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722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 250 333 408 500 500 833 778 180 333 333 500 564 250 333 250 278 500 500 500 500 500 500 500 500 500 500 278 278 564 564 564 444 921 722 667 667 722 611 556 722 722 333 389 722 611 889 722 722 556 722 667 556 611 722 722 944 722 722 611 333 278 333 469 500 333 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 480 200 480 541 350 744 350 333 500 444 1000 500 500 333 1000 556 333 889 350 611 350 350 333 333 444 444 350 500 1000 333 980 389 333 722 350 444 722 250 333 500 500 744 500 200 500 333 760 276 500 564 333 760 333 400 549 300 300 333 576 453 250 333 300 310 500 750 750 750 444 722 722 722 722 722 722 889 667 611 611 611 611 333 333 333 333 722 722 722 722 722 722 722 564 722 722 722 722 722 722 556 500 444 444 444 444 444 444 667 444 444 444 444 444 278 278 278 278 500 500 500 500 500 500 500 549 500 500 500 500 500 500 500 500] endobj 1503 0 obj <> endobj 1504 0 obj <> endobj 1505 0 obj <> endobj 1506 0 obj <> endobj 1507 0 obj <> endobj 1508 0 obj <> endobj 1509 0 obj <> endobj 1510 0 obj <> endobj 1511 0 obj <> endobj 1512 0 obj <> endobj 1513 0 obj <> endobj 1514 0 obj <> endobj 1515 0 obj <> endobj 1516 0 obj <> endobj 1517 0 obj <> endobj 1 0 obj <>/ProcSet[/PDF/Text]/ExtGState<>>>/Type/Page>> endobj 2 0 obj <>stream q 0.9700012 0 0 0.9700012 9 12 cm 0 0 m 612 0 l 612 792 l 0 792 l 0 0 l W n 1.0309265 0 0 1.0309265 -9.2783388 -12.3711185 cm BT 0 0 0 rg /GS0 gs /TT0 1 Tf 0.0022 Tc 0.1378 Tw 9.701 0 0 9.7194 69.7608 725.0083 Tm [(Pan )-6(et)4( al)4( [6])5( obt)4(ai)4(ned a new set)4( of param)12(e)2(t)4(e)2(rs based on )]TJ 0.0024 Tc 0.7855 Tw -1.44 -1.168 Td [(t)4(h)-1(ei)4(r )-6(experi)4(m)12(e)2(nt)4(s for SnAgCu sol)4(d)-1(ered com)12(ponent)4(s, )]TJ 0.0021 Tc -0.0001 Tw 0 -1.168 TD [(i)4(n)-2(cl)4(udi)4(ng ceram)12(i)4(c)2( Bal)4(l)4( Gri)4(d)-2( Array)4( \(CBGA\) com)12(ponent)4(s, Chi)4(p)-2( )]TJ 0.0003 Tc 0.3676 Tw T* [(Scale Pack)-4(ag)-4(es \(CSP\), an)-4(d)-4( Th)-4(in)-4( Sm)10(all-O)-3(u)-4(tlin)-4(e Pack)-4(ag)-4(es )]TJ 0.0014 Tc 0.0006 Tw T* (\(TSOP\). The new set of coefficients are )Tj 0.0029 Tc -0.0009 Tw 0 -1.868 TD [(m)13(=)3(0.136, n=2.65, and E)]TJ 0 Tc 0 Tw 6.2736 0 0 6.2856 150.426 659.9988 Tm (a)Tj 0.0025 Tc -0.0005 Tw 9.701 0 0 9.7194 153.2196 661.4538 Tm [(/)4(k)-1( = 2185 )-240( )-3348( )-3348( \(5\) )]TJ 0.0021 Tc 0.4318 Tw -8.603 -1.766 Td [(Engel)4(m)12(ai)4(er )-6([10])5( )-6(proposed )-6(an anal)4(y)4(t)4(i)4(cal)4( form)12( of t)4(h)-2(e )]TJ 0.0023 Tc 0.1917 Tw -1.44 -1.168 Td [(Coffi)4(n-M)4(a)2(nson\222s equat)4(i)4(on t)4(o)-2( obt)4(ai)4(n t)4(h)-2(e pl)4(ast)4(i)4(c)2( st)4(rai)4(n)-2( )6(range )]TJ 0.0005 Tc 0.5594 Tw 0 -1.168 TD (analytically. The original fo)Tj 0.0012 Tc 0.5587 Tw 12.857 0 Td [(rm)11( of Engelm)11(aier\222s )6(m)11(o)-3(del )]TJ 0.0019 Tc 0.0661 Tw -12.857 -1.168 Td [(consi)4(s)1(t)4(s)1( )-6(of t)4(w)-2(o part)4(s:)4( t)4(h)-2(e phy)4(si)4(cal)4( part)4( and t)4(h)-2(e st)4(at)4(i)4(s)1(t)4(i)4(cal)4( part)4( )]TJ 0.0026 Tc 0.2154 Tw T* [(by)5( a 2-param)13(e)3(t)5(e)3(r W)-7(e)3(i)5(bul)5(l)5( di)5(st)5(ri)5(but)5(i)5(on. )6(The )6(com)13(b)-1(i)5(n)-1(at)5(i)5(on )6(of )]TJ 0.0015 Tc 0.0065 Tw T* [(these two parts can be presented as a )6(num)11(ber )6(of )6(cycles )]TJ /TT1 1 Tf -0.0011 Tc 0 Tw 22.186 0 Td (N )Tj /TT0 1 Tf 0 Tc 0.918 0 Td (\()Tj /TT1 1 Tf 0.336 0 Td (x)Tj /TT0 1 Tf 0.002 Tc (%\) )Tj 0.0014 Tc 0.0006 Tw -23.439 -1.168 Td (until x% of the population have failed as )Tj ET q 0.9700012 0 0 0.9700012 103.4587097 546.6840363 cm 0 0 0 RG 0.501 w 1 j 1 J 0 0 m 7.26 0 l 15.12 0 m 33.66 0 l S Q q 0.9700012 0 0 0.9700012 147.1087646 562.9800568 cm 0 0 0 RG 0.25 w 1 j 1 J 0 0 m 3.84 0 l S Q q 0.9700012 0 0 0.9700012 158.6905823 546.6840363 cm 0 0 0 RG 0.501 w 1 j 1 J 0 0 m 59.82 0 l S Q q 0.9700012 0 0 0.9700012 223.6418457 559.8954468 cm 0 0 0 RG 0.25 w 1 j 1 J 0 0 m 5.58 0 l S Q BT /C2_0 1 Tf 0 Tc 0 Tw 6.8174 0 2.3317 6.8303 224.1654 552.678 Tm <0045>Tj 11.687 0 3.9972 11.7094 120.6858 534.5779 Tm <0048>Tj -0.181 1.446 Td <0048>Tj /TT0 1 Tf 6.8174 0 0 6.8303 224.631 562.6302 Tm (1)Tj -11.337 0.452 Td (1)Tj 11.687 0 0 11.7094 194.7162 534.5779 Tm [(5)749(.)748(0)1416(ln)]TJ 1.509 1.412 Td [(\))1782(01)1244(.)748(0)1840(1)1506(ln\()]TJ -7.993 0.035 Td (2)Tj -1.255 -1.446 Td (2)Tj -0.015 1.412 Td (1)Tj -2.291 -0.631 Td [(%\))2033(\()]TJ /C2_0 1 Tf 12.051 -0.085 Td <00B8>Tj 0 -0.815 TD <00B9>Tj 0 1.456 TD <00B7>Tj -5.602 -0.641 Td <00A8>Tj 0 -0.815 TD <00A9>Tj 0 1.456 TD <00A7>Tj 2.181 0.075 Td <0010>Tj -3.471 -1.153 Td <00B8>Tj 0 0.701 TD <00B8>Tj 0 -1.342 TD <00B9>Tj 0 1.983 TD <00B7>Tj -2.181 -1.342 Td <00A8>Tj 0 0.701 TD <00A8>Tj 0 -1.342 TD <00A9>Tj 0 1.983 TD <00A7>Tj -1.564 -0.82 Td <0020>Tj 6.8174 0 0 6.8303 142.9764 561.2334 Tm <0010>Tj /TT1 1 Tf 11.687 0 0 11.7094 206.88 551.1066 Tm (x)Tj -11.548 -0.631 Td [(x)1624(N)]TJ 6.8174 0 0 6.8303 147.516 555.7626 Tm (c)Tj -2.843 -3.528 Td (p)Tj 0.401 2.471 Td (c)Tj /TT0 1 Tf 0.0025 Tc -0.0005 Tw 9.701 0 0 9.7194 231.1494 527.1283 Tm [( )-3270( \(6\))]TJ 0 Tc 0 Tw 5.705 1.695 Td ( )Tj 0.0018 Tc -23.782 -3.03 Td (where )Tj /C2_0 1 Tf 0 Tc 2.88 0 Td <0048>Tj /TT0 1 Tf 6.2736 0 0 6.2856 87.9774 512.6947 Tm (p)Tj /TT1 1 Tf 9.701 0 0 9.7194 91.1202 514.1497 Tm ( )Tj /TT0 1 Tf -0.0008 Tc 0.1708 Tw 0.426 0 Td [(is th)-5(e p)-5(o)-5(t)1(en)-5(tial cyclic fatig)-5(u)-5(e)-1( d)-5(a)-1(m)9(a)-1(g)-5(e)-1( at co)-5(m)9(p)-5(lete )]TJ 0.002 Tc 0.09 Tw -4.068 -1.233 Td [(st)4(ress rel)4(a)2(xat)4(i)4(on, and )]TJ /C2_0 1 Tf 0 Tc 0 Tw <0048>Tj /TT0 1 Tf 6.2736 0 0 6.2856 146.9922 500.7054 Tm (c)Tj -0.0005 Tc 0.0925 Tw 9.701 0 0 9.7194 149.7858 502.1604 Tm [( is th)-4(e fatig)-4(u)-4(e)-1( d)-4(u)-4(c)-1(tility )6(co)-4(efficien)-4(t, )]TJ /TT1 1 Tf 0.0001 Tc 0 Tw 14.92 0 Td (c )Tj /TT0 1 Tf 0.0011 Tc 0.0489 Tw -24.609 -1.168 Td (is the fatigue ductility exponent, and )Tj /C2_1 1 Tf 0 Tc 0 Tw 15.19 0 Td <0215>Tj /TT0 1 Tf 0.0011 Tc 0.0429 Tw 0.51 0 Td [( )-6(is the shape param)11(e)1(ter )]TJ 0.0028 Tc 0.1672 Tw -15.7 -1.233 Td [(of t)5(h)-1(e W)-7(e)3(i)5(bul)5(l)5( di)5(st)5(ri)5(but)5(i)5(on. )]TJ /C2_0 1 Tf 0 Tc 0 Tw 11.855 0 Td <0048>Tj /TT0 1 Tf 6.2736 0 0 6.2856 175.0446 477.3672 Tm (p)Tj 0.0014 Tc 0.1626 Tw 9.701 0 0 9.7194 178.1874 478.8222 Tm [( )-6(for leadless packages can be )]TJ 0.0016 Tc 0.0004 Tw -12.617 -1.168 Td (presented as )Tj ET q 0.9700012 0 0 0.9700012 82.215683 441.9239044 cm 0 0 0 RG 0.501 w 1 j 1 J 0 0 m 49.26 0 l S Q BT /TT1 1 Tf 0 Tc 0 Tw 11.6759 0 0 11.6982 103.284 429.8178 Tm (h)Tj 1.311 1.443 Td [(T)3572(FL)]TJ 6.811 0 0 6.8239 124.818 443.7858 Tm (e)Tj -8.861 -1.134 Td (p)Tj /C2_0 1 Tf 11.6759 0 0 11.6982 111.4902 446.6958 Tm [<0027>1852<0027>]TJ -3.33 -0.662 Td <0020>Tj 11.6759 0 3.9933 11.6982 104.0988 446.6958 Tm <0044>Tj -3.806 -0.662 Td <0048>Tj /TT0 1 Tf 0.0023 Tc -0.0003 Tw 9.701 0 0 9.7194 132.2676 427.257 Tm [( )-2664( )-3348( )-2592( )-3348( \(7\))]TJ 0 Tc 0 Tw 15.898 1.198 Td ( )Tj 0.0008 Tc 0.2771 Tw -23.782 -2.964 Td [(where F is em)11(pirical non-ideality)]TJ 0.0013 Tc 0.2766 Tw 14.399 0 Td [( factor, L is half of )6(the )]TJ 0.0023 Tc 0.7976 Tw -14.399 -1.168 Td [(m)12(a)2(xi)4(m)12(u)-2(m)12( )-6(di)4(st)4(ance )-6(bet)4(w)-1(een com)12(ponent)4( sol)4(d)-2(er joi)4(n)-2(t)4(s)2( )]TJ 0.0017 Tc 0.0063 Tw 0 -1.168 TD [(\(Distance form)12( Nnutral point\), )]TJ /C2_1 1 Tf -0.0011 Tc 0 Tw 12.533 0 Td <01FB012E>Tj /TT0 1 Tf 0 Tc 0.008 Tw [( is th)-4(e ab)-4(so)-4(lu)-4(te )6(d)-4(i)2(fferen)-4(ce )6(in)-4( )]TJ 0.0023 Tc 0.1497 Tw -12.533 -1.168 Td [(coeffi)4(ci)4(ent)4(s)2( )-6(of )-6(t)4(h)-2(erm)12(a)2(l)4( expansi)4(o)-2(n of t)4(h)-2(e com)12(ponent)4( and t)4(h)-2(e )]TJ 0.0011 Tc 0.0789 Tw T* (substrate, )Tj /C2_1 1 Tf 0 Tc 0 Tw 4.475 0 Td <01FB>Tj /TT0 1 Tf 0.642 0 Td (T)Tj 6.2736 0 0 6.2856 111.3738 363.237 Tm (e)Tj 0.0023 Tc 0.0717 Tw 9.701 0 0 9.7194 114.1674 364.692 Tm [( )-6(i)4(s)2( )-6(equi)4(val)4(e)2(nt)4( )-6(cy)4(cl)4(i)4(n)-2(g t)4(e)2(m)12(p)-2(erat)4(ure range and h )]TJ -0.0001 Tc 0.0021 Tw -6.017 -1.168 Td [(is so)-4(ld)-4(er j)-4(o)-4(in)-4(t h)-4(eig)-4(h)-4(t)2(. )]TJ /C2_1 1 Tf 0 Tc 0 Tw 8.729 0 Td <01FB>Tj /TT0 1 Tf 0.642 0 Td (T)Tj 6.2736 0 0 6.2856 152.6376 351.888 Tm (e)Tj 0.0016 Tc 0.0004 Tw 9.701 0 0 9.7194 155.4312 353.343 Tm ( can be presented as )Tj ET q 0.9700012 0 0 0.9700012 103.8079071 326.8623657 cm 0 0 0 RG 0.499 w 1 j 1 J 0 0 m 74.1 0 l -1.44 15.18 m -1.44 -15.18 l 75.3 15.18 m 75.3 -15.18 l S Q BT /C2_0 1 Tf 0 Tc 0 Tw 11.6373 0 3.9801 11.6593 139.1352 314.8146 Tm <0044>Tj -0.038 1.443 Td [<0044>4126<0044>]TJ 11.6373 0 0 11.6593 132.0348 314.8146 Tm <0027>Tj 2.156 1.443 Td [<0027>2371<0010>2293<0027>]TJ -5.546 -0.664 Td [<0020>2358<0027>]TJ /TT1 1 Tf 6.7883 0 0 6.8012 170.4468 328.7244 Tm [(c)3016(c)3848(s)2953(s)]TJ -12.603 -1.138 Td (e)Tj 11.6373 0 0 11.6593 164.2194 331.6344 Tm [(T)4062(T)]TJ -7.357 -0.664 Td (T)Tj /TT0 1 Tf 3.3496 Tc 9.701 0 0 9.7194 179.526 309.3438 Tm [( )1956( \()3347(8)3346(\))]TJ 0 Tc 10.019 1.497 Td ( )Tj -21.334 -3.264 Td ( )Tj 0.0021 Tc 0.3118 Tw -1.44 -1.27 Td [(where )-6(s denot)4(es subst)4(r)-1(at)4(e and c denot)4(e)2(s com)12(ponent)4(. For )]TJ 0.0014 Tc 0.0006 Tw T* [(leaded packages, the strain range is approxim)11(a)1(ted as )]TJ ET q 0.9700012 0 0 0.9700012 96.1255035 242.0066681 cm 0 0 0 RG 0.497 w 1 j 1 J 0 0 m 79.2 0 l S Q BT /TT1 1 Tf 0 Tc 0 Tw 11.6388 0 0 11.6611 128.6592 229.9591 Tm (Ah)Tj 1.98 1.442 Td [(T)2971(L)2811(FK)]TJ 6.7894 0 0 6.8021 157.9338 243.8689 Tm (e)Tj -6.575 0 Td (d)Tj -5.135 -1.138 Td (p)Tj /TT0 1 Tf 13.116 2.336 Td (2)Tj 11.6388 0 0 11.6611 162.7062 246.7789 Tm [(\))4083(\()]TJ /C2_0 1 Tf -1.55 0 Td [<0027>1861<0027>]TJ -4.99 -0.664 Td <0020>Tj 11.6388 0 3.9808 11.6611 137.2146 246.7789 Tm <0044>Tj -5.463 -0.664 Td <0048>Tj /TT0 1 Tf 3.3496 Tc 9.701 0 0 9.7194 175.161 227.3983 Tm [( )1506( \()3347(9)3346(\))]TJ 0 Tc 10.469 1.198 Td ( )Tj 0.0018 Tc 0.1142 Tw -22.774 -2.964 Td (where K)Tj 0 Tc 0 Tw 6.2736 0 0 6.2856 90.189 208.7742 Tm (d)Tj 0.0021 Tc 0.1139 Tw 9.701 0 0 9.7194 93.3318 210.2292 Tm [( i)4(s)1( t)4(h)-2(e di)4(agonal)4( fl)4(exural)4( l)4(ead st)4(i)4(ffness and )6(A )6(i)4(s)1( )6(t)4(h)-2(e )]TJ 0.0016 Tc 0.3663 Tw -3.87 -1.168 Td (effective solder bond area. Sa)Tj 0.0006 Tc 0.3673 Tw 13.367 0 Td [(lm)11(ela [12] recalibrated the )]TJ -0.0007 Tc 0.7286 Tw -13.367 -1.168 Td [(En)-5(g)-5(e)-1(lm)9(aier )-6(m)9(o)-5(d)-5(e)-1(l )-6(b)-5(y)1( rep)-5(l)1(acin)-5(g)-5( th)-5(e fatig)-5(u)-5(e)-1( d)-5(u)-5(c)-1(tility )]TJ 0.001 Tc 0.4209 Tw T* [(coefficient by tem)11(p)-3(erature-de)]TJ 0.0023 Tc 0.4196 Tw 12.689 0 Td [(pendent)4( and sol)4(d)-2(er m)12(a)2(t)4(e)2(ri)4(al)4( )]TJ 0.0012 Tc 0.0068 Tw -12.689 -1.168 Td [(specific correction term)11(. Osterm)11(an)]TJ 0.0029 Tc 0.0051 Tw 13.919 0 Td [( [11])6( present)5(e)3(d a new set)5( of )]TJ 0.0022 Tc -0.0002 Tw -13.919 -1.168 Td [(const)4(a)2(nt)4(s based on t)4(h)-2(e Engel)4(m)12(ai)4(er m)12(o)-2(del)4( for SnAgCu sol)4(d)-2(er. )]TJ -0.0009 Tc 0.0389 Tw 1.44 -1.27 Td [(A)-5(n)-5( )-6(ex)-5(ten)-5(s)-2(io)-5(n)-5( )-6(to)-5( )-6(th)-5(e o)-5(r)-4(ig)-5(in)-5(al Co)-5(ffin)-5(-)-4(Man)-5(s)-2(o)-5(n)-5( eq)-5(u)-5(a)-1(tio)-5(n)-5( is to)-5( )]TJ 0.0007 Tc 0.2532 Tw -1.44 -1.168 Td (use the plastic strain energy )Tj -0.0009 Tc 0.2548 Tw 12.647 0 Td [(d)-5(e)-1(n)-5(s)-2(ity in)-5(stead)-5( o)-5(f)-4( )6(th)-5(e )6(p)-5(l)1(astic )]TJ -0.0003 Tc 0.2362 Tw -12.647 -1.168 Td [(strain)-4( )-6(ran)-4(g)-4(e )-6(to)-4( )-6(rep)-4(r)-3(esen)-4(t th)-4(e cu)-4(m)10(u)-4(lativ)-4(e d)-4(am)10(ag)-4(e o)-4(n)-4( so)-4(ld)-4(er )]TJ 0.0026 Tc 0.0954 Tw T* [(joi)5(n)-1(t)5(.)1( Equat)5(i)5(on \(1\) and \(2\) based )6(on )6(t)5(h)-1(e )6(pl)5(ast)5(i)5(c)3( )6(st)5(rai)5(n)-1( )6(energy)5( )]TJ 0.0006 Tc 0.0014 Tw T* [(d)-3(e)1(n)-3(sity ran)-3(g)-3(e)1( can)-3( b)-3(e)1( re-w)-3(ritten)-3( as )]TJ /TT1 1 Tf 0 Tc 0 Tw 11.7805 0 0 11.8028 117.8922 73.9249 Tm [(C)4012(W)2562(N)]TJ 6.8719 0 0 6.8849 99.21 79.221 Tm (m)Tj -1.474 -1.192 Td (p)Tj /C2_0 1 Tf 11.7805 0 0 11.8028 126.6222 74.6233 Tm <0063>Tj -1.517 -0.059 Td [<0020>3720<0027>]TJ /TT0 1 Tf -1.22 0 Td [(\))2640(\()]TJ 3.3496 Tc 9.701 0 0 9.7194 131.4528 67.0572 Tm [( )600( \()3347(1)3346(0)3346(\))]TJ 0 Tc 15.478 0.701 Td ( )Tj ET q 0.9700012 0 0 0.9700012 343.4757996 710.9246216 cm 0 0 0 RG 0.499 w 1 j 1 J 0 0 m 16.2 0 l 35.34 0 m 64.86 0 l S Q BT /TT1 1 Tf 6.768 0 0 6.7808 413.2572 726.4633 Tm (m)Tj -2.511 -4.652 Td (p)Tj 0.095 2.841 Td (p)Tj 11.6023 0 0 11.6243 385.6704 697.8288 Tm (W)Tj 0.055 1.657 Td (W)Tj -3.577 -1.562 Td (N)Tj 0.055 1.437 Td (N)Tj -2.583 -0.656 Td (AF)Tj /C2_0 1 Tf 7.961 -0.616 Td <00B8>Tj 0 0.886 TD <00B8>Tj 0 -1.527 TD <00B9>Tj 0 2.168 TD <00B7>Tj -3.11 -1.527 Td <00A8>Tj 0 0.886 TD <00A8>Tj 0 -1.527 TD <00A9>Tj 0 2.168 TD <00A7>Tj 0.587 -1.787 Td <0027>Tj 0.055 1.657 Td <0027>Tj -1.425 -0.781 Td [<0020>3036<0020>]TJ /TT0 1 Tf 6.768 0 0 6.7808 400.9188 703.8816 Tm (2)Tj -0.017 2.841 Td (1)Tj -6.957 -4 Td (2)Tj -0.017 2.463 Td (1)Tj 3.3496 Tc 9.701 0 0 9.7194 420.474 690.5538 Tm [( )300( \()3347(1)3346(1)3346(\))]TJ 0 Tc 12.179 1.796 Td ( )Tj 0.0022 Tc 0.1198 Tw -21.838 -3.563 Td [(It)4( )-6(i)4(s)1( )-6(not)4(ed t)4(h)-2(at)4( t)4(h)-2(e em)12(pi)4(ri)4(cal)4( m)12(a)2(t)4(e)2(ri)4(al)4( const)4(a)2(nt)4( \(exponent)4( )]TJ 0 Tc 0.062 Tw -1.44 -1.168 Td [(m)10(\))-3( w)-4(ill b)-4(e d)-4(i)2(fferen)-4(t)2( fro)-4(m)10( th)-4(at w)-4(h)-4(en)-4( th)-4(e p)-4(l)2(astic )6(strain)-4( )6(ran)-4(g)-4(e )6(is )]TJ 0.0021 Tc -0.0001 Tw 0 -1.168 TD (used. )Tj 0.09 Tw 1.44 -1.27 Td [(Cl)4(ech [13])5( devel)4(oped an )6(anal)]TJ 0.0003 Tc 0.0857 Tw 12.113 0 Td [(ytical m)10(odel to com)10(p)-4(ute the )]TJ 0.0018 Tc 0.0302 Tw -13.553 -1.168 Td [(pl)4(ast)4(i)4(c)2( )-6(st)4(rai)4(n)-2( energy)4( range. The st)4(abi)4(l)4(i)4(zed hy)4(st)4(eresi)4(s)1( l)4(oops are )]TJ 0.0021 Tc 0.1679 Tw T* [(com)12(puted for shear deform)12(ations)]TJ 0.1619 Tw 13.787 0 Td [( )-6(dri)4(v)-2(en by)4( t)4(h)-2(e gl)4(obal)4( CTE )]TJ 0.0025 Tc 0.3114 Tw -13.787 -1.168 Td [(m)12(i)4(sm)12(at)4(ch bet)4(w)-1(een board and com)12(ponent)4(, and )6(for )6(norm)12(a)2(l)4( )]TJ 0.0013 Tc 0.0607 Tw T* (stresses and strains driven by )Tj 0.0007 Tc 0.0553 Tw 12.257 0 Td [(local CTE m)11(i)3(sm)11(atches between )]TJ 0.0022 Tc 0.2337 Tw -12.257 -1.168 Td [(sol)4(d)-2(er )-6(and )-6(t)4(h)-2(e i)4(n)-2(t)4(e)2(rconnect)4(ed part)4(s. The m)12(e)2(t)4(hodol)4(ogy)4( was )]TJ 0.0025 Tc 0.0235 Tw T* [(fi)4(rst)4( devel)4(oped by)5( Hal)4(l)4( [14, 15])6( i)4(n)-1( t)4(h)-1(e si)4(m)12(u)-1(l)4(a)2(t)4(i)4(o)-1(n of m)12(easured )]TJ 0.0022 Tc 0.1078 Tw T* [(hy)4(st)4(eresi)4(s)1( l)4(oops for SnPb assem)12(b)-2(l)4(i)4(e)2(s. The m)12(e)2(t)4(hod appl)4(i)4(e)2(s )6(t)4(o)-2( )]TJ 0.001 Tc 0.4989 Tw T* [(any )-6(shape of a periodic tem)11(p)]TJ 0.0015 Tc 0.4984 Tw 14.051 0 Td (erature profile, including )Tj 0.0023 Tc -0.0003 Tw -14.051 -1.168 Td [(t)4(r)-1(apezoi)4(d)-2(al)4(, saw-t)4(oot)4(h and si)4(ne profi)4(l)4(e)2(s. )]TJ -0.0001 Tc 0.692 Tw 1.44 -1.27 Td [(Fin)-4(ite Elem)10(en)-4(t A)-4(n)-4(alysis \(FEA)-4(\) h)-4(as b)-4(een)-4( u)-4(tilized)-4( )]TJ -0.0007 Tc 0.3026 Tw -1.44 -1.168 Td [(ex)-5(ten)-5(s)-1(iv)-5(ely )-6(to)-5( calcu)-5(late th)-5(e p)-5(l)1(astic strain)-5( ran)-5(g)-5(e)-1( o)-5(r)-4( p)-5(l)1(astic )]TJ 0.0022 Tc 0.1318 Tw T* [(st)4(rai)4(n)-2( densi)4(t)4(y)4( range [1-5, 16-19])5(. Fi)4(ni)4(t)4(e)2( el)4(em)12(ent)4( m)12(o)-2(del)4(s)1( can )]TJ 0.0023 Tc 0.1137 Tw T* [(t)4(a)2(ke )-6(i)4(n)-2(t)4(o)-2( consi)4(d)-2(erat)4(i)4(on t)4(h)-2(e i)4(n)-2(t)4(e)2(ract)4(i)4(on am)12(ong com)12(p)-2(onent)4(s)2( i)4(n)-2( )]TJ -0.0007 Tc 0.0747 Tw T* [(an)-5( assem)9(b)-5(ly w)-4(ith)-5( little o)-5(r)-4( n)-5(o)-5( g)-5(e)-1(o)-5(m)9(etric sim)9(p)-5(lificatio)-5(n)-5(.)-3( It also)-5( )]TJ 0.0023 Tc 0.2816 Tw T* [(offers t)4(h)-2(e advant)4(age of bei)4(ng )]TJ -0.0005 Tc 0.2844 Tw 13.379 0 Td [(ab)-4(le to)-4( so)-4(lv)-4(e th)-4(e )6(fu)-4(ll )6(field)-4( )]TJ 0.0024 Tc 0.1436 Tw -13.379 -1.168 Td [(equat)4(i)4(ons and provi)4(de st)4(ress/)4(st)4(rai)4(n)-2( i)4(n)-2(form)12(at)4(i)4(on on al)4(l)4( sol)4(d)-1(er )]TJ -0.0001 Tc 0.1401 Tw T* [(j)-4(o)-4(in)-4(ts. H)-4(o)-4(w)-4(ev)-4(er, th)-4(is d)-4(o)-4(es n)-4(o)-4(t)2( n)-4(ecessarily tran)-4(slate )6(th)-4(e )6(FEA)-4( )]TJ 0.002 Tc 0.204 Tw T* [(approach )-6(into one with superi)]TJ 0.0012 Tc 0.2048 Tw 12.761 0 Td (or accuracy in predicting the )Tj 0.0022 Tc 0.0718 Tw -12.761 -1.168 Td [(fat)4(i)4(gue l)4(i)4(f)-1(e over ot)4(her si)4(m)12(p)-2(l)4(i)4(f)-1(i)4(e)]TJ 0.001 Tc 0.067 Tw 12.809 0 Td [(d em)11(pirical m)11(o)-3(dels. There are )]TJ 0.0021 Tc 0.0779 Tw -12.809 -1.168 Td [(several)4( FEA based SnAgCu fat)4(i)4(g)-2(ue l)4(i)4(f)-1(e m)12(o)-2(del)4(s)1( such as [17])5(, )]TJ 0.0029 Tc 0.359 Tw T* [([18])6(, and [19])6(. However, m)13(a)3(ny)5( of )6(t)5(h)-1(em)13( )6(showed )6(l)5(i)5(m)13(i)5(t)5(e)3(d )]TJ 0.0012 Tc 0.0008 Tw T* (success. )Tj /TT2 1 Tf 0.0016 Tc 0.0004 Tw 0 -1.886 TD (3. Experimental Data Collection )Tj /TT0 1 Tf 0.0003 Tc 0.3796 Tw 1.44 -1.258 Td [(In)-4( th)-4(e fo)-4(llo)-4(w)-3(i)2(n)-4(g)-4(,)-2( )6(th)-4(e )6(ex)-4(p)-4(eri)]TJ 0.0015 Tc 0.3724 Tw 12.461 0 Td [(m)11(e)1(ntal data from)11( various )]TJ 0.0012 Tc 0.3067 Tw -13.901 -1.168 Td [(sources )-6(will )-6(be listed, and us)]TJ 0.001 Tc 0.3069 Tw 13.079 0 Td (ed to recalibrate the Norris )Tj 0.002 Tc 0.078 Tw -13.079 -1.168 Td [(Landzberg m)12(odel)4(. In order t)4(o)-2( achi)4(e)2(ve t)4(h)-2(i)4(s)1(, t)4(h)-2(e t)4(e)2(st)4( dat)4(a)2( )6(m)12(u)-2(st)4( )]TJ -0.0003 Tc 0.0023 Tw 0 -1.168 TD [(th)-4(e fo)-4(llo)-4(w)-4(i)2(n)-4(g)-4( criteria: )]TJ 0.0039 Tc 0 Tw 1.8 -1.27 Td (1.)Tj /TT3 1 Tf 0 Tc 0.756 0 Td ( )Tj /TT0 1 Tf 0.0005 Tc 0.0195 Tw 1.044 0 Td [(The )-6(experim)10(ental )-6(data )-6(m)10(u)-3(st be available to calculate )]TJ -0.0002 Tc 0.0442 Tw T* [(th)-4(e life w)-4(ith)-4( 5)-4(0)-4(%)-1( failu)-4(re rate an)-4(d)-4( th)-4(e req)-4(u)-4(i)2(rem)10(en)-4(t)2( )6(o)-4(n)-4( )]TJ -0.0004 Tc 0.0024 Tw T* [(th)-4(e statistical p)-4(attern)-4( is m)10(et; )]TJ 0.0039 Tc 0 Tw -1.8 -1.27 Td (2.)Tj /TT3 1 Tf 0 Tc 0.756 0 Td ( )Tj /TT0 1 Tf 0.0008 Tc 0.1392 Tw 1.044 0 Td [(The test data m)11(u)-3(st include two tem)11(p)-3(erature )6(cycling )]TJ -0.0008 Tc 0.2727 Tw T* [(co)-5(n)-5(d)-5(itio)-5(n)-5(s)-2(, w)-5(ith)-5( all sp)-5(ecific cyclic lo)-5(ad)-5(in)-5(g)-5( )6(d)-5(e)-1(tails )]TJ 0.0021 Tc 0.1139 Tw T* [(i)4(n)-2(cl)4(uded t)4(o)-2( obt)4(ai)4(n t)4(h)-2(e t)4(e)2(m)12(p)-2(erat)4(ure range, m)12(a)2(xi)4(m)12(u)-2(m)12( )]TJ 0.001 Tc 0.001 Tw T* [(tem)11(p)-3(erature and the cyclic frequency. )]TJ 0.0024 Tc 0.0236 Tw -2.16 -1.27 Td [(Tabl)4(e )-6(1 )-6(shows )-6(t)4(hose t)4(e)2(st)4( dat)4(a)2( t)4(a)2(ken from)12( publ)4(i)4(s)2(hed papers )]TJ 0.0021 Tc 0.2158 Tw -1.44 -1.168 Td [(by)4( )-6(Int)4(e)2(l)4( on FCBGA, socket)4(, and di)4(e si)4(de capaci)4(t)4(o)-2(r \(DSC\) )]TJ 0.0024 Tc 0.3115 Tw T* [(packages. Bot)4(h)-1( SAC105 and SAC405 dat)4(a)2( are )6(shown )6(i)4(n)-2( )]TJ 0.0023 Tc 0.0657 Tw T* [(Tabl)4(e 1 and t)4(h)-2(e t)4(e)2(m)12(p)-2( behavi)4(or i)4(s)2( si)4(m)12(i)4(l)4(a)2(r for bot)4(h)-2( al)4(l)4(o)-2(y)4(s)2(. )6(The )]TJ 0.0025 Tc 0.1675 Tw T* [(experi)4(m)12(e)2(nt)4(al)4( t)4(e)2(st)4( procedures were provi)4(ded i)4(n)-1( )6(our )6(previ)4(ous )]TJ 0.0017 Tc 0.0723 Tw T* [(paper [1])5(. An Air )6(to )6(air )6(tem)12(p)-2(er)]TJ 0.0007 Tc 0.0673 Tw (ature cycle test was used. The )Tj -0.0002 Tc 0.0382 Tw T* [(in)-4(-situ)-4( m)10(o)-4(n)-4(ito)-4(rin)-4(g)-4( o)-4(n)-4( th)-4(e resistan)-4(ce )6(ch)-4(an)-4(g)-4(e )6(w)-4(ere )6(co)-4(rrelated)-4( )6(to)-4( )]TJ 0.0023 Tc 0.1377 Tw T* [(sol)4(d)-2(er joi)4(n)-2(t)4( cracks usi)4(ng dy)4(e and )6(pul)4(l)4( )6(t)4(e)2(st)4( )6(and )6(cross-sect)4(i)4(o)-2(n )]TJ -0.0001 Tc 0.614 Tw T* [(an)-4(alysis. In)-4( o)-4(r)-3(d)-4(er to)-4( in)-4(v)-4(estig)-4(ate )6(th)-4(e )6(Sn)-4(A)-4(g)-4(Cu)-4( )6(fatig)-4(u)-4(e )]TJ 0.0016 Tc 0.1924 Tw T* [(perform)12(ance )-6(under t)4(h)-2(e ext)4(e)2(nded cy)4(cl)4(e t)4(i)4(m)12(e, several)4( speci)4(al)4( )]TJ 0.0008 Tc 0.0792 Tw T* [(tem)11(p)-3(erature cycle profiles have )]TJ 0.0017 Tc 0.0723 Tw (been defined. For socket, the )Tj 0.0013 Tc 0.1807 Tw T* [(t)3(o)-3(t)3(a)1(l)3( )-6(cy)3(cl)3(e )-6(t)3(i)3(m)11(e )-6(i)3(s)1( 480 m)11(i)3(nut)3(es per cy)3(cl)3(e t)3(o)-3( i)3(nvest)3(i)3(g)-3(at)3(e t)3(h)-3(e )]TJ 0.0024 Tc -0.0004 Tw T* [(SnAgCu perform)12(ance i)4(n)-1( power cy)5(cl)4(i)4(ng condi)4(t)4(i)4(ons. )]TJ 0 Tc 0 Tw 1.44 -1.27 Td ( )Tj 8.7134 0 0 8.73 312.804 63.6234 Tm ( )Tj ET Q BT /GS1 gs /TT4 1 Tf 10 0 0 10 298.5 40.29 Tm (140)Tj /TT5 1 Tf 2.704 0 Td (2008 Electronic Components and Technology Conference)Tj ET endstream endobj 3 0 obj [722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 250 333 408 500 500 833 778 180 333 333 500 564 250 333 250 278 500 500 500 500 500 500 500 500 500 500 278 278 564 564 564 444 921 722 667 667 722 611 556 722 722 333 389 722 611 889 722 722 556 722 667 556 611 722 722 944 722 722 611 333 278 333 469 500 333 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 480 200 480 541 350 744 350 333 500 444 1000 500 500 333 1000 556 333 889 350 611 350 350 333 333 444 444 350 500 1000 333 980 389 333 722 350 444 722 250 333 500 500 744 500 200 500 333 760 276 500 564 333 760 333 400 549 300 300 333 576 453 250 333 300 310 500 750 750 750 444 722 722 722 722 722 722 889 667 611 611 611 611 333 333 333 333 722 722 722 722 722 722 722 564 722 722 722 722 722 722 556 500 444 444 444 444 444 444 667 444 444 444 444 444 278 278 278 278 500 500 500 500 500 500 500 549 500 500 500 500 500 500 500 500] endobj 4 0 obj [722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 250 333 408 500 500 833 778 180 333 333 500 564 250 333 250 278 500 500 500 500 500 500 500 500 500 500 278 278 564 564 564 444 921 722 667 667 722 611 556 722 722 333 389 722 611 889 722 722 556 722 667 556 611 722 722 944 722 722 611 333 278 333 469 500 333 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 480 200 480 541 350 744 350 333 500 444 1000 500 500 333 1000 556 333 889 350 611 350 350 333 333 444 444 350 500 1000 333 980 389 333 722 350 444 722 250 333 500 500 744 500 200 500 333 760 276 500 564 333 760 333 400 549 300 300 333 576 453 250 333 300 310 500 750 750 750 444 722 722 722 722 722 722 889 667 611 611 611 611 333 333 333 333 722 722 722 722 722 722 722 564 722 722 722 722 722 722 556 500 444 444 444 444 444 444 667 444 444 444 444 444 278 278 278 278 500 500 500 500 500 500 500 549 500 500 500 500 500 500 500 500] endobj 5 0 obj <>/ProcSet[/PDF/Text]/ExtGState<>>>/Type/Page>> endobj 6 0 obj <>stream q 0.9700012 0 0 0.9700012 9 12 cm 0 0 m 612 0 l 612 792 l 0 792 l 0 0 l W n 1.0309265 0 0 1.0309265 -9.2783388 -12.3711185 cm BT 0 0 0 rg /GS0 gs /TT0 1 Tf 0.002 Tc 0.0018 Tw 8.7134 0 0 8.73 55.7928 725.9976 Tm [(Table 1: SAC thermal cy)-12(cling data collection from Intel \(refs.1, 3\) )]TJ 0.0018 Tc 0 Tw 7.7259 0 0 7.7406 55.7928 706.3842 Tm (Solder )Tj 0.0003 Tc -0.0017 Tw 0 -1.181 TD (Alloy )Tj 0.0029 Tc -0.0043 Tw 5.424 0.586 Td (Package )Tj 9.605 0 Td [(T)4(C)-1( Conditions 1 &)5( 2 )]TJ 0.0012 Tc 0 Tw 12.43 0.654 Td (AF )Tj 0.0007 Tc -0.0021 Tw 0 -1.308 TD (test )Tj ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 723.84 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 727.44 43.2 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 723.84 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84.48 727.44 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 723.84 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 727.44 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 723.84 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.98 727.44 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 723.84 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 727.44 0.48 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 699.36 0.48 24.