
Using the General LogLinear Model in ALTA PRO for Thermal Cycling
Having higher reliability than competitors is one of the key factors for success. This is especially true for the electronics industry. The reliability of electronic products can be predicted based on the design, the manufacturing process and the expected operating conditions. There are many different approaches for reliability estimation such as standards based reliability prediction, physics of failure and life testing. ReliaSoft's ALTA PRO employs a physics of failure approach and can be used to analyze test data for single or multiple stress conditions. In this article, we will analyze accelerated test data using the NorrisLandzberg model for leadfree solder joint lowcycle fatigue, by using the general loglinear (GLL) model in ALTA PRO.
Comparing the NorrisLandzberg Model and the GLL Model
In electronic devices, failures can occur due to fatigue caused by temperature cycling and thermal shock. These fatigue failures are often a result of cyclical stresses that are induced during the device’s normal powerup and powerdown cycles. These stresses lead to weakened materials that may fail due to several different causes, including dielectric/thinfilm cracking, lifted bonds and solder fatigue. The CoffinManson model and a modified version of it known as the NorrisLandzberg model have been used successfully to model crack growth in solder joints due to repeated temperature cycling as the device is switched on and off. The number of cycles to failure in the NorrisLandzberg model is represented as:
Where:
N_{f} is the number of cycles to failure
C is a coefficient
f is the cycling frequency [cycles/day]
ΔT is the temperature range during a cycle [K]
T_{max} is the maximum temperature during each cycle [K]
E_{a} is the activation energy [eV]
K is the Boltzmann's constant [8.617 × 10^{5} eV/K]
p and m are the model parameters
The cycling frequency (f), the temperature range (ΔT) and the maximum temperature (T_{max}) are the stresses considered for testing. The activation energy (E_{a}) can be determined by test data and it is usually related to certain failure mechanisms and failure modes. Typical parameters of the NorrisLandzberg model have been published for various solder types. For example, for tinlead (SnPb) solder and tinsilvercopper (SnAgCu or SAC) solder, the parameters are: p = 0.33, m = 1.9, and E_{a} = 0.122.
Acceleration factor can also be calculated as:
The general loglinear (GLL) model in ALTA PRO assumes a loglinear relation for the life characteristic, t_{p}, and is formulated as:
where:
t_{p} is the life characteristic
α_{0}, α_{1}, ... α_{n} are the parameters of the lifestress relationship
χ_{1}, χ_{2}, ... χ_{n} are the covariates
This equation can be rewritten in a more compact form as:
And we can express this in terms of the life characteristic as:
The life characteristic, t_{p}, can represent any percentile of the assumed underlying life distribution. It can be the scale parameter eta (Weibull distribution), mean (exponential distribution) or median (lognormal distribution).
The advantage of representing the life characteristic with the loglinear relationship is that lifestress relationship models can be assumed for the covariates by performing a simple transformation. Therefore, the NorrisLandzberg model, which is a combination of a power model for f, a power model for ΔT, and an exponential model for T_{max}, can be formulated via the GLL model by applying a logarithmic transformation to f and ΔT, and a reciprocal transformation to T_{max}. Hence, for three stresses the GLL model becomes:
Applying the transformations:
where the relationships between the parameters of the NorrisLandzberg and GLL models are described as:
p = −α_{1}
m = −α_{2}
^{Eα}⁄_{K} = α_{3}
Example
40 electronic components were tested to failure due to crack growth in solder joints as a result of repeated temperature cycling at three different elevated stress conditions. The associated data set is entered into an ALTA PRO standard folio, as shown below.
To represent the NorrisLandzberg model, choose the GLLLognormal model on the control panel, and then use the following stress transformations for the three stresses.
You can then use the GLL results from ALTA PRO to calculate the parameters of the NorrisLandzberg model, as shown next:
Conclusion
In this article, we introduced the NorrisLandzberg physics of failure model for crack growth in solder joints resulting from repeated temperature cycling in electronic devices. The relationship between the NorrisLandzberg model and the general loglinear model was presented, and ALTA PRO was used to estimate the NorrisLandzberg parameters for a given data set. A similar process can be used to analyze accelerated test data in ALTA for many physics of failure models with multiple stresses.
References
 Wayne Nelson, Accelerated Testing: Statistical Models, Test Plans and Data Analyses. New York: Wiley, 1990.
 "Reliability Prediction Methods for Electronic Products," Reliability Edge 9, no. 1: http://www.ReliaSoft.com/newsletter/v9i1/prediction_methods.htm?_ga=1.123553672.244422347.1440020929
 "Introduction to Accelerated Life Testing", ReliaWiki.org, accessed June 3, 2016, http://reliawiki.org/index.php/Introduction_to_Accelerated_Life_Testing
 M. Osterman, "Effect of Temperature Cycling Parameters (Dwell and Mean Temperature) on the Durability of Pbfree solders." Paper presented at the IMAPS Chesapeake Winter Technical Symposium, University of Maryland, January 27, 2010.
 "General LogLinear Model for Accelerated Life Data Analysis," Reliability Edge 2, no. 2: http://www.ReliaSoft.com/newsletter/2q2001/general_loglinear.htm
 "Using ALTA with MultiStress Physics of Failure Models", HotWire 90 (August 2008): http://www.weibull.com/hotwire/issue90/hottopics90.htm
 Putaala, J. et. al., "Aspects for Accelerated Testing and Reliable Lifetime Estimation of LeadFree Solder Interconnections," Paper presented at the IMAPS Nordic Conference, 2014
 K. C. Norris and A. H. Landzberg, "Reliability of controlled collapse interconnections," IBM Journal of Research and Development 13, no. 3 (1969): 266–271.
 Jinhua Mi, YanFeng Li, YuanJian Yang, Weiwen Peng, and HongZhong Huang, "Thermal Cycling Life Prediction of Sn3.0Ag0.5Cu Solder Joint Using TypeI Censored Data," The Scientific World Journal 2014 (2014).