SSER estimation on benchmark circuits

For charge strength Q2 = 99fC and Q3 = 132fC in Static (SPICE) or in Statistical (SPICE), very little difference can be found between static and statistical results. Therefore, we can take Q2 = 99fC and Q3 = 132fC as a static value and only run static SPICE once.

As a result, almost an half of time in SPICE simulation is saved.

Table 5.3 lists the total number of nodes, the name, and the total number of outputs for each circuit in the first three columns. Table 5.4 reports the SSER values required by the MC, QMC and QMC-IS (QMC + importance sampling) frameworks considering spatial correlation, respectively. The last column compute the SSER difference, by comparing re-sults from the MC frameworks considering spatial correlation. Moreover, Table 5.5 reports the runtime required by the MC, QMC and QMC-IS (QMC + importance sampling) frame-works considering spatial correlation, respectively. The last column compute the speedup, by comparing results from the MC frameworks considering spatial correlation.

From Table 5.3 and Table 5.4, SSER is clearly related to the number of nodes and primary outputs of a circuit, which correspond to the possibility of the circuit struck by radiation particles and the possibility of the transient faults observed at primary outputs, respectively. The runtime, however, depend not only on the number of strike nodes, but also the number of convolutions between nodes.

From Table 5.4, SSER difference is computed by |SSER_{M C}−SSER_{QM C}|/SSER_{M C}

Table 5.4: Benchmark circuits, SER from the baseline MC, QMC and QMC-IS frameworks considering spatial correlations

MC QMC QMC-IS

circuit SSER (FIT) SSER (FIT) SSER diff. (%) SSER (FIT) SSER diff. (%)

c432 897.37E-05 908.53E-05 1.24 905.01E-05 0.85

c499 1102.24E-05 1161.77E-05 0.97 1082.18E-05 1.82

c880 1199.94E-05 1193.65E-05 0.52 1191.71E-05 0.69

c1355 1111.32E-05 1127.01E-05 1.41 1087.1E-05 2.18

c1908 907.23E-05 917.83E-05 1.17 866.17E-05 4.53

c2670 2988.66E-05 2992.9E-05 0.14 2992.7E-05 0.14

c3540 2113.85E-05 2090.39E-05 1.11 2122.44E-05 0.41

c5315 7845.95E-05 7862.43E-05 0.21 7848.76E-05 0.04

c6288 3733.71E-05 3661.51E-05 2.35 3656.12E-05 2.08

c7552 5929.5E-05 6263.61E-05 5.63 5905.00E-05 0.41

m4 828.2E-05 829.74E-05 0.19 786.3E-05 5.06

m8 1973.04E-05 1988.19E-05 0.77 1977.49E-05 0.23

m16 4409.17E-05 4550.25E-05 3.20 4459.3E-05 1.14

m24 6927.18E-05 7109.2E-05 2.09 7036.49E-05 2.56

Average 1.59 1.68

and the average of 1.59% difference implies that the QMC and MC frameworks are of the same quality. SSER difference is computed by |SSERM C − SSERQM C−IS|/SSERM C

and the average of 1.68% difference implies that the QMC-IS and MC frameworks are of the same quality. And From Table 5.5, for all benchmark circuits, the overall speedup brought by QMC is 2.55X in average. For all benchmark circuits, the overall speedup brought by QMC-IS is 3.72X in average.

Table 5.5: Benchmark circuits, runtime from the baseline MC, QMC and QMC-IS frame-works considering spatial correlations

MC QMC QMC-IS

circuit TM C(sec) TQM C(sec) speedup (X) TQM C−IS(sec) speedup (X)

c432 145.20 44.76 3.24 31.04 4.68

c499 870.61 269.71 2.75 153.09 5.71

c880 174.43 49.62 3.51 31.93 5.46

c1355 913.07 280.46 3.26 198.36 4.60

c1908 341.71 139.59 2.45 103.46 3.30

c2670 463.91 142.52 3.26 96.11 4.83

c3540 1176.2 383.92 3.06 348.14 3.38

c5315 881.85 595.41 1.48 482.31 1.83

c6288 16111.8 4183.31 1.93 3671.84 4.39

c7552 1533.25 400.74 3.83 316.45 4.85

m4 114.23 47.65 2.4 37.159 3.07

m8 676.65 342.43 1.97 277.89 2.43

m16 9925.51 5636.89 1.76 2422.43 4.09

m24 37894.21 26687.6 1.42 10670.5 3.55

Average 2.55 3.72

Chapter 6

Conclusion

6.1 Conclusion

Due to the presence of process variation, all static techniques tend to unavoidably under-estimate true SERs and the statistical SER analysis is built. In this paper, we adopt quality statistical cell models, based on which a Monte Carlo SSER framework is developed and consider spatial correlations into our framework. We further apply importance sampling to the framework for reducing variance and faster converging SSER. According to the ex-perimental results, the average of SSER errors are within 1.68% compared to Monte Carlo SPICE simulations, more accurate than those from previous works. Furthermore, the use of quasi-random sequences and importance sampling demonstrates an average of 3.72X run-time improvement over the baseline MC framework considering spatial correlations while preserving the same SSER quality.

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