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Life Distributions

Reliability engineers are in many ways like soothsayers - they are expected to predict many things for the semiconductor company: how many failures from this and that lot will occur within x number of years, how much of this and that lot will survive after x number of years, what will happen if a device is operated under these conditions, etc.

To many people, such questions seem overwhelmingly difficult to answer, half-expecting reliability engineers to demonstrate some supernatural powers of their own to come up with the right figures.

Fortunately for reliability engineers, they don't need any paranormal abilities to give intelligent responses to questions involving failures that have not yet happened. All they need is a good understanding of statistics and reliability mathematics to be up to the task.

Reliability assessment, or the process of determining to a certain degree of confidence the probability of a lot being able to survive for a specified period of time under specified conditions, applies various statistical analysis techniques to analyze reliability data. If properly done, a reliability prediction using such techniques will match the survival behavior of a lot, many years after the prediction was made.

A good understanding of life distributions is a must-have for every reliability engineer who expects to exercise sound reliability engineering judgment whenever the need for it arises. A life distribution is simply a collection of time-to-failure data, or life data, graphically presented as a plot of the number of failures versus time. It is just like any statistical distribution, except that the data involved are life data.

By looking at the time-to-failure data or life distribution of a set of samples taken from a given population of devices after they have undergone reliability testing, the reliability engineer is able to assess how the rest of the population will fail in time when they are operated in the field. Based on this reliability assessment, the company can make the decision as to whether it would be safe to release the lot to its customers or not, and what risks are involved in doing so.

All new engineers in the semiconductor industry are acquainted with the bath tub curve, which represents the over-all failure rate curve generally observed in a very large population of semiconductor devices from the time they are released to the time they all fail. The bath-tub curve has three components: the early life phase, the steady-state phase, and the wear-out phase.

The failure rate is highest at the beginning of the early life phase and the end of the wear-out phase. On the other hand, it is lowest and constant in the long steady-state phase at the middle part of the curve. Collectively, these phases make the curve look like a bath tub (where it obviously got its name).

The bath tub curve takes into account all possible failure mechanisms that the population will encounter. Some failure mechanisms are more pronounced in the early life phase (such as early life dielectric breakdown), while others are more pronounced in the steady-state or wear-out phases. Failures that occur in the early life phase are known as infant mortality, which are screened out in production by burn-in.

In real life, it is not always practical to evaluate the failure or survival rate of a population of devices in terms of the bath tub curve. Reliability assessments are often conducted to evaluate only the known weaknesses of a given lot or, if the lot has no known weaknesses, to determine if it is vulnerable to any of the critical failure mechanisms dreaded in the semiconductor industry today.

Such reliability assessments are conducted by running a set of industry-standard reliability tests, generating life data along the way. These life data are then analyzed according to what type of life distribution they fit.

There are currently four (4) life distributions being used in semiconductor reliability engineering today, namely, the normal distribution, the exponential distribution, the lognormal distribution, and the Weibull distribution. Different failure mechanisms will result in time-to-failure data that fit different life distributions, so it is up to the reliability engineer to select which life distribution would best model the failure mechanism of interest.

<Proceed to Page 2 - Distribution Functions and the Normal Life Distribution>

<Proceed to Page 3 - Exponential and Lognormal Life Distributions>

<Proceed to Page 4 - Weibull Life Distribution>

Reliability Modeling; Failure Analysis; LTPD/AQL Sampling

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