Arrhenius equation (for reliability)

An equation used to calculate thermal acceleration factors for semiconductor device time-to-failure distributions:

A_T = exp [(-E_aa/k) (1/T₁ - 1/T₂)]

where

A_T is the acceleration factor due to changes in temperature;
E_aa is the apparent activation energy (eV);
k is Boltzmann's constant (8.62 × 10^-5 eV/K);
T₁ is the absolute temperature of the test (K);
T₂ is the absolute temperature of the system (K).

NOTE 1 The original Arrhenius equation (for atomic or molecular processes and chemical reactions) used the gas constant, not an activation energy, in the exponent. The "Arrhenius equation (for reliability)", used to calculate a thermal acceleration factor for a given observed time-to-failure distribution and E_aa, is in the form of the quotient of two Arrhenius equations, so that the acceleration factor for two different temperatures can be calculated.

NOTE 2  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.