Weibull

A Weibull function provides a convenient parametrization of accelerator SEE cross-section data, after correction for geometric effects. The Weibull function is widely used to fit direct ionization ("heavy-ion") SEE cross-section data, since it provides great flexibility in fitting the "turn-on" in the cross-section and naturally levels to a plateau or limiting value.

The functional form of the Weibull is:

F(x) = A (1- exp{-[(x-x₀)/W]^s})

where

• x = effective LET in MeV-cm²/milligram;
• F(x) = SEE cross-section in square-microns/bit;
• A = limiting or plateau cross-section;
• x₀ = onset parameter, such that F(x) = 0 for x < x0;
• W = width parameter;
• s = a dimensionless exponent.

As noted above, the Weibull distribution is generally used to describe heavy-ion (ie., direct-ionization) induced SEE cross-sections. However, it has been shown that in some devices, a Weibull function also gives a better empirical description of the proton-induced SEE cross-section than the Bendel 1- and Bendel 2-parameter fits which are generally used for this purpose. The CREME96 software therefore also allows you to use Weibull fits in calculating proton-induced SEE rates. In this case,

• x = proton energy in MeV
• F(x) = proton-induced SEE cross-section in units of 10^-12 cm²/bit

For more information on the Weibull function, see:

"Rate Prediction for Single Event Effects -- a Critique" by E.L. Petersen, J.C. Pickel, J.H. Adams, Jr., and E.C. Smith, IEEE Transactions on Nuclear Science NS-39, No. 6, pp. 1577-1599, December 1992.

For more information on Weibull fits to proton-SEE cross-sections, see:

"Single Event Upsets Caused by Solar Energetic Heavy Ions" by A.J. Tylka,W.F. Dietrich, P.R. Boberg, E.C. Smith, and J.H. Adams, Jr., IEEE Transactions on Nuclear Science, December 1996 (in press).