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 699.36 0.48 24.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 699.36 0.48 24.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 699.36 0.48 24.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 699.36 0.48 24.48 re f Q BT /TT0 1 Tf 0.0027 Tc -0.0041 Tw 7.7259 0 0 7.7406 141.3468 677.226 Tm [(-)4(40\260)3(C to 85\260)3(C,)4( cy)6(cle tim)20(e 46m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 695.28 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 41.28 698.88 42.72 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 695.28 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84.48 698.88 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 695.28 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 698.88 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 695.28 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.98 698.88 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 695.28 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 677.28 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 677.28 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 677.28 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 677.28 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 677.28 0.48 18 re f Q BT /TT0 1 Tf 7.7259 0 0 7.7406 55.7928 668.496 Tm [(SAC405 )-1461(FCBGA )]TJ 11.074 -1.639 Td [(-)4(40\260)3(C to 85\260)3(C,)4( cy)6(cle tim)20(e 76m)20(in )]TJ 0.0047 Tc -0.0061 Tw 16.385 1.639 Td [(1.)6(2 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 673.2 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 673.2 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 673.2 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 676.8 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 673.2 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 673.2 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 655.2 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 655.2 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 655.2 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 655.2 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 655.2 0.48 18 re f Q BT /TT0 1 Tf 0.0028 Tc -0.0042 Tw 7.7259 0 0 7.7406 141.3468 634.3908 Tm [(-)4(40\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 30m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 651.12 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 41.28 654.72 42.72 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 651.12 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84.48 654.72 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 651.12 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 654.72 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 651.12 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.98 654.72 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 651.12 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 633.12 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 633.12 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 633.12 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 633.12 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 633.12 0.48 18 re f Q BT /TT0 1 Tf 0.0035 Tc -0.0049 Tw 7.7259 0 0 7.7406 55.7928 625.6608 Tm (SAC105 )Tj 0.0019 Tc 0 Tw 5.424 0.594 Td (CSP-)Tj 0.0016 Tc -0.003 Tw 0 -1.18 TD (BGA )Tj 0.0028 Tc -0.0042 Tw 5.65 -1.053 Td [(-)4(25\260)3(C to 100\260)3(C,)4( cy)6(cle tim)20(e 30m)20(in )]TJ 0.0047 Tc -0.0061 Tw 16.385 1.639 Td [(2.)6(5 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 629.04 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 629.04 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 629.04 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 632.64 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 629.04 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 629.04 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 611.04 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 611.04 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 611.04 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 611.04 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 611.04 0.48 18 re f Q BT /TT0 1 Tf 0.0028 Tc -0.0042 Tw 7.7259 0 0 7.7406 141.3468 591.5556 Tm [(-)4(25\260)3(C to 100\260)3(C,)4( cy)6(cle tim)20(e 60m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 606.96 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 41.28 610.56 42.72 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 606.96 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84.48 610.56 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 606.96 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 610.56 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 606.96 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.98 610.56 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 606.96 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 588.96 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 588.96 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 588.96 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 588.96 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 588.96 0.48 18 re f Q BT /TT0 1 Tf 0.0029 Tc -0.0043 Tw 7.7259 0 0 7.7406 55.7928 582.8256 Tm [(SAC405 )-1461(Socket )]TJ 0.0028 Tc -0.0042 Tw 11.074 -1.639 Td [(-)4(25\260)3(C to 100\260)3(C,)4( cy)6(cle tim)20(e 480m)20(in )]TJ 0.0047 Tc -0.0061 Tw 16.385 1.639 Td [(2.)6(1 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 584.88 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 584.88 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 584.88 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 588.48 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 584.88 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 584.88 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 566.88 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 566.88 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 566.88 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 566.88 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 566.88 0.48 18 re f Q BT /TT0 1 Tf 0.0027 Tc -0.0041 Tw 7.7259 0 0 7.7406 141.3468 548.7204 Tm [(-)4(40\260)3(C to 85\260)3(C,)4( cy)6(cle tim)20(e 46m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 562.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 41.28 566.4 42.72 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 562.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84.48 566.4 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 562.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 566.4 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 562.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.98 566.4 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 562.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 544.8 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 544.8 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 544.8 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 544.8 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 544.8 0.48 18 re f Q BT /TT0 1 Tf 0.0029 Tc -0.0043 Tw 7.7259 0 0 7.7406 55.7928 539.9905 Tm [(SAC405 )-1461(CSP )]TJ 0.0028 Tc -0.0042 Tw 11.074 -1.639 Td [(0\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 120m)20(in )]TJ 0.0047 Tc -0.0061 Tw 16.385 1.639 Td [(1.)6(4 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 540.72 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 540.72 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 540.72 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 544.32 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 540.72 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 540.72 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 522.72 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 522.72 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 522.72 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 522.72 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 522.72 0.48 18 re f Q BT /TT0 1 Tf 0.0027 Tc -0.0041 Tw 7.7259 0 0 7.7406 141.3468 505.8852 Tm [(-)4(40\260)3(C to 85\260)3(C,)4( cy)6(cle tim)20(e 46m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 518.64 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 41.28 522.24 42.72 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 518.64 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84.48 522.24 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 518.64 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 522.24 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 518.64 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.98 522.24 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 518.64 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 500.64 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 500.64 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 500.64 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 500.64 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 500.64 0.48 18 re f Q BT /TT0 1 Tf 7.7259 0 0 7.7406 55.7928 497.1552 Tm [(SAC405 )-1461(FCBGA )]TJ 11.074 -1.639 Td [(0\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 120m)20(in )]TJ 0.0047 Tc -0.0061 Tw 16.385 1.639 Td [(3.)6(2 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 496.56 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 496.56 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 496.56 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 500.16 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 496.56 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 496.56 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 478.56 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 478.56 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 478.56 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 478.56 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 478.56 0.48 18 re f Q BT /TT0 1 Tf 0.0027 Tc -0.0041 Tw 7.7259 0 0 7.7406 141.3468 463.05 Tm [(-)4(40\260)3(C to 85\260)3(C,)4( cy)6(cle tim)20(e 46m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 474.48 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 41.28 478.08 42.72 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 474.48 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84.48 478.08 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 474.48 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 478.08 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 474.48 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.98 478.08 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 474.48 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 456.48 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 456.48 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 456.48 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 456.48 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 456.48 0.48 18 re f Q BT /TT0 1 Tf 7.7259 0 0 7.7406 55.7928 454.32 Tm [(SAC405 )-1461(FCBGA )]TJ 11.074 -1.639 Td [(0\260)3(C to 125C,)4( cy)6(cle tim)20(e 120m)20(in )]TJ 0.0047 Tc -0.0061 Tw 16.385 1.639 Td [(2.)6(5 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 452.4 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 452.4 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 452.4 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 456 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 452.4 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 452.4 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 434.4 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 434.4 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 434.4 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 434.4 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 434.4 0.48 18 re f Q BT /TT0 1 Tf 0.0028 Tc -0.0042 Tw 7.7259 0 0 7.7406 141.3468 420.2148 Tm [(-)4(25\260)3(C to 100\260)3(C,)4( cy)6(cle tim)20(e 30m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 430.32 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 41.28 433.92 42.72 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 430.32 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84.48 433.92 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 430.32 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 433.92 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 430.32 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.98 433.92 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 430.32 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 412.32 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 412.32 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 412.32 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 412.32 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 412.32 0.48 18 re f Q BT /TT0 1 Tf 0.0035 Tc -0.0049 Tw 7.7259 0 0 7.7406 55.7928 411.4848 Tm (SAC405 )Tj 0.0012 Tc 0 Tw 5.424 1.181 Td (Die-side )Tj 0.0011 Tc 0 -1.181 TD (capacitor )Tj 0.0021 Tc -0.0035 Tw T* (package )Tj 0.0028 Tc -0.0042 Tw 5.65 -0.459 Td [(-)4(25\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 30m)20(in )]TJ 0.0047 Tc -0.0061 Tw 16.385 1.639 Td [(1.)6(5 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 408.24 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 408.24 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 408.24 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 411.84 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 408.24 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 408.24 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 390.24 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 390.24 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 390.24 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 390.24 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 390.24 0.48 18 re f Q BT /TT0 1 Tf 0.0028 Tc -0.0042 Tw 7.7259 0 0 7.7406 141.3468 377.3796 Tm [(-)4(25\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 30m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 386.16 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 41.28 389.76 42.72 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 386.16 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84.48 389.76 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 386.16 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 389.76 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 386.16 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.98 389.76 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 386.16 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 368.16 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 368.16 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 368.16 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 368.16 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 368.16 0.48 18 re f Q BT /TT0 1 Tf 0.0035 Tc -0.0049 Tw 7.7259 0 0 7.7406 55.7928 368.6496 Tm (SAC405 )Tj 0.0012 Tc 0 Tw 5.424 1.181 Td (Die-side )Tj 0.0011 Tc T* (capacitor )Tj 0.0021 Tc T* (package )Tj 0.0028 Tc -0.0042 Tw 5.65 -0.459 Td [(-)4(55\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 30m)20(in )]TJ 0.0047 Tc -0.0061 Tw 16.385 1.639 Td [(1.)6(9 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 40.8 364.08 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 364.08 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 364.08 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 367.68 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 364.08 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 364.08 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 345.6 0.48 18.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 40.8 345.6 43.2 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84 345.6 0.48 18.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 84.48 345.6 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129 345.6 0.48 18.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 129.48 345.6 130.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.5 345.6 0.48 18.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 259.98 345.6 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 345.6 0.48 18.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 286.5 345.6 0.48 0.48 re f Q BT /TT0 1 Tf 0 Tc 0 Tw 9.701 0 0 9.7194 55.7928 338.0946 Tm ( )Tj 0.0021 Tc 0.0959 Tw 1.44 -1.27 Td [(Tabl)4(e 2 gi)4(ves t)4(h)-2(e t)4(e)2(st)4( dat)4(a)2( used by)4( Zhang and )6(Cl)4(ech )6([7])5(. )]TJ 0.0008 Tc 0.6311 Tw -1.44 -1.168 Td [(For )-6(PBGA assem)11(b)-3(ly, the accelerated therm)11(a)1(l cycling )]TJ 0.0021 Tc 0.0239 Tw 0 -1.168 TD [(condi)4(t)4(i)4(ons were t)4(h)-2(erm)12(a)2(l)4( cy)4(cl)4(i)4(n)-2(g bet)4(w)-2(een 0\260C and 100\260C )6(wi)4(t)4(h)-2( )]TJ 0.0027 Tc 0.0953 Tw T* [(10 )-6(m)13(i)5(nut)5(es )-6(ram)13(p)-1(s \(up and down\), 10 m)13(i)5(nut)5(es dwel)5(l)5(s)2( at)5( 0\260C, )]TJ 0.0024 Tc 0.2335 Tw T* [(and )-6(10 )-6(m)12(i)4(nut)4(es or 60 m)12(i)4(nut)4(es at)4( 100\260C, respect)4(i)4(v)-1(el)4(y)5(. For )]TJ 0.0005 Tc 0.0855 Tw T* [(CBGA, three tem)10(p)-3(erature cyclic )]TJ 0.0025 Tc 0.0835 Tw 13.541 0 Td [(profi)4(l)4(e)2(s were used, but)4( )6(wi)4(t)4(h)-1( )]TJ 0.0004 Tc 0.0496 Tw -13.541 -1.168 Td [(the )-6(fixed )-6(total )-6(cycle )-6(tim)10(e as 80 m)10(i)2(nutes. Total cycle tim)10(e was )]TJ 0.0012 Tc 0.0008 Tw T* (used for acceleration factor calculation. )Tj 0.0021 Tc 0.0017 Tw 8.7134 0 0 8.73 55.7928 229.1442 Tm [(Table 2: Test conditions and acceleration factors from)5( test \(ref. 7\) )]TJ 0.0018 Tc 0 Tw 7.7259 0 0 7.7406 69.4698 209.9965 Tm (Solder )Tj 0.0003 Tc -0.0017 Tw 0 -1.181 TD (Alloy )Tj 0.0029 Tc -0.0043 Tw 5.349 0.594 Td [(Package )-3126(T)4(C)-1( Conditions 1 &)5( 2 )]TJ 0.0012 Tc 0 Tw 20.98 0.586 Td (AF )Tj 0.0007 Tc -0.0021 Tw T* (test )Tj ET q 0.9700012 0 0 0.9700012 9 12 cm 54.9 211.62 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 54.9 215.22 42.6 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 211.62 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.98 215.22 40.62 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 211.62 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 139.08 215.22 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 211.62 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 265.08 215.22 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 211.62 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 215.22 0.48 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 54.9 188.16 0.48 23.46 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 188.16 0.48 23.46 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 188.16 0.48 23.46 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 188.16 0.48 23.46 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 188.16 0.48 23.46 re f Q BT /TT0 1 Tf 0.0027 Tc -0.0041 Tw 7.7259 0 0 7.7406 150.6588 181.3621 Tm [(0\260)3(C to 100\260)3(C,)4( cy)6(cle tim)20(e 90m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 54.9 184.08 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 55.38 187.68 42.12 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 184.08 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.98 187.68 40.62 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 184.08 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 139.08 187.68 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 184.08 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 265.08 187.68 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 184.08 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 54.9 166.08 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 166.08 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 166.08 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 166.08 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 166.08 0.48 18 re f Q BT /TT0 1 Tf 7.7259 0 0 7.7406 69.4698 172.6321 Tm [(SAC305 )-1386(PBGA )]TJ 10.509 -1.639 Td [(0\260)3(C to 100\260)3(C,)4( cy)6(cle tim)20(e 48m)20(in )]TJ 0.0047 Tc -0.0061 Tw 15.82 1.639 Td [(1.)6(2 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 54.9 162 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 162 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 162 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 139.08 165.6 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 162 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 162 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 54.9 144 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 144 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 144 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 144 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 144 0.48 18 re f Q BT /TT0 1 Tf 0.0027 Tc -0.0041 Tw 7.7259 0 0 7.7406 150.6588 138.5268 Tm [(0\260)3(C to 100\260)3(C,)4( cy)6(cle tim)20(e 80m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 54.9 139.92 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 55.38 143.52 42.12 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 139.92 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.98 143.52 40.62 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 139.92 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 139.08 143.52 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 139.92 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 265.08 143.52 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 139.92 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 54.9 121.92 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 121.92 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 121.92 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 121.92 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 121.92 0.48 18 re f Q BT /TT0 1 Tf 0.0029 Tc -0.0043 Tw 7.7259 0 0 7.7406 69.4698 129.7968 Tm [(SAC305 )-1386(CBGA )]TJ 0.0027 Tc -0.0041 Tw 10.509 -1.639 Td [(30\260)3(C to 80\260)3(C,)4( cy)6(cle tim)20(e 80m)20(in )]TJ 0.0047 Tc -0.0061 Tw 15.82 1.639 Td [(2.)6(5 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 54.9 117.84 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 117.84 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 117.84 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 139.08 121.44 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 117.84 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 117.84 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 54.9 99.84 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 99.84 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 99.84 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 99.84 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 99.84 0.48 18 re f Q BT /TT0 1 Tf 0.0028 Tc -0.0042 Tw 7.7259 0 0 7.7406 150.6588 95.6917 Tm [(-)4(40\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 80m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 54.9 95.76 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 55.38 99.36 42.12 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 95.76 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.98 99.36 40.62 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 95.76 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 139.08 99.36 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 95.76 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 265.08 99.36 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 95.76 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 54.9 77.76 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 77.76 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 77.76 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 77.76 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 77.76 0.48 18 re f Q BT /TT0 1 Tf 0.0029 Tc -0.0043 Tw 7.7259 0 0 7.7406 69.4698 86.9617 Tm [(SAC305 )-1386(CBGA )]TJ 0.0027 Tc -0.0041 Tw 10.509 -1.639 Td [(30\260)3(C to 80\260)3(C,)4( cy)6(cle tim)20(e 80m)20(in )]TJ 0.0047 Tc -0.0061 Tw 15.82 1.639 Td [(2.)6(1 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 54.9 73.68 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 73.68 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 73.68 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 139.08 77.28 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 73.68 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 73.68 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 54.9 55.2 0.48 18.