic strain is the thermal strain induced due to the Coefficient of Thermal Expansion (CTE) mismatch between different materials = ∆α .T.
Typically, within the thermal operating range for most of the electronic devices, the coefficient of thermal expansion doesn’t change much with temperature and Coffin-Manson in its simplest form takes into account only the temperature differences.
n
stress env use
Ts Tu AF
−
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·¸¸
¨¨
¨¨©
¨¨
§¨¨
∆
= ∆ (32)
where
∆T = Entire temperature cycle range within which a device operates n = Material dependent inverse power law coefficient ( e.g. ~1.9 for
eutectic solders)
Chapter 7 will describe more in details how Coffin-Manson type of model is derived and used for the reliability prediction for solder joints.
4.5 Norris-Landzberg Model
The simple form of the Coffin-Manson Equation doesn’t account for the dependent material behaviours. To account for the effect of these time-dependent properties (strain rate effects, stress relaxation etc.) on fatigue life, Norris and Landzberg (IBM, 1969) introduced an empirical frequency factor into the original Coffin-Manson equation. In addition, they also observed that specifically for eutectic solders when strain is applied at a continuously changing temperature, the fatigue life would decrease in the upper tempe-rature regions of the cycle due to tempetempe-rature-related effects such as increased grain boundary sliding. Hence, an empirical peak temperature factor was also introduced.Norris-Landzberg model is given by:
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∆
= ∆
−
stress env
use m
stress env use n
stress env use
T T
k ¨
©¨¨
s env use
Q fs
fu Ts
Tu
AF 1 1
exp (33)
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Where
∆T = Entire temperature cycle range within which a device operates n = Material dependent inverse power law coefficient ( e.g. ~1.9 for
eutectic solders) f = frequency of cycling
m = frequency inverse power law coefficient (~0.33 for eutectic solders) Q = Activation Energy (eV)
k = Boltzmann’s constant (8.617 x 101010 eV/K)05
T = Temperature in the hot zone of temperature cycle inoK (oC + 273.16)