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positively skewed distributions. A right skewed distribution will

be a good model for data in a histogram with an extended right

tail. The Weibull distribution is sometimes referred to as a

distribution of minima. An example of a Weibull distribution is

the strength to break a chain where the weakest link describes

the strength of the chain. The extreme value distribution is a

distribution of maxima. It is the least utilized of the four life

distributions.

For means of example, the Weibull distribution will be used.

The Weibull lifetime distribution has the form:

F(t,

θ, β) + 1 * e

(1)

The two parameters for the Weibull distribution are q and b.

Theta is the scale parameter, or characteristic life. It

represents the 63.2 percentile of the life distribution. Beta is

the shape parameter. In order to determine the parameters for

the Weibull distribution, testing must be performed produce

failure on the devices. The failure data can be used to

calculate the maximum likelihood estimates or determined

graphically. It has not always been customary to perform

reliability demonstration testing until failures occur. In regards

to media testing, this seems to be the only method to derive

lifetime estimates that reflect a true understanding of the

device capability.

(2)

+ e

low

high

•

high

low

A media test typically needs to take results received in

weeks or months to predict lifetime in years. Acceleration

models are used to determine the relationship between the

accelerated test and the normal lifetime. Literature has

reported numerous models to equate testing to lifetime

including the Peck model for temperature and humidity [25].

The acceleration equation based on Peck’s model is where Ea

is 0.9eV and n is –3.0. The value K is Boltzmann’s constant

which is equal to 8.6171x10–5 eV/K. The relative humidity is

entered as a whole number, i.e. 85 for 85%. Using this sample

model, test results from humidity testing can be related to the

lifetime. The methods to equate test time to lifetime first

involves fitting the failure data to a lifetime distribution. For an

example, humidity data at 60

°C, 90% relative humidity and

bias was tested to failure. The failure data fit a Weibull

distribution with a characteristic life of 40,000 hours.

applying the acceleration factor equation shown above,

quantification of the lifetime in the use conditions can be

calculated. Figure 15 shows the cumulative failure distribution

for the test and use conditions for a 15 year lifetime. This

technique is key for media testing since the range of use

conditions is very broad. The consumer can determine the

attributes for the sensor to use for the application. The

attributes might include cost, performance, and possibility for

replacement.

Figure 15. Probability of failure versus time for humidity testing with bias on an integrated sensor device.

10%

30%

20%

40%

50%

60%

70%

80%

90%

100%

TIME (YEARS)

Test Condition

(60 C, 90% RH)

(30 C, 85% RH)

(25 C, 60% RH)

The

failure

distribution

example

shown

typically

represents one failure mechanism. The failure mechanism

that typifies humidity testing is mobile ions. An elevated

test temperature, humidity and bias contributes to the

mobility of the ions and the ability to create a surface

charge. By lowering the temperature, humidity or

switching the bias, an improvement in the lifetime can be

obtained. If a device manufacturer would test to failure and

report the lifetimes, the customer could select the

appropriate product for their application. Following a

template of reliability tests that have not been verified and

do not coincide with the applicable failure mechanism may

put the application at risk for surviving.

Humidity testing was used as an example above, but a

similar case could be made of other attributes involved

with media testing. Other attributes of the media test may

include the bias level and duty cycle, the pH or conductivity

of the solution, and any stress such as a pressure

differential. By modeling these attributes against the

various solutions, models for media compatibility can be

developed.

Freescale Semiconductor, Inc.

For More Information On This Product,

Go to: www.freescale.com

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