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 54.9 55.2 42.6 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.5 55.2 0.48 18.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 97.98 55.2 40.62 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 138.6 55.2 0.48 18.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 139.08 55.2 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 264.6 55.2 0.48 18.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 265.08 55.2 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 55.2 0.48 18.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 291.6 55.2 0.48 0.48 re f Q BT /TT0 1 Tf 0 Tc 0.14 Tw 9.701 0 0 9.7194 326.772 725.0083 Tm [(Tab)-4(l)2(e )-6(3)-4( )-6(lists )-6(th)-4(e )-6(p)-4(ack)-4(ag)-4(e in)-4(fo)-4(rm)10(atio)-4(n)-4( an)-4(d)-4( test d)-4(ata fro)-4(m)10( )]TJ 0.0026 Tc 0.1014 Tw -1.44 -1.168 Td [(ref. [18] for SAC305/405. )6(In )6(or)]TJ 0.0004 Tc 0.0976 Tw (der to evaluate the reliability )Tj 0.0012 Tc 0.3487 Tw 0 -1.168 TD [(of solder joints, )6(accelerated )]TJ 0.0003 Tc 0.3436 Tw 12.665 0 Td [(tem)10(p)-4(erature cycle tests were )]TJ 0.0024 Tc 0.1196 Tw -12.665 -1.168 Td [(conduct)4(e)2(d on vari)4(ous packages. )6(Th)]TJ 0.0021 Tc 0.1139 Tw [(e dat)4(a)2( were generat)4(e)2(d on )]TJ 0.0022 Tc 0.0898 Tw T* [(packages of sizes varying from)12( )6(8x8m)12(m)12( )6(to )6(27m)12(m)12(x)-2(27m)12(m)12( )6(and )]TJ 0.001 Tc 0.3789 Tw T* (various die sizes. All packages)Tj -0.001 Tc 0.3749 Tw 13.853 0 Td [( u)-5(s)-2(ed)-5( in)-5( th)-5(is stu)-5(d)-5(y u)-5(s)-2(ed)-5( )]TJ -0.0004 Tc 0.0444 Tw -13.853 -1.168 Td [(electro)-4(lytic )-6(N)-4(i)2(A)-4(u)-4( )-6(p)-4(l)2(atin)-4(g)-4( o)-4(n)-4( th)-4(e b)-4(all lan)-4(d)-4(s an)-4(d)-4( th)-4(e test b)-4(o)-4(ard)-4(s )]TJ 0.0015 Tc 0.1745 Tw T* [(had )-6(OSP )-6(surface finish. Three te)]TJ 0.0014 Tc 0.1746 Tw 13.931 0 Td (st conditions were used to )Tj 0.0017 Tc 0.0423 Tw -13.931 -1.168 Td [(generat)4(e)2( t)4(h)-2(e t)4(e)2(st)4( dat)4(a)2( as shown i)4(n)-2( Tabl)4(e 3. These )6(t)4(e)2(m)12(p)-2(erat)4(ure )]TJ 0.0012 Tc 0.2587 Tw T* (cycle conditions cover the ra)Tj 0.2526 Tw 12.563 0 Td [(nge )-6(of accelerated conditions )]TJ 0.0022 Tc 0.4737 Tw -12.563 -1.168 Td [(t)4(y)4(pi)4(cal)4(l)4(y)4( used by)4( t)4(h)-2(e i)4(ndust)4(r)-1(y)4( t)4(o)-2( eval)4(uat)4(e)2( )6(sol)4(d)-2(er )6(joi)4(n)-2(t)4( )]TJ 0.0001 Tc 0.0019 Tw T* [(reliab)-4(ility fo)-4(r v)-4(ario)-4(u)-4(s)-1( ap)-4(p)-4(licatio)-4(n)-4(s)-1(. )]TJ 0.0024 Tc 0.0014 Tw 8.7134 0 0 8.73 312.804 583.0002 Tm (Table 3, Test conditions and accelera)Tj 0.0018 Tc 0.002 Tw 14.975 0 Td [(tion factors from)5( test \(ref. 18\) )]TJ -0.0014 Tc 0 Tw 7.7259 0 0 7.7406 327.5868 563.3286 Tm ( )Tj 0.0019 Tc 0 -1.181 TD (Alloy)Tj 0.0027 Tc -0.0041 Tw 3.947 0.586 Td [(Package )-4090(T)3(e)2(st conditions T)3(C)-1(1 &)5( T)3(C)-1(2 )]TJ 0.001 Tc 0 Tw 21.372 0.594 Td (AF)Tj 0.0009 Tc -0.218 -1.181 Td (Test )Tj ET q 0.9700012 0 0 0.9700012 9 12 cm 327.96 576.72 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 327.96 580.02 22.5 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 576.72 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.94 580.02 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 576.72 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.94 580.02 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 576.72 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.94 580.02 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 576.72 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 580.02 0.48 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 327.96 551.82 0.48 24.9 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 551.82 0.48 24.9 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 551.82 0.48 24.9 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 551.82 0.48 24.9 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 551.82 0.48 24.9 re f Q BT /TT0 1 Tf 0.0027 Tc -0.0041 Tw 7.7259 0 0 7.7406 404.2944 534.4033 Tm [(0\260)3(C to 100\260)3(C,)4( cy)6(cle tim)20(e 30m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 327.96 548.04 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 328.44 551.34 22.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 548.04 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.94 551.34 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 548.04 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.94 551.34 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 548.04 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.94 551.34 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 548.04 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 327.96 530.34 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 530.34 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 530.34 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 530.34 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 530.34 0.48 17.7 re f Q BT /TT0 1 Tf 0 Tc 0 Tw 7.7259 0 0 7.7406 345.2214 530.9112 Tm ( )Tj 0.0012 Tc -1.876 -1.308 Td (SAC)Tj 0.0023 Tc 3.375 0.654 Td (flexBGA )Tj 0.0028 Tc -0.0042 Tw 5.725 -1.586 Td [(-)4(55\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 30m)20(in )]TJ 0.0047 Tc 0 Tw 15.827 1.586 Td [(3.)6(5 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 327.96 526.56 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 526.56 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 526.56 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.94 529.86 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 526.56 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 526.56 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 327.96 508.86 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 508.86 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 508.86 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 508.86 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 508.86 0.48 17.7 re f Q BT /TT0 1 Tf 0.0027 Tc -0.0041 Tw 7.7259 0 0 7.7406 404.2944 492.732 Tm [(0\260)3(C to 100\260)3(C,)4( cy)6(cle tim)20(e 30m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 327.96 505.08 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 328.44 508.38 22.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 505.08 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.94 508.38 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 505.08 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.94 508.38 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 505.08 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.94 508.38 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 505.08 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 327.96 487.38 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 487.38 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 487.38 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 487.38 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 487.38 0.48 17.7 re f Q BT /TT0 1 Tf 0.0017 Tc 0 Tw 7.7259 0 0 7.7406 330.7296 484.1766 Tm [(SAC)-1425(f)-4(lexBGA )]TJ 0.0028 Tc -0.0042 Tw 9.1 -1.586 Td [(-)4(40\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 60m)20(in )]TJ 0.0047 Tc 0 Tw 15.827 1.586 Td [(3.)6(7 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 327.96 483.6 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 483.6 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 483.6 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.94 486.9 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 483.6 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 483.6 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 327.96 465.9 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 465.9 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 465.9 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 465.9 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 465.9 0.48 17.7 re f Q BT /TT0 1 Tf 0.0028 Tc -0.0042 Tw 7.7259 0 0 7.7406 401.0352 451.0608 Tm [(-)4(40\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 60m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 327.96 462.12 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 328.44 465.42 22.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 462.12 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.94 465.42 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 462.12 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.94 465.42 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 462.12 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.94 465.42 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 462.12 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 327.96 444.42 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 444.42 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 444.42 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 444.42 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 444.42 0.48 17.7 re f Q BT /TT0 1 Tf 0.0012 Tc 0 Tw 7.7259 0 0 7.7406 330.7296 442.5054 Tm (SAC)Tj 0.0011 Tc 3.88 0.586 Td (Plastic )Tj 0.0019 Tc 0.445 -1.181 Td (CSP )Tj 0.0028 Tc -0.0042 Tw 4.776 -0.992 Td [(-)4(55\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 30m)20(in )]TJ 0.0047 Tc 0 Tw 15.827 1.586 Td [(1.)6(5 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 327.96 440.64 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 440.64 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 440.64 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.94 443.94 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 440.64 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 440.64 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 327.96 422.94 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 422.94 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 422.94 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 422.94 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 422.94 0.48 17.7 re f Q BT /TT0 1 Tf 0.0027 Tc -0.0041 Tw 7.7259 0 0 7.7406 404.2944 409.3896 Tm [(0\260)3(C to 100\260)3(C,)4( cy)6(cle tim)20(e 30m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 327.96 419.16 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 328.44 422.46 22.02 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 419.16 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.94 422.46 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 419.16 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.94 422.46 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 419.16 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.94 422.46 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 419.16 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 327.96 401.46 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 401.46 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 401.46 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 401.46 0.48 17.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 401.46 0.48 17.7 re f Q BT /TT0 1 Tf 0.0018 Tc 0 Tw 7.7259 0 0 7.7406 330.7296 400.8342 Tm [(SAC)-1870(CBGA )]TJ 0.0028 Tc -0.0042 Tw 8.852 -1.586 Td [(-)4(40\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 60m)20(in )]TJ 0.0047 Tc 0 Tw 16.076 1.586 Td [(2.)6(5 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 327.96 397.68 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 397.68 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 397.68 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.94 400.98 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 397.68 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 397.68 0.48 3.78 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 327.96 379.5 0.48 18.18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 327.96 379.5 22.5 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.46 379.5 0.48 18.18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 350.94 379.5 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.46 379.5 0.48 18.18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 395.94 379.5 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.46 379.5 0.48 18.18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 521.94 379.5 26.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 379.5 0.48 18.18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 548.46 379.5 0.48 0.48 re f Q BT /TT0 1 Tf 0 Tc 9.701 0 0 9.7194 312.804 365.1576 Tm ( )Tj 0.0018 Tc 0.2341 Tw 1.44 -1.27 Td [(CALCE [11])5( i)4(nvest)4(i)4(g)-2(at)4(ed )]TJ 0.0021 Tc 0.2278 Tw 11.249 0 Td [(the SnAgCu perform)12(ance for )]TJ 0.0017 Tc 0.0963 Tw -12.689 -1.168 Td [(CLCC, TQFP and TSOP packages under t)4(h)-2(erm)12(a)2(l)4( cy)4(cl)4(i)4(n)-2(g, as )]TJ 0.0022 Tc 0.2817 Tw 0 -1.168 TD [(shown )-6(i)4(n)-2( )-6(Tabl)4(e 4. In t)4(h)-2(at)4( st)4(udy)4(, t)4(w)-2(o t)4(e)2(m)12(p)-2(erat)4(ure-cy)4(cl)4(i)4(n)-2(g )]TJ 0.0027 Tc 0.5092 Tw T* [(condi)5(t)5(i)5(ons were appl)5(i)5(e)3(d t)5(o)-1( i)5(ndependent)5( )6(groups )6(of )6(t)5(e)3(st)5( )]TJ 0.0005 Tc 0.0015 Tw T* [(assem)10(b)-3(lies. )-6(The )-6(first )-6(test )-6(subjected a set of test assem)10(b)-3(lies to a )]TJ 0.0014 Tc 0.0666 Tw 0 -1.233 TD [(tem)11(p)-3(erature cycle of -55 to 125)]TJ /C2_0 1 Tf 0 Tc 0 Tw 12.947 0 Td <0071>Tj /TT0 1 Tf 0.0017 Tc 0.0663 Tw 0.402 0 Td [(C. The second )6(t)4(e)2(st)4( )6(subject)4(ed )]TJ 0.0007 Tc 0.0133 Tw -13.349 -1.168 Td [(another )-6(set )-6(of )-6(test )-6(specim)11(e)1(ns to a sm)11(aller tem)11(p)-3(erature cycle of )]TJ 0.0038 Tc 0.1302 Tw T* [(-20 t)6(o 80)]TJ /C2_0 1 Tf 0 Tc 0 Tw <0071>Tj /TT0 1 Tf -0.0004 Tc 0.1344 Tw 4.302 0 Td [(C. Fo)-4(r b)-4(o)-4(th)-4( tests, th)-4(e d)-4(w)-4(ell )6(tim)10(e )6(at )6(th)-4(e )6(m)10(ax)-4(i)2(m)10(u)-4(m)10( )]TJ 0.0009 Tc 0.1151 Tw -4.301 -1.168 Td [(tem)11(p)-3(erature )-6(was 30 m)11(i)3(nutes and dwell tim)11(e at the m)11(i)3(nim)11(u)-3(m)11( )]TJ 0.002 Tc 0 Tw 0 -1.168 TD [(t)4(e)2(m)12(p)-2(erat)4(ure was 10 m)12(i)4(nut)4(es. )]TJ 0.0023 Tc 0.0015 Tw 8.7134 0 0 8.73 312.804 232.2289 Tm (Table 4 Test conditions and accelera)Tj 0.0018 Tc 0.002 Tw 14.721 0 Td [(tion factors from)5( test \(ref. 11\) )]TJ 0 Tw 7.7259 0 0 7.7406 324.3276 213.081 Tm (Solder )Tj 0.0003 Tc -0.0017 Tw 0 -1.181 TD (Alloy )Tj 0.0029 Tc -0.0043 Tw 5.062 0.594 Td [(Package )-3616(T)4(C)-1( Conditions 1 &)5( 2 )]TJ 0.0012 Tc 0 Tw 21.47 0.586 Td (AF )Tj 0.0009 Tc T* (Test )Tj ET q 0.9700012 0 0 0.9700012 9 12 cm 317.64 214.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 317.64 218.4 40.32 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 214.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 358.44 218.4 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 214.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 403.44 218.4 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 214.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 529.44 218.4 29.4 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 214.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 218.4 0.48 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 317.64 191.34 0.48 23.46 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 191.34 0.48 23.46 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 191.34 0.48 23.46 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 191.34 0.48 23.46 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 191.34 0.48 23.46 re f Q BT /TT0 1 Tf 0.0027 Tc -0.0041 Tw 7.7259 0 0 7.7406 407.088 184.4466 Tm [(-)4(20\260)3(C to 80\260)3(C,)4( cy)6(cle tim)20(e 76m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 317.64 187.26 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 318.12 190.86 39.84 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 187.26 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 358.44 190.86 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 187.26 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 403.44 190.86 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 187.26 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 529.44 190.86 29.4 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 187.26 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 317.64 169.26 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 169.26 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 169.26 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 169.26 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 169.26 0.48 18 re f Q BT /TT0 1 Tf 0.0023 Tc -0.0037 Tw 7.7259 0 0 7.7406 324.3276 186.3673 Tm (SAC )Tj 0.0041 Tc 0 Tw T* [(Sn3.)6(9 )]TJ -0.0055 Tw T* [(Ag 0.)6(7 )]TJ 0 Tw T* (Cu )Tj 0.0034 Tc 5.062 2.03 Td (CLCC20 )Tj 0.0028 Tc -0.0042 Tw 5.65 -1.639 Td [(-)4(55\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 60m)20(in )]TJ 0.0047 Tc -0.0061 Tw 15.82 1.639 Td [(1.)6(2 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 317.64 165.18 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 165.18 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 165.18 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 403.44 168.78 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 165.18 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 165.18 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 317.64 144.96 0.48 20.22 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 144.96 0.48 20.22 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 144.96 0.48 20.22 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 144.96 0.48 20.22 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 144.96 0.48 20.22 re f Q BT /TT0 1 Tf 0.0027 Tc -0.0041 Tw 7.7259 0 0 7.7406 407.088 139.4581 Tm [(-)4(20\260)3(C to 80\260)3(C,)4( cy)6(cle tim)20(e 70m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 317.64 140.88 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 318.12 144.48 39.84 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 140.88 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 358.44 144.48 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 140.88 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 403.44 144.48 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 140.88 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 529.44 144.48 29.4 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 140.88 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 317.64 122.88 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 122.88 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 122.88 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 122.88 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 122.88 0.48 18 re f Q BT /TT0 1 Tf 0.0023 Tc -0.0037 Tw 7.7259 0 0 7.7406 324.3276 141.3786 Tm (SAC )Tj 0.0041 Tc 0 Tw 0 -1.18 TD [(Sn3.)6(9 )]TJ -0.0055 Tw T* [(Ag 0.)6(7 )]TJ 0 Tw T* (Cu )Tj 0.0008 Tc 5.062 2.684 Td (TQFP )Tj 0.0047 Tc -0.0061 Tw 0 -1.308 TD (144 )Tj 0.0028 Tc -0.0042 Tw 5.65 -0.985 Td [(-)4(55\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 60m)20(in )]TJ 0.0047 Tc -0.0061 Tw 15.82 1.639 Td [(2.)6(5 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 317.64 118.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 118.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 118.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 403.44 122.4 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 118.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 118.8 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 317.64 98.58 0.48 20.22 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 98.58 0.48 20.22 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 98.58 0.48 20.22 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 98.58 0.48 20.22 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 98.58 0.48 20.22 re f Q BT /TT0 1 Tf 0.0027 Tc -0.0041 Tw 7.7259 0 0 7.7406 407.088 94.4695 Tm [(-)4(20\260)3(C to 80\260)3(C,)4( cy)6(cle tim)20(e 76m)20(in )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 317.64 94.5 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 318.12 98.1 39.84 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 94.5 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 358.44 98.1 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 94.5 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 403.44 98.1 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 94.5 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 529.44 98.1 29.4 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 94.5 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 317.64 76.5 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 76.5 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 76.5 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 76.5 0.48 18 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 76.5 0.48 18 re f Q BT /TT0 1 Tf 0.0023 Tc -0.0037 Tw 7.7259 0 0 7.7406 324.3276 96.3901 Tm (SAC )Tj 0.0041 Tc 0 Tw 0 -1.181 TD [(Sn3.)6(9 )]TJ -0.0055 Tw T* [(Ag 0.)6(7 )]TJ 0 Tw T* (Cu )Tj 0.0033 Tc 5.062 2.03 Td [(T)4(S)2(OP50 )]TJ 0.0028 Tc -0.0042 Tw 5.65 -1.639 Td [(-)4(55\260)3(C to 125\260)3(C,)4( cy)6(cle tim)20(e 60m)20(in )]TJ 0.0047 Tc -0.0061 Tw 15.82 1.639 Td [(2.)6(1 )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 317.64 72.42 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 72.42 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 72.42 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 403.44 76.02 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 72.42 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 72.42 0.48 4.08 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 317.64 51.72 0.48 20.