# Peck’s Relationship for Temperature & Humidity Testing

High temperature & humidity is a common test condition. For specific failure mechanisms, there are models available (or you can create a model) to determine the translation from test to use conditions.

These acceleration models generally only apply to one specific failure mechanisms and do not apply to a system level estimate of life. If the failure mechanism is the dominant failure mechanism for the product, then an ALT exploring just that mechanisms would provide a life estimate.

Peck’s relationship is an acceleration model for the effect of humidity on the metallization elements of integrated circuits within plastic enclosures (typically an epoxy over molding).

## Peck’s Relationship for Temperature & Humidity

When electronic components moved from small metal cans to epoxy packaging, one of the issues was moisture ingress leading to the silicon device failing quickly. If the epoxy over-molding did not form an adequate seal the application of a relatively high humidity at an elevated temperature could determine if the package would survive nominal temperature and humidity conditions for an extended time.

Peck and colleagues gathered reports and studies of the effects of temperature and humidity on the time to failure behavior for a range of epoxy based packages. The model they developed is empirically derived from a large number of different life studies.

$$ \large\displaystyle {{t}_{f}}=A{{\left( RH \right)}^{-n}}{{e}^{{}^{{{E}_{a}}}\!\!\diagup\!\!{}_{kT}\;}}$$

Where $- {{t}_{f}}-$ is the time to failure

A is a constant dependent on the materials, process, and conditions

RH is relative humidity

n is a constant

E_{a} is the activation energy

k is Boltzmann’s constant, 8.617 x 10^{-5} eV/K

T is temperature in Kelvin

## Acceleration Factor or Model

Using Peck’s relationship as a ratio of test conditions over use conditions we are able to eliminate the constant A, it simply cancels out.

$$ \large\displaystyle AF={{\left( \frac{R{{H}_{u}}}{R{{H}_{t}}} \right)}^{-n}}\exp \left[ \frac{{{E}_{a}}}{k}\left( \frac{1}{{{T}_{u}}}-\frac{1}{{{T}_{t}}} \right) \right]$$

The ratio results in the acceleration factor, AF, or the number of times one can multiply the test, subscript *t*, determined time to failure data to estimate the use condition, subscript *u*, expected time to failure duration.

Note the model is a form of an Erying model being the product of the inverse power law for humidity and the Arrhenius equation for the temperature elements.

## The Constants n and Ea

The constants were determined fitting the data from hundreds of studies using simple regression techniques. The constants vary depending on the:

- Geometry
- Material set
- Process conditions
- Testing conditions
- Use conditions

The values in Peck’s paper and in subsequent papers or books are only a starting point providing a rough model. You should determine the appropriate constants for your particular circumstance when ever possible.

In Peck’s paper he reports n = 2.7 and E_{a} = 0.79 eV. These values are also listed in Nelson’s discussion of the model.

Wayne Condra discusses Peck’s relationship and uses n = 3 and E_{a} = 0.9 eV.

## Summary

You acceleration factor may differ. Peck’s relationship is a great place to start when evaluating the longevity of moisture induce IC failure with epoxy over molded components. You can improve your acceleration model by determining the fitted constants for your specific system.

Finally, keep in mind Peck’s relationship is an acceleration model for temperature & humidity evaluation of moisture induce IC failure within epoxy over-molded components. It is not a general model for any application of temperature & humidity testing.

Peck, D Stewart. “Comprehensive Model for Humidity Testing Correlation.”* Reliability Physics Symposium, 1986. 24th Annual *(1986): 44-50.

Nelson, Wayne. *Accelerated Testing: Statistical Models, Test Plans, and Data Analysis.* Edited by S S Wilks Samuel. Wiley Series in Probability and Mathematical Statistics. New York: John Wiley & Sons, 1990.

Condra, Lloyd W. *Reliability Improvement with Design of Experiments.* New York: Marcel Dekker, 2001.

*
Also published on Medium. *

RAMKUMAR N says

Hello, I want to know n – constant, how to derive that plz define it.

Fred Schenkelberg says

In the work that Peck did reviewing hundreds of studies he found n = 2.7… that is an grand average fit. It is a regression analysis with your data at different humidity levels and different temperatures to determine the constants that work for your situation. n = 2.7 is a starting point for planning. The differences in materials and assembly processes will likely change these constants, yet I’ve not seen papers published in this area for some time.

A good starting point to design such an experiment would be to review the papers Peck references in his work.

Cheers,

Fred

Vishnu says

Thanks for your reply Mr. fred.

Can you show any proof. Please i need for my study.

Fred Schenkelberg says

The best place for details on the relationship is Peck’s paper

Peck, D Stewart. “Comprehensive Model for Humidity Testing Correlation.” Reliability Physics Symposium, 1986. 24th Annual (1986): 44-50.

Cheers,

Fred

Fred Schenkelberg says

Not sure there is a proof or derivation for the formula – it was empirically fit to hundreds of studies of temperature and humidity testing determining time to failure. Peck used regressional analysis to find the fitting parameters, n and Ea.

bita says

how can i find n and a constant for nimonic alloy?

can i use this equation for creep?

Fred Schenkelberg says

Not sure you could find constants for nemonic alloy and no, this equation is not suitable as is for creep. Cheers,

Fred

Raju Nalluri says

Hello Fred,

Thank you for such simple yet understandable article.

So, when i have to choose between Lawson model and Peck model, what should i Pick?

I see that in Lawson model, both the humidity and temperature factor are raised to the power of exponential where as it is not in case of Humidity factor in Peck´s model.

Regards,

Raju Nalluri

Fred Schenkelberg says

Hi Raju,

I’m not familiar with Lawson’s model and a quick search found the formula, yet I’ll have to research a bit more to understand what Lawson was modeling – specifically what failure mechanism.

In selecting any model for estimating the acceleration factor the choice is based on how well the model describes the stress to time to failure relationship for a specific failure mechanism. Temperature and humidity excite many different failure mechanisms that likely have different stress/time to failure relationships.

The best way to select a model is after you have failures and can confirm the mechanism at work… without that knowledge, it is engineering judgment.

Cheers,

Fred