with Multi-Stress Physics of Failure Models
In the "Reliability
Prediction Methods for Electronic Products" article in
Volume 9, Issue 1 of the Reliability Edge newsletter, we
presented several physics of failure models for electronic
components. The article included an example of data analysis
ALTA software using
an Arrhenius model. However, many physics of failure models are
formulated such that they cannot be used with the one- and
two-stress models available in ALTA Standard. In this
article, we will analyze accelerated test data using the Peck
model for corrosion in aluminum devices, using the General Log
Linear model in ALTA 7 PRO.
Comparing the Peck Model and
the GLL Model in ALTA PRO
The Peck model is widely used in the semiconductor industry to
model the effect of three stresses on the life of a device. Each
of these stresses affects the rate of corrosion in devices
containing aluminum or aluminum alloys. The model considers
relative humidity, voltage, and temperature, and it ignores
interactions between the stresses. In addition, the form of the
voltage term has not been experimentally determined. The Peck
model has been applied to failure mechanisms other than
corrosion by changing some of the model parameters.
The Peck model for corrosion is
is the time to failure of the device.
is a scale factor.
is the relative humidity in percent.
is an unknown function of voltage in volts.
is the activation energy in eV.
is the Boltzmann constant (8.617385x10-5 eV/K).
is the temperature in Kelvin.
The General Log Linear (GLL)
model in ALTA PRO is given by:
The three-stress form of the GLL
is the life of the component subjected to a vector of
are model parameters.
Comparing the Peck model to the
three-stress form of the GLL, we obtain the following
Making the substitutions
Note that we have assumed an
inverse power law relationship for the dependence of time to
failure on voltage, i.e.
f(V) = Vn.
Therefore, if we enter the stresses relative humidity (R),
and temperature (U),
in separate columns of an ALTA Data Sheet, the GLL model
will be related to the Peck equation through:
Twenty-seven tests were performed at elevated stress
conditions, and the data set is given in Table 1. The data are
copied and pasted directly into an
ALTA folio, and the column headings are customized to
reflect the data, as shown in Figure 1.
Accelerated Corrosion Test Data
Figure 1: Original Test Data in ALTA
[Click to Enlarge]
data were obtained in Celsius; however, absolute temperature
units must be used in the ALTA model. In order to convert
the temperature stress values to Kelvin, the Temperature column
is selected and the Convert Stress Values feature in the
Data menu is used to automatically convert the temperature
values to Kelvin (see Figure 2).
Figure 2: Automatic Conversion of Temperature Stress Values from
Celsius to Kelvin
In addition, the Put Current
Values in Subset ID option is enabled, and the column
headings for the temperature stress column and the subset ID are
changed to reflect the unit conversion, as shown in Figure 3.
The GLL model and the associated stress columns are selected, as
is the Weibull distribution.
Figure 3: Accelerated Corrosion Test Data with Temperature in
[Click to Enlarge]
Figure 4 shows the
settings used for the transformation of the three stresses that
are selected by clicking Stress Transformation... in the
Figure 4: Defining the Stress Transformations
The parameters are
computed by clicking the Calculate
button in the Control Panel, and Table 2 shows the results
Initial Computed ALTA Parameters
Recall that in the Peck model,
the value of the relative humidity exponent is defined as -2.7.
To change this, select Alter One Parameter (and Recalculate)
then Alter Alpha and then Alter Alpha(1) from the
Data menu. Change Alpha(1) to -2.7, as shown in Figure 5.
Figure 5: Altering Alpha(1) in the GLL Model to Match the Peck
Table 3 shows the final
parameters, along with the corresponding Peck model parameters.
Final Computed ALTA Parameters
The General Log Linear model in
ALTA 7 PRO was used to compute parameters for the Peck
model for corrosion in devices with aluminum and aluminum
alloys. One of the parameters in ALTA was altered and the
other parameters were recomputed in order to mimic the form of
the Peck model. A similar process can be used to analyze
accelerated test data in ALTA for many physics of failure
models with multiple stresses found in the electronics