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 317.64 51.72 40.32 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 357.96 51.72 0.48 20.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 358.44 51.72 44.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 402.96 51.72 0.48 20.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 403.44 51.72 125.52 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 528.96 51.72 0.48 20.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 529.44 51.72 29.4 0.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 51.72 0.48 20.7 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 558.84 51.72 0.48 0.48 re f Q Q BT /GS1 gs /TT1 1 Tf 10 0 0 10 298.5 40.29 Tm (141)Tj /TT2 1 Tf 2.704 0 Td (2008 Electronic Components and Technology Conference)Tj ET endstream endobj 7 0 obj [722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 250 333 408 500 500 833 778 180 333 333 500 564 250 333 250 278 500 500 500 500 500 500 500 500 500 500 278 278 564 564 564 444 921 722 667 667 722 611 556 722 722 333 389 722 611 889 722 722 556 722 667 556 611 722 722 944 722 722 611 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0.0006 Tw 9.701 0 0 9.7194 55.7928 724.8336 Tm ( 4. Acceleration Model )Tj /TT1 1 Tf 0.3005 Tw 1.44 -1.258 Td [(SAC solder is m)11(o)-2(re creep re)]TJ -0.0002 Tc 0.2961 Tw 12.833 0 Td [(sistan)-4(t )-6(th)-4(an)-4( Sn)-4(/Pb)-4( so)-4(ld)-4(er )]TJ 0.002 Tc 0.012 Tw -14.273 -1.168 Td [(under m)12(o)-2(st conditions. However, )]TJ 0.0004 Tc 0.0136 Tw 13.655 0 Td [(tem)10(p)-4(erature, and cycle )6(tim)10(e )]TJ -0.0004 Tc 0.0024 Tw -13.655 -1.168 Td [(still )-6(h)-4(av)-4(e )-6(sig)-4(n)-4(i)2(fican)-4(t )-6(im)10(p)-4(act o)-4(n)-4( th)-4(e th)-4(erm)10(al fatig)-4(u)-4(e life o)-4(f)-3( SA)-4(C )]TJ 0.002 Tc 0.102 Tw 0 -1.168 TD [(sol)4(d)-2(er joi)4(n)-2(t)4(s)1(, as shown from)12( t)4(h)-2(e )6(t)4(e)2(st)4( )6(dat)4(a)2( )6(above. )6(The )6(i)4(m)12(pact)4( )]TJ -0.0004 Tc 0.0864 Tw T* [(o)-4(f)-3( th)-4(e ex)-4(ten)-4(d)-4(ed)-4( cycle tim)10(e o)-4(n)-4( so)-4(ld)-4(er j)-4(o)-4(in)-4(t reliab)-4(ility )6(fo)-4(r )6(b)-4(o)-4(t)2(h)-4( )]TJ 0.0021 Tc 0.0779 Tw T* [(Sn/)4(Pb )-6(and )-6(SAC 405 has been charact)4(eri)4(zed by)4( Vasudevan et)4( )]TJ 0.0028 Tc 0.0472 Tw T* [(al)5( [1])6( and showed no cross-over )6(for )6(bot)5(h )6(Sn/)5(P)1(b )6(and )6(LF )6(even )]TJ 0.0008 Tc 0.2351 Tw T* [(after )-6(8 hrs cycle tim)11(e. Both )]TJ 0.0026 Tc 0.2333 Tw 12.563 0 Td [(Sn/)5(P)1(b and LF sol)5(d)-1(er showed )]TJ 0.0014 Tc 0.2106 Tw -12.563 -1.168 Td [(decrease in fatigue perform)11(ance )]TJ -0.0008 Tc 0.2068 Tw 13.925 0 Td [(w)-5(ith)-5( )-6(th)-5(e )-6(in)-5(crease in)-5( d)-5(w)-5(ell )]TJ -0.0005 Tc 0.2784 Tw -13.925 -1.168 Td [(tim)9(e. )-6(So)-4(ld)-4(er )-6(j)-5(o)-4(in)-4(t fatig)-4(u)-4(e)-1( life scales in)-4(v)-4(e)-1(rsely w)-4(ith)-4( cyclic )]TJ 0.0014 Tc 0.1566 Tw T* (shear strain range \()Tj /C2_0 1 Tf -0.0011 Tc 0 Tw 8.135 0 Td <01FB012B>Tj /TT1 1 Tf 0.0032 Tc 0.1548 Tw 1.224 0 Td [(\) for bot)5(h Sn/)5(P)1(b and )6(LF.)]TJ 0 Tc 0 Tw 11.618 0 0 11.64 249.4824 599.1216 Tm ( )Tj 0.0027 Tc 0.1493 Tw 9.701 0 0 9.7194 253.8474 599.1216 Tm [(Hi)5(gh st)5(rai)5(n)-1( )]TJ 0.0025 Tc 0.0055 Tw -20.416 -1.353 Td [(com)12(ponent)4(s \()]TJ /C2_0 1 Tf -0.0011 Tc 0 Tw 5.435 0 Td <01FB012B>Tj /TT1 1 Tf 0 Tc 0.002 Tw 1.224 0 Td (= {)Tj 0.0003 Tc 0 Tw 11.618 0 0 11.64 132.966 585.9684 Tm (L.)Tj 0 Tc 9.701 0 0 9.7194 142.9764 585.9684 Tm ( )Tj /C2_0 1 Tf 0.252 0 Td <01FB>Tj /C2_1 1 Tf 11.618 0 0 11.64 151.6482 585.9684 Tm <012E>Tj /TT1 1 Tf 0.581 0 Td (.)Tj 9.701 0 0 9.7194 161.3094 585.9684 Tm ( )Tj /C2_0 1 Tf 0.252 0 Td <01FB>Tj /TT1 1 Tf 0.0012 Tc 11.618 0 0 11.64 169.9812 585.9684 Tm (T/h\))Tj 0.0007 Tw 9.701 0 0 9.7194 190.0602 585.9684 Tm [( such as large ceram)11(ic BGA )]TJ 0.0023 Tc 0.0177 Tw -13.841 -1.21 Td [(and CLCC showed a t)4(e)2(m)12(p)-2(erat)4(ure-dependent)4( )6(behavi)4(or )6([20])5( )6(for )]TJ 0.0015 Tc 0.0485 Tw T* [(solder fatigue perform)11(ance. )6( )6(Oste)]TJ 0.0017 Tc 0.0423 Tw [(rm)12(an [20] showed that there )]TJ 0.0012 Tc 0.2407 Tw T* [(is a cross-over in )6(tem)11(p)-3(erat)]TJ 0.0015 Tc 0.2345 Tw 11.531 0 Td [(ure cycle perform)11(ance for SAC )]TJ 0.0021 Tc 0.1859 Tw -11.531 -1.168 Td [(solder com)12(p)-2(ared to Sn/Pb for )]TJ 0.0016 Tc 0.1864 Tw 12.947 0 Td [(high strain packages )6(such )6(as )]TJ 0.0017 Tc 0.2582 Tw -12.947 -1.168 Td [(CLCC. Thei)4(r st)4(udy)4( showed t)4(h)-2(at)]TJ 0.0011 Tc 0.2528 Tw 13.817 0 Td [( for the sam)11(e)1( tem)11(p)-3(erature )]TJ 0.0004 Tc 0.1756 Tw -13.817 -1.168 Td [(ran)-3(g)-3(e, if th)-3(e Tm)10(ax)-3( is 1)-3(0)-3(0)]TJ 0 Tc 0 Tw 6.2736 0 0 6.2856 162.066 521.832 Tm (o)Tj 0.0017 Tc 0.1683 Tw 9.701 0 0 9.7194 165.2088 517.467 Tm [(C )-6(or lower, LF perform)12(ed better )]TJ 0.0024 Tc 0.2096 Tw -11.279 -1.168 Td [(t)4(h)-1(an Sn/)4(P)1(b. However, when Tm)12(ax was )6(125)]TJ 0 Tc 0 Tw 6.2736 0 0 6.2856 236.7948 510.483 Tm (o)Tj 0.002 Tc 0.204 Tw 9.701 0 0 9.7194 239.9376 506.118 Tm (C, LF showed )Tj 0.0024 Tc 0.3055 Tw -18.982 -1.168 Td [(poor perform)12(ance com)12(p)-1(ared t)4(o)-1( Sn/)4(P)1(b. Thi)4(s)2( behavi)4(or was )]TJ 0.0022 Tc 0.2577 Tw T* [(hy)4(pot)4(hesi)4(zed as a pot)4(ent)4(i)4(a)2(l)4( shi)4(f)-1(t)4( i)4(n)-2( sol)4(d)-2(er fat)4(i)4(gue )6(dam)12(a)2(ge )]TJ 0 Tc 0.098 Tw T* [(m)10(ech)-4(an)-4(ism)10(.)-2( )-6(Based)-4( )-6(o)-4(n)-4( In)-4(tel test d)-4(ata, w)-4(h)-4(en)-4( Tm)10(ax)-4( w)-4(as b)-4(elo)-4(w)-4( )]TJ 0.0039 Tc 0 Tw T* (100)Tj 0 Tc 6.2736 0 0 6.2856 70.4592 465.087 Tm (o)Tj 0.0019 Tc 0.396 Tw 9.701 0 0 9.7194 73.602 460.722 Tm [(C )-6(and )-6(t)4(h)-2(e ram)12(p)-2( rat)4(e)2( was bel)4(o)-2(w 15)]TJ 0 Tc 0 Tw 6.2736 0 0 6.2856 233.3028 465.087 Tm (o)Tj 0.0008 Tc 0.3971 Tw 9.701 0 0 9.7194 236.4456 460.722 Tm [(C/m)11(i)3(n, the LF )]TJ 0.3191 Tw -18.622 -1.168 Td [(tem)11(p)-3(erature cycle results show)]TJ 0.0025 Tc 0.3114 Tw [(ed )-6(i)4(m)12(proved sol)4(d)-1(er fat)4(i)4(gue )]TJ 0.002 Tc 0.186 Tw T* [(perform)12(ance com)12(p)-2(ared to Sn/Pb )]TJ 0.0003 Tc 0.1817 Tw 13.943 0 Td [([1]. )-6(Typically when cyclic )]TJ -0.0002 Tc 0.0862 Tw -13.943 -1.168 Td [(sh)-4(ear )-6(strain)-4( )-6(is )-6(lo)-4(w)-4(er th)-4(an)-4( ~6)-4(%, th)-4(e SA)-4(C allo)-4(y sh)-4(o)-4(w)-4(ed)-4( b)-4(etter )]TJ 0.002 Tc 0.5279 Tw T* [(fat)4(i)4(gue )-6(perform)12(ance. )-6(As )-6(a general)4( desi)4(gn pract)4(i)4(ce for )]TJ 0 Tc 0.074 Tw T* [(reliab)-4(ility, )-6(th)-4(e )-6(reco)-4(m)10(m)10(en)-4(d)-4(ed)-4( )-6(strain)-4( ran)-4(g)-4(es are lo)-4(w)-4(er th)-4(an)-4( 6)-4(%)-1( )]TJ 0.0014 Tc 0.0726 Tw T* [(\(1-2% range ty)4(pical\). The failure)]TJ 0.0001 Tc 0.0739 Tw [( m)10(o)-4(d)-4(e, failu)-4(re sig)-4(n)-4(atu)-4(re, )6(th)-4(e )]TJ 0.0012 Tc 0.0248 Tw T* (location, and the interface separa)Tj 0.0014 Tc 0.0246 Tw 13.325 0 Td [(tion for LF solder are sim)11(ilar )]TJ -0.0002 Tc 0.1762 Tw -13.325 -1.168 Td [(to)-4( Sn)-4(/Pb)-4( so)-4(ld)-4(er in)-4( tem)10(p)-4(eratu)-4(r)]TJ 0.0009 Tc 0.1751 Tw 12.449 0 Td [(e cycle test, even )6(in )6(extended )]TJ 0.0007 Tc 0.0133 Tw -12.449 -1.168 Td [(cycle )-6(tim)11(e testing [1]. Therefor)]TJ 0.0026 Tc 0.0114 Tw 12.539 0 Td [(e, t)5(h)-1(e m)13(odi)5(fi)5(ed Coffi)5(n-M)4(a)3(nson )]TJ 0.002 Tc 0.084 Tw -12.539 -1.168 Td (equation proposed by Norris a)Tj 0.0016 Tc 0.0844 Tw (nd Landzberg should still be a )Tj 0.0006 Tc 0.1154 Tw T* [(viable em)11(pirical acceleration m)]TJ 0.0012 Tc 0.1088 Tw 12.917 0 Td (odel for SAC alloys. For this )Tj 0.002 Tc 0.018 Tw -12.917 -1.168 Td [(reason, we used the sam)12(e)2( form)12( as in equation \(3\) for our SAC )]TJ 0.0011 Tc 0.0909 Tw T* [(solder acceleration m)11(odel. The co)]TJ 0.0005 Tc 0.0915 Tw [(efficient in the tem)10(p)-3(erature )]TJ 0.0024 Tc 0.6235 Tw T* [(range, frequency)5(, and T)]TJ -0.0078 Tc 0 Tw 6.2736 0 0 6.2856 166.7802 300.381 Tm [(ma)-9(x)-9( )]TJ 0.0011 Tc 0.6248 Tw 9.701 0 0 9.7194 185.1714 301.836 Tm [(term)11(s were fit from)11( )6(the )]TJ 0.0001 Tc 0.0859 Tw -13.337 -1.168 Td [(ex)-4(p)-4(erim)10(en)-4(t)2(al resu)-4(lts fo)-4(r SA)-4(C so)-4(ld)-4(er j)-4(o)-4(in)-4(ts at v)-4(ario)-4(u)-4(s)-1( )6(th)-4(erm)10(al )]TJ 0.002 Tc 0.2339 Tw T* [(cy)4(cl)4(e )-6(condi)4(t)4(i)4(ons. )-6(Di)4(fferent)4( from)12( Pan et)4( al)4(\222s ext)4(e)2(nsi)4(on, t)4(h)-2(e )]TJ -0.0005 Tc 0.4344 Tw T* [(cyclic )-6(freq)-4(u)-4(e)-1(n)-4(c)-1(y )-6(is )-6(sill u)-4(s)-1(ed)-4( o)-4(t)1(h)-4(e)-1(r th)-4(an)-4( d)-4(w)-4(ell tim)9(e. A)-4( )]TJ 0 Tc 0.182 Tw T* [(n)-4(o)-4(n)-4(lin)-4(ear )-6(cu)-4(rv)-4(e fit w)-4(as p)-4(erfo)-4(rm)10(ed)-4( to)-4( sim)10(u)-4(ltan)-4(eo)-4(u)-4(s)-1(ly fit th)-4(e )]TJ -0.0005 Tc 0.0145 Tw T* [(th)-4(ree co)-4(efficien)-4(ts w)-4(ith)-4( th)-4(e th)-4(erm)9(a)-1(l cyclin)-4(g)-4( test resu)-4(lts )6(g)-4(i)1(v)-4(e)-1(n)-4( )6(in)-4( )]TJ 0.0021 Tc 0.1379 Tw T* [(Tabl)4(es )-6(1-4. In order t)4(o)-2( have a consi)4(s)1(t)4(e)2(ncy)4( wi)4(t)4(h)-2( t)4(h)-2(e ori)4(g)-2(i)4(n)-2(al)4( )]TJ 0.0023 Tc 0.2396 Tw T* [(Norri)4(s-Landzberg )-6(m)12(odel)4(, )-6(som)12(e)2( adjust)4(m)12(e)2(nt)4( has been m)12(a)2(de. )]TJ 0.0012 Tc 0.0008 Tw T* [(The resulting acceleration m)11(odel is given as follows )]TJ ET q 0.9700012 0 0 0.9700012 99.675705 178.6268005 cm 0 0 0 RG 0.501 w 1 j 1 J 0 0 m 17.52 0 l 35.88 0 m 48.36 0 l 71.28 0 m 90.9 0 l S Q q 0.9700012 0 0 0.9700012 214.2134399 189.4520111 cm 0 0 0 RG 0.25 w 1 j 1 J 0 0 m 8.52 0 l 12.66 0 m 29.1 0 l 33.72 0 m 50.94 0 l S Q BT /C2_2 1 Tf 0 Tc 0 Tw 11.683 0 0 11.705 269.5032 165.2407 Tm <00B8>Tj 0 0.467 TD <00B8>Tj 0 0.97 TD <00B8>Tj 0 -2.088 TD <00B9>Tj 0 2.735 TD <00B7>Tj -5.709 -2.083 Td <00A8>Tj 0 0.467 TD <00A8>Tj 0 0.97 TD <00A8>Tj 0 -2.088 TD <00A9>Tj 0 2.735 TD <00A7>Tj -1.166 -1.571 Td <00B8>Tj 0 0.408 TD <00B8>Tj 0 -1.054 TD <00B9>Tj 0 1.7 TD <00B7>Tj -2.247 -1.054 Td <00A8>Tj 0 0.408 TD <00A8>Tj 0 -1.054 TD <00A9>Tj 0 1.7 TD <00A7>Tj 0.578 -1.447 Td <0027>Tj 0.05 1.397 Td <0027>Tj -1.913 -1.004 Td <00B8>Tj 0 0.408 TD <00B8>Tj 0 -1.054 TD <00B9>Tj 0 1.7 TD <00B7>Tj -1.654 -1.054 Td <00A8>Tj 0 0.408 TD <00A8>Tj 0 -1.054 TD <00A9>Tj 0 1.7 TD <00A7>Tj -0.757 -0.671 Td [<0020>3064<0020>]TJ 6.8151 0 0 6.8278 264.789 184.2139 Tm <00B8>Tj 0 0.673 TD <00B8>Tj 0 -1.313 TD <00B9>Tj 0 1.96 TD <00B7>Tj -6.174 -1.321 Td <00A8>Tj 0 0.673 TD <00A8>Tj 0 -1.313 TD <00A9>Tj 0 1.96 TD <00A7>Tj 2.955 -0.801 Td <0010>Tj -7.148 0.571 Td <0010>Tj -6.063 0 Td <0010>Tj /TT1 1 Tf 4.8679 0 0 4.877 260.424 180.6637 Tm [(2)2556(max,)4208(1)2449(max,)]TJ 6.8151 0 0 6.8278 253.6728 192.0708 Tm [(1)3557(1)]TJ -10.402 -4.151 Td (2)Tj -0.009 2.395 Td (1)Tj -6.055 -2.395 Td (2)Tj 0 2.395 TD (1)Tj -4.526 0 Td (1)Tj 11.683 0 0 11.705 110.4426 166.6374 Tm (2)Tj /TT2 1 Tf 6.8151 0 0 6.8278 247.038 182.3515 Tm [(T)3554(T)2016(k)]TJ -4.722 1.423 Td (E)Tj -2.451 -0.06 Td (n)Tj -6.055 0 Td (m)Tj 4.8679 0 0 4.877 219.0438 190.3831 Tm (a)Tj 11.683 0 0 11.705 208.335 175.7166 Tm (e)Tj -2.695 -0.776 Td (T)Tj 0.045 1.397 Td (T)Tj -3.417 -1.397 Td (f)Tj 0.05 1.397 Td (f)Tj -3.178 -1.397 Td (N)Tj 0.13 1.397 Td (N)Tj -2.571 -0.621 Td (AF)Tj /TT1 1 Tf 3.3496 Tc 9.701 0 0 9.7194 55.7928 132.8233 Tm [( \()3347(1)3346(2)3346(\))]TJ 0 Tc 23.278 2.198 Td ( )Tj -0.0019 Tc -23.278 -3.964 Td [(w)-6(ith)-6( )]TJ 0.0027 Tc -0.0007 Tw 1.44 -1.868 Td [(m)13(=)3(0.33, n= 1.9, and E)]TJ 0 Tc 0 Tw 6.2736 0 0 6.2856 157.0608 96.0408 Tm (a)Tj 0.0027 Tc -0.0007 Tw 9.701 0 0 9.7194 159.8544 97.4958 Tm [(/)5(k)-1( = 1414 )]TJ 0.0009 Tc 0.427 Tw -9.287 -1.766 Td (Surprisingly, the coefficients)Tj -0.0001 Tc 0.422 Tw 12.467 0 Td [( )-6(are )-6(v)-4(ery sim)10(ilar to)-4( th)-4(e )]TJ 0.0024 Tc 0.3235 Tw -13.907 -1.168 Td [(ori)4(g)-1(i)4(n)-1(al)4( )-6(val)4(u)-1(es of t)4(h)-1(e Norri)4(s-Landzberg m)12(odel)4( for Sn/)4(P)1(b )]TJ -0.0004 Tc 0.1164 Tw 26.493 67.497 Td [(assem)10(b)-4(ly w)-4(h)-4(en)-4( all th)-4(e d)-4(ata w)-4(ere u)-4(s)-1(ed)-4(. A)-4(lth)-4(o)-4(u)-4(g)-4(h)-4( it )6(h)-4(as )6(b)-4(een)-4( )]TJ 0.0011 Tc 0.1209 Tw 0 -1.168 TD (generally accepted that SnAgCu )Tj 0.0017 Tc 0.1143 Tw 13.679 0 Td [(perform)12(s better than Sn/Pb, )]TJ 0.0011 Tc 0.0669 Tw -13.679 -1.168 Td (the acceleration factor, in particul)Tj 0.0015 Tc 0.0665 Tw 13.763 0 Td [(ar, in term)11(s of )6(the )6(extended )]TJ 0.0006 Tc 0.0914 Tw -13.763 -1.168 Td [(cycle tim)11(e and m)11(a)1(xim)11(u)-3(m)11( tem)11(p)-3(erature range effect, is )6(sim)11(ilar )]TJ -0.0001 Tc 0.26 Tw T* [(to)-4( Sn)-4(/Pb)-4(.)-2( Th)-4(e in)-4(d)-4(i)2(v)-4(i)2(d)-4(u)-4(al d)-4(ata fit fo)-4(r a p)-4(articu)-4(l)2(ar )6(set )6(w)-4(ith)-4( )]TJ 0.0005 Tc 0.0255 Tw T* [(respect to the cycle tim)10(e or m)10(axim)10(u)-3(m)10( tem)10(p)-3(erature m)10(ay not )6(be )]TJ 0.0021 Tc 0.1979 Tw T* [(i)4(d)-2(eal)4( usi)4(ng t)4(h)-2(e above coeffi)4(ent)4(s)1(, but)4( t)4(h)-2(e )6(overal)4(l)4( )6(fi)4(t)4( )6(i)4(s)1( )6(very)4( )]TJ 0.0016 Tc 0.1683 Tw T* [(good. )-6(The )-6(acceleration )-6(m)12(odel in equation \(12\) was used to )]TJ 0.0604 Tw T* [(com)12(p)-2(are )-6(the predicted and obser)1(ved acceleration factor \(AF\), )]TJ 0.1745 Tw T* [(as shown in Figure 1. Figure 1 )6(shows )6(that )6(the )6(acceleration )]TJ -0.0003 Tc 0.0503 Tw T* [(m)10(o)-4(d)-4(el )-6(g)-4(i)2(v)-4(es )-6(satisfacto)-4(r)-3(y resu)-4(lts w)-4(h)-4(en)-4( co)-4(m)10(p)-4(ared)-4( w)-4(ith)-4( th)-4(e d)-4(ata )]TJ 0.0023 Tc 0.1077 Tw T* [(generat)4(e)2(d from)12( vari)4(ous sources. The error i)4(n)-2( m)12(ean based on )]TJ 0.002 Tc 0.024 Tw T* [(t)4(h)-2(e 17 dat)4(a)2( set)4(s)1( for t)4(h)-2(e new m)12(odel)4( i)4(s)1( 5.8%. It)4( )6(can )6(be )6(seen )6(t)4(h)-2(at)4( )]TJ 0.2879 Tw T* [(t)4(h)-2(e t)4(e)2(st)4( condi)4(t)4(i)4(ons and dat)4(a)2( col)4(l)4(ect)4(ed above )6(have )6(a )6(wi)4(de )]TJ 0.0013 Tc 0.1147 Tw T* [(spread, with different tem)11(p)-3(er)]TJ 0.0023 Tc 0.1137 Tw [(at)4(ure range, di)4(fferent)4( m)12(a)2(xi)4(m)12(u)-2(m)12( )]TJ 0.0024 Tc 0.0056 Tw T* [(t)4(e)2(m)12(p)-2(erat)4(ure )-6(and, i)4(n)-1( part)4(i)4(c)2(ul)4(ar)]TJ 0.0012 Tc 0.0068 Tw 11.879 0 Td [(, the cycle tim)11(e ranging from)11( 45 )]TJ 0.0027 Tc 0.0593 Tw -11.879 -1.168 Td [(m)13(i)5(nut)5(es t)5(o)-1( 480 m)13(i)5(nut)5(es. The newl)5(y)5( proposed m)13(odel)5( )6(fi)5(t)5( )6(al)5(l)5( )6(17 )]TJ -0.0003 Tc 0.0803 Tw T* [(p)-4(airs o)-4(f)-3( test d)-4(ata w)-4(ith)-4( an)-4( av)-4(erag)-4(e d)-4(ev)-4(i)2(atio)-4(n)-4( less )6(th)-4(an)-4( )6(6)-4(%)-1( )6(an)-4(d)-4( )78( )]TJ 0.002 Tc 0.03 Tw T* [(dat)4(a)2( used were from)12( LF SAC al)4(l)4(o)-2(y)4( sy)4(st)4(em)12( \(3 t)4(o)-2( 4.0% )6(Ag )6(and )]TJ 0.0019 Tc 0.0661 Tw T* [(0.5 to 0.7 % Cu range\). One can )6(perform)12( )6(sim)12(ilar )6(analy)4(s)1(is )6(for )]TJ 0.0013 Tc 0.0307 Tw T* [(low cyclic strain com)11(ponents and )]TJ 0.0009 Tc 0.0251 Tw 13.817 0 Td [(expected )-6(n values will be at )]TJ 0.0025 Tc 0.1015 Tw -13.817 -1.168 Td [(t)4(h)-1(e )-6(hi)4(gher )-6(end of Sn/)4(P)1(b C-M)4( coeffi)4(ci)4(ent)4(s)2( \(2.1 t)4(o)-1( 2.2 range\). )102( )]TJ -0.0002 Tc 0.1042 Tw T* [(It )-6(is )-6(su)-4(rp)-4(risin)-4(g)-4( )-6(to)-4( )-6(see a g)-4(en)-4(eral fit to)-4( th)-4(e o)-4(r)-3(ig)-4(in)-4(al N)-4(o)-4(rris an)-4(d)-4( )]TJ 0.0022 Tc 0.0478 Tw T* [(Landzberg m)12(odel)4( and hence for LF )6(sol)4(d)-2(er, )6(t)4(h)-2(e )6(ori)4(g)-2(i)4(n)-2(al)4( )6(Sn/)4(Pb )]TJ 0.0778 Tw T* [(sol)4(d)-2(er fat)4(i)4(gue m)12(odel)4( can be used. Dependi)4(ng on )6(t)4(h)-2(e )6(package )]TJ 0.0008 Tc 0.0972 Tw T* [(type )-6(and m)11(a)1(terial choices, the )]TJ 0.0009 Tc 0.0971 Tw 12.665 0 Td [(fatigue m)11(odel coefficients can )]TJ -0.0002 Tc 0.0022 Tw -12.665 -1.168 Td [(v)-4(ary slig)-4(h)-4(tly. )]TJ ET q 0.9700012 0 0 0.9700012 329.507782 423.998291 cm 1 1 1 rg 0 0 m 228.42 0 l 228.42 -202.14 l 0 -202.14 l f Q q 0.9700012 0 0 0.9700012 9 12 cm 0.801 1 1 rg 356.1 250.86 180.9 164.82 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 561.18 427.56 -233.58 -207.3 re 327.6 427.56 m h 489 415.62 -132.84 -28.56 re W* n 1 0 0 1 356.0999685 415.6799591 cm 0.5 0.5 0.5 RG 0.397 w 1 j 1 J 0 0 m 180.9 0 l S Q q 0.9700012 0 0 0.9700012 529.8906097 415.2100677 cm 0.5 0.5 0.5 RG 0.397 w 1 j 1 J 0 0 m 0 -164.82 l -180.9 -164.82 l S Q q 0.9700012 0 0 0.9700012 9 12 cm 561.18 427.56 -233.58 -207.3 re 327.6 427.56 m h 489 415.62 -132.84 -28.56 re W* n 1 0 0 1 356.0999685 250.8599811 cm 0.5 0.5 0.5 RG 0.397 w 1 j 1 J 0 0 m 0 164.82 l S Q q 0.9700012 0 0 0.9700012 354.4174042 415.2100677 cm 0 0 0 RG 0.06 w 1 j 1 J 0 0 m 0 -164.82 l -1.98 -164.82 m 0 -164.82 l -1.98 -141.42 m 0 -141.42 l -1.98 -117.54 m 0 -117.54 l -1.98 -94.14 m 0 -94.14 l -1.98 -70.68 m 0 -70.68 l -1.98 -47.28 m 0 -47.28 l -1.98 -23.46 m 0 -23.46 l -1.98 0 m 0 0 l 0 -164.82 m 180.9 -164.82 l 0 -166.8 m 0 -164.82 l 25.8 -166.8 m 25.8 -164.82 l 51.6 -166.8 m 51.6 -164.82 l 77.34 -166.8 m 77.34 -164.82 l 103.56 -166.8 m 103.56 -164.82 l 129.3 -166.8 m 129.3 -164.82 l 155.1 -166.8 m 155.1 -164.82 l 180.9 -166.8 m 180.9 -164.82 l S Q q 0.9700012 0 0 0.9700012 354.4174042 255.3344879 cm 0.602 0.199 0.398 RG 1.19 w 1 j 1 J 0 0 m 180.9 164.82 l S Q q 0.9700012 0 0 0.9700012 372.5176239 270.524704 cm 1 0.398 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 1.02 -0.9 1.8 -1.98 1.8 c -3.06 1.8 -3.96 1.02 -3.96 0 c -3.96 -0.96 -3.06 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -0.96 0 0 c h B* Q q 0.9700012 0 0 0.9700012 409.067276 304.4553375 cm 1 0.398 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.9 1.8 -1.98 1.8 c -3.06 1.8 -3.96 0.96 -3.96 0 c -3.96 -1.02 -3.06 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -1.02 0 0 c h B* Q q 0.9700012 0 0 0.9700012 524.1288147 409.6228638 cm 1 0.398 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.9 1.8 -2.04 1.8 c -3.12 1.8 -4.02 0.96 -4.02 0 c -4.02 -1.02 -3.12 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -1.02 0 0 c h B* Q q 0.9700012 0 0 0.9700012 400.2208557 297.8787384 cm 1 0.398 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 1.02 -0.9 1.8 -1.98 1.8 c -3.06 1.8 -3.96 1.02 -3.96 0 c -3.96 -0.96 -3.06 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -0.96 0 0 c h B* Q q 0.9700012 0 0 0.9700012 402.8980713 300.2067413 cm 1 0.398 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.84 1.8 -1.98 1.8 c -3.06 1.8 -3.96 0.96 -3.96 0 c -3.96 -0.96 -3.06 -1.8 -1.98 -1.8 c -0.84 -1.8 0 -0.96 0 0 c h B* Q q 0.9700012 0 0 0.9700012 375.1948242 265.9268951 cm 1 0.398 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.84 1.8 -1.98 1.8 c -3.06 1.8 -3.96 0.96 -3.96 0 c -3.96 -1.02 -3.06 -1.8 -1.98 -1.8 c -0.84 -1.8 0 -1.02 0 0 c h B* Q q 0.9700012 0 0 0.9700012 387.5332489 300.2067413 cm 1 0.398 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.9 1.8 -1.98 1.8 c -3.06 1.8 -3.96 0.96 -3.96 0 c -3.96 -0.96 -3.06 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -0.96 0 0 c h B* Q q 0.9700012 0 0 0.9700012 414.0724792 311.3811493 cm 1 0.398 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.9 1.8 -1.98 1.8 c -3.06 1.8 -3.96 0.96 -3.96 0 c -3.96 -0.96 -3.06 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -0.96 0 0 c h B* Q q 0.9700012 0 0 0.9700012 414.0724792 311.3811493 cm 1 0.398 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.9 1.8 -1.98 1.8 c -3.06 1.8 -3.96 0.96 -3.96 0 c -3.96 -0.96 -3.06 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -0.96 0 0 c h B* Q q 0.9700012 0 0 0.9700012 406.3900757 311.3811493 cm 1 0.398 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.9 1.8 -1.98 1.8 c -3.12 1.8 -3.96 0.96 -3.96 0 c -3.96 -0.96 -3.12 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -0.96 0 0 c h B* Q q 0.9700012 0 0 0.9700012 371.3536224 269.3607025 cm 1 1 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 1.02 -0.84 1.8 -1.98 1.8 c -3.06 1.8 -3.96 1.02 -3.96 0 c -3.96 -0.96 -3.06 -1.74 -1.98 -1.74 c -0.84 -1.74 0 -0.96 0 0 c h B* Q q 0.9700012 0 0 0.9700012 387.5332489 279.371109 cm 1 1 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 1.02 -0.9 1.8 -1.98 1.8 c -3.06 1.8 -3.96 1.02 -3.96 0.06 c -3.96 -0.96 -3.06 -1.74 -1.98 -1.74 c -0.9 -1.74 0 -0.96 0 0 c h B* Q q 0.9700012 0 0 0.9700012 382.5280457 278.2653198 cm 1 1 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.9 1.74 -1.98 1.74 c -3.06 1.74 -3.96 0.96 -3.96 0 c -3.96 -1.02 -3.06 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -1.02 0 0 c h B* Q q 0.9700012 0 0 0.9700012 374.089035 278.2653198 cm 1 1 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.9 1.74 -1.98 1.74 c -3.12 1.74 -4.02 0.96 -4.02 0 c -4.02 -1.02 -3.12 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -1.02 0 0 c h B* Q q 0.9700012 0 0 0.9700012 396.3796539 278.2653198 cm 1 1 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.9 1.74 -1.98 1.74 c -3.06 1.74 -3.96 0.96 -3.96 0 c -3.96 -1.02 -3.06 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -1.02 0 0 c h B* Q q 0.9700012 0 0 0.9700012 387.5332489 278.2653198 cm 1 1 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.9 1.74 -1.98 1.74 c -3.06 1.74 -3.96 0.96 -3.96 0 c -3.96 -1.02 -3.06 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -1.02 0 0 c h B* Q q 0.9700012 0 0 0.9700012 375.1948242 271.281311 cm 1 1 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 1.02 -0.84 1.8 -1.98 1.8 c -3.06 1.8 -3.96 1.02 -3.96 0.06 c -3.96 -0.96 -3.06 -1.74 -1.98 -1.74 c -0.84 -1.74 0 -0.96 0 0 c h B* Q q 0.9700012 0 0 0.9700012 380.2000427 275.9373169 cm 1 1 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.84 1.8 -1.98 1.8 c -3.06 1.8 -3.96 0.96 -3.96 0 c -3.96 -0.96 -3.06 -1.8 -1.98 -1.8 c -0.84 -1.8 0 -0.96 0 0 c h B* Q BT /TT3 1 Tf 0 Tc 0 Tw 5.7677 0 0 5.7786 346.7928 253.1808 Tm (0)Tj 0 3.938 TD (2)Tj 0 3.998 TD (4)Tj 0 3.938 TD (6)Tj 0 3.928 TD (8)Tj -0.0214 Tc -0.535 3.938 Td (10)Tj 0 3.998 TD (12)Tj 0 3.928 TD (14)Tj 3.7828 Tc 1.604 -29.127 Td [(0)10(246)-61(8)272(1)3804(0)535(1)3804(2)545(1)3804(4)]TJ 0 0 1 rg /TT4 1 Tf 0.0098 Tc -0.031 Tw 8.8439 0 0 8.8608 425.6538 232.8108 Tm [(T)-31(est)-6( A)-12(F)]TJ -0.0151 Tc -0.0061 Tw 0 8.8439 -8.8608 0 339.576 307.7142 Tm [(Pr)-14(e)-25(d)-16(ic)-25(t)-31(e)-25(d)-16( A)-37(F)]TJ ET q 128.5055847 0 0 27.7032013 354.4751587 387.4482117 cm /Im0 Do Q q 0.9700012 0 0 0.9700012 9 12 cm 0 0 0 RG 0.06 w 1 j 1 J 489.06 415.62 -132.9 -28.62 re S Q q 0.9700012 0 0 0.9700012 359.07341 410.5540619 cm 0.602 0.199 0.398 RG 1.19 w 1 j 1 J 0 0 m 14.28 0 l S Q BT 0 0 0 rg /TT4 1 Tf -0.0223 Tc 0.0383 Tw 6.5368 0 0 6.5493 374.496 407.5272 Tm [(M)45(a)9(st)-36(er)-43( l)15(i)24(ne)]TJ ET q 0.9700012 0 0 0.9700012 367.9198303 401.5330658 cm 1 0.398 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.9 1.8 -1.98 1.8 c -3.12 1.8 -3.96 0.96 -3.96 0 c -3.96 -1.02 -3.12 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -1.02 0 0 c h B* Q BT /TT4 1 Tf -0.0234 Tc 0.0394 Tw 6.5368 0 0 6.5493 374.496 398.6808 Tm [(Pr)-53(opos)7(ed LF m)38(odel)23( \()-46(I)23(ndu)-9(s)7(t)-46(r)-44(y)8( d)-9(a)7(t)-46(a)7(\))]TJ ET q 0.9700012 0 0 0.9700012 367.9198303 392.2792511 cm 1 1 0 rg 1 0.398 0 RG 0.397 w 1 j 1 J 0 0 m 0 0.96 -0.9 1.8 -1.98 1.8 c -3.12 1.8 -3.96 0.96 -3.96 0 c -3.96 -0.96 -3.12 -1.8 -1.98 -1.8 c -0.9 -1.8 0 -0.96 0 0 c h B* Q BT /TT4 1 Tf 0.0393 Tw 6.5368 0 0 6.5493 374.496 389.427 Tm [(Pr)-53(opos)8(ed LF m)38(odel)23( \()-46(I)23(nt)-46(e)8(l)14( dat)-37(a)-1(\))]TJ /TT1 1 Tf 0 Tc 0 Tw 9.701 0 0 9.7194 553.752 225.2449 Tm ( )Tj 0.0016 Tc 0.2583 Tw -24.837 -1.042 Td [(Figure 1 Acceleration factor )6(\(A)]TJ 0.2523 Tw 13.679 0 Td (F\) predicted with equation )Tj 0.0024 Tc -0.0004 Tw -13.679 -1.168 Td [(\(12\) vs. observed AF from)12( t)4(e)2(st)4( dat)4(a)2( i)4(n)-1( vari)4(ous sources )]TJ /TT0 1 Tf 0.0012 Tc 0.0008 Tw 0 -1.886 TD (5. Extended Cycle Time Effect and Failure Analysis )Tj 0.002 Tc 0 Tw 0 -1.856 TD ( )Tj /TT1 1 Tf 0.0016 Tc 0.1684 Tw [(One )-6(of )-6(the key concerns fo)]TJ 0.0011 Tc 0.1689 Tw 13.469 0 Td (r the LF acceleration factor )Tj -0.0008 Tc 0.0808 Tw -13.469 -1.168 Td [(estim)9(atio)-5(n)-5( is th)-5(e in)-5(co)-5(rp)-5(o)-5(r)-4(atio)-5(n)-5( )6(o)-5(f)]TJ 0.0013 Tc 0.0727 Tw 13.613 0 Td ( the effect of LF creep. The )Tj 0.0007 Tc 0.6852 Tw -13.613 -1.168 Td [(effect of extended cycle tim)11(e on tem)11(p)-3(erature cycle )]TJ 0.0019 Tc 0.0181 Tw 0 -1.168 TD [(perform)12(ance )-6(of )-6(LF solder was com)12(p)]TJ -0.0002 Tc 0.0202 Tw 14.669 0 Td [(ared)-4( w)-4(ith)-4( Sn)-4(/Pb)-4( in)-4( Fig)-4(.)