1246:
1022:
1461:
Each of the equations above uses a combination of knowledge of the degradation mechanisms and test experience to develop first-order equations that allow the design or reliability engineer to be able to predict time to failure behavior based on information on the design architecture, materials, and
481:
The resources and successes with integrated circuits, and a review of some of the drivers of field failures, subsequently motivated the reliability physics community to initiate physics of failure investigations into package-level degradation mechanisms. An extensive amount of work was performed to
57:
An approach to the design and development of reliable product to prevent failure, based on the knowledge of root cause failure mechanisms. The
Physics of Failure (PoF) concept is based on the understanding of the relationships between requirements and the physical characteristics of the product and
1482:
There are some limitations with the use of physics of failure in design assessments and reliability prediction. The first is physics of failure algorithms typically assume a 'perfect design'. Attempting to understand the influence of defects can be challenging and often leads to
Physics of Failure
1483:(PoF) predictions limited to end of life behavior (as opposed to infant mortality or useful operating life). In addition, some companies have so many use environments (think personal computers) that performing a PoF assessment for each potential combination of temperature / vibration / humidity /
67:
The concept of
Physics of Failure, also known as Reliability Physics, involves the use of degradation algorithms that describe how physical, chemical, mechanical, thermal, or electrical mechanisms evolve over time and eventually induce failure. While the concept of Physics of Failure is common in
92:
funded an extensive amount of effort to especially improve the reliability of electronics, with the initial efforts focused on after-the-fact or statistical methodology. Unfortunately, the rapid evolution of electronics, with new designs, new materials, and new manufacturing processes, tended to
1411:
1087:
37:
A science-based approach to reliability that uses modeling and simulation to design-in reliability. It helps to understand system performance and reduce decision risk during design and after the equipment is fielded. This approach models the root causes of failure such as
830:
97:(RADC). Under the auspices of the RADC, the first Physics of Failure in Electronics Symposium was held in September 1962. The goal of the program was to relate the fundamental physical and chemical behavior of materials to reliability parameters.
93:
quickly negate approaches and predictions derived from older technology. In addition, the statistical approach tended to lead to expensive and time-consuming testing. The need for different approaches led to the birth of
Physics of Failure at the
482:
develop algorithms that could accurately predict the reliability of interconnects. Specific interconnects of interest resided at 1st level (wire bonds, solder bumps, die attach), 2nd level (solder joints), and 3rd level (plated through holes).
608:
58:
their variation in the manufacturing processes, and the reaction of product elements and materials to loads (stressors) and interaction under loads and their influence on the fitness for use with respect to the use conditions and time.
881:
254:
Physics of failure is typically designed to predict wearout, or an increasing failure rate, but this initial success by Black focused on predicting behavior during operational life, or a constant failure rate. This is because
1252:
485:
Just as integrated circuit community had four major successes with physics of failure at the die-level, the component packaging community had four major successes arise from their work in the 1970s and 1980s. These were
1712:
Raghavan, N.; Prasad, K.; "Statistical outlook into the physics of failure for copper low-k intra-metal dielectric breakdown", Reliability
Physics Symposium, 2009 IEEE International, vol., no., pp. 819–824, 26–30 April
1722:
Bukowski, J.V.; Johnson, D.A.; Goble, W.M.; "Software-reliability feedback: a physics-of-failure approach", Reliability and
