Semiconductor glossary · Test and reliability

What Is Activation Energy?

Activation energy, Ea, is the height of the energy barrier on the way from a normal state to a degraded state. It controls how strongly a particular failure mechanism accelerates with temperature.

Energy is needed to cross the barrier

Atoms and molecules must receive enough energy from their environment to cross an energy barrier. As temperature rises, the proportion with enough energy increases. This is why temperature can accelerate degradation.

The Renesas reliability handbook expresses the temperature-dependent reaction rate as K＝Λexp(−Ea/kT). Here K is the reaction rate, Λ is a prefactor, T is absolute temperature in kelvin, and Ea is expressed in electronvolts (eV). The handbook reports 8.6157×10⁻⁵ eV/K for the Boltzmann constant k; this is the value used in its examples.

The barrier diagram illustrates the concept; its shape and vertical height are schematic rather than a measurement of a particular device.

A schematic energy barrier separates a normal state from a degraded state. Ea measures the energy needed to reach the activated state.

The value depends on the failure mechanism

The handbook reports 0.6〜1.0 eV for electromigration (EM). In a humidity-resistance calculation with no observed failures and no independently determined activation energy, it assumes 1.0 eV based on prior experience. These are a reported range and an example assumption, respectively. They are not a universal activation energy for every semiconductor or humidity failure.

Different failure mechanisms have different representative activation energies. Select or measure Ea for the mechanism and conditions that the accelerated test is intended to reproduce.

The cited handbook reports 0.6 to 1.0 eV for electromigration and assumes 1.0 eV in a humidity-resistance calculation example.

Estimate Ea from the measured slope

Measure lifetime at several temperatures and fit a line. The Arrhenius lifetime model is L＝A exp(Ea/kT); taking the natural logarithm gives ln L＝ln A＋Ea/kT.

With x = 1/T (K⁻¹) and y = ln L, slope m = Ea/k, so Ea = k × m.

With x = 1/(kT), the slope is Ea. The axis definition must be stated before interpreting a slope.

Two temperatures determine a line; three or more help test whether a straight-line model is appropriate over the measured range. This corrects the Japanese source's shorthand that the slope itself is Ea: that statement needs the energy-scaled reciprocal-temperature axis.

Other stresses introduce additional parameters

The Arrhenius model focuses on temperature. The handbook also discusses an Eyring model that incorporates other stresses. Its humidity-resistance form is L＝C・e^(Ea/kTb)・(RH)^−n・V^−α, where RH is relative humidity, V is applied voltage, and n and α are fitted stress parameters.

Adding humidity or voltage does not remove the need to identify the failure mechanism. The ROHM EcoGaN lifetime paper uses device-specific accelerated tests to connect stress, failure mechanisms and application conditions.

Trade-offs

A larger assumed Ea gives a larger temperature acceleration factor and can make a short test appear to cover a longer use period. If that assumption is too high for the actual mechanism, the lifetime estimate can be optimistic. A smaller Ea generally requires a longer test to cover the same use exposure.

For a failure-rate estimate that divides by accelerated equivalent exposure, an error in the acceleration factor propagates inversely into the calculated failure rate, provided the other inputs and the model stay the same. A mechanism change can invalidate that simple conversion altogether.

Frequently asked questions

What is activation energy?

It is the height of the energy barrier between a normal state and a degraded state. Energy from the environment is needed to cross that barrier.

What units are used?

Ea is expressed in electronvolts (eV). The Renesas handbook reports 8.6157×10⁻⁵ eV/K for k in its calculation examples.

Why does a higher temperature accelerate degradation?

A greater proportion of atoms or molecules has enough energy to cross the barrier. The Arrhenius equation describes this temperature dependence.

What values are typical?

The cited handbook reports 0.6〜1.0 eV for electromigration and assumes 1.0 eV in a humidity-resistance example. Neither should be applied indiscriminately to other mechanisms.

Does Ea change with the failure mechanism?

Yes. A representative activation energy is associated with a particular mechanism, and the relevant mechanism must be established for the test and use conditions.

How is Ea estimated?

Fit ln lifetime against reciprocal absolute temperature. The slope against 1/T is Ea/k; multiply that slope by k to obtain Ea. Against 1/(kT), the slope is Ea.

What happens if Ea is wrong?

The acceleration factor is wrong, changing the equivalent exposure and the calculated failure-rate estimate. Extrapolation can also fail if the dominant mechanism changes.

Compare the concepts

An acceleration factor is a lifetime ratio; activation energy is the mechanism-specific model parameter that helps determine that ratio. Black’s equation is a failure model for electromigration, not a universal model for every mechanism.