The Effect of Temperature on Failure Rate

A companion piece to "What Causes Semiconductor Devices to Fail?" from our November 1999 issue.

Jon Titus, Editorial Director -- Test & Measurement World, 11/1/1999 2:24:00 PM

You may recall hearing in a chemistry class that increasing the temperature of a reaction by 10°C increases the reaction’s rate twofold. That type of observation led Swedish chemist Svante Arrhenius (1859–1927) to develop the chemical-kinetics equation that bears his name. Arrhenius made other discoveries, too, and he won the Nobel Prize in Chemistry in 1903.

The Arrhenius equation relates the rate of a temperature-dependent process to temperature with the equation explained in "Models Predict Failure Rates":

R = Ae^{(–E_a /kT)}

The activation energy (E_a) and the Boltzmann constant (k) appear in units of electron volts, which are more appropriate for failure analysis than another unit of energy such as ergs or joules.

As stated in the section labeled “Thermal Overstress” in the main article, reducing the temperature of a semiconductor junction from 160°C to 135°C will cut the rate of failures by about half. Here is how the Arrhenius equation predicts this behavior. First, convert the equation to its logarithmic equivalent. You can use base-e or base-10 logarithms:

Then differentiate the equation:

and rearrange it so you can insert values for two temperatures, T₂ and T₁:

Now use an activation energy of about 0.4 eV, which is typical for electronic failures (see the table in "Models Predict Failure Rates"), and substitute the value 160°C for T₂ and 135°C for T₁. Also use the Boltzmann constant listed earlier and solve the equation for the logarithm of the ratio of the rates. The ratio should be about 2, thus the log should be about 0.301.

Go back to"What Causes Semiconductor Devices to Fail?"