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2019 | OriginalPaper | Chapter

9. Accelerated Degradation

Author : J. W. McPherson

Published in: Reliability Physics and Engineering

Publisher: Springer International Publishing

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Abstract

In Chap. 2 we learned that a stressed material was at a higher Gibbs Potential and therefore more unstable. The stressed material will spontaneously degrade, but at what rate? We might suspect, and rightfully so, that higher stress levels will make a material even more unstable and therefore accelerate the degradation rate; also, our intuition might suggest that the degradation rate for a material is temperature dependent. This chapter will develop the needed equations that show that this is indeed the case.

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previous chapter Failure Rate Modeling

next chapter Acceleration Factor Modeling

Equation (9.1) represents the Boltzmann probability that atoms in the initial state will obtain the necessary energy to go over the barrier to the degraded state. It is possible that the atoms can tunnel through the barrier, but the tunneling probability is very small except for the very lightest of elements such as hydrogen. For nearly all other elements, the Boltzmann probability is usually much greater than the tunneling probability. Boltzmann’s constant is 8.62 × 10⁻⁵ eV/K.

sinh(x) ~ x for small x and sinh(x) ~ exp(x)/2 for large x.

Note that since it was assumed that the free energy difference between the initial state and the degraded state was zero, when ξ = 0 then the net degradation rate at low stress levels goes to zero when b is zero.

A Maclaurin series expansion is carried out (keeping only the first term).

Schrodinger, E.: Statistical Thermodynamics, Dover Publications, (1952).

Desloge, E.: Thermal Physics, Holt, Rinehart and Winston, Inc., (1968).

Haase, R.: Thermodynamics of Irreversible Processes, Dover Publications, (1969).

Barret, C., et al.: The Principles of Engineering Materials, Prentice Hall, (1973).

Sears, F. and Salinger, G: Thermodynamics, Kinetic Theory, and Statistical Thermodynamics, 3^rd Ed. , Addison-Wesley Publishing, (1975).

Kittel, C. and H. Kroemer: Thermal Physics, 2^nd Edition, W.H. Freeman and Co., (1980).

McPherson, J.: Stress Dependent Activation Energy, IEEE International Reliability Physics Symposium Proceedings, 12 (1986).

McPherson, J., Accelerated Testing. In: Electronic Materials Handbook, Vol. 1 Packaging, ASM International, 887 (1989a).

McPherson, J.: Accelerated Testing and VLSI Failure Mechanisms, Tutorial, IEEE International Symposium on Physical and Failure Analysis of Integrated Circuits, (1989b).

Title: Accelerated Degradation
Author: J. W. McPherson
Publisher: Springer International Publishing
Book: Reliability Physics and Engineering
Print ISBN: 978-3-319-93682-6

Electronic ISBN: 978-3-319-93683-3

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-319-93683-3_9