-2( 2)-4(.)-2( )]TJ 0.002 Tc 0.036 Tw -14.669 -1.168 Td [(The i)4(m)12(proved fat)4(i)4(gue perform)12(ance i)4(n)-2( 8 hrs cy)4(cl)4(e )6(t)4(i)4(m)12(e )6(t)4(e)2(st)4( )6(for )]TJ 0.0022 Tc 0.2277 Tw T* [(LF )-6(was observed. Sol)4(d)-2(er joi)4(n)]TJ 0.0014 Tc 0.2285 Tw 12.725 0 Td [(t analysis was perform)11(ed for )]TJ 0.0023 Tc 0.2396 Tw -12.725 -1.168 Td [(bot)4(h)-2( )-6(passi)4(ng and fai)4(l)4(i)4(ng sam)12(p)-2(l)4(e)2(s t)4(o)-2( underst)4(a)2(nd t)4(h)-2(e fai)4(l)4(u)-2(re )]TJ 0.0012 Tc 0.0788 Tw T* [(m)11(echanism)11(,)-1( m)11(ode, location etc. )]TJ 0.0018 Tc 0.0722 Tw 13.229 0 Td [( )-6(Both X-section and dye and )]TJ 0.0662 Tw -13.229 -1.168 Td [(peel)4( t)4(e)2(st)4(s were used t)4(o)-2( underst)4(a)2(nd t)4(h)-2(e sol)4(d)-2(er )6(crack )6(si)4(gnat)4(u)-2(re, )]TJ 0.2581 Tw T* [(si)4(ze, )-6(frequency)4( )-6(and l)4(o)-2(cat)4(i)4(on. The fai)4(l)4(u)-2(re si)4(gnat)4(u)-2(re, fai)4(l)4(u)-2(re )]TJ ET Q BT /GS1 gs /TT5 1 Tf 10 0 0 10 298.5 40.29 Tm (142)Tj /TT6 1 Tf 2.704 0 Td (2008 Electronic Components and Technology Conference)Tj ET endstream endobj 11 0 obj <>stream HB)P_-2$%[Y{+3Wܷ{8Np8nn7z^V???rXl6N&x<Fp0^v;gnZfhZVV+J\.JbP(|||\.f3L:NRd2HX,F#H8B`0~z=v\NpvfZ___-ˋl6LF`0秧'Nj5ZVTJRPGL J%X,DBP |r9fXL&`tFRooo) L&HD"@ xb1FPH$@p B!9 @ggg@ ߿'<- endstream endobj 12 0 obj <>stream H[lsb^5(//#q@zDL&A5U)QT(2QGl֔u.ATVJ\ԃ_MstZFRa=dRS1El5_ӺZ}MzTa=T\"ZS Zz(Bkޗ״d4z[M}|ikKssSc Fs kM;MPGi>YtwuvG ѣGb4_Mz{ vdTi5<D!Kp58 ^}.a)\S驩 cҍ]yvvf@z5meT5]̙ͳ3࠿iQ>stream HVy\SW/ ȮAs_}A Ep!B$쌒 .BUQRQjE-Qpb P"Vym37y~sϹw "D-db0>7-qbQ I(B٢ 5 s>>,K $ƠAlA2Fy<f騯2w_tgs9j2E?^.do 1y)% K~@vX nYbi sJw$-1=3.t)y>;Ʒ>ܼ_Tq7>Ӝ6l䋰I(01gìnkd\ȯ[䥣!E%4\q w?'q@ "3xKFk&U==ufRo,xf={o?ssR~n>f5qd w{]床|ͺZ–4{bܽOUhbN zK:1y]5bA %R"!TҹkyQZ&=~:b4 ĥK|wwg h +Dyh2EhH:XYX&BْZ LiC#3Q}JOq,A$ә[ t̴iܰ8/[ٖ&yhr"}0bv}}?=O~waY{M:{yQh4;yhg#*24+;5RׯQ05 3J3YXwۯK2h|U;4(qr(}jpOggLe`|{rCqB0Fy4"IQF*&gQR5Lk K#2L]kuH>[[Mu۳3ONVsEZz to$ǶaSth܉nqHWSHwOfL[-Xt1}XGVoyH+8IяP| K%?1XIߞGIDi wв~q1:6VrDᆋ̾mmzFC-]q-jël)Ck[{}%*)5]Gj8JQ[=E##eֱ ^ͱDd~ l4ߡ6mۺ?f=$GB_}Z_զn:)ɥ3r͎*t衒*=I—%QQvݺp9lݟTR]B~78nPDoU{W6)h<ӂ݇ '0' A?/x7Yi˔5jD˙A )c+%E#-f*NW"C*)]RnZ(e䞡myWϙ~.<(oJa}B˄#; ڧa~m8Ml~r -4(CA5&s4ݏuiERgI:t]Np=%>n8RIX,VzOID)7t Ifc ;lUM˯7'ڌyiQwF] lnPmd*:R0ZY[EYNF2eqNJ1="$òQ6%&_= Y=:1̓NVlmWͤ"L&U0A2 g5D| ÃfV~ [3P9=G=Y!ذy|/"~Ĉ},?0(s(r1RZl}M "z+AHJU2` rl{00;u:"_{\m%o8jKj~qȞ}NL Җ[\ѸS4q܁]kM,ow~5JL2cŬCH7ai5fdGc]n3@R s Ɲ4˩9&VÁ3Unϧjڕs]swR5,|QK W(C<Ӱڳ(ʉ@O?O="~rF?#?Ө鵆d޳Ը..#鰿>)c鶕S[azՒ\dž۞4նͭ)RM5͜۸B7Zĵ5"?v.ߦ򧱷޳6ƭ+̹5뷡ߴͧϱ"s¥((±Л7*鴽&ǏUٖ\4م6۴ǬD#z׻e¸鸿'5.Ud{S#&ĚMxDڟyJD^ vɴkǫo2vX>ֶangFnќ֔*=T)srdq4 p/ƳPK!)t_H_IԐP3_b%*iM6^ Ԙ7 CjdЃrt C^$̏ttR1z*VT+K-!tpq(cKSU LWeWsCixO$zѮp&}P\)?pQ/dĪ2?u13T4!Ud0~9{ֹ(8gk[^֮"Gͼmuoi_u]Oxm7: M7/W7ajkUهO_z=-Μ%7f _APdtcxPX*ŵSOvJp&o)|lI&*!^E;/Da`<~_ 6mcFW|b)Su#0rZ|bl ĞdW" _<-V(+ew"WB.r~A;!8Q %ІY%IU7,X,gFd߳x$v>^IQaBR(Wzeҩ[np||}Mfy TJ̢L`0 Se,…Twco#Tϱba1?L?M$X[6f-<%?&1=ژ?`<ɾ+tWoT̄up ^[1P&WV!6{)8^"^v30E )vEtP%"->1iU!FR*4>Ls` &Jux4!МAtǧ;$3P `|ʙ0[n$,7cY9L֮"d$egX>|R0 #hMG!F5Shn(|MY@VHM`2ϡ|A#c D8- [쎌ɓ8F:uTÇ MA'%>zMbQ}34$8(GEUDDьx!q̽^L{C#R2iK:HttI:%1LKԤDͥkFSZpjN@3l?ޏn*wjz48\cP`QAfDs12 t42 tѺӌqR#'rlIf3 Ӎvdja*l`֘]37!IibvTТۑB "*M!0 dlDreBBV|ٶ]rm2( Vs:qQrQ{is PKo:ʃ5V#69>ocnwZJ8f.sE!&:Qu:'WX oJGTy`݋gaciD7H gIPʘTذ:Cڦb]CO7gdt=˘/[rJbgN(3,T2|͒BT1+%f>/k' Ƭ5K2XE(,7L |{ԘiVu\۶=X仜{y''VpgOav鷚]e5;X[܏qu@h5lv޵y\r"Уei>S n NjZ[I6Ko ays@}7jr~UBž@ 6i̥_D@'oK%xMd9KxxGćks|Vhbh|S}~|&iyB|IDVw w?Oi^r>'9ٴDz92հ.˰DZci19dwީaϻO'wM=³<;ΛCu)'Ӻ}rf}~QFzbDp r'gjPiXb~^x *F݃f!3,{%{dbh0Df?e fz" jTFx8|-"%v ֪D~d9@]ȜKq-7Zp7gS5/u\< >jV}X־t* $F<=qs 娡9yQ7z68^byA%B]P6;E5a72y_h[...e-H#J? 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Fi)4(g. 3 shows t)4(h)-1(e X-sect)4(i)4(on i)4(m)12(ages for )6(Sn/)4(P)1(b )]TJ 0.0021 Tc 0.0119 Tw T* [(and LF sam)12(p)-2(l)4(e)2(s post)4( 1400 cy)4(cl)4(es of 8 hrs t)4(e)2(st)4( wi)4(t)4(h)-2( bi)4(gger si)4(ze )]TJ 0.006 Tw T* [(solder crack for Sn/Pb com)12(p)-2(ared )]TJ 0.0017 Tc 0.0003 Tw 13.439 0 Td [(to )-6(LF. )-6( There is no change in )]TJ 0.0012 Tc 0.2767 Tw -13.439 -1.168 Td [(failure )-6(location, )-6(m)11(ode, or the type of interface separation )]TJ 0.0021 Tc 0.1139 Tw T* [(\(board )-6(si)4(de )-6(cracks\) )-6(bet)4(w)-2(een )-6(60 and 480 m)12(i)4(nut)4(es cy)4(cl)4(e t)4(i)4(m)12(e. )114( )]TJ 0.042 Tw T* [(Fi)4(g. 3 showed for t)4(h)-2(e sam)12(e)2( t)4(e)2(m)12(p)-2(erat)4(ure cy)4(cl)4(e readout)4( )6(LF )6(had )]TJ 0.0017 Tc 0.0843 Tw T* [(a l)4(o)-2(wer crack si)4(ze com)12(p)-2(ared t)4(o)-2( Sn/)4(Pb even at)4( 480 m)12(i)4(n )6(cy)4(cl)4(e )]TJ 0.002 Tc 0.174 Tw T* [(t)4(i)4(m)12(e. Thi)4(s)1( suggest)4(s t)4(h)-2(e frequency)4( t)4(e)2(rm)12( for )6(LF )6(i)4(s)1( )6(si)4(m)12(i)4(l)4(a)2(r )6(t)4(o)-2( )]TJ 0.0003 Tc 0.0017 Tw T* [(Sn)-4(/Pb)-4( fo)-4(r th)-4(e ex)-4(ten)-4(d)-4(ed)-4( cycle tim)10(e \(u)-4(se co)-4(n)-4(d)-4(itio)-4(n)-4(\))-3(. )]TJ /TT1 1 Tf 0 Tc 0 Tw 25.095 -16.964 Td ( )Tj -25.095 -1.659 Td ( )Tj /TT0 1 Tf 0.0026 Tc 0.5333 Tw 0 -1.258 TD [(Fi)5(g.2 )-6(LF \(SAC 405\) sol)5(d)-1(er showed i)5(m)13(proved fat)5(i)5(gue )]TJ 0.0007 Tc 0.2113 Tw 0 -1.168 TD [(perform)11(ance in tem)11(p)-3( cycle test )]TJ -0.0002 Tc 0.2062 Tw 13.637 0 Td [(co)-4(m)10(p)-4(ared)-4( )-6(to)-4( Sn)-4(/Pb)-4( in)-4( th)-4(e )]TJ 0.002 Tc 0.06 Tw -13.637 -1.168 Td [(ext)4(e)2(nded )-6(cy)4(cl)4(e )-6(t)4(i)4(m)12(e t)4(e)2(st)4( \( 60 m)12(i)4(n vs. 480 m)12(i)4(n cy)4(cl)4(e t)4(i)4(m)12(e and )]TJ 0.0023 Tc 0.1257 Tw T* [(t)4(e)2(m)12(p)-2(erat)4(ure range i)4(s)2( from)12( -25 t)4(o)-2( + 100)]TJ 0 Tc 0 Tw 6.2736 0 0 6.2856 215.4936 399.9612 Tm (o)Tj 0.0022 Tc 0.1258 Tw 9.701 0 0 9.7194 218.6364 395.5962 Tm [(C.\). The )6(com)12(ponent)4( )]TJ 0.0011 Tc 0.0009 Tw -16.786 -1.168 Td (tested is BGA socket )Tj -0.0003 Tc 0.0023 Tw 8.687 0 Td [(w)-4(ith)-4( en)-4(ab)-4(lin)-4(g)-4( lo)-4(ad)-4(. )]TJ 0 Tc 0 Tw -8.687 -1.27 Td ( )Tj 19.258 -11.443 Td ( )Tj /TT1 1 Tf -19.258 -1.659 Td ( )Tj /TT0 1 Tf 0.0021 Tc 0.3658 Tw 0 -1.856 TD [(Fi)4(gure )-6(3 )-6(X-sect)4(i)4(on )-6(i)4(m)12(ages of post)4( 1400 cy)4(cl)4(es sam)12(p)-2(l)4(e)2(s )]TJ 0.0015 Tc 0.0665 Tw 0 -1.168 TD [(showed the full solder )6(crack )6(fo)]TJ 0.0019 Tc 0.0601 Tw 12.731 0 Td [(r Sn/Pb \(top im)12(age\) com)12(p)-2(ared )]TJ 0.0027 Tc 0.0833 Tw -12.731 -1.168 Td [(LF \(SAC 405\) sol)5(d)-1(er whi)5(c)3(h showed )6(onl)5(y)5( )6(m)13(i)5(nor )6(crack )6(\(10%, )]TJ 0.0008 Tc 0.0312 Tw T* [(bottom)11( im)11(age\)\) at board side. The tem)11(p)-3( cycle test )6(param)11(e)1(ters: )]TJ 0.002 Tc 0.054 Tw T* [(cy)4(cl)4(e )-6(t)4(i)4(m)12(e )-6(i)4(s)1( )-6(480 )-6(m)12(i)4(n )-6(and t)4(e)2(m)12(p)-2(erat)4(ure range i)4(s)1( from)12( -25 t)4(o)-2( + )]TJ 0.0039 Tc 0 Tw T* (100 )Tj 0 Tc 6.2736 0 0 6.2856 73.7766 174.1452 Tm (o)Tj 0.0022 Tc 0.0838 Tw 9.701 0 0 9.7194 76.9194 169.7802 Tm [(C\). )-6(The com)12(ponent)4( t)4(e)2(st)4(ed i)4(s)1( BGA socket)4( wi)4(t)4(h)-2( enabl)4(i)4(ng )]TJ -0.0009 Tc 0 Tw -2.178 -1.186 Td [(lo)-5(ad)]TJ /TT1 1 Tf 0.002 Tc 1.728 0 Td (. )Tj 0.0014 Tc 0.0006 Tw -1.728 -1.886 Td (6. Discussion )Tj /TT0 1 Tf 0.0022 Tc 0.1018 Tw 1.44 -1.258 Td [(As we have di)4(scussed earl)4(i)4(e)2(r, Pan et)4( al)4( )6([17])5( )6(proposed )6(an )]TJ 0.0012 Tc 0.2947 Tw -1.44 -1.168 Td [(acceleration m)11(odel based on )6(th)]TJ 0.0019 Tc 0.288 Tw 13.583 0 Td [(e Norris-Landzberg m)12(odel. )]TJ 0.0025 Tc 0.1135 Tw -13.583 -1.168 Td [(Fi)4(g. )-6(4 )-6(pl)4(ot)4(t)4(e)2(d )-6(t)4(h)-1(e com)12(p)-1(ari)4(s)2(on bet)4(w)-1(een t)4(h)-1(ese t)4(w)-1(o m)12(odel)4(s)2( for )]TJ -0.0003 Tc 0.0143 Tw T* [(th)-4(e av)-4(ailab)-4(l)2(e test d)-4(ata. )6(It )6(is )6(o)-4(b)-4(s)]TJ 0.001 Tc 0.007 Tw [(erved that the Pan et al\222s m)11(o)-3(del )]TJ 0.0013 Tc 0.0667 Tw T* (presented a reasonable fit when )Tj 0.0007 Tc 0.0613 Tw 13.235 0 Td [(the )-6(acceleration factor is less )]TJ 0.0023 Tc 0.4916 Tw -13.235 -1.168 Td [(t)4(h)-2(an )-6(3.5. )-6(Bey)4(ond )-6(t)4(h)-2(i)4(s)2( range, t)4(h)-2(e m)12(odel)4( showed l)4(a)2(rge )]TJ 0.0022 Tc 0.1678 Tw 26.493 67.293 Td [(di)4(screpanci)4(e)2(s )-6(wi)4(t)4(h)-2( )-6(t)4(h)-2(e experi)4(m)12(e)2(nt)4(al)4( resul)4(t)4(s)1(. Al)4(t)4(h)-2(ough Pan\222s )]TJ -0.0004 Tc 0.0564 Tw T* [(o)-4(w)-4(n)-4( d)-4(ata fit v)-4(ery w)-4(ell w)-4(ith)-4( th)-4(e p)-4(r)-3(ed)-4(icted)-4( v)-4(alu)-4(es, Syed)-4(\222s d)-4(ata, )]TJ 0.0001 Tc 0.0619 Tw T* [(CA)-4(LCE\222s )-6(d)-4(ata d)-4(o)-4( n)-4(o)-4(t)2( fit th)-4(e lin)-4(e v)-4(ery w)-4(ell [1)-4(2)-4(])3(. Th)-4(e erro)-4(r in)-4( )]TJ 0.0025 Tc 0.1495 Tw T* [(m)12(ean based on al)4(l)4( 17 dat)4(a)2( set)4( was pl)4(ot)4(t)4(e)2(d i)4(n)-1( )6(Fi)4(g. )6(4 )6(for )6(t)4(h)-1(e )]TJ 0.002 Tc 0 Tw T* [(m)12(odel)4( proposed here agai)4(nst)4( Pan et)4( al)4(\222s m)12(odel)4(. )]TJ 0 Tc 1.44 -1.27 Td ( )Tj 24.297 -21.814 Td ( )Tj 0.0021 Tc -0.0001 Tw -17.626 -1.042 Td [(Fi)4(g.4. Pan et)4( al)4(\222 m)12(odel)4( fi)4(t)4( )]TJ 0 Tc 0 Tw -6.671 -1.27 Td ( )Tj ET q 0.9700012 0 0 0.9700012 9 12 cm 330.48 303.54 225.36 124.38 re W n 1 0 0 1 330.4799748 427.9199622 cm 1 1 1 rg 0 0 m 225.36 0 l 225.36 -139.86 l 0 -139.86 l f Q q 0.9700012 0 0 0.9700012 9 12 cm 0.801 1 1 rg 358.5 309.42 192.42 95.04 re f Q q 1.0213165 0 0 -0.9212494 356.7429352 404.3232422 cm 0.5 0.5 0.5 RG 0.386 w 1 j 1 J 0 0 m 182.75 0 l 182.75 100.068 l 0 100.068 l 0 0 l S Q q 0.9700012 0 0 0.9700012 9 12 cm 1 0.398 0 rg 387.36 309.42 38.64 7.68 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 387.12 309.36 39.3 7.98 re W n 1.0529023 0 0 -0.9497404 0 0 cm 0 0 1 RG 0.386 w 1 j 1 J 367.894 -333.878 36.698 8.086 re S Q q 0.9700012 0 0 0.9700012 9 12 cm 1 0.398 0 rg 483.78 309.42 38.22 82.2 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 483.54 309.36 38.88 82.5 re W n 1.0529023 0 0 -0.9497404 0 0 cm 0 0 1 RG 0.386 w 1 j 1 J 459.469 -412.341 36.299 86.549 re S Q q 0.9700012 0 0 0.9700012 356.7454071 404.3266602 cm 0 0 0 RG 0.06 w 1 j 1 J 0 0 m 0 -95.04 l -2.46 -95.04 m 0 -95.04 l -2.46 -81.48 m 0 -81.48 l -2.46 -67.86 m 0 -67.86 l -2.46 -54.3 m 0 -54.3 l -2.46 -40.74 m 0 -40.74 l -2.46 -27.12 m 0 -27.12 l -2.46 -13.56 m 0 -13.56 l -2.46 0 m 0 0 l 0 -95.04 m 192.42 -95.04 l 0 -97.26 m 0 -95.04 l 96.42 -97.26 m 96.42 -95.04 l 192.42 -97.26 m 192.42 -95.04 l S Q BT /TT2 1 Tf 0.0705 Tc -0.0563 Tw 8.1723 0 0 8.1878 406.0986 413.7546 Tm [(E)18(r)25(r)18(o)12(r)25( i)7(n)-38( m)41(ean)-45( )7(\()12(%)91(\))]TJ 1 0 0 rg /TT3 1 Tf 0.0777 Tc 0 Tw -1.887 -10.918 Td [(5.)71(7)7(9%)]TJ 0.0705 Tc 11.11 8.828 Td [(60.)56(66%)]TJ 0 0 0 rg 0.0581 Tc 7.1063 0 0 7.1197 339.4014 309.6348 Tm (0%)Tj -0.614 1.847 Td (10%)Tj 0 1.847 TD (20%)Tj 0 1.856 TD (30%)Tj 0 1.847 TD (40%)Tj T* (50%)Tj 0 1.856 TD (60%)Tj 0 1.847 TD (70%)Tj /TT0 1 Tf 0 Tc 9.701 0 0 9.7194 550.9002 306.4338 Tm ( )Tj 0.0022 Tc -0.0002 Tw -19.504 -1.042 Td [(Proposed LF m)12(odel)4( )-942( )-3348(Pan et)4( al)4(\222 m)12(odel)4( )]TJ 0 Tc 0 Tw 9.359 -1.27 Td ( )Tj 0.0023 Tc 0.0537 Tw -14.399 -1.27 Td [(Fi)4(g. 5 t)4(h)-2(e com)12(p)-2(ari)4(s)2(on of t)4(h)-2(e proposed m)12(odel)4( wi)4(t)4(h)-2( Pan et)4( )6(al)4(\222s )]TJ 0.0026 Tc 0 Tw 0 -1.168 TD [(m)13(odel)5( )]TJ 0 Tc 1.44 -1.27 Td ( )Tj 0.0015 Tc 0.3064 Tw 0 -1.27 TD [(There )-6(are )-6(a num)11(b)-2(er of ther)]TJ -0.0008 Tc 0.3087 Tw 12.269 0 Td [(m)9(a)-1(l fatig)-5(u)-5(e)-1( life p)-5(r)-4(ed)-5(ictio)-5(n)-5( )]TJ 0.002 Tc 0.2699 Tw -13.709 -1.168 Td [(m)12(odel)4(s)1( )-6(based )-6(on t)4(h)-2(e FEA anal)4(y)4(s)1(i)4(s)1( or anal)4(y)4(t)4(i)4(cal)4( sol)4(u)-2(t)4(i)4(ons )]TJ 0.0023 Tc 0.1617 Tw 0 -1.168 TD [(usi)4(ng st)4(rai)4(n)-2( energy)4( densi)4(t)4(y)4( range or pl)4(ast)4(i)4(c)2( st)4(rai)4(n)-2( )6(range )6(\(or )]TJ 0.2276 Tw T* [(nonl)4(i)4(n)-2(ear st)4(rai)4(n)-2( range\). It)4( i)4(s)2( )6(cl)4(ear )6(t)4(h)-2(at)4( )6(when )6(runni)4(ng )6(FEA )]TJ 0.0003 Tc 0.0977 Tw T* [(sim)10(u)-4(lations, it is easier to take )]TJ 0.0008 Tc 0.0912 Tw 12.947 0 Td [(into )-6(account structural details )]TJ -0.0006 Tc 0.2485 Tw -12.947 -1.168 Td [(th)-4(an)-4( )-6(th)-4(e relativ)-4(ely sim)9(p)-4(le an)-4(alytical m)9(o)-4(d)-4(e)-1(ls. H)-4(o)-5(w)-4(e)-1(v)-4(e)-1(r, th)-4(e )]TJ 0.001 Tc 0.055 Tw T* [(accuracy of the FEA-based m)11(o)-3(dels is not )6(always )6(satisfactory. )]TJ 0.0026 Tc 0.0294 Tw T* [(Fi)5(g. 6 sum)13(m)13(a)3(ri)5(zed som)13(e)3( FEA resul)5(t)5(s)2( )6(predi)5(c)3(t)5(i)5(ons. )6(It)5( )6(shoul)5(d )6(be )]TJ -0.0005 Tc 0.0625 Tw T* [(n)-4(o)-4(ted)-4( th)-4(at th)-4(e FEA)-4( resu)-4(lts o)-4(r)-3( an)-4(alytical )6(resu)-4(lts )6(p)-4(l)1(o)-4(tted)-4( )6(in)-4( )6(Fig)-4(.)-2( )]TJ 0.0004 Tc 0.0436 Tw T* [(6)-3( )-6(are )-6(fro)-3(m)10( d)-3(i)2(fferen)-4(t)2( FEA)-3( b)-3(ased)-4( life p)-3(r)-3(ed)-3(ictio)-3(n)-4( m)10(o)-3(d)-3(els b)-4(u)-3(t are )]TJ 0.0013 Tc 0.0007 Tw T* (consistent with each of their predictions. )Tj 0 Tc 0 Tw 1.44 -1.27 Td ( )Tj ET q 0.9700012 0 0 0.9700012 9 12 cm 48.24 367.74 192.42 -111.3 re W* n q 1.6799906 0 0 0.1800063 136.4397829 365.3995281 cm /Im0 Do Q q 2.8799906 0 0 0.1800063 142.3797861 365.3995281 cm /Im1 Do Q q 0.9599969 0 0 0.1800063 145.9797861 365.3995281 cm /Im2 Do Q q 2.4 0 0 0.1800063 136.0797861 365.2195375 cm /Im3 Do Q q 2.8799906 0 0 0.1800063 142.3797861 365.2195375 cm /Im4 Do Q q 0.9599969 0 0 0.1800063 145.9797861 365.2195375 cm /Im5 Do Q q 0.9599969 0 0 0.1800063 135.8997955 365.039547 cm /Im2 Do Q q 1.2 0 0 0.1800063 137.6997955 365.039547 cm /Im6 Do Q q 0.7199937 0 0 0.1800063 142.3797861 365.039547 cm /Im7 Do Q q 1.2 0 0 0.1800063 144.3597924 365.039547 cm /Im6 Do Q q 0.9599969 0 0 0.1800063 145.9797861 365.039547 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 135.8997955 364.8595564 cm /Im2 Do Q q 1.2 0 0 0.1800063 137.6997955 364.8595564 cm /Im6 Do Q q 0.7199937 0 0 0.1800063 142.3797861 364.8595564 cm /Im7 Do Q q 1.2 0 0 0.1800063 144.3597924 364.8595564 cm /Im6 Do Q q 0.9599969 0 0 0.1800063 145.9797861 364.8595564 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 135.8997955 364.6795344 cm /Im8 Do Q q 0.9599969 0 0 0.1800063 137.8797861 364.6795344 cm /Im9 Do Q q 0.7199937 0 0 0.1800063 142.3797861 364.6795344 cm /Im10 Do Q q 0.9599969 0 0 0.1800063 144.5397829 364.6795344 cm /Im11 Do Q q 0.9599969 0 0 0.1800063 145.9797861 364.6795344 cm /Im5 Do Q q 0.7199937 0 0 0.1800063 135.7198049 364.4995438 cm /Im7 Do Q q 1.2 0 0 0.1800063 137.8797861 364.4995438 cm /Im6 Do Q q 0.7199937 0 0 0.1800063 142.3797861 364.4995438 cm /Im7 Do Q q 0.7199937 0 0 0.1800063 144.8997798 364.4995438 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 145.9797861 364.4995438 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 135.7198049 364.3195532 cm /Im12 Do Q q 0.9599969 0 0 0.1800063 138.0597924 364.3195532 cm /Im13 Do Q q 2.1599969 0 0 0.1800063 139.3197892 364.3195532 cm /Im14 Do Q q 0.7199937 0 0 0.1800063 142.3797861 364.3195532 cm /Im7 Do Q q 0.7199937 0 0 0.1800063 144.8997798 364.3195532 cm /Im15 Do Q q 2.1599969 0 0 0.1800063 145.9797861 364.3195532 cm /Im16 Do Q q 0.9599969 0 0 0.1800063 135.7198049 364.1395627 cm /Im2 Do Q q 2.6400031 0 0 0.1800063 139.3197892 364.1395627 cm /Im17 Do Q q 0.7199937 0 0 0.1800063 142.3797861 364.1395627 cm /Im7 Do Q q 0.7199937 0 0 0.1800063 144.8997798 364.1395627 cm /Im7 Do Q q 2.6400031 0 0 0.1800063 145.9797861 364.1395627 cm /Im17 Do Q q 0.9599969 0 0 0.1800063 135.8997955 363.9595249 cm /Im18 Do Q q 1.4400031 0 0 0.1800063 139.3197892 363.9595249 cm /Im19 Do Q q 0.9599969 0 0 0.1800063 140.9397829 363.9595249 cm /Im20 Do Q q 0.7199937 0 0 0.1800063 142.3797861 363.9595249 cm /Im21 Do Q q 0.7199937 0 0 0.1800063 144.8997798 363.9595249 cm /Im22 Do Q q 1.4400031 0 0 0.1800063 145.9797861 363.9595249 cm /Im23 Do Q q 1.2 0 0 0.1800063 147.5997798 363.9595249 cm /Im24 Do Q q 1.4400031 0 0 0.1800063 136.0797861 363.7795344 cm /Im25 Do Q q 1.2 0 0 0.1800063 139.3197892 363.7795344 cm /Im6 Do Q q 0.9599969 0 0 0.1800063 141.1197892 363.7795344 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 142.3797861 363.7795344 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 144.5397829 363.7795344 cm /Im2 Do Q q 1.2 0 0 0.1800063 145.9797861 363.7795344 cm /Im6 Do Q q 0.7199937 0 0 0.1800063 147.9597766 363.7795344 cm /Im7 Do Q q 2.1599969 0 0 0.1800063 136.2597924 363.5995438 cm /Im26 Do Q q 0.7199937 0 0 0.1800063 139.3197892 363.5995438 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 141.1197892 363.5995438 cm /Im9 Do Q q 0.7199937 0 0 0.1800063 142.3797861 363.5995438 cm /Im10 Do Q q 1.2 0 0 0.1800063 144.3597924 363.5995438 cm /Im27 Do Q q 0.9599969 0 0 0.1800063 145.9797861 363.5995438 cm /Im5 Do Q q 0.7199937 0 0 0.1800063 147.9597766 363.5995438 cm /Im28 Do Q q 2.1599969 0 0 0.1800063 136.2597924 363.4195532 cm /Im26 Do Q q 0.7199937 0 0 0.1800063 139.3197892 363.4195532 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 141.1197892 363.4195532 cm /Im9 Do Q q 0.7199937 0 0 0.1800063 142.3797861 363.4195532 cm /Im10 Do Q q 1.2 0 0 0.1800063 144.3597924 363.4195532 cm /Im27 Do Q q 0.9599969 0 0 0.1800063 145.9797861 363.4195532 cm /Im5 Do Q q 0.7199937 0 0 0.1800063 147.9597766 363.4195532 cm /Im28 Do Q q 2.1599969 0 0 0.1800063 136.7997798 363.2395312 cm /Im29 Do Q q 0.7199937 0 0 0.1800063 139.3197892 363.2395312 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 141.1197892 363.2395312 cm /Im2 Do Q q 2.8799906 0 0 0.1800063 142.3797861 363.2395312 cm /Im1 Do Q q 0.9599969 0 0 0.1800063 145.9797861 363.2395312 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 148.1397829 363.2395312 cm /Im7 Do Q q 1.4400031 0 0 0.1800063 137.6997955 363.0595407 cm /Im19 Do Q q 0.7199937 0 0 0.1800063 139.3197892 363.0595407 cm /Im12 Do Q q 0.9599969 0 0 0.1800063 141.1197892 363.0595407 cm /Im9 Do Q q 2.6400031 0 0 0.1800063 142.3797861 363.0595407 cm /Im30 Do Q q 0.9599969 0 0 0.1800063 145.9797861 363.0595407 cm /Im5 Do Q q 0.7199937 0 0 0.1800063 148.1397829 363.0595407 cm /Im15 Do Q q 0.9599969 0 0 0.1800063 138.0597924 362.8795501 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 139.3197892 362.8795501 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 141.1197892 362.8795501 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 142.3797861 362.8795501 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 145.9797861 362.8795501 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 148.1397829 362.8795501 cm /Im7 Do Q q 0.5400031 0 0 0.1800063 135.7198049 362.6995595 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 138.0597924 362.6995595 cm /Im11 Do Q q 0.7199937 0 0 0.1800063 139.3197892 362.6995595 cm /Im31 Do Q q 0.9599969 0 0 0.1800063 141.1197892 362.6995595 cm /Im9 Do Q q 0.7199937 0 0 0.1800063 142.3797861 362.6995595 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 145.9797861 362.6995595 cm /Im5 Do Q q 0.7199937 0 0 0.1800063 148.1397829 362.6995595 cm /Im15 Do Q q 0.7199937 0 0 0.1800063 135.7198049 362.519569 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 138.0597924 362.519569 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 139.3197892 362.519569 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 141.1197892 362.519569 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 142.3797861 362.519569 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 145.9797861 362.519569 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 148.1397829 362.519569 cm /Im7 Do Q q 0.7199937 0 0 0.1800063 135.7198049 362.339547 cm /Im12 Do Q q 0.9599969 0 0 0.1800063 138.0597924 362.339547 cm /Im11 Do Q q 0.7199937 0 0 0.1800063 139.3197892 362.339547 cm /Im31 Do Q q 0.9599969 0 0 0.1800063 141.1197892 362.339547 cm /Im9 Do Q q 0.7199937 0 0 0.1800063 142.3797861 362.339547 cm /Im10 Do Q q 0.9599969 0 0 0.1800063 145.9797861 362.339547 cm /Im5 Do Q q 0.7199937 0 0 0.1800063 147.9597766 362.339547 cm /Im32 Do Q q 0.9599969 0 0 0.1800063 135.7198049 362.1595407 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 138.0597924 362.1595407 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 139.3197892 362.1595407 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 141.1197892 362.1595407 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 142.3797861 362.1595407 cm /Im7 Do Q q 1.2 0 0 0.1800063 145.9797861 362.1595407 cm /Im6 Do Q q 0.7199937 0 0 0.1800063 147.9597766 362.1595407 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 135.8997955 361.9795501 cm /Im5 Do Q q 1.2 0 0 0.1800063 137.6997955 361.9795501 cm /Im6 Do Q q 0.7199937 0 0 0.1800063 139.3197892 361.9795501 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 141.1197892 361.9795501 cm /Im9 Do Q q 0.7199937 0 0 0.1800063 142.3797861 361.9795501 cm /Im10 Do Q q 1.4400031 0 0 0.1800063 145.9797861 361.9795501 cm /Im23 Do Q q 0.9599969 0 0 0.1800063 147.5997798 361.9795501 cm /Im33 Do Q q 0.9599969 0 0 0.1800063 135.8997955 361.7995595 cm /Im5 Do Q q 1.2 0 0 0.1800063 137.6997955 361.7995595 cm /Im6 Do Q q 0.7199937 0 0 0.1800063 139.3197892 361.7995595 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 141.1197892 361.7995595 cm /Im9 Do Q q 0.7199937 0 0 0.1800063 142.3797861 361.7995595 cm /Im10 Do Q q 1.4400031 0 0 0.1800063 145.9797861 361.7995595 cm /Im23 Do Q q 0.9599969 0 0 0.1800063 147.5997798 361.7995595 cm /Im33 Do Q q 2.4 0 0 0.1800063 136.0797861 361.6195375 cm /Im3 Do Q q 0.7199937 0 0 0.1800063 139.3197892 361.6195375 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 141.1197892 361.6195375 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 142.3797861 361.6195375 cm /Im7 Do Q q 2.6400031 0 0 0.1800063 145.9797861 361.6195375 cm /Im17 Do Q q 1.6799906 0 0 0.1800063 136.4397829 361.439547 cm /Im34 Do Q q 0.7199937 0 0 0.1800063 139.3197892 361.439547 cm /Im12 Do Q q 0.9599969 0 0 0.1800063 141.1197892 361.439547 cm /Im9 Do Q q 0.7199937 0 0 0.1800063 142.3797861 361.439547 cm /Im10 Do Q q 2.1599969 0 0 0.1800063 145.9797861 361.439547 cm /Im16 Do Q q 187.9197263 0 0 0.1800063 51.1199308 360.1795344 cm /Im35 Do Q q 187.919742 0 0 0.1800063 51.1199308 359.9995438 cm /Im36 Do Q q 187.919742 0 0 0.1800063 51.1199308 359.8195532 cm /Im37 Do Q q 187.919742 