Two-Parameter Model for Estimation of SEE Sensitivity of VLSI Circuits under Ion Irradiation
Two-parameter model for estimation SEE sensitivity of VLSI circuits under ion irradiation is discussed. An approach to IC SEE sensitivity parameters estimation based on charge collection by a point node is considered. The improved model takes into account finite sizes of sensitive volume and allows more correct estimation of an angle dependence of threshold LET. The standard approach for estimation of single event effect (SEE) sensitivity assumes that the area of charge collection from the charged particle track is fixed, while sensitivity of IC elements has a spread reflecting experimental dependency of SEE cross section change on linear energy transfer (LET). It is clear, that it is vice versa in practice. Sensitive volume may vary, but the critical charge is constant for the same type of VLSI elements. The point node model of charge collection allows overcoming this contradiction. The value of collection charge (ionizing response) decreases as exponential function of the distance between points of sensitive node and charge generation. In case of incidence of ion particle at a distance from the center of the point sensitive area, LET needed for SEE is determined by integrating along the track length. Two parameters are needed to describe the dependence of SEE cross section as a function of LET : the effective collection length (l<sub>c</sub>) and the threshold LET (L<sub>zo</sub>). Unfortunately, this model gives changes in threshold LET dependencies on an angle of incidence that are smaller than the experimental results. The effect of finite sizes of the sensitive area allows overcoming this obstacle. SEE cross section at the corresponding value of LET increases. One can see a satisfactory correlation between experimental results and simulation results for different SEEs: SEUs, SEFIs, SELs and SETs for various VLSI, but the extra parameter, namely radius of sensitive area (r<sub>s</sub>) is added. Moreover, the effective collection length l<sub>c</sub> is correlated with design rules, thus the diffusion processes of charge collection predominate on drift processes. The analysis showed that acceptable accuracy can be obtained within the two-parameter model if it is assumed that r<sub>s</sub>=l<sub>c</sub>. We can observe change of LET threshold depending on the angle of incidence practically as 1/cos0 until 0<60<sup>o</sup>. In this case it is not always possible to obtain satisfactory agreement with experimental data in subthreshold area. However, the error in this area does not lead to noticeable errors in the estimates of the SEE rate under the cosmic ion irradiation.