Maintainability Symposium, 1992. Proceedings., Annual, vol., no., pp. 285–289, 21–23 Jan
1537:, Gas Turbine Materials/Components Life Evaluation & Extension Programs, Dr. Prakash Patnaik, Director SMPL, National Research Council Canada, Institute for Aerospace Research, Ottawa, Canada, 21 October 2008
1747:, McLeish, J.G.; "Enhancing MIL-HDBK-217 reliability predictions with physics of failure methods", Reliability and Maintainability Symposium (RAMS), 2010 Proceedings – Annual, vol., no., pp. 1–6, 25–28 Jan. 2010
203:
1241:{\displaystyle \sigma ={\frac {(\alpha _{\text{E}}-\alpha _{\text{Cu}})\Delta TA_{\text{E}}E_{\text{E}}E_{\text{Cu}}}{A_{\text{E}}E_{\text{E}}+A_{\text{Cu}}E_{\text{Cu}}}},\quad {\text{for }}\sigma \leq S_{Y}}
1664:
Engelmaier, W.; "Fatigue Life of
Leadless Chip Carrier Solder Joints During Power Cycling", Components, Hybrids, and Manufacturing Technology, IEEE Transactions on, vol. 6, no. 3, pp. 232–237, Sep 1983
1646:
Chen, Y.F. Lin, M.H. Chou, C.H. Chang, W.C. Huang, S.C. Chang, Y.J. Fu, K.Y. "Negative Bias
Temperature Instability (NBTI) in Deep Sub-micron p+-gate pMOSFETS", 2000 IRW Final Report, p98-101
1703:
O. Salmela, K. Andersson, A. Perttula, J. Sarkka and M. Tammenmaa "Modified
Engelmaier's model taking account of different stress levels", Microelectron. Reliab., vol. 48, p. 773, 2008
1567:
J. Spiegel and E.M. Bennett, Military System
Reliability: Department of Defense Contributions, IRE Transactions on Reliability and Quality Control, Dec. 1960, Volume: RQC-9 Issue:3
659:
1694:, N. Blattau and C. Hillman "An Engelmaier model for leadless ceramic chip devices with Pb-free solder", J. Reliab. Inf. Anal. Cntr., vol. First Quarter, p. 7, 2007.
501:
259:
in traces can be designed out by following design rules, while electromigration at vias are primarily interfacial effects, which tend to be defect or process-driven.
1470:
More recent work in the area of physics of failure has been focused on predicting the time to failure of new materials (i.e., lead-free solder, high-K dielectric ),
109:. This was primarily because the rapid evolution of the technology created a need to capture and predict performance several generations ahead of existing product.
1619:, E. Wyrwas, L. Condra, and A. Hava, Accurate Quantitative Physics-of-Failure Approach to Integrated Circuit Reliability, IPC APEX Expo, Las Vegas, NV, April 2011
1017:{\displaystyle Z_{0}={\frac {9.8\times 3{\sqrt {\pi /2\times {\text{PSD}}\times f_{n}\times Q}}}{f_{n}^{2}}}\quad Z_{\text{c}}={\frac {0.00022B}{chr{\sqrt {L}}}}}
274:) in modern integrated circuits (equations shown below). More recent work has attempted to aggregate these discrete algorithms into a system-level prediction.
1637:
Takeda, E. Suzuki, N. "An empirical model for device degradation due to Hot-Carrier Injection", IEEE Electron Device Letters, Vol 4, Num 4, 1983, pp. 111–113.
1534:
68:
many structural fields, the specific branding evolved from an attempt to better predict the reliability of early generation electronic parts and systems.
124:. Electromigration occurs when collisions of electrons cause metal atoms in a conductor to dislodge and move downstream of current flow (proportional to
1406:{\displaystyle N_{\text{f}}^{-0.6}D_{\text{f}}^{0.75}+0.9{\frac {S_{\text{u}}}{E}}\left^{0.1785\log {\frac {10^{5}}{N_{\text{f}}}}}-\Delta \epsilon =0}
1496:
1673:
D. S. Steinberg, Vibration Analysis For Electronic Equipment, John Wiley & Sons Inc., New York, first ed. 1973, second ed. 1988, third ed. 2000
1607:
James Black, Mass Transport of Aluminum by Momentum Exchange with Conducting Electrons, 6th Annual Reliability Physics Symposium, November 1967
1576:
George H. Ebel, Reliability Physics in Electronics: A Historical View, IEEE TRANSACTIONS ON RELIABILITY, VOL 47, NO. 3-SP 1998 SEPTEMBER SP-379
271:
1655:
Peck, D.S.; "New concerns about integrated circuit reliability", Electron Devices, IEEE Transactions on, vol. 26, no. 1, pp. 38–43, Jan 1979
262:
Leveraging this success, additional physics-of-failure based algorithms have been derived for the three other major degradation mechanisms (
1474:, using the algorithms for prognostic purposes, and integrating physics of failure predictions into system-level reliability calculations.
