The life expectancy of most products is estimated at some point prior to their introduction. Reliability analyses are an integral part of the design cycle of a product. In all reliability calculations, temperature is the key driver. The predicted life span from these calculations is often the deciding factor for introducing the product or investing more resources in redesign.
The questions that linger are: to what level of accuracy can we determine the temperature magnitude, and what is the impact of temperature uncertainty on the predicted reliability (i.e., the expected life of the product)?
When a system is operating, it incessantly experiences temperature and power-cycling. Such fluctuations, resulting from system design and operation or from complex thermal transport in electronic systems, create large bandwidths in temperature response. Whether it happens in the course of an analysis or a compliance/ stress testing, we often overlook the accuracy by which temperature is measured or calculated. Yet to truly obtain an adequate measure of a systems reliability in the field, such temperature data is essential.
To demonstrate the impact of temperature on reliability, consider the two models commonly used in practice. The Arrhenius model [1], often referred to as Erroneous, is perhaps the most broadly used model in the field. Equation 1 shows the reaction rate (failure rate) k and the acceleration factor AT. KB is the Boltzmann constant (8.617 x 10-5 eV/K) and Ea is the activation energy. All temperatures are in Kelvin. Activation energy depends on the failure mechanism and the materials (for example, 0.3 – 0.5 for oxide defects, and 1.0 for contamination).
[1]
The second model, Eyring, often referred to as More Erroneous, is shown by Equation 2.
[2]
The data shows that the uncertainty band is between 7 to 51%. These numbers by themselves are alarming, yet they are commonly encountered in the field. In either case, Stand-Alone or Device-In-System, being able to accurately determine the temperature or air velocity in a highly three-dimensional thermal transport environment is not a task to be treated casually.
To measure the impact of such uncertainty on the reliability prediction, it’s best to calculate its impact on the Acceleration factor AT.
Let us consider the case when:
T1 = 40oC
T2 = 150oC
Ea = 0.4 eV
kB = 8.6×10-5 eV/K
This results in AT = 48. Now, let us impose a 10% and 35% uncertainty on the temperature measurement of T2. Table 1 shows the result of this error on the acceleration factor.
Table 1 clearly demonstrates how a small degree of uncertainty in temperature measurement can negatively impact the Acceleration Factor and, thus, the reliability predictions where AT is often used. The first row shows the correct temperature. The second row shows the result of a 10% error in temperature measurement (i.e., 165oC instead of 150oC). The last row shows the impact of a 35% error (i.e., 202oC vs. the 158.6oC that the device is actually experiencing). The end result of this error in measurement is a 230% error in the Acceleration Factor.
One may think such an error is rare, but the contrary is true! In a simple device-case-temperature measurement, the temperature gradient could be in excess of 20oC from the die to the edge of the device. Or the air temperature variation in a channel formed by two PCBs could exceed 30oC. Of course, there are variations due to geometry, material and power dissipation that are observed in any electronics system. If we add to these the effects of improperly designed instruments, the combination of physical variation and the instrument error could certainly be detrimental to a products launch.
Longevity and life cycle in the market are keys for a products success. Therefore, to determine system performance, a reliability analysis must be performed. Since time is of the essence, and first-to-market is advantageous, the quickest reliability prediction models (analysis in general) will continue to be popular. To make such models, the use of Equations 1 and 2, or others more meaningful, must include accurate component and fluid temperature data. Measurement is heavily relied upon for temperature and air velocity determination. It is imperative to employ instruments designed for use in electronics systems with the highest level of accuracy and repeatability. High-grade instruments with quality output will enhance the reliability of the product you are working on.
SUMMARY
Small errors in temperature and air flow measurements can have a significant effect on reliability predictions. The origin of these errors lies in the measurement process or the use of inaccurate instruments. The former depends on the knowledge-base of the experimenter. That is why a good experimentalist is even a better analyst. You must know where to measure and the variations that exist in the field of measurement. Electronics system environments are notorious for such variations. It is repeatedly seen that, in one square centimeter of air flow passage between two PCBs, you can have temperature variations in excess of 30oC. Therefore, measurement practices and instrument selection must address these changes and not introduce further errors because of inferior design. Besides its design, an instrument’s construction and calibration should not introduce more errors. Accurate and high-quality instruments are not only essential for any engineering practice, their absence will adversely impact reliability predictions of a product at hand. No company wants to have its products returned, especially because of thermally induced failures.
References:
1. Klinger, D., Nakada, Y., and Menendez, M., AT&T Reliability Manual, Van Nostrand Reinhold, 1990.
2. Azar, K., The Effect of Uncertainty Analysis on Temperature Prediction, Therminic Conference, 2002.