0 0 0.1800063 51.1199308 359.6395627 cm /Im38 Do Q q 187.919742 0 0 0.1800063 51.1199308 359.4595407 cm /Im39 Do Q q 187.919742 0 0 0.1800063 51.1199308 359.2795501 cm /Im40 Do Q q 187.919742 0 0 0.1800063 51.1199308 359.0995595 cm /Im41 Do Q q 187.9197263 0 0 0.1800063 51.1199308 358.9195532 cm /Im42 Do Q q 187.9197263 0 0 0.1800063 51.1199308 358.7395312 cm /Im42 Do Q q 187.9197263 0 0 0.1800063 51.1199308 358.5595407 cm /Im43 Do Q q 187.919742 0 0 0.1800063 51.1199308 358.3795501 cm /Im44 Do Q q 187.919742 0 0 0.1800063 51.1199308 358.1995595 cm /Im45 Do Q q 187.919742 0 0 0.1800063 51.1199308 358.019569 cm /Im46 Do Q q 187.919742 0 0 0.1800063 51.1199308 357.839547 cm /Im47 Do Q q 187.919742 0 0 0.1800063 51.1199308 357.6595564 cm /Im48 Do Q q 187.919742 0 0 0.1800063 51.1199308 357.4795658 cm /Im49 Do Q q 187.919742 0 0 0.1800063 51.1199308 357.2995753 cm /Im49 Do Q q 187.9197263 0 0 0.1800063 51.1199308 357.1195375 cm /Im50 Do Q q 187.9197263 0 0 0.1800063 51.1199308 356.939547 cm /Im51 Do Q q 187.919742 0 0 0.1800063 51.1199308 356.7595564 cm /Im52 Do Q q 187.919742 0 0 0.1800063 51.1199308 356.5795658 cm /Im53 Do Q q 187.919742 0 0 0.1800063 51.1199308 356.3995438 cm /Im54 Do Q q 187.919742 0 0 0.1800063 51.1199308 356.2195532 cm /Im55 Do Q q 187.919742 0 0 0.1800063 51.1199308 356.0395627 cm /Im56 Do Q q 187.919742 0 0 0.1800063 51.1199308 355.8595721 cm /Im57 Do Q q 187.919742 0 0 0.1800063 51.1199308 355.6795501 cm /Im57 Do Q q 187.9197263 0 0 0.1800063 51.1199308 355.4995595 cm /Im58 Do Q q 187.9197263 0 0 0.1800063 51.1199308 355.3195532 cm /Im59 Do Q q 187.919742 0 0 0.1800063 51.1199308 355.1395627 cm /Im60 Do Q q 187.919742 0 0 0.1800063 51.1199308 354.9595407 cm /Im61 Do Q q 187.919742 0 0 0.1800063 51.1199308 354.7795501 cm /Im62 Do Q q 187.919742 0 0 0.1800063 51.1199308 354.5995595 cm /Im63 Do Q q 187.919742 0 0 0.1800063 51.1199308 354.419569 cm /Im64 Do Q q 187.919742 0 0 0.1800063 51.1199308 354.239547 cm /Im64 Do Q q 187.919742 0 0 0.1800063 51.1199308 354.0595564 cm /Im65 Do Q q 187.9197263 0 0 0.1800063 51.1199308 353.8795658 cm /Im66 Do Q q 187.9197263 0 0 0.1800063 51.1199308 353.6995595 cm /Im59 Do Q q 187.919742 0 0 0.1800063 51.1199308 353.519569 cm /Im67 Do Q q 187.919742 0 0 0.1800063 51.1199308 353.339547 cm /Im68 Do Q q 187.919742 0 0 0.1800063 51.1199308 353.1595564 cm /Im69 Do Q q 187.919742 0 0 0.1800063 51.1199308 352.9795658 cm /Im63 Do Q q 187.919742 0 0 0.1800063 51.1199308 352.7995753 cm /Im70 Do Q q 187.919742 0 0 0.1800063 51.1199308 352.6195532 cm /Im70 Do Q q 187.919742 0 0 0.1800063 51.1199308 352.4395627 cm /Im71 Do Q q 187.9197263 0 0 0.1800063 51.1199308 352.2595721 cm /Im72 Do Q q 187.9197263 0 0 0.1800063 51.1199308 352.0795658 cm /Im59 Do Q q 187.919742 0 0 0.1800063 51.1199308 351.8995438 cm /Im73 Do Q q 187.919742 0 0 0.1800063 51.1199308 351.7195532 cm /Im74 Do Q q 187.919742 0 0 0.1800063 51.1199308 351.5395627 cm /Im75 Do Q q 187.919742 0 0 0.1800063 51.1199308 351.3595721 cm /Im76 Do Q q 187.919742 0 0 0.1800063 51.1199308 351.1795501 cm /Im77 Do Q q 187.919742 0 0 0.1800063 51.1199308 350.9995595 cm /Im77 Do Q q 187.919742 0 0 0.1800063 51.1199308 350.819569 cm /Im78 Do Q q 187.9197263 0 0 0.1800063 51.1199308 350.6395784 cm /Im79 Do Q q 187.9197263 0 0 0.1800063 51.1199308 350.4595564 cm /Im80 Do Q q 187.919742 0 0 0.1800063 51.1199308 350.2795501 cm /Im81 Do Q q 187.919742 0 0 0.1800063 51.1199308 350.0995595 cm /Im82 Do Q q 187.919742 0 0 0.1800063 51.1199308 349.919569 cm /Im83 Do Q q 187.919742 0 0 0.1800063 51.1199308 349.739547 cm /Im84 Do Q q 187.919742 0 0 0.1800063 51.1199308 349.5595564 cm /Im84 Do Q q 187.919742 0 0 0.1800063 51.1199308 349.3795658 cm /Im85 Do Q q 187.919742 0 0 0.1800063 51.1199308 349.1995753 cm /Im86 Do Q q 187.9197263 0 0 0.1800063 51.1199308 349.0195532 cm /Im87 Do Q q 187.9197263 0 0 0.1800063 51.1199308 348.8395627 cm /Im88 Do Q q 187.919742 0 0 0.1800063 51.1199308 348.6595564 cm /Im89 Do Q q 187.919742 0 0 0.1800063 51.1199308 348.4795658 cm /Im90 Do Q q 187.919742 0 0 0.1800063 51.1199308 348.2995753 cm /Im91 Do Q q 187.919742 0 0 0.1800063 51.1199308 348.1195532 cm /Im92 Do Q q 187.919742 0 0 0.1800063 51.1199308 347.9395627 cm /Im92 Do Q q 187.919742 0 0 0.1800063 51.1199308 347.7595721 cm /Im93 Do Q q 187.919742 0 0 0.1800063 51.1199308 347.5795816 cm /Im94 Do Q q 187.9197263 0 0 0.1800063 51.1199308 347.3995595 cm /Im95 Do Q q 187.9197263 0 0 0.1800063 51.1199308 347.219569 cm /Im96 Do Q q 187.919742 0 0 0.1800063 51.1199308 347.0395784 cm /Im97 Do Q q 187.919742 0 0 0.1800063 51.1199308 346.8595721 cm /Im98 Do Q q 187.919742 0 0 0.1800063 51.1199308 346.6795501 cm /Im99 Do Q q 187.919742 0 0 0.1800063 51.1199308 346.4995595 cm /Im99 Do Q q 187.919742 0 0 0.1800063 51.1199308 346.319569 cm /Im100 Do Q q 187.919742 0 0 0.1800063 51.1199308 346.1395784 cm /Im101 Do Q q 187.919742 0 0 0.1800063 51.1199308 345.9595564 cm /Im102 Do Q q 187.9197263 0 0 0.1800063 51.1199308 345.7795658 cm /Im103 Do Q q 187.9197263 0 0 0.1800063 51.1199308 345.5995753 cm /Im104 Do Q q 187.919742 0 0 0.1800063 51.1199308 345.4195847 cm /Im105 Do Q q 187.919742 0 0 0.1800063 51.1199308 345.2395627 cm /Im106 Do Q q 187.919742 0 0 0.1800063 51.1199308 345.0595564 cm /Im107 Do Q q 187.919742 0 0 0.1800063 51.1199308 344.8795658 cm /Im107 Do Q q 187.919742 0 0 0.1800063 51.1199308 344.6995753 cm /Im108 Do Q q 187.919742 0 0 0.1800063 51.1199308 344.5195532 cm /Im109 Do Q q 187.919742 0 0 0.1800063 51.1199308 344.3395627 cm /Im110 Do Q q 187.9197263 0 0 0.1800063 51.1199308 344.1595721 cm /Im111 Do Q q 187.9197263 0 0 0.1800063 51.1199308 343.9795816 cm /Im112 Do Q q 187.919742 0 0 0.1800063 51.1199308 343.799591 cm /Im113 Do Q q 187.919742 0 0 0.1800063 51.1199308 343.619569 cm /Im114 Do Q q 187.919742 0 0 0.1800063 51.1199308 343.4395627 cm /Im114 Do Q q 187.919742 0 0 0.1800063 51.1199308 343.2595721 cm /Im115 Do Q q 187.919742 0 0 0.1800063 51.1199308 343.0795816 cm /Im116 Do Q q 187.919742 0 0 0.1800063 51.1199308 342.8995595 cm /Im117 Do Q q 187.919742 0 0 0.1800063 51.1199308 342.719569 cm /Im118 Do Q q 187.9197263 0 0 0.1800063 51.1199308 342.5395784 cm /Im119 Do Q q 187.9197263 0 0 0.1800063 51.1199308 342.3595879 cm /Im120 Do Q q 187.919742 0 0 0.1800063 51.1199308 342.1795658 cm /Im121 Do Q q 187.919742 0 0 0.1800063 51.1199308 341.9995753 cm /Im122 Do Q q 187.919742 0 0 0.1800063 51.1199308 341.819569 cm /Im122 Do Q q 187.919742 0 0 0.1800063 51.1199308 341.6395784 cm /Im123 Do Q q 187.919742 0 0 0.1800063 51.1199308 341.4595564 cm /Im124 Do Q q 187.919742 0 0 0.1800063 51.1199308 341.2795658 cm /Im125 Do Q q 187.919742 0 0 0.1800063 51.1199308 341.0995753 cm /Im126 Do Q q 187.9197263 0 0 0.1800063 51.1199308 340.9195847 cm /Im127 Do Q q 187.9197263 0 0 0.1800063 51.1199308 340.7395627 cm /Im128 Do Q q 187.919742 0 0 0.1800063 51.1199308 340.5595721 cm /Im129 Do Q q 187.919742 0 0 0.1800063 51.1199308 340.3795816 cm /Im129 Do Q q 187.919742 0 0 0.1800063 51.1199308 340.199591 cm /Im130 Do Q q 187.919742 0 0 0.1800063 51.1199308 340.0195532 cm /Im131 Do Q q 187.919742 0 0 0.1800063 51.1199308 339.8395627 cm /Im132 Do Q q 187.919742 0 0 0.1800063 51.1199308 339.6595721 cm /Im133 Do Q q 187.919742 0 0 0.1800063 51.1199308 339.4795816 cm /Im134 Do Q q 187.9197263 0 0 0.1800063 51.1199308 339.299591 cm /Im135 Do Q q 187.9197263 0 0 0.1800063 51.1199308 339.119569 cm /Im136 Do Q q 187.919742 0 0 0.1800063 51.1199308 338.9395784 cm /Im137 Do Q q 187.919742 0 0 0.1800063 51.1199308 338.7595879 cm /Im137 Do Q q 187.919742 0 0 0.1800063 51.1199308 338.5795973 cm /Im138 Do Q q 187.919742 0 0 0.1800063 51.1199308 338.3995595 cm /Im139 Do Q q 187.919742 0 0 0.1800063 51.1199308 338.219569 cm /Im140 Do Q q 187.919742 0 0 0.1800063 51.1199308 338.0395784 cm /Im141 Do Q q 187.919742 0 0 0.1800063 51.1199308 337.8595879 cm /Im142 Do Q q 187.9197263 0 0 0.1800063 51.1199308 337.6795658 cm /Im143 Do Q q 187.9197263 0 0 0.1800063 51.1199308 337.4995753 cm /Im144 Do Q q 187.9197263 0 0 0.1800063 51.1199308 337.3195847 cm /Im144 Do Q q 187.919742 0 0 0.1800063 51.1199308 337.1395941 cm /Im145 Do Q q 187.919742 0 0 0.1800063 51.1199308 336.9595721 cm /Im146 Do Q q 187.919742 0 0 0.1800063 51.1199308 336.7795816 cm /Im147 Do Q q 187.919742 0 0 0.1800063 51.1199308 336.5995753 cm /Im148 Do Q q 187.919742 0 0 0.1800063 51.1199308 336.4195847 cm /Im149 Do Q q 187.919742 0 0 0.1800063 51.1199308 336.2395627 cm /Im150 Do Q q 187.9197263 0 0 0.1800063 51.1199308 336.0595721 cm /Im151 Do Q q 187.9197263 0 0 0.1800063 51.1199308 335.8795816 cm /Im152 Do Q q 187.9197263 0 0 0.1800063 51.1199308 335.699591 cm /Im152 Do Q q 187.919742 0 0 0.1800063 51.1199308 335.519569 cm /Im153 Do Q q 187.919742 0 0 0.1800063 51.1199308 335.3395784 cm /Im154 Do Q q 187.919742 0 0 0.1800063 51.1199308 335.1595879 cm /Im155 Do Q q 187.919742 0 0 0.1800063 51.1199308 334.9795816 cm /Im156 Do Q q 187.919742 0 0 0.1800063 51.1199308 334.799591 cm /Im157 Do Q q 187.919742 0 0 0.1800063 51.1199308 334.619569 cm /Im158 Do Q q 187.9197263 0 0 0.1800063 51.1199308 334.4395784 cm /Im159 Do Q q 187.9197263 0 0 0.1800063 51.1199308 334.2595879 cm /Im160 Do Q q 187.9197263 0 0 0.1800063 51.1199308 334.0795973 cm /Im160 Do Q q 187.919742 0 0 0.1800063 51.1199308 333.8995753 cm /Im161 Do Q q 187.919742 0 0 0.1800063 51.1199308 333.7195847 cm /Im162 Do Q q 187.919742 0 0 0.1800063 51.1199308 333.5395941 cm /Im163 Do Q q 187.919742 0 0 0.1800063 51.1199308 333.3595879 cm /Im164 Do Q q 187.919742 0 0 0.1800063 51.1199308 333.1795658 cm /Im165 Do Q q 187.919742 0 0 0.1800063 51.1199308 332.9995753 cm /Im166 Do Q q 187.9197263 0 0 0.1800063 51.1199308 332.8195847 cm /Im167 Do Q q 187.9197263 0 0 0.1800063 51.1199308 332.6395941 cm /Im167 Do Q q 187.9197263 0 0 0.1800063 51.1199308 332.4595721 cm /Im168 Do Q q 187.919742 0 0 0.1800063 51.1199308 332.2795816 cm /Im169 Do Q q 187.919742 0 0 0.1800063 51.1199308 332.099591 cm /Im170 Do Q q 187.919742 0 0 0.1800063 51.1199308 331.9196004 cm /Im171 Do Q q 187.919742 0 0 0.1800063 51.1199308 331.7395784 cm /Im172 Do Q q 187.919742 0 0 0.1800063 51.1199308 331.5595721 cm /Im173 Do Q q 187.919742 0 0 0.1800063 51.1199308 331.3795816 cm /Im174 Do Q q 187.9197263 0 0 0.1800063 51.1199308 331.199591 cm /Im175 Do Q q 187.9197263 0 0 0.1800063 51.1199308 331.019569 cm /Im175 Do Q q 187.9197263 0 0 0.1800063 51.1199308 330.8395784 cm /Im176 Do Q q 187.919742 0 0 0.1800063 51.1199308 330.6595879 cm /Im177 Do Q q 187.919742 0 0 0.1800063 51.1199308 330.4795973 cm /Im178 Do Q q 187.919742 0 0 0.1800063 51.1199308 330.2996067 cm /Im179 Do Q q 187.919742 0 0 0.1800063 51.1199308 330.1195847 cm /Im180 Do Q q 187.919742 0 0 0.1800063 51.1199308 329.9395941 cm /Im181 Do Q q 187.919742 0 0 0.1800063 51.1199308 329.7595879 cm /Im182 Do Q q 187.919742 0 0 0.1800063 51.1199308 329.5795973 cm /Im182 Do Q q 187.9197263 0 0 0.1800063 51.1199308 329.3995753 cm /Im183 Do Q q 187.9197263 0 0 0.1800063 51.1199308 329.2195847 cm /Im184 Do Q q 187.919742 0 0 0.1800063 51.1199308 329.0395941 cm /Im185 Do Q q 187.919742 0 0 0.1800063 51.1199308 328.8596036 cm /Im186 Do Q q 187.919742 0 0 0.1800063 51.1199308 328.6795816 cm /Im187 Do Q q 187.919742 0 0 0.1800063 51.1199308 328.499591 cm /Im188 Do Q q 187.919742 0 0 0.1800063 51.1199308 328.3196004 cm /Im189 Do Q q 187.919742 0 0 0.1800063 51.1199308 328.1395941 cm /Im190 Do Q q 187.919742 0 0 0.1800063 51.1199308 327.9595721 cm /Im190 Do Q q 187.9197263 0 0 0.1800063 51.1199308 327.7795816 cm /Im191 Do Q q 187.9197263 0 0 0.1800063 51.1199308 327.599591 cm /Im192 Do Q q 187.919742 0 0 0.1800063 51.1199308 327.4196004 cm /Im193 Do Q q 187.919742 0 0 0.1800063 51.1199308 327.2395784 cm /Im194 Do Q q 187.919742 0 0 0.1800063 51.1199308 327.0595879 cm /Im195 Do Q q 187.919742 0 0 0.1800063 51.1199308 326.8795973 cm /Im196 Do Q q 187.919742 0 0 0.1800063 51.1199308 326.6996067 cm /Im197 Do Q q 187.919742 0 0 0.1800063 51.1199308 326.5195847 cm /Im197 Do Q q 187.919742 0 0 0.1800063 51.1199308 326.3395784 cm /Im198 Do Q q 187.9197263 0 0 0.1800063 51.1199308 326.1595879 cm /Im199 Do Q q 187.9197263 0 0 0.1800063 51.1199308 325.9795973 cm /Im200 Do Q q 187.919742 0 0 0.1800063 51.1199308 325.7996067 cm /Im201 Do Q q 187.919742 0 0 0.1800063 51.1199308 325.6195847 cm /Im202 Do Q q 187.919742 0 0 0.1800063 51.1199308 325.4395941 cm /Im203 Do Q q 187.919742 0 0 0.1800063 51.1199308 325.2596036 cm /Im204 Do Q q 187.919742 0 0 0.1800063 51.1199308 325.079613 cm /Im205 Do Q q 187.919742 0 0 0.1800063 51.1199308 324.899591 cm /Im205 Do Q q 187.919742 0 0 0.1800063 51.1199308 324.7195847 cm /Im206 Do Q q 187.9197263 0 0 0.1800063 51.1199308 324.5395941 cm /Im207 Do Q q 187.9197263 0 0 0.1800063 51.1199308 324.3596036 cm /Im208 Do Q q 187.919742 0 0 0.1800063 51.1199308 324.1795816 cm /Im209 Do Q q 187.919742 0 0 0.1800063 51.1199308 323.999591 cm /Im210 Do Q q 187.919742 0 0 0.1800063 51.1199308 323.8196004 cm /Im211 Do Q q 187.919742 0 0 0.1800063 51.1199308 323.6396099 cm /Im212 Do Q q 187.919742 0 0 0.1800063 51.1199308 323.4595879 cm /Im212 Do Q q 187.919742 0 0 0.1800063 51.1199308 323.2795973 cm /Im213 Do Q q 187.919742 0 0 0.1800063 51.1199308 323.0996067 cm /Im214 Do Q q 187.9197263 0 0 0.1800063 51.1199308 322.9196004 cm /Im215 Do Q q 187.9197263 0 0 0.1800063 51.1199308 322.7395784 cm /Im216 Do Q q 187.919742 0 0 0.1800063 51.1199308 322.5595879 cm /Im217 Do Q q 187.919742 0 0 0.1800063 51.1199308 322.3795973 cm /Im218 Do Q q 187.919742 0 0 0.1800063 51.1199308 322.1996067 cm /Im219 Do Q q 187.919742 0 0 0.1800063 51.1199308 322.0195847 cm /Im220 Do Q q 187.919742 0 0 0.1800063 51.1199308 321.8395941 cm /Im220 Do Q q 187.919742 0 0 0.1800063 51.1199308 321.6596036 cm /Im221 Do Q q 187.919742 0 0 0.1800063 51.1199308 321.479613 cm /Im222 Do Q q 187.9197263 0 0 0.1800063 51.1199308 321.2996067 cm /Im223 Do Q q 187.9197263 0 0 0.1800063 51.1199308 321.1195847 cm /Im224 Do Q q 187.919742 0 0 0.1800063 51.1199308 320.9395941 cm /Im225 Do Q q 187.919742 0 0 0.1800063 51.1199308 320.7596036 cm /Im226 Do Q q 187.919742 0 0 0.1800063 51.1199308 320.579613 cm /Im227 Do Q q 187.919742 0 0 0.1800063 51.1199308 320.399591 cm /Im227 Do Q q 187.919742 0 0 0.1800063 51.1199308 320.2196004 cm /Im228 Do Q q 187.919742 0 0 0.1800063 51.1199308 320.0396099 cm /Im229 Do Q q 187.919742 0 0 0.1800063 51.1199308 319.8596193 cm /Im230 Do Q q 187.9197263 0 0 0.1800063 51.1199308 319.6795816 cm /Im231 Do Q q 187.9197263 0 0 0.1800063 51.1199308 319.499591 cm /Im232 Do Q q 187.919742 0 0 0.1800063 51.1199308 319.3196004 cm /Im233 Do Q q 187.919742 0 0 0.1800063 51.1199308 319.1396099 cm /Im234 Do Q q 187.919742 0 0 0.1800063 51.1199308 318.9595879 cm /Im235 Do Q q 187.919742 0 0 0.1800063 51.1199308 318.7795973 cm /Im235 Do Q q 187.919742 0 0 0.1800063 51.1199308 318.5996067 cm /Im236 Do Q q 187.919742 0 0 0.1800063 51.1199308 318.4196162 cm /Im237 Do Q q 187.919742 0 0 0.1800063 51.1199308 318.2395941 cm /Im238 Do Q q 187.9197263 0 0 0.1800063 51.1199308 318.0596036 cm /Im239 Do Q q 187.9197263 0 0 0.1800063 51.1199308 317.8795973 cm /Im240 Do Q q 187.919742 0 0 0.1800063 51.1199308 317.6996067 cm /Im241 Do Q q 187.919742 0 0 0.1800063 51.1199308 317.5195847 cm /Im242 Do Q q 187.919742 0 0 0.1800063 51.1199308 317.3395941 cm /Im243 Do Q q 187.919742 0 0 0.1800063 51.1199308 317.1596036 cm /Im243 Do Q q 187.919742 0 0 0.1800063 51.1199308 316.979613 cm /Im244 Do Q q 0.3599969 0 0 0.1800063 51.1199308 316.799591 cm /Im245 Do Q q 0.3599969 0 0 0.1800063 51.8399245 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 52.7399245 316.799591 cm /Im245 Do Q q 0.3599969 0 0 0.1800063 53.4599182 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 54.3599182 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 55.0799276 316.799591 cm /Im247 Do Q q 0.3599969 0 0 0.1800063 55.9799276 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 56.6999213 316.799591 cm /Im247 Do Q q 0.3599969 0 0 0.1800063 57.5999213 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 58.3199151 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 59.2199151 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 59.9399088 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 60.8399088 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 61.7399088 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 62.4599182 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 63.3599025 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 64.0799119 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 64.9799119 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 65.6999056 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 66.5999056 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 67.3199151 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 68.2199151 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 68.939893 316.799591 cm /Im247 Do Q q 0.3599969 0 0 0.1800063 69.8399088 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 70.5599025 316.799591 cm /Im247 Do Q q 0.3599969 0 0 0.1800063 71.4599025 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 72.1798962 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 73.0798962 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 73.7998899 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 74.6998899 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 75.5998899 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 76.3198993 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 77.2198993 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 77.939893 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 78.839893 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 79.5598867 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 80.4598867 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 81.1798962 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 82.0798962 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 82.7998899 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 83.6998899 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 84.4198836 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 85.3198836 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 86.0398773 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 86.939893 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 87.659871 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 88.559871 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 89.459871 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 90.1798804 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 91.0798804 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 91.7998742 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 92.6998742 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 93.4198679 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 94.3198679 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 95.0398773 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 95.9398616 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 96.6598553 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 97.5598553 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 98.279849 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 99.179849 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 99.8998584 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 100.7998584 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 101.5198521 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 102.4198521 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 103.3198521 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 104.0398458 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 104.9398458 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 105.6598395 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 106.5598395 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 107.2798333 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 108.179849 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 108.8998427 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 109.7998427 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 110.5198364 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 111.4198364 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 112.1398301 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 113.0398301 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 113.7598395 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 114.6598395 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 115.3798333 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 116.2798333 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 117.1798333 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 117.899827 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 118.799827 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 119.5198207 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 120.4198207 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 121.1398301 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 122.0398301 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 122.7598238 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 123.6598081 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 124.3798018 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 125.2798018 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 125.9997955 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 126.8998112 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 127.6198049 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 128.5197892 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 129.2397986 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 130.1397986 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 131.0397986 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 131.7597924 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 132.6597924 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 133.3797861 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 134.2798018 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 134.9997955 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 135.8997955 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 136.6197892 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 137.5197892 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 138.2397829 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 139.1397986 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 139.8597924 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 140.7597924 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 141.4797861 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 142.3797861 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 143.0997798 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 143.9997955 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 144.8997798 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 145.6197735 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 146.5197735 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 147.2397672 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 148.1397829 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 