Abstract
Generally, materials/devices exist in metastable states. These states are referred to as being metastable because they are only apparently stable. Metastable states will change/degrade with time. The rate of degradation of the materials (and eventual time-to-failure for the device) can be accelerated by an elevated stress (e.g., mechanical stress, electrical stress, electrochemical stress, etc.) and/or elevated temperature.
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Notes
- 1.
A few exceptions to this general degradation rule exist. Very shallow charge-traps in MOSFETs can sometimes be filled more efficiently at lower temperatures. This will be discussed more in detail when the hot carrier injection (HCI) failure mechanism is discussed in Chap. 10.
- 2.
Equation (3) 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 other elements, the Boltzmann probability is usually much greater than the tunneling probability. Boltzmann’s constant is 8.62 × 10–5 eV/K.
- 3.
Our hypotheses are: (1) the stress \( \xi \) will serve to lower the activation energy (a will be positive as written) and (2) the stress may also serve to increase the free energy difference between the initial state and the degraded state (b will be positive as written). The actual degradation rate data will tell us if our hypotheses are correct.
- 4.
Sinh (x)Â ~Â x for small x and sinh (x)Â ~Â exp (x)/2 for large x.
- 5.
Note that since it was assumed that the free energy difference between the initial state and the degraded state was zero, when \( \xi \, = \,0, \) then the net degradation rate at low-stress levels goes to zero when b is zero.
- 6.
A Maclaurin Series expansion is carried out (keeping only the first term).
Bibliography
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McPherson, J., Accelerated Testing. In: Electronic Materials Handbook, Vol. 1 Packaging, ASM International, 887 (1989).
McPherson, J.: Accelerated Testing and VLSI Failure Mechanisms, Tutorial, IEEE International Symposium on Physical and Failure Analysis of Integrated Circuits, (1989).
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McPherson, J.W. (2013). Accelerated Degradation . In: Reliability Physics and Engineering. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00122-7_8
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DOI: https://doi.org/10.1007/978-3-319-00122-7_8
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