To find the failure rate at different junction temperatures from your reliability report http://www.atmel.com/dyn/resou...9C2051.pdf you must take the Arrhenius' formula and do some statistics:

'Retention bake test' at 150°C, which simulates a highly accelerated stress for devices, yielded the following total device hours (t) without any failure:

AT89C2051: 3,535,000 hours

According theory gives an Arrhenius' acceleration factor of:

Af = exp [Ea / k x (1 / Tu - 1 / Tt)] = exp [0.5 / 8.6171D-5 x (1 / (40 + 273.16) - 1 / (150 + 273.16)] = 124

Ea = 0.5eV is the activation energy of failure mechanism, k = 8.6171D-5 is Boltzmann's constant, Tu is use condition junction temperature (40°C in this example here) and Tt is test condition junction temperature.

The failures in time (FITs) are estimated by the help of chi-square distribution:

lambda = chi-square / 2 / Af / t x 1D+9 = 1.833 / 2 / 124 / t x 1D+9 = 7,391,129 / t = 7,391,129 / 3,535,000 = 2.1 FITs

chi-square = 1.833 represents 'zero failures' and '60% confidence level'.

2.1 FITs means 2.1 failures per 10^9 hours, or 0.0000021 failures per 1,000 hours or lambda = 0.00021% per 1,000 hours, which is the unit presented in your reliability report.

2.1 FITs also corresponds to a MTTF (mean time to failure) of 54,360 years.

Keep in mind, though, that using a different confidence level will have some influence on failure rate. When chosing 99% confidence level, MTTF is 5 times smaller!

With the scheme above you can estimate the failure rate for any other junction temperature.


Atmel states here http://www.atmel.com/dyn/produ...aq_id=1685 , that the data retention rate for all FLASH/EEPROM devices is a minimum of 10 years. Why is this so much smaller than the 54,360 years from above?

Atmel might specify this data retention time for the full operating temperature range. So, we should calculate the failure rate for Tu = 125°C and a confidence level of 60%, which yields:

Af = exp [Ea / k x (1 / Tu - 1 / Tt)] = exp [0.5 / 8.6171D-5 x (1 / (125 + 273.16) - 1 / (150 + 273.16)] = 2.4

lambda = chi-square / 2 / Af / t x 1D+9 = 1.833 / 2 / 2.4 / 3,535,000 x 1D+9 = 108 FITS

This corresponds to a MTTF of 1057 years.

Now, we must take into account, that Atmel specifies the data retention time for all their FLASH/EEPROM products. And as the failure rate is proprtional to integration, we must assume that a 2KB FLASH must show a much lower failure rate than a 128KB FLASH, about 64 times smaller. This degradation with higher integration can indeed be seen from other reliability reports. So, finally, for a 128KB product we roughly estimate a failure rate at 125°C junction temperature and 60% confidence level of about 7000 FITs corresponding to a MTTF of about 16 years.


Kai