As the temperature of a gas rises, the motion velocity increases in the molecules that make up the gas. However, the gas contains a mixture of fast-moving and slow-moving molecules, and if we posit that the velocity distribution conforms to the negative exponential distribution in relation to (1/T), then in particular the activated molecules abounding in energy are what is actually contributing to the reaction, and the proportion of activated molecules increases markedly along with rising temperature. It has been proposed that the chemical reaction between two gases can only be contributed to by molecules with relative motion energy that exceeds activation energy level E. Therefore, in isothermal reactions in this type of molecular collision between two gases, the explanation of formula (3.1) applies to the proportion of exp(-E/RT), which is the proportion of activated molecules with energy above a certain energy limit value. However, because this theory cannot be properly applied to more complex reactions in which numerous molecules participate, in 1935 H. Eyring and E.H. Eyring proposed the absolute reaction theory that was developed from this approach.
  This approach holds that activation energy is the main factor in reaction velocity, and that this can be separated into activation energy and activation entropy. When T represents temperature stress and S represents other stress, reaction velocity K becomes



  This is known as the Eyring formula. This formula is frequently used in the field of electrical and electronic equipment. However, no theory has yet been established that can account for all chemical reactions. Here, becomes the constant.

3-3 Applying chemical kinetics
  Let's try to adapt these formulas to the field of electrical and electronic equipment reliability. Using the aforementioned stress-strength model, we can conceptually grasp the process in which physical changes resulting from stress such as temperature and voltage reduce durability and lead to failure. Can chemical kinetics be applied to explain this type of phenomenon?
  If we express the level of stress applied to a product as x and the level of resulting deterioration as y, and if we regard y as a function of x, then we can express the following relationship.



  When there are multiple sources of stress, we must regard x as a vector, but to simplify matters, we can make it scalar. Deterioration with age dy/dt signify reaction velocity, so we can express this as



  Here, when K is a constant, if we integrate formula (3.4), we get y = Kt. Now, if we set L as the time in which deterioration level y reaches product proof stress limit r, then the y = Kt relationship yields the relationship



  Next, if we substitute formula (3.3) for this formula, we get



  At this point, we can think of the product being operated. If we have the following two instances,
(1) Stress voltage is V1, operating temperature is T1 and the corresponding life is L1, and the failure rate is 1
(2) Stress voltage is V2, operating temperature is T2 and the corresponding life is L2, and the failure rate is 2
Using formula (3.6), we can show both relationships as

  If we attempt to express this as a failure rate, the mean life L and the failure rate of the electrical and electronic equipment have an inverse function relationship, and so the above formula becomes



  In the above formula, V2/V1 = S is called the stress ratio.
  When = 0 in formula (3.7), this becomes the Arrhenius formula, and is often adapted to temperature-dependent deterioration phenomena, and is useful for establishing the acceleration factor when performing accelerated testing.
  In other words, formula (3.7) can be rewritten in the following way.



  In other words, the rate of acceleration (the acceleration factor) can be found with the following formula.



  The Arrehnius model is widely applied to reliability testing and failure analysis of electrical and electronic equipment, especially to semiconductor devices. That is to say, semiconductor devices are manufactured using physical and chemical changes in the surface layers of material, and rather than having a structure of complete crystallization or solidification, they are combined in an amorphous state. Because of this, the changes that appear tend to be chemical rather than physical changes, and so chemical theory is considered easier to apply.