134:
1525:
JEDEC JEP148, April 2004, Reliability Qualification of Semiconductor Devices Based on Physics of Failure Risk and Opportunity Assessment
89:
1471:
1586:
128:). Black used this knowledge, in combination with experimental findings, to describe the failure rate due to electromigration as
1682:
IPC-TR-579, Round Robin Reliability Evaluation of Small Diameter Plated-Through Holes in Printed Wiring Boards, September 1988
1598:
Vaccaro “Reliability and the physics of failure program at RADC”, Physics of Failure in Electronics, 1963, pp. 4–10; Spartan.
1535:
http://www.iagtcommittee.com/downloads/08-3-1%20Prakash%20Patnaik%20-%20Life%20Evaluation%20and%20Extension%20Program.pdf
263:
1763:
94:
1732:
1691:
228:
825:{\displaystyle N_{\text{f}}(50\%)={\frac {1}{2}}\left^{\frac {-1}{c}}\quad \Delta D({\text{leadless}})=\left}
81:
1501:
23:
1744:
1558:
R. Lusser, Unreliability of Electronics – Cause and Cure, Redstone Arsenal, Huntsville, AL, DTIC Document
267:
1616:
492:: Predicts time to failure of wire bond / bond pad connections when exposed to elevated temperature /
105:
The initial focus of physics of failure techniques tended to be limited to degradation mechanisms in
77:
1546:
113:
106:
1440:
is plating thickness, and E and Cu label corresponding board and copper properties, respectively,
26:
design that leverages the knowledge and understanding of the processes and mechanisms that induce
603:{\displaystyle {\text{TTF}}=A_{0}(RH)^{-2.7}f(V)\exp \left({\frac {E_{a}}{k_{\text{B}}T}}\right)}
236:
39:
112:
One of the first major successes under predictive physics of failure was a formula developed by
256:
121:
80:, the major driver for the implementation of Physics of Failure was the poor performance of
1628:
Schuegraf and Hu, "A Model for Gate Oxide Breakdown", IEEE Trans. Electron Dev., May 1994.
1506:
217:
125:
248:
1757:
1484:
1059:
is the length of PCB edge parallel to component located at the center of the board,
85:
1081:: Predicts time to failure of plated through holes exposed to temperature cycling
1692:
http://www.dfrsolutions.com/uploads/publications/2006_Blattau_IPC_working.pdf
51:
653:: Predicts time to failure of solder joints exposed to temperature cycling
493:
117:
43:
1745:
http://www.dfrsolutions.com/uploads/publications/2010_01_RAMS_Paper.pdf
440:) where A is determined empirically by normalizing the above equation,
27:
1048:
is transmissibility (assumed to be square root of natural frequency),
212:
is a constant based on the cross-sectional area of the interconnect,
1617:
http://www.dfrsolutions.com/uploads/publications/ICWearout_Paper.pdf
198:{\displaystyle {\text{MTTF}}=A(J^{-n})e^{\frac {E_{\text{a}}}{kT}}}
875:: Predicts time to failure of solder joints exposed to vibration
394:
is the activation energy of HCI, typically −0.2 to −0.1 eV,
1547:
http://theriac.org/DeskReference/PDFs/2011Q1/2011Q1-article2.pdf
47:
1055:
is the critical displacement (20 million cycles to failure),
1031:
is maximum displacement, PSD is the power spectral density (
1487:/ etc. would be onerous and potentially of limited value.
629:) is a voltage function (often cited as voltage squared),
30:
to predict reliability and improve product performance.
1255:
1090:
884:
662:
504:
137:
1405:
1240:
1016:
824:
602:
197:
33:Other definitions of Physics of Failure include:
227:is the activation energy (e.g. 0.7 eV for
1585:This would eventually evolve into the current
846:is a time and temperature dependent constant,
8:
1587:International Reliability Physics Symposium
1420:is coefficient of thermal expansion (CTE),
1454:being ductility of the plated copper, and
861:is the coefficient of thermal expansion, Δ
1378:
1368:
1362:
1352:
1333:
1317:
1301:
1295:
1283:
1278:
1265:
1260:
1254:
1232:
1217:
1204:
1194:
1181:
1171:
1159:
1149:
1139:
1120:
1107:
1097:
1089:
1004:
984:
975:
962:
957:
938:
926:
915:
910:
898:
889:
883:
788:
778:
763:
737:
713:
703:
688:
667:
661:
584:
573:
567:
536:
517:
505:
503:
178:
172:
156:
138:
136:
1497:List of finite element software packages
1447:being the ultimate tensile strength and
857:is the distance from the neutral point,
1518:
251:(usually set to 2 according to Black).