148.8597766 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 149.7597766 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 150.4797703 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 151.3797703 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 152.099764 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 152.9997798 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 153.7197735 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 154.6197735 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 155.3397672 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 156.2397672 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 156.9597609 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 157.8597766 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 158.7597609 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 159.4797703 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 160.3797546 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 161.099764 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 161.999764 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 162.7197577 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 163.6197577 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 164.3397515 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 165.2397515 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 165.9597452 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 166.8597609 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 167.5797546 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 168.4797546 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 169.1997483 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 170.0997483 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 170.819742 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 171.7197577 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 172.619742 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 173.3397515 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 174.2397357 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 174.9597452 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 175.8597452 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 176.5797546 316.799591 cm /Im249 Do Q q 0.3599969 0 0 0.1800063 177.4797389 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 178.1997483 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 179.0997326 316.799591 cm /Im249 Do Q q 0.5400031 0 0 0.1800063 179.819742 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 180.719742 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 181.4397357 316.799591 cm /Im250 Do Q q 0.3599969 0 0 0.1800063 182.3397357 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 183.0597294 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 183.9597294 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 184.6797231 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 185.5797389 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 186.4797231 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 187.1997326 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 188.0997168 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 188.8197263 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 189.7197263 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 190.4397357 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 191.33972 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 192.0597294 316.799591 cm /Im247 Do Q q 0.3599969 0 0 0.1800063 192.9597137 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 193.6797231 316.799591 cm /Im247 Do Q q 0.3599969 0 0 0.1800063 194.5797231 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 195.2997326 316.799591 cm /Im247 Do Q q 0.3599969 0 0 0.1800063 196.1997168 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 196.9197263 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 197.8197106 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 198.53972 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 199.43972 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 200.33972 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 201.0597137 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 201.9597137 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 202.6797074 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 203.5797074 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 204.2997168 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 205.1997011 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 205.9197106 316.799591 cm /Im247 Do Q q 0.3599969 0 0 0.1800063 206.8196948 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 207.5397043 316.799591 cm /Im247 Do Q q 0.3599969 0 0 0.1800063 208.4397043 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 209.1597137 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 210.059698 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 210.7797074 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 211.6796917 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 212.3997011 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 213.2997011 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 214.1997011 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 214.9196948 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 215.8196948 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 216.5396885 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 217.4397043 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 218.159698 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 219.059698 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 219.7796917 316.799591 cm /Im247 Do Q q 0.3599969 0 0 0.1800063 220.6796759 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 221.3996854 316.799591 cm /Im247 Do Q q 0.3599969 0 0 0.1800063 222.2996854 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 223.0196948 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 223.9196791 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 224.6396885 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 225.5396728 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 226.2596822 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 227.1596822 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 228.0596822 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 228.7796759 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 229.6796759 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 230.3996697 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 231.2996854 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 232.0196791 316.799591 cm /Im246 Do Q q 0.3599969 0 0 0.1800063 232.9196791 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 233.6396728 316.799591 cm /Im247 Do Q q 0.3599969 0 0 0.1800063 234.5396728 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 235.2596665 316.799591 cm /Im247 Do Q q 0.3599969 0 0 0.1800063 236.1596822 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 236.8796759 316.799591 cm /Im248 Do Q q 0.3599969 0 0 0.1800063 237.7796759 316.799591 cm /Im246 Do Q q 0.5400031 0 0 0.1800063 238.4996697 316.799591 cm /Im251 Do Q q 1.6799906 0 0 0.1800063 140.9397829 309.779613 cm /Im252 Do Q q 0.9599969 0 0 0.1800063 144.8997798 309.779613 cm /Im13 Do Q q 1.6799906 0 0 0.1800063 148.6797703 309.779613 cm /Im252 Do Q q 1.6799906 0 0 0.1800063 140.9397829 309.5996225 cm /Im252 Do Q q 0.9599969 0 0 0.1800063 144.8997798 309.5996225 cm /Im13 Do Q q 1.6799906 0 0 0.1800063 148.6797703 309.5996225 cm /Im252 Do Q q 2.4 0 0 0.1800063 140.5797861 309.4196162 cm /Im3 Do Q q 0.9599969 0 0 0.1800063 144.8997798 309.4196162 cm /Im2 Do Q q 2.1599969 0 0 0.1800063 148.3197735 309.4196162 cm /Im29 Do Q q 0.9599969 0 0 0.1800063 140.3997798 309.2395941 cm /Im253 Do Q q 0.9599969 0 0 0.1800063 142.1997798 309.2395941 cm /Im254 Do Q q 1.4400031 0 0 0.1800063 144.5397829 309.2395941 cm /Im255 Do Q q 1.2 0 0 0.1800063 147.9597766 309.2395941 cm /Im256 Do Q q 1.4400031 0 0 0.1800063 149.7597766 309.2395941 cm /Im257 Do Q q 0.7199937 0 0 0.1800063 140.3997798 309.0596036 cm /Im258 Do Q q 0.7199937 0 0 0.1800063 142.3797861 309.0596036 cm /Im258 Do Q q 1.4400031 0 0 0.1800063 144.5397829 309.0596036 cm /Im25 Do Q q 0.7199937 0 0 0.1800063 147.9597766 309.0596036 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 150.1197735 309.0596036 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 140.0397829 308.879613 cm /Im2 Do Q q 1.2 0 0 0.1800063 142.3797861 308.879613 cm /Im259 Do Q q 1.6799906 0 0 0.1800063 144.5397829 308.879613 cm /Im260 Do Q q 0.9599969 0 0 0.1800063 147.5997798 308.879613 cm /Im33 Do Q q 0.9599969 0 0 0.1800063 150.299764 308.879613 cm /Im13 Do Q q 0.9599969 0 0 0.1800063 140.0397829 308.6996225 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 142.5597924 308.6996225 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 144.3597924 308.6996225 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 145.4397672 308.6996225 cm /Im7 Do Q q 1.2 0 0 0.1800063 147.4197892 308.6996225 cm /Im6 Do Q q 0.9599969 0 0 0.1800063 150.299764 308.6996225 cm /Im2 Do Q q 1.2 0 0 0.1800063 140.0397829 308.5196004 cm /Im261 Do Q q 0.9599969 0 0 0.1800063 144.3597924 308.5196004 cm /Im9 Do Q q 0.7199937 0 0 0.1800063 145.4397672 308.5196004 cm /Im12 Do Q q 0.9599969 0 0 0.1800063 147.4197892 308.5196004 cm /Im11 Do Q q 0.9599969 0 0 0.1800063 140.3997798 308.3396099 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 144.3597924 308.3396099 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 145.6197735 308.3396099 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 147.4197892 308.3396099 cm /Im2 Do Q q 1.4400031 0 0 0.1800063 140.5797861 308.1596193 cm /Im25 Do Q q 0.9599969 0 0 0.1800063 144.1797861 308.1596193 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 145.6197735 308.1596193 cm /Im9 Do Q q 0.9599969 0 0 0.1800063 147.4197892 308.1596193 cm /Im2 Do Q q 1.4400031 0 0 0.1800063 140.5797861 307.9796288 cm /Im25 Do Q q 0.9599969 0 0 0.1800063 144.1797861 307.9796288 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 145.6197735 307.9796288 cm /Im9 Do Q q 0.9599969 0 0 0.1800063 147.4197892 307.9796288 cm /Im2 Do Q q 2.1599969 0 0 0.1800063 140.7597924 307.7996067 cm /Im29 Do Q q 0.9599969 0 0 0.1800063 144.1797861 307.7996067 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 145.6197735 307.7996067 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 147.4197892 307.7996067 cm /Im2 Do Q q 1.9199937 0 0 0.1800063 141.2997798 307.6196004 cm /Im262 Do Q q 0.9599969 0 0 0.1800063 143.9997955 307.6196004 cm /Im5 Do Q q 0.9599969 0 0 0.1800063 145.7997798 307.6196004 cm /Im13 Do Q q 0.9599969 0 0 0.1800063 147.4197892 307.6196004 cm /Im13 Do Q q 1.4400031 0 0 0.1800063 142.1997798 307.4396099 cm /Im25 Do Q q 0.9599969 0 0 0.1800063 143.9997955 307.4396099 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 145.7997798 307.4396099 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 147.4197892 307.4396099 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 142.5597924 307.2596193 cm /Im263 Do Q q 2.8799906 0 0 0.1800063 143.9997955 307.2596193 cm /Im264 Do Q q 0.9599969 0 0 0.1800063 147.4197892 307.2596193 cm /Im13 Do Q q 0.7199937 0 0 0.1800063 140.0397829 307.0796288 cm /Im265 Do Q q 0.9599969 0 0 0.1800063 142.5597924 307.0796288 cm /Im2 Do Q q 3.1199937 0 0 0.1800063 143.8197735 307.0796288 cm /Im266 Do Q q 0.9599969 0 0 0.1800063 147.4197892 307.0796288 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 150.4797703 307.0796288 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 140.0397829 306.8996067 cm /Im13 Do Q q 0.9599969 0 0 0.1800063 142.5597924 306.8996067 cm /Im267 Do Q q 0.7199937 0 0 0.1800063 143.8197735 306.8996067 cm /Im268 Do Q q 0.9599969 0 0 0.1800063 145.9797861 306.8996067 cm /Im5 Do Q q 0.9599969 0 0 0.1800063 147.5997798 306.8996067 cm /Im269 Do Q q 0.9599969 0 0 0.1800063 150.299764 306.8996067 cm /Im270 Do Q q 0.9599969 0 0 0.1800063 140.0397829 306.7196162 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 142.5597924 306.7196162 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 143.8197735 306.7196162 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 146.1597766 306.7196162 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 147.5997798 306.7196162 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 150.299764 306.7196162 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 140.0397829 306.5396256 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 142.5597924 306.5396256 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 143.8197735 306.5396256 cm /Im7 Do Q q 0.9599969 0 0 0.1800063 146.1597766 306.5396256 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 147.5997798 306.5396256 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 150.299764 306.5396256 cm /Im2 Do Q q 1.2 0 0 0.1800063 140.0397829 306.359635 cm /Im6 Do Q q 0.9599969 0 0 0.1800063 142.5597924 306.359635 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 143.6397829 306.359635 cm /Im10 Do Q q 0.9599969 0 0 0.1800063 146.1597766 306.359635 cm /Im11 Do Q q 0.7199937 0 0 0.1800063 147.9597766 306.359635 cm /Im31 Do Q q 0.9599969 0 0 0.1800063 150.1197735 306.359635 cm /Im9 Do Q q 0.9599969 0 0 0.1800063 140.3997798 306.179613 cm /Im2 Do Q q 0.9599969 0 0 0.1800063 142.1997798 306.179613 cm /Im2 Do Q q 0.7199937 0 0 0.1800063 143.6397829 306.179613 cm /Im7 Do Q q 1.2 0 0 0.1800063 146.1597766 306.179613 cm /Im6 Do Q q 1.2 0 0 0.1800063 147.9597766 306.179613 cm /Im6 Do Q q 1.4400031 0 0 0.1800063 149.7597766 306.179613 cm /Im25 Do Q q 2.4 0 0 0.1800063 140.5797861 305.9996067 cm /Im271 Do Q q 0.9599969 0 0 0.1800063 143.4597766 305.9996067 cm /Im272 Do Q q 0.7199937 0 0 0.1800063 146.5197735 305.9996067 cm /Im15 Do Q q 2.4 0 0 0.1800063 148.1397829 305.9996067 cm /Im273 Do Q q 1.6799906 0 0 0.1800063 140.9397829 305.8196162 cm /Im0 Do Q q 0.7199937 0 0 0.1800063 143.4597766 305.8196162 cm /Im7 Do Q q 0.7199937 0 0 0.1800063 146.5197735 305.8196162 cm /Im7 Do Q q 1.9199937 0 0 0.1800063 148.4997798 305.8196162 cm /Im274 Do Q q 187.9197263 0 0 0.1800063 52.7399245 305.0996225 cm /Im275 Do Q q 187.9197263 0 0 0.1800063 52.7399245 304.9196319 cm /Im275 Do Q q 187.9197263 0 0 0.1800063 52.7399245 304.7396099 cm /Im276 Do Q q 187.919742 0 0 0.1800063 52.7399245 304.5596193 cm /Im277 Do Q q 187.919742 0 0 0.1800063 52.7399245 304.379613 cm /Im278 Do Q q 187.9197263 0 0 0.1800063 52.7399245 304.1996225 cm /Im279 Do Q q 187.9197263 0 0 0.1800063 52.7399245 304.0196004 cm /Im280 Do Q q 187.919742 0 0 0.1800063 52.7399245 303.8396099 cm /Im281 Do Q q 187.919742 0 0 0.1800063 52.7399245 303.6596193 cm /Im282 Do Q q 187.9197263 0 0 0.1800063 52.7399245 303.4796288 cm /Im283 Do Q q 187.9197263 0 0 0.1800063 52.7399245 303.2996067 cm /Im283 Do Q q 187.9197263 0 0 0.1800063 52.7399245 303.1196162 cm /Im284 Do Q q 187.919742 0 0 0.1800063 52.7399245 302.9396256 cm /Im285 Do Q q 187.919742 0 0 0.1800063 52.7399245 302.759635 cm /Im286 Do Q q 187.9197263 0 0 0.1800063 52.7399245 302.5796288 cm /Im287 Do Q q 187.9197263 0 0 0.1800063 52.7399245 302.3996067 cm /Im288 Do Q q 187.919742 0 0 0.1800063 52.7399245 302.2196162 cm /Im289 Do Q q 187.919742 0 0 0.1800063 52.7399245 302.0396256 cm /Im290 Do Q q 187.919742 0 0 0.1800063 52.7399245 301.859635 cm /Im290 Do Q q 187.9197263 0 0 0.1800063 52.7399245 301.679613 cm /Im291 Do Q q 187.9197263 0 0 0.1800063 52.7399245 301.4996225 cm /Im292 Do Q q 187.919742 0 0 0.1800063 52.7399245 301.3196319 cm /Im293 Do Q q 187.919742 0 0 0.1800063 52.7399245 301.1396413 cm /Im294 Do Q q 187.9197263 0 0 0.1800063 52.7399245 300.9596193 cm /Im295 Do Q q 187.9197263 0 0 0.1800063 52.7399245 300.779613 cm /Im296 Do Q q 187.919742 0 0 0.1800063 52.7399245 300.5996225 cm /Im297 Do Q q 187.919742 0 0 0.1800063 52.7399245 300.4196319 cm /Im298 Do Q q 187.919742 0 0 0.1800063 52.7399245 300.2396413 cm /Im298 Do Q q 187.9197263 0 0 0.1800063 52.7399245 300.0596508 cm /Im299 Do Q q 187.9197263 0 0 0.1800063 52.7399245 299.8796602 cm /Im300 Do Q q 187.919742 0 0 0.1800063 52.7399245 299.6996697 cm /Im301 Do Q q 187.919742 0 0 0.1800063 52.7399245 299.5196476 cm /Im302 Do Q q 187.9197263 0 0 0.1800063 52.7399245 299.3396413 cm /Im303 Do Q q 187.9197263 0 0 0.1800063 52.7399245 299.1596508 cm /Im304 Do Q q 187.919742 0 0 0.1800063 52.7399245 298.9796602 cm /Im305 Do Q q 187.919742 0 0 0.1800063 52.7399245 298.7996382 cm /Im305 Do Q q 187.919742 0 0 0.1800063 52.7399245 298.6196476 cm /Im306 Do Q q 187.9197263 0 0 0.1800063 52.7399245 298.4396571 cm /Im307 Do Q q 187.9197263 0 0 0.1800063 52.7399245 298.2596665 cm /Im308 Do Q q 187.919742 0 0 0.1800063 52.7399245 298.0796445 cm /Im309 Do Q q 187.919742 0 0 0.1800063 52.7399245 297.8996539 cm /Im310 Do Q q 187.9197263 0 0 0.1800063 52.7399245 297.7196634 cm /Im311 Do Q q 187.9197263 0 0 0.1800063 52.7399245 297.5396571 cm /Im312 Do Q q 187.919742 0 0 0.1800063 52.7399245 297.3596665 cm /Im313 Do Q q 187.919742 0 0 0.1800063 52.7399245 297.1796445 cm /Im313 Do Q q 187.919742 0 0 0.1800063 52.7399245 296.9996539 cm /Im314 Do Q q 187.9197263 0 0 0.1800063 52.7399245 296.8196634 cm /Im315 Do Q q 187.9197263 0 0 0.1800063 52.7399245 296.6396728 cm /Im316 Do Q q 187.919742 0 0 0.1800063 52.7399245 296.4596508 cm /Im317 Do Q q 187.919742 0 0 0.1800063 52.7399245 296.2796602 cm /Im318 Do Q q 187.9197263 0 0 0.1800063 52.7399245 296.0996697 cm /Im319 Do Q q 187.9197263 0 0 0.1800063 52.7399245 295.9196634 cm /Im320 Do Q q 187.9197263 0 0 0.1800063 52.7399245 295.7396413 cm /Im320 Do Q q 187.919742 0 0 0.1800063 52.7399245 295.5596508 cm /Im321 Do Q q 187.919742 0 0 0.1800063 52.7399245 295.3796602 cm /Im322 Do Q q 187.9197263 0 0 0.1800063 52.7399245 295.1996697 cm /Im323 Do Q q 187.9197263 0 0 0.1800063 52.7399245 295.0196476 cm /Im324 Do Q q 187.919742 0 0 0.1800063 52.7399245 294.8396571 cm /Im325 Do Q q 187.919742 0 0 0.1800063 52.7399245 294.6596665 cm /Im326 Do Q q 187.9197263 0 0 0.1800063 52.7399245 294.4796759 cm /Im327 Do Q q 187.9197263 0 0 0.1800063 52.7399245 294.2996539 cm /Im328 Do Q q 187.9197263 0 0 0.1800063 52.7399245 294.1196476 cm /Im328 Do Q q 187.919742 0 0 0.1800063 52.7399245 293.9396571 cm /Im329 Do Q q 187.919742 0 0 0.1800063 52.7399245 293.7596665 cm /Im330 Do Q q 187.9197263 0 0 0.1800063 52.7399245 293.5796445 cm /Im331 Do Q q 187.9197263 0 0 0.1800063 52.7399245 293.3996539 cm /Im332 Do Q q 187.919742 0 0 0.1800063 52.7399245 293.2196634 cm /Im333 Do Q q 187.919742 0 0 0.1800063 52.7399245 293.0396728 cm /Im334 Do Q q 187.9197263 0 0 0.1800063 52.7399245 292.8596822 cm /Im335 Do Q q 187.9197263 0 0 0.1800063 52.7399245 292.6796602 cm /Im335 Do Q q 187.9197263 0 0 0.1800063 52.7399245 292.4996539 cm /Im336 Do Q q 187.919742 0 0 0.1800063 52.7399245 292.3196634 cm /Im337 Do Q q 187.919742 0 0 0.1800063 52.7399245 292.1396728 cm /Im338 Do Q q 187.9197263 0 0 0.1800063 52.7399245 291.9596508 cm /Im339 Do Q q 187.9197263 0 0 0.1800063 52.7399245 291.7796602 cm /Im340 Do Q q 187.919742 0 0 0.1800063 52.7399245 291.5996697 cm /Im341 Do Q q 187.919742 0 0 0.1800063 52.7399245 291.4196948 cm /Im342 Do Q q 187.9197263 0 0 0.1800063 52.7399245 291.2396571 cm /Im343 Do Q q 187.9197263 0 0 0.1800063 52.7399245 291.0596822 cm /Im343 Do Q q 187.9197263 0 0 0.1800063 52.7399245 290.8796917 cm /Im344 Do Q q 187.919742 0 0 0.1800063 52.7399245 290.6996854 cm /Im345 Do Q q 187.919742 0 0 0.1800063 52.7399245 290.5196634 cm /Im346 Do Q q 187.9197263 0 0 0.1800063 52.7399245 290.3396728 cm /Im347 Do Q q 187.9197263 0 0 0.1800063 52.7399245 290.1596822 cm /Im348 Do Q q 187.919742 0 0 0.1800063 52.7399245 289.9796917 cm /Im349 Do Q q 187.919742 0 0 0.1800063 52.7399245 289.7996697 cm /Im350 Do Q q 187.919742 0 0 0.1800063 52.7399245 289.6196791 cm /Im350 Do Q q 187.9197263 0 0 0.1800063 52.7399245 289.4396885 cm /Im351 Do Q q 187.9197263 0 0 0.1800063 52.7399245 289.259698 cm /Im352 Do Q q 187.919742 0 0 0.1800063 52.7399245 289.0796759 cm /Im353 Do Q q 187.919742 0 0 0.1800063 52.7399245 288.8996697 cm /Im354 Do Q q 187.9197263 0 0 0.1800063 52.7399245 288.7196791 cm /Im355 Do Q q 187.9197263 0 0 0.1800063 52.7399245 288.5396885 cm /Im356 Do Q q 187.919742 0 0 0.1800063 52.7399245 288.359698 cm /Im357 Do Q q 187.919742 0 0 0.1800063 52.7399245 288.1796759 cm /Im358 Do Q q 187.919742 0 0 0.1800063 52.7399245 287.9996854 cm /Im358 Do Q q 187.9197263 0 0 0.1800063 52.7399245 287.8196948 cm /Im359 Do Q q 187.9197263 0 0 0.1800063 52.7399245 287.6397043 cm /Im360 Do Q q 187.919742 0 0 0.1800063 52.7399245 287.4596822 cm /Im361 Do Q q 187.919742 0 0 0.1800063 52.7399245 287.2796759 cm /Im362 Do Q q 187.9197263 0 0 0.1800063 52.7399245 287.0996854 cm /Im363 Do Q q 187.9197263 0 0 0.1800063 52.7399245 286.9196948 cm /Im364 Do Q q 187.919742 0 0 0.1800063 52.7399245 286.7396728 cm /Im365 Do Q q 187.919742 0 0 0.1800063 52.7399245 286.5596822 cm /Im366 Do Q q 187.919742 0 0 0.1800063 52.7399245 286.3796917 cm /Im366 Do Q q 187.9197263 0 0 0.1800063 52.7399245 286.1997011 cm /Im367 Do Q q 187.9197263 0 0 0.1800063 52.7399245 286.0196791 cm /Im368 Do Q q 187.919742 0 0 0.1800063 52.7399245 285.8396885 cm /Im369 Do Q q 187.919742 0 0 0.1800063 52.7399245 285.6596822 cm /Im370 Do Q q 187.9197263 0 0 0.1800063 52.7399245 285.4796917 cm /Im371 Do Q q 187.9197263 0 0 0.1800063 52.7399245 285.2996697 cm /Im372 Do Q q 187.919742 0 0 0.1800063 52.7399245 285.1196791 cm /Im373 Do Q q 187.919742 0 0 0.1800063 52.7399245 284.9396885 cm /Im373 Do Q q 187.919742 0 0 0.1800063 52.7399245 284.759698 cm /Im374 Do Q q 187.9197263 0 0 0.1800063 52.7399245 284.5796759 cm /Im375 Do Q q 187.9197263 0 0 0.1800063 52.7399245 284.3996854 cm /Im376 Do Q q 187.919742 0 0 0.1800063 52.7399245 284.2196948 cm /Im377 Do Q q 187.919742 0 0 0.1800063 52.7399245 284.0397043 cm /Im378 Do Q q 187.9197263 0 0 0.1800063 52.7399245 283.8596665 cm /Im379 Do Q q 187.9197263 0 0 0.1800063 52.7399245 283.6796759 cm /Im380 Do Q q 187.919742 0 0 0.1800063 52.7399245 283.4996854 cm /Im381 Do Q q 187.919742 0 0 0.1800063 52.7399245 283.3196948 cm /Im381 Do Q q 187.919742 0 0 0.1800063 52.7399245 283.1397043 cm /Im382 Do Q q 187.9197263 0 0 0.1800063 52.7399245 282.9596822 cm /Im383 Do Q q 187.9197263 0 0 0.1800063 52.7399245 282.7796917 cm /Im384 Do Q q 187.919742 0 0 0.1800063 52.7399245 282.5997011 cm /Im385 Do Q q 187.919742 0 0 0.1800063 52.7399245 282.4197106 cm /Im386 Do Q q 187.9197263 0 0 0.1800063 52.7399245 282.2396728 cm /Im387 Do Q q 187.9197263 0 0 0.1800063 52.7399245 282.0596822 cm /Im388 Do Q q 187.9197263 0 0 0.1800063 52.7399245 281.8796917 cm /Im388 Do Q q 187.919742 0 0 0.1800063 52.7399245 281.6997011 cm /Im389 Do Q q 187.919742 0 0 0.1800063 52.7399245 281.5196791 cm /Im390 Do Q q 187.9197263 0 0 0.1800063 52.7399245 281.3396885 cm /Im391 Do Q q 187.9197263 0 0 0.1800063 52.7399245 281.159698 cm /Im392 Do Q q 187.919742 0 0 0.1800063 52.7399245 280.9797074 cm /Im393 Do Q q 187.919742 0 0 0.1800063 52.7399245 280.7996854 cm /Im394 Do Q q 187.9197263 0 0 0.1800063 52.7399245 280.6196948 cm /Im395 Do Q q 187.9197263 0 0 0.1800063 52.7399245 280.4396885 cm /Im396 Do Q q 187.9197263 0 