Arrhenius equation (for reliability)

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

AT = exp [(-Eaa/k) (1/T1 - 1/T2)]


AT is the acceleration factor due to changes in temperature;
Eaa 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 Eaa, 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  λs = λtAT, where λs is the quoted (predicted) system failure rate at some system temperature Ts and λt is the observed failure rate at some test temperature Tt.


JESD91A, 8/01