 Activation Energy

Activation Energy , usually denoted by its symbol Ea, is defined as the minimum amount of energy required to initiate a particular process. It is usually used in the context of chemical reactions, i.e., as the minimum amount of energy that chemical reactants must possess before they can undergo a chemical reaction.  In the context of semiconductor device reliability, however, activation energy refers to the minimum amount of energy required to trigger a temperature-accelerated failure mechanism.

A failure mechanism is defined as a physical phenomenon that can lead to device failure if triggered and given enough time to progress.  This is not the same as the failure mode, which is the type of failure that a device exhibits.  The failure mechanism, in essence, is the physical phenomenon behind the failure mode. A single failure mechanism can result in several different failure modes, in the same way that similar failure modes can be due to different failure mechanisms. During failure analysis, the ability to identify the correct failure mechanism is the key to preventing the problem from happening again.

A discussion on activation energy is never complete without mentioning the Arrhenius Equation, which gives the basic relationship between the rate at which a failure mechanism occurs, the temperature, and the activation energy of the failure mechanism.  The Arrhenius Equation is as follows: R = Ae(-Ea/kT)  where R is the rate at which the failure mechanism occurs, A is a constant, Ea is the activation energy of the failure mechanism, k is Boltzmann’s constant (8.6e-5 eV/K), and T is the absolute temperature at which the mechanism occurs. Ea is expressed in electron volts (eV).  If one were to collect the median lifetime (time it takes for 50% of a set of samples to fail) data of different sets of samples accelerated to fail by the same, specific failure mechanism at different temperatures, the natural logarithms (ln) of these median lifetimes can be plotted against 1/T (T is the temperature in deg K) to yield a straight line whose slope is equal to Ea/k.  This is how reliability engineers estimate the activation energy of a given failure mechanism.

The value of activation energy indicates the relative tendency of a failure mechanism to be accelerated by temperature, i.e., the lower the Ea, the easier it is to trigger a failure mechanism with temperature. A negative Ea means that the failure mechanism is accelerated by decreasing the temperature. Hot carrier injection is an example of a failure mechanism with a negative activation energy.

Table 1 shows some activation energy values obtained by various researchers for various failure mechanisms commonly encountered in the semiconductor industry.

Table 1. Activation Energies of some Failure Mechanisms

 Failure Mechanism Accelerating Factors Activation Energy Electric Field, Temperature 0.2 - 1.0 eV Humidity, Temperature, Voltage 0.3 - 1.1 eV Temperature, Current Density 0.5 - 1.2 eV Au-Al Intermetallic Growth Temperature 1.0 - 1.05 eV Electric Field, Temperature -1 eV Slow Charge Trapping Electric Field, Temperature 1.3 eV Temperature 1.0 - 1.05 eV

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