Reliability HotWire

Issue 90, August 2008

Hot Topics

Using ALTA 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 with ReliaSoft's 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 given by:

where:

  • TTF is the time to failure of the device.
  • A0 is a scale factor.
  • RH is the relative humidity in percent.
  • f(V) is an unknown function of voltage in volts.
  • Ea is the activation energy in eV.
  • kB is the Boltzmann constant (8.617385x10-5 eV/K).
  • T is the temperature in Kelvin.

The General Log Linear (GLL) model in ALTA PRO is given by:

where:

  • L(X) is the life of the component subjected to a vector of stresses, X, and
  • αi are model parameters.
The three-stress form of the GLL model becomes:

.

Comparing the Peck model to the three-stress form of the GLL, we obtain the following relationships:

Making the substitutions X1 = log (R), X2 = log S, and X3 = 1/U yields:

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), voltage (S), and temperature (U), in separate columns of an ALTA Data Sheet, the GLL model parameters α1 and α3 will be related to the Peck equation through:

Example:
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.

Table 1: Accelerated Corrosion Test Data


Figure 1: Original Test Data in ALTA
[Click to Enlarge]

The temperature 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 Absolute Units
[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 Control Panel.


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 obtained.

Table 2: 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 Model

Table 3 shows the final parameters, along with the corresponding Peck model parameters.

Table 3: Final Computed ALTA Parameters

Conclusion:
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 literature.

Copyright 2008 ReliaSoft Corporation, ALL RIGHTS RESERVED