1044:is the natural frequency of the CCA,
272:negative bias temperature instability
22:is a technique under the practice of
7:
1735:NASA Prognostic Center of Excellence
842:is a fatigue ductility coefficient,
88:. During the subsequent decade, the
1071:is a relative position factor, and
1063:is a component packaging constant,
380:is an empirical fitting parameter,
376:is an empirical fitting parameter,
264:time dependent dielectric breakdown
101:Early history – integrated circuits
90:United States Department of Defense
1391:
1129:
865:is the change in temperature, and
803:
794:
754:
724:
679:
465:is the activation energy of NBTI,
458:is the surface mobility constant,
14:
1549:, A Short History of Reliability.
477:Next stage – electronic packaging
1216:
970:
753:
643:is the Boltzmann constant, and
469:is the Boltzmann constant, and
398:is the Boltzmann constant, and
323:, and εox is the permittivity.
1339:
1326:
1126:
1100:
809:
797:
768:
760:
682:
673:
554:
548:
533:
523:
165:
149:
1:
473:is the absolute temperature.
369:is the failure rate of HCI,
120:to describe the behavior of
869:is solder joint thickness.
95:Rome Air Development Center
1780:
850:is an empirical constant,
636:is the activation energy,
621:is the relative humidity,
16:Mechanical design approach
647:is absolute temperature.
402:is absolute temperature.
451:is the thermal voltage,
229:grain boundary diffusion
1502:Critical plane analysis
243:is the temperature and
82:military weapon systems
1407:
1242:
1018:
826:
604:
387:is the drain voltage,
199:
1458:is the strain range.
1408:
1243:
1075:is component length.
1019:
827:
605:
268:hot carrier injection
200:
1432:is board thickness,
1428:is elastic modules,
1253:
1088:
882:
660:
502:
135:
78:electronics industry
1288:
1273:
967:
721:
107:integrated circuits
1764:Mechanical failure
1436:is hole diameter,
1403:
1274:
1256:
1238:
1067:is PCB thickness,
1014:
953:
822:
709:
600:
237:Boltzmann constant
195:
20:Physics of failure
1472:software programs
1384:
1381:
1346:
1336:
1310:
1304:
1281:
1263:
1220:
1211:
1207:
1197:
1184:
1174:
1162:
1152:
1142:
1123:
1110:
1012:
1009:
978:
968:
950:
929:
816:
791:
766:
750:
731:
716:
696:
670:
594:
587:
508:
192:
181:
141:
1771:
1748:
1742:
1736:
1730:
1724:
1720:
1714:
1710:
1704:
1701:
1695:
1689:
1683:
1680:
1674:
1671:
1665:
1662:
1656:
1653:
1647:
1644:
1638:
1635:
1629:
1626:
1620:
1614:
1608:
1605:
1599:
1596:
1590:
1583:
1577:
1574:
1568:
1565:
1559:
1556:
1550:
1544:
1538:
1532:
1526:
1523:
1424:is temperature,
1412:
1410:
1409:
1404:
1387:
1386:
1385:
1383:
1382:
1379:
1373:
1372:
1363:
1351:
1347:
1342:
1338:
1337:
1334:
1318:
1311:
1306:
1305:
1302:
1296:
1287:
1282:
1279:
1272:
1264:
1261:
1247:
1245:
1244:
1239:
1237:
1236:
1221:
1218:
1212:
1210:
1209:
1208:
1205:
1199:
1198:
1195:
1186:
1185:
1182:
1176:
1175:
1172:
1165:
1164:
1163:
1160:
1154:
1153:
1150:
1144:
1143:
1140:
1125:
1124:
1121:
1112:
1111:
1108:
1098:
1023:
1021:
1020:
1015:
1013:
1011:
1010:
1005:
993:
985:
980:
979:
976:
969:
966:
961:
952:
951:
943:
942:
930:
927:
919:
911:
899:
894:
893:
831:
829:
828:
823:
821:
817:
812:
793:
792:
789:
779:
767:
764:
752:
751:
746:
738:
736:
732:
730:
722:
717:
714:
704:
697:
689:
672:
671:
668:
609:
607:
606:
601:
599:
595:
593:
589:
588:
585:
578:
577:
568:
544:
543:
522:
521:
509:
506:
299:
297:
257:electromigration
204:
202:
201:
196:
194:
193:
191:
183:
182:
179:
173:
164:
163:
142:
139:
122:electromigration
1779:
1778:
1774:
1773:
1772:
1770:
1769:
1768:
1754:
1753:
1752:
1751:
1743:
1739:
1731:
1727:
1721:
1717:
1711:
1707:
1702:
1698:
1690:
1686:
1681:
1677:
1672:
1668:
1663:
1659:
1654:
1650:
1645:
1641:
1636:
1632:
1627:
1623:
1615:
1611:
1606:
1602:
1597:
1593:
1584:
1580:
1575:
1571:
1566:
1562:
1557:
1553:
1545:
1541:
1533:
1529:
1524:
1520:
1515:
1507:Maintainability
1493:
1480:
1468:
1453:
1446:
1374:
1364:
1329:
1319:
1313:
1312:
1297:
1251:
1250:
1228:
1200:
1190:
1177:
1167:
1166:
1155:
1145:
1135:
1116:
1103:
1099:
1086:
1085:
1054:
1043:
994:
986:
971:
934:
900:
885:
880:
879:
856:
841:
784:
780:
774:
739:
723:
705:
699:
698:
663:
658:
657:
642:
635:
617:is a constant,
580:
579:
569:
563:
532:
513:
500:
499:
479:
464:
457:
450:
435:
428:
422:
393:
386:
375:
368:
357:
342:
335:
306:
295:
293:
288:) exp where τo(
226:
218:current density
184:
174:
168:
152:
133:
132:
126:current density
103:
74:
65:
17:
12:
11:
5:
1777:
1775:
1767:
1766:
1756:
1755:
1750:
1749:
1737:
1725:
1715:
1705:
1696:
1684:
1675:
1666:
1657:
1648:
1639:
1630:
1621:
1609:
1600:
1591:
1578:
1569:
1560:
1551:
1539:
1527:
1517:
1516:
1514:
1511:
1510:
1509:
1504:
1499:
1492:
1489:
1479:
1476:
1467:
1464:
1451:
1444:
1414:
1413:
1402:
1399:
1396:
1393:
1390:
1377:
1371:
1367:
1361:
1358:
1355:
1350:
1345:
1341:
1332:
1328:
1325:
1322:
1316:
1309:
1300:
1294:
1291:
1286:
1277:
1271:
1268:
1259:
1248:
1235:
1231:
1227:
1224:
1215:
1203:
1193:
1189:
1180:
1170:
1158:
1148:
1138:
1134:
1131:
1128:
1119:
1115:
1106:
1102:
1096:
1093:
1052:
1039:
1025:
1024:
1008:
1003:
1000:
997:
992:
989:
983:
974:
965:
960:
956:
949:
946:
941:
937:
933:
925:
922:
918:
914:
909:
906:
903:
897:
892:
888:
854:
839:
833:
832:
820:
815:
811:
808:
805:
802:
799:
796:
787:
783:
777:
773:
770:
762:
759:
756:
749:
745:
742:
735:
729:
726:
720:
712:
708:
702:
695:
692:
687:
684:
681:
678:
675:
666:
640:
633:
611:
610:
598:
592:
583:
576:
572:
566:
562:
559:
556:
553:
550:
547:
542:
539:
535:
531:
528:
525:
520:
516:
512:
478:
475:
462:
455:
448:
433:
426:
420:
391:
384:
373:
366:
355:
340:
333:
319:) = 120 + 5.8/
304:
249:scaling factor
231:in aluminum),
224:
206:
205:
190:
187:
177:
171:
167:
162:
159:
155:
151:
148:
145:
102:
99:
73:
70:
64:
61:
60:
59:
55:
15:
13:
10:
9:
6:
4:
3:
2:
1776:
1765:
1762:
1761:
1759:
1746:
1741:
1738:
1734:
1729:
1726:
1719:
1716:
1709:
1706:
1700:
1697:
1693:
1688:
1685:
1679:
1676:
1670:
1667:
1661:
1658:
1652:
1649:
1643:
1640:
1634:
1631:
1625:
1622:
1618:
1613:
1610:
1604:
1601:
1595:
1592:
1588:
1582:
1579:
1573:
1570:
1564:
1561:
1555:
1552:
1548:
1543:
1540:
1536:
1531:
1528:
1522:
1519:
1512:
1508:
1505:
1503:
1500:
1498:
1495:
1494:
1490:
1488:
1486:
1485:power cycling
1477:
1475:
1473:
1465:
1463:
1462:environment.
