Statistical Treatment of Damage Factors for Semiconductor Devices

By fitting a lognormal distribution to the data of Messenger and Steele a statistical analysis derives a formula for the survival probability, with 90 percent confidence, of a silicon transistor exposed to the neutron flux ϕ as: Ps(ϕ)=Fn[ln(C.T.F.-1)+ln(fTmin/ßmin/ϕ)+16.38/0.493] where Fn is the standard normal cumulative distribution function, C.T.F. is the circuit tolerance factor, fTmin is the minimum gain band width product specified by the manufacturer and ßmin is the minimum current gain specified by the manufacturer. The present analysis is similar to the previous one except that the analysis here accounts for the fact that a lognormal distribution does not exactly fit the data. The formula shown above differs from the one presented in reference 2 in that their denominator of 0.444 has been replaced by 0.493. The new denominator can increase previously estimated failure probabilities by a factor of 2.5. The method shown here is generally applicable to cases where distributions other than the lognormal ones are fitted to a set data.