acceleration factor, temperature (A_T)

The acceleration factor due to changes in temperature.

NOTE 1 This is the acceleration factor most often referenced. The Arrhenius equation for reliability is commonly used to calculate the acceleration factor that applies to the acceleration of time-to-failure distributions for microcircuits and other semiconductor devices:

A_T = λ_T1/ λ_T2 = exp[(-E_a/k)(1/T₁ - 1/T₂)]

where

E_a is the activation energy (eV);
k is Boltzmann's constant (8.62 × 10^-5 eV/K);
T₁ is the absolute temperature of test 1 (K);
T₂ is the absolute temperature of test 2 (K);
λ_T1 is the observed failure rate at test temperature T₁ (h^-1);
λ_T2 is the observed failure rate at the test temperature T_{2 n}(h^-1).

NOTE 2 Other acceleration factors can be calculated for electrical, mechanical, environmental, and other stresses that can affect the reliability of a device. Acceleration factors can be a function of one or more of the basic stresses. A plot of the reciprocal of absolute temperature, 1/T (K), versus the log of percent failed is linear for the lognormal distribution.

NOTE 3  λ_s = λ_t ∙ A_T, where λ_s is the quoted (predicted) system failure rate at some system temperature T_s and λ_t is the observed failure rate at some test temperature T_t, and A_T is the temperature acceleration factor due to the change from T_t to T_s.

References

JEP122E, 3/09
JEP143B.01, 6/08
JESD74A, 2/07