1459:
1457:
1450:
1443:
1439:
1435:
1431:
1427:
1423:
1419:
1400:
1397:
1394:
1388:
1375:
1369:
1365:
1359:
1356:
1353:
1348:
1343:
1330:
1323:
1320:
1314:
1307:
1298:
1292:
1289:
1284:
1275:
1269:
1266:
1257:
1249:
1233:
1229:
1225:
1222:
1213:
1201:
1191:
1187:
1178:
1168:
1156:
1146:
1136:
1132:
1117:
1113:
1104:
1094:
1091:
1084:
1083:
1082:
1080:
1076:
1074:
1070:
1066:
1062:
1058:
1051:
1047:
1042:
1038:
1034:
1030:
1006:
1001:
998:
995:
990:
987:
981:
972:
963:
958:
954:
947:
944:
939:
935:
931:
923:
920:
916:
912:
907:
904:
901:
895:
890:
886:
878:
877:
876:
874:
870:
868:
864:
860:
853:
849:
845:
838:
818:
813:
806:
800:
785:
781:
775:
771:
757:
747:
743:
740:
733:
727:
718:
710:
706:
700:
693:
690:
685:
676:
664:
656:
655:
654:
652:
648:
646:
639:
632:
628:
624:
620:
616:
596:
590:
581:
574:
570:
564:
560:
557:
551:
545:
540:
537:
529:
526:
518:
514:
510:
498:
497:
496:
495:
491:
487:
483:
476:
474:
472:
468:
461:
454:
447:
443:
439:
432:
425:
419:
415:
411:
407:
403:
401:
397:
390:
383:
379:
372:
365:
361:
354:
350:
346:
339:
332:
328:
324:
322:
318:
314:
310:
303:
291:
287:
283:
279:
275:
273:
269:
265:
260:
258:
252:
250:
246:
242:
238:
234:
230:
223:
219:
215:
211:
188:
185:
175:
169:
160:
157:
153:
146:
143:
131:
130:
129:
127:
123:
119:
115:
110:
108:
100:
98:
96:
91:
87:
83:
79:
72:The beginning
71:
69:
62:
56:
53:
49:
45:
41:
36:
35:
34:
31:
29:
25:
21:
1740:
1728:
1718:
1708:
1699:
1687:
1678:
1669:
1660:
1651:
1642:
1633:
1624:
1612:
1603:
1594:
1581:
1572:
1563:
1554:
1542:
1530:
1521:
1481:
1469:
1460:
1455:
1448:
1441:
1437:
1433:
1429:
1425:
1421:
1417:
1415:
1078:
1077:
1072:
1068:
1064:
1060:
1056:
1049:
1045:
1040:
1036:
1032:
1028:
1026:
872:
871:
866:
862:
858:
851:
847:
843:
836:
834:
650:
649:
644:
637:
630:
626:
622:
618:
614:
612:
489:
488:
484:
480:
470:
466:
459:
452:
445:
441:
437:
430:
423:
417:
413:
409:
405:
404:
399:
395:
388:
381:
377:
370:
363:
359:
352:
348:
344:
337:
330:
326:
325:
320:
316:
312:
308:
301:
289:
285:
281:
277:
276:
261:
253:
244:
240:
232:
221:
213:
209:
207:
111:
104:
86:World War II
75:
66:
32:
19:
18:
1478:Limitations
1466:Recent work
114:James Black
76:Within the
24:reliability
1513:References
1079:IPC-TR-579
651:Engelmaier
1395:ϵ
1392:Δ
1389:−
1360:
1324:
1267:−
1226:≤
1223:σ
1219:for
