Critical Charge Method

The CREME96 software allows you to calculate the direct-ionization ("heavy-ion") -induced SEU rate as a function of critical charge, Q_c, the minimum charge deposition required to produce an upset. In this method, the SEU cross-section is treated as a step-function:

• SEU cross-section = 0 for Q_deposited < Q_c
• SEU cross-section = constant for Q_deposited > Q_c

However, because the amount of charge needed to upset a bit also depends on where the ionizing particle traverses the bit's sensitive volume, a single critical-charge value is generally inadequate to characterize the upset cross-section. Instead of a step-function, real SEU cross-sections generally show a gradual "turn-on" with increasing charge deposition: with increasing charge deposition, the bit is vulnerable to upset over a larger portion of its sensitive volume. For accurate SEU rate calculations, this "turn-on" must be taken into account, using a parametrization of the SEU cross-section data, such as the Weibull fit.

In general, the critical charge method does not give accurate SEU rates for space applications. However, it still may be useful for order-of-magnitude estimates by chip designers.

See additional information on converting from threshold LET to critical charge and on scaling of critical charge with feature size.

In using the critical charge method in the CREME96/HUP module:

• The critical charge must be specified in picoColoumbs (10^-12 Coulombs).
• The limiting cross-section must be specified in square-microns/bit.
• If you enter "0" in the limiting cross-section input field, the limiting cross-section will be set to "xy", the product of the lateral RPP dimensions.
• Alternatively, if you set x=y=0 in the RPP dimension input fields, they will be reset automatically to the square root of the limiting cross-section.
• If you set x=y=0 and the limiting cross-section=0, HUP will return an SEU rate of zero.

It should be noted that there is some confusion in the language which describes charge deposition in microelectronic devices. The term "critical charge", as characterized above, is widely used in the space-engineering literature. However, perhaps more appropriately, the charge described above should be called "deposited charge", since "critical charge" is also used by circuit designers to specify the amount of charge which must actually be collected at a sensitive node. Amplification and/or collection-efficiency effects can cause the "deposited" and "collected" charges to be significantly different.

Finally, it should also be noted that there is no uniform definition of what constitutes the "threshold LET". In some cases, authors define the threshold as the lowest effective LET at which SEEs are observed; in other cases, the "threshold" is defined as the point at which the SEE cross-section has reached ~50% of its limiting value. In cases where there is insufficient information to determine the complete LET-dependence of the SEE cross-section (as given by a Weibull fit, for example), the later usage is preferred, since the former generally gives predictions which are too conservative.

For further discussion, see E.L. Petersen, "Cross-Section Measurements and Upset Rate Calculations", IEEE Transactions on Nuclear Science, NS-43, 2805 (1996).