Models Predict Failure Rates
A companion piece to "What Causes Semiconductor Devices to Fail?" from our November 1999 issue.
V. Lakshminarayanan, Centre for Development of Telematics, Bangalore, India -- Test & Measurement World, 11/1/1999 2:07:00 PM
The Arrhenius equation, one of the best-known rate models, relates temperature to semiconductor reliability. The equation predicts the rate of failure, not the failure of a specific device. (Keep in mind that reliability also depends upon factors such as operating current and voltage.) Assuming that electrical conditions remain within spec, you can use the Arrhenius equation below to model the rate of electrical failures induced by temperature. (The equation results from many years of experimental chemistry, which led Arrhenius to formulate the equation.)
R = Ae(–Ea/kT)
where,
R = failure or reaction rate
A = empirical constant
Ea = activation energy (eV)
k = Boltzmann’s constant (8.6 x 10-5 eV/K)
T = temperature in Kelvin (°C + 273.16°C)
As temperature increases, so does the failure rate, so more devices fail at higher temperatures than at lower ones. (For semiconductors, T represents a device’s junction temperature.) Of course, several independent failure mechanisms can act in concert, thus making it difficult to compute an absolute failure rate for a component.
Nevertheless, the Arrhenius equation lets you estimate failure rates. Different failure mechanisms have different activation energies that range from 0.3 eV to 1.0 eV (see the table, below).
To model the effects of other stresses, you’ll need other models. The Eyring equation models thermal and environmental mechanisms, and the Reich Hakim, the Lawson model, and the Peck equations model temperature and humidity. (For more information about these models, see "Using Models to Predict Semiconductor Failures.")
By applying these models, you can determine in advance the rate at which a specific mechanism will cause devices to fail. If devices seem to fail at a particularly high rate, the models can help you gain insight into the conditions that users have subjected them to.
Table. Activation Energies for Failure Mechanisms
| Failure Mechanism | Activation Energy, Ea (eV) |
| Oxide defects | 0.3 to 0.5 |
| Bulk silicon defects | 0.3 to 0.5 |
| Corrosion | 0.45 |
| Assembly defects | 0.5 to 0.7 |
| Electromigration | 0.6 (Al line) 0.9 (Contact) |
| Mask or photoresist defect | 0.7 |
| Contamination | 1.0 |
| Change injection | 1.3 |
Go back to "What Causes Semiconductor Devices to Fail?"
See also, "The Effect of Temperature on Failure Rate"