1130:Δ
1118:α
1114:−
1105:α
1092:σ
945:×
932:×
924:×
913:π
905:×
873:Steinberg
804:Δ
801:α
795:Δ
755:Δ
741:−
725:Δ
711:ϵ
680:%
561:
538:−
362:) where
158:−
52:corrosion
1758:Category
1733:NASA.gov
1491:See also
765:leadless
719:′
494:humidity
118:Motorola
63:Overview
44:fracture
988:0.00022
444:= 2.9,
351:) exp(−
235:is the
216:is the
84:during
40:fatigue
28:failure
1589:(IRPS)
1416:where
1354:0.1785
1035:/Hz),
1027:where
835:where
613:where
270:, and
208:where
50:, and
429:exp(−
416:εoxm
343:exp(−
300:exp(−
284:= τo(
247:is a
1723:1992
1713:2009
1344:0.36
1285:0.75
490:Peck
406:NBTI
292:) =
278:TDDB
140:MTTF
48:wear
1357:log
1321:exp
1293:0.9
1270:0.6
928:PSD
902:9.8
558:exp
541:2.7
507:TTF
367:HCI
334:HCI
327:HCI
311:),
294:5.4
116:of
1760::
1456:De
1366:10
1206:Cu
1196:Cu
1161:Cu
1122:Cu
677:50
619:RH
438:kT
436:/
412:=
408::
360:kT
358:/
349:VD
336:=
329::
321:kT
309:kT
307:/
298:10
280::
266:,
239:,
220:,
46:,
42:,
1452:f
1449:D
1445:u
1442:S
1438:t
1434:d
1430:h
1426:E
1422:T
1418:a
1401:0
1398:=
1380:f
1376:N
1370:5
1349:]
1340:)
1335:f
1331:D
1327:(
1315:[
1308:E
1303:u
1299:S
1290:+
1280:f
1276:D
1262:f
1258:N
1234:Y
1230:S
1214:,
1202:E
1192:A
1188:+
1183:E
1179:E
1173:E
1169:A
1157:E
1151:E
1147:E
1141:E
1137:A
1133:T
1127:)
1109:E
1101:(
1095:=
1073:L
1069:r
1065:h
1061:c
1057:B
1053:c
1050:Z
1046:Q
1041:n
1037:f
1033:g
1029:Z
1007:L
1002:r
999:h
996:c
991:B
982:=
977:c
973:Z
964:2
959:n
955:f
948:Q
940:n
936:f
921:2
917:/
908:3
896:=
891:0
887:Z
867:h
863:T
859:α
855:D
852:L
848:F
844:c
840:f
837:ε
819:]
814:h
810:)
807:T
798:(
790:D
786:L
782:F
776:[
772:=
769:)
761:(
758:D
748:c
744:1
734:]
728:D
715:f
707:2
701:[
694:2
691:1
686:=
683:)
674:(
669:f
665:N
645:T
641:B
638:k
634:a
631:E
627:V
625:(
623:f
615:A
597:)
591:T
586:B
582:k
575:a
571:E
565:(
555:)
552:V
549:(
546:f
534:)
530:H
527:R
524:(
519:0
515:A
511:=
471:T
467:k
463:a
460:E
456:p
453:μ
449:T
446:V
442:m
434:a
431:E
427:p
424:μ
421:T
418:V
414:A
410:λ
400:T
396:k
392:a
389:E
385:D
382:V
378:β
374:3
371:A
364:λ
356:a
353:E
347:/
345:β
341:3
338:A
331:λ
317:T
315:(
313:G
305:a
302:E
296:×
290:T
286:T
282:τ
245:n
241:T
233:k
225:a
222:E
214:J
210:A
189:T
186:k
180:a
176:E
170:e
166:)
161:n
154:J
150:(
147:A
144:=
54:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.