0 0.1800063 52.7399245 280.259698 cm /Im396 Do Q q 187.919742 0 0 0.1800063 52.7399245 280.0796759 cm /Im397 Do Q q 187.919742 0 0 0.1800063 52.7399245 279.8996854 cm /Im398 Do Q q 187.9197263 0 0 0.1800063 52.7399245 279.7196948 cm /Im399 Do Q q 187.9197263 0 0 0.1800063 52.7399245 279.5397043 cm /Im400 Do Q q 187.919742 0 0 0.1800063 52.7399245 279.3596822 cm /Im401 Do Q q 187.919742 0 0 0.1800063 52.7399245 279.1796917 cm /Im402 Do Q q 187.9197263 0 0 0.1800063 52.7399245 278.9997011 cm /Im403 Do Q q 187.9197263 0 0 0.1800063 52.7399245 278.8196948 cm /Im403 Do Q q 187.9197263 0 0 0.1800063 52.7399245 278.6397043 cm /Im404 Do Q q 187.919742 0 0 0.1800063 52.7399245 278.4596822 cm /Im405 Do Q q 187.919742 0 0 0.1800063 52.7399245 278.2796917 cm /Im406 Do Q q 187.9197263 0 0 0.1800063 52.7399245 278.0997011 cm /Im407 Do Q q 187.9197263 0 0 0.1800063 52.7399245 277.9197106 cm /Im408 Do Q q 187.919742 0 0 0.1800063 52.7399245 277.7396885 cm /Im409 Do Q q 187.919742 0 0 0.1800063 52.7399245 277.559698 cm /Im410 Do Q q 187.9197263 0 0 0.1800063 52.7399245 277.3797074 cm /Im411 Do Q q 187.9197263 0 0 0.1800063 52.7399245 277.1997011 cm /Im411 Do Q q 187.9197263 0 0 0.1800063 52.7399245 277.0196791 cm /Im412 Do Q q 187.919742 0 0 0.1800063 52.7399245 276.8396885 cm /Im413 Do Q q 187.919742 0 0 0.1800063 52.7399245 276.659698 cm /Im414 Do Q q 187.9197263 0 0 0.1800063 52.7399245 276.4797074 cm /Im415 Do Q q 187.9197263 0 0 0.1800063 52.7399245 276.2996854 cm /Im416 Do Q q 187.919742 0 0 0.1800063 52.7399245 276.1196948 cm /Im417 Do Q q 187.919742 0 0 0.1800063 52.7399245 275.9397043 cm /Im418 Do Q q 187.919742 0 0 0.1800063 52.7399245 275.7597137 cm /Im418 Do Q q 187.9197263 0 0 0.1800063 52.7399245 275.5796917 cm /Im419 Do Q q 187.9197263 0 0 0.1800063 52.7399245 275.3996854 cm /Im420 Do Q q 187.919742 0 0 0.1800063 52.7399245 275.2196948 cm /Im421 Do Q q 187.919742 0 0 0.1800063 52.7399245 275.0397043 cm /Im422 Do Q q 187.9197263 0 0 0.1800063 52.7399245 274.8596822 cm /Im423 Do Q q 187.9197263 0 0 0.1800063 52.7399245 274.6796917 cm /Im424 Do Q q 187.919742 0 0 0.1800063 52.7399245 274.4997011 cm /Im425 Do Q q 187.919742 0 0 0.1800063 52.7399245 274.3197106 cm /Im426 Do Q q 187.919742 0 0 0.1800063 52.7399245 274.13972 cm /Im426 Do Q q 187.9197263 0 0 0.1800063 52.7399245 273.959698 cm /Im427 Do Q q 187.9197263 0 0 0.1800063 52.7399245 273.7797074 cm /Im428 Do Q q 187.919742 0 0 0.1800063 52.7399245 273.5997011 cm /Im429 Do Q q 187.919742 0 0 0.1800063 52.7399245 273.4197106 cm /Im430 Do Q q 187.9197263 0 0 0.1800063 52.7399245 273.2396885 cm /Im431 Do Q q 187.9197263 0 0 0.1800063 52.7399245 273.059698 cm /Im432 Do Q q 187.919742 0 0 0.1800063 52.7399245 272.8797074 cm /Im433 Do Q q 187.919742 0 0 0.1800063 52.7399245 272.6997168 cm /Im433 Do Q q 187.919742 0 0 0.1800063 52.7399245 272.5196948 cm /Im434 Do Q q 187.9197263 0 0 0.1800063 52.7399245 272.3397043 cm /Im435 Do Q q 187.9197263 0 0 0.1800063 52.7399245 272.1597137 cm /Im436 Do Q q 187.919742 0 0 0.1800063 52.7399245 271.9797074 cm /Im437 Do Q q 187.919742 0 0 0.1800063 52.7399245 271.7996854 cm /Im438 Do Q q 187.9197263 0 0 0.1800063 52.7399245 271.6196948 cm /Im439 Do Q q 187.9197263 0 0 0.1800063 52.7399245 271.4397043 cm /Im440 Do Q q 187.919742 0 0 0.1800063 52.7399245 271.2597137 cm /Im441 Do Q q 187.919742 0 0 0.1800063 52.7399245 271.0796917 cm /Im441 Do Q q 187.919742 0 0 0.1800063 52.7399245 270.8997011 cm /Im442 Do Q q 187.9197263 0 0 0.1800063 52.7399245 270.7197106 cm /Im443 Do Q q 187.9197263 0 0 0.1800063 52.7399245 270.53972 cm /Im444 Do Q q 187.919742 0 0 0.1800063 52.7399245 270.3596822 cm /Im445 Do Q q 187.919742 0 0 0.1800063 52.7399245 270.1796917 cm /Im446 Do Q q 187.9197263 0 0 0.1800063 52.7399245 269.9997011 cm /Im447 Do Q q 187.9197263 0 0 0.1800063 52.7399245 269.8197106 cm /Im448 Do Q q 187.919742 0 0 0.1800063 52.7399245 269.63972 cm /Im449 Do Q q 187.919742 0 0 0.1800063 52.7399245 269.459698 cm /Im449 Do Q q 187.919742 0 0 0.1800063 52.7399245 269.2797074 cm /Im450 Do Q q 187.9197263 0 0 0.1800063 52.7399245 269.0997168 cm /Im451 Do Q q 187.9197263 0 0 0.1800063 52.7399245 268.9197263 cm /Im452 Do Q q 187.919742 0 0 0.1800063 52.7399245 268.7397043 cm /Im453 Do Q q 187.919742 0 0 0.1800063 52.7399245 268.559698 cm /Im454 Do Q q 187.9197263 0 0 0.1800063 52.7399245 268.3797074 cm /Im455 Do Q q 187.9197263 0 0 0.1800063 52.7399245 268.1997168 cm /Im456 Do Q q 187.9197263 0 0 0.1800063 52.7399245 268.0196948 cm /Im456 Do Q q 187.919742 0 0 0.1800063 52.7399245 267.8397043 cm /Im457 Do Q q 187.919742 0 0 0.1800063 52.7399245 267.6597137 cm /Im458 Do Q q 187.9197263 0 0 0.1800063 52.7399245 267.4797231 cm /Im459 Do Q q 187.9197263 0 0 0.1800063 52.7399245 267.2997011 cm /Im460 Do Q q 187.919742 0 0 0.1800063 52.7399245 267.1197106 cm /Im461 Do Q q 187.919742 0 0 0.1800063 52.7399245 266.9397043 cm /Im462 Do Q q 187.9197263 0 0 0.1800063 52.7399245 266.7597137 cm /Im463 Do Q q 187.9197263 0 0 0.1800063 52.7399245 266.5796917 cm /Im464 Do Q q 187.9197263 0 0 0.1800063 52.7399245 266.3997011 cm /Im464 Do Q q 187.919742 0 0 0.1800063 52.7399245 266.2197106 cm /Im465 Do Q q 187.919742 0 0 0.1800063 52.7399245 266.03972 cm /Im466 Do Q q 187.9197263 0 0 0.1800063 52.7399245 265.859698 cm /Im467 Do Q q 187.9197263 0 0 0.1800063 52.7399245 265.6797074 cm /Im468 Do Q q 187.919742 0 0 0.1800063 52.7399245 265.4997168 cm /Im469 Do Q q 187.919742 0 0 0.1800063 52.7399245 265.3197106 cm /Im470 Do Q q 187.9197263 0 0 0.1800063 52.7399245 265.13972 cm /Im471 Do Q q 187.9197263 0 0 0.1800063 52.7399245 264.959698 cm /Im471 Do Q q 187.9197263 0 0 0.1800063 52.7399245 264.7797074 cm /Im472 Do Q q 187.919742 0 0 0.1800063 52.7399245 264.5997168 cm /Im473 Do Q q 187.919742 0 0 0.1800063 52.7399245 264.4197263 cm /Im474 Do Q q 187.9197263 0 0 0.1800063 52.7399245 264.2397043 cm /Im475 Do Q q 187.9197263 0 0 0.1800063 52.7399245 264.0597137 cm /Im476 Do Q q 187.919742 0 0 0.1800063 52.7399245 263.8797231 cm /Im477 Do Q q 187.919742 0 0 0.1800063 52.7399245 263.6997326 cm /Im478 Do Q q 187.9197263 0 0 0.1800063 52.7399245 263.5196948 cm /Im479 Do Q q 187.9197263 0 0 0.1800063 52.7399245 263.3397043 cm /Im479 Do Q q 187.9197263 0 0 0.1800063 52.7399245 263.1597137 cm /Im480 Do Q q 187.919742 0 0 0.1800063 52.7399245 262.9797231 cm /Im481 Do Q q 187.919742 0 0 0.1800063 52.7399245 262.7997011 cm /Im482 Do Q q 187.9197263 0 0 0.1800063 52.7399245 262.6197106 cm /Im483 Do Q q 187.9197263 0 0 0.1800063 52.7399245 262.43972 cm /Im484 Do Q q 187.919742 0 0 0.1800063 52.7399245 262.2597294 cm /Im485 Do Q q 187.919742 0 0 0.1800063 52.7399245 262.0797074 cm /Im486 Do Q q 187.919742 0 0 0.1800063 52.7399245 261.8997168 cm /Im486 Do Q q 187.9197263 0 0 0.1800063 52.7399245 261.7197106 cm /Im487 Do Q q 187.9197263 0 0 0.1800063 52.7399245 261.53972 cm /Im488 Do Q q 187.919742 0 0 0.1800063 52.7399245 261.359698 cm /Im489 Do Q q 187.919742 0 0 0.1800063 52.7399245 261.1797074 cm /Im490 Do Q q 187.9197263 0 0 0.1800063 52.7399245 260.9997168 cm /Im491 Do Q q 187.9197263 0 0 0.1800063 52.7399245 260.8197263 cm /Im492 Do Q q 187.919742 0 0 0.1800063 52.7399245 260.6397357 cm /Im493 Do Q q 187.919742 0 0 0.1800063 52.7399245 260.4597137 cm /Im494 Do Q q 187.919742 0 0 0.1800063 52.7399245 260.2797231 cm /Im494 Do Q q 187.9197263 0 0 0.1800063 52.7399245 260.0997168 cm /Im495 Do Q q 187.9197263 0 0 0.1800063 52.7399245 259.9197263 cm /Im496 Do Q q 187.919742 0 0 0.1800063 52.7399245 259.7397043 cm /Im497 Do Q q 187.919742 0 0 0.1800063 52.7399245 259.5597137 cm /Im498 Do Q q 187.9197263 0 0 0.1800063 52.7399245 259.3797231 cm /Im499 Do Q q 187.9197263 0 0 0.1800063 52.7399245 259.1997326 cm /Im500 Do Q q 187.919742 0 0 0.1800063 52.7399245 259.0197106 cm /Im501 Do Q q 187.919742 0 0 0.1800063 52.7399245 258.83972 cm /Im501 Do Q q 187.919742 0 0 0.1800063 52.7399245 258.6597294 cm /Im502 Do Q q 187.9197263 0 0 0.1800063 52.7399245 258.4797231 cm /Im503 Do Q q 187.9197263 0 0 0.1800063 52.7399245 258.2997011 cm /Im504 Do Q q 187.919742 0 0 0.1800063 52.7399245 258.1197106 cm /Im505 Do Q q 0.3599969 0 0 0.1800063 52.7399245 257.93972 cm /Im245 Do Q q 0.3599969 0 0 0.1800063 53.4599182 257.93972 cm /Im245 Do Q q 0.3599969 0 0 0.1800063 54.3599182 257.93972 cm /Im245 Do Q q 0.5400031 0 0 0.1800063 55.0799276 257.93972 cm /Im251 Do Q q 0.3599969 0 0 0.1800063 55.9799276 257.93972 cm /Im245 Do Q q 0.5400031 0 0 0.1800063 56.6999213 257.93972 cm /Im251 Do Q q 0.3599969 0 0 0.1800063 57.5999213 257.93972 cm /Im245 Do Q q 0.5400031 0 0 0.1800063 58.3199151 257.93972 cm /Im251 Do Q q 0.3599969 0 0 0.1800063 59.2199151 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 59.9399088 257.93972 cm /Im251 Do Q q 0.3599969 0 0 0.1800063 60.8399088 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 61.7399088 257.93972 cm /Im245 Do Q q 0.3599969 0 0 0.1800063 62.4599182 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 63.3599025 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 64.0799119 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 64.9799119 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 65.6999056 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 66.5999056 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 67.3199151 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 68.2199151 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 68.939893 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 69.8399088 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 70.5599025 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 71.4599025 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 72.1798962 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 73.0798962 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 73.7998899 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 74.6998899 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 75.5998899 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 76.3198993 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 77.2198993 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 77.939893 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 78.839893 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 79.5598867 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 80.4598867 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 81.1798962 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 82.0798962 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 82.7998899 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 83.6998899 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 84.4198836 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 85.3198836 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 86.0398773 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 86.939893 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 87.659871 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 88.559871 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 89.459871 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 90.1798804 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 91.0798804 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 91.7998742 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 92.6998742 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 93.4198679 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 94.3198679 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 95.0398773 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 95.9398616 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 96.6598553 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 97.5598553 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 98.279849 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 99.179849 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 99.8998584 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 100.7998584 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 101.5198521 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 102.4198521 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 103.3198521 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 104.0398458 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 104.9398458 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 105.6598395 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 106.5598395 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 107.2798333 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 108.179849 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 108.8998427 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 109.7998427 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 110.5198364 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 111.4198364 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 112.1398301 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 113.0398301 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 113.7598395 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 114.6598395 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 115.3798333 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 116.2798333 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 117.1798333 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 117.899827 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 118.799827 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 119.5198207 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 120.4198207 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 121.1398301 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 122.0398301 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 122.7598238 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 123.6598081 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 124.3798018 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 125.2798018 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 125.9997955 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 126.8998112 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 127.6198049 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 128.5197892 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 129.2397986 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 130.1397986 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 131.0397986 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 131.7597924 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 132.6597924 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 133.3797861 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 134.2798018 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 134.9997955 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 135.8997955 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 136.6197892 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 137.5197892 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 138.2397829 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 139.1397986 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 139.8597924 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 140.7597924 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 141.4797861 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 142.3797861 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 143.0997798 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 143.9997955 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 144.8997798 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 145.6197735 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 146.5197735 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 147.2397672 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 148.1397829 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 148.8597766 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 149.7597766 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 150.4797703 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 151.3797703 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 152.099764 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 152.9997798 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 153.7197735 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 154.6197735 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 155.3397672 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 156.2397672 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 156.9597609 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 157.8597766 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 158.7597609 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 159.4797703 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 160.3797546 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 161.099764 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 161.999764 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 162.7197577 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 163.6197577 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 164.3397515 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 165.2397515 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 165.9597452 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 166.8597609 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 167.5797546 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 168.4797546 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 169.1997483 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 170.0997483 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 170.819742 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 171.7197577 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 172.619742 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 173.3397515 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 174.2397357 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 174.9597452 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 175.8597452 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 176.5797546 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 177.4797389 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 178.1997483 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 179.0997326 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 179.819742 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 180.719742 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 181.4397357 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 182.3397357 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 183.0597294 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 183.9597294 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 184.6797231 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 185.5797389 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 186.4797231 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 187.1997326 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 188.0997168 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 188.8197263 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 189.7197263 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 190.4397357 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 191.33972 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 192.0597294 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 192.9597137 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 193.6797231 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 194.5797231 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 195.2997326 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 196.1997168 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 196.9197263 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 197.8197106 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 198.53972 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 199.43972 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 200.33972 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 201.0597137 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 201.9597137 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 202.6797074 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 203.5797074 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 204.2997168 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 205.1997011 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 205.9197106 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 206.8196948 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 207.5397043 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 208.4397043 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 209.1597137 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 210.059698 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 210.7797074 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 211.6796917 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 212.3997011 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 213.2997011 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 214.1997011 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 214.9196948 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 215.8196948 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 216.5396885 257.93972 cm /Im245 Do Q q 0.3599969 0 0 0.1800063 217.4397043 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 218.159698 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 219.059698 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 219.7796917 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 220.6796759 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 221.3996854 257.93972 cm /Im251 Do Q q 0.3599969 0 0 0.1800063 222.2996854 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 223.0196948 257.93972 cm /Im251 Do Q q 0.3599969 0 0 0.1800063 223.9196791 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 224.6396885 257.93972 cm /Im251 Do Q q 0.3599969 0 0 0.1800063 225.5396728 257.93972 cm /Im506 Do Q q 0.5400031 0 0 0.1800063 226.2596822 257.93972 cm /Im251 Do Q q 0.3599969 0 0 0.1800063 227.1596822 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 228.0596822 257.93972 cm /Im245 Do Q q 0.3599969 0 0 0.1800063 228.7796759 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 229.6796759 257.93972 cm /Im245 Do Q q 0.3599969 0 0 0.1800063 230.3996697 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 231.2996854 257.93972 cm /Im245 Do Q q 0.3599969 0 0 0.1800063 232.0196791 257.93972 cm /Im506 Do Q q 0.3599969 0 0 0.1800063 232.9196791 257.93972 cm /Im245 Do Q q 0.5400031 0 0 0.1800063 233.6396728 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 234.5396728 257.93972 cm /Im245 Do Q q 0.5400031 0 0 0.1800063 235.2596665 257.93972 cm /Im507 Do Q q 0.3599969 0 0 0.1800063 236.1596822 257.93972 cm /Im245 Do Q q 0.5400031 0 0 0.1800063 236.8796759 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 237.7796759 257.93972 cm /Im245 Do Q q 0.5400031 0 0 0.1800063 238.4996697 257.93972 cm /Im508 Do Q q 0.3599969 0 0 0.1800063 239.3996697 257.93972 cm /Im245 Do Q q 0.3599969 0 0 0.1800063 240.1196634 257.93972 cm /Im245 Do Q Q q 243.0431671 0 0 155.8595734 55.7927856 457.9866028 cm /Im509 Do Q q 0.9700012 0 0 0.9700012 9 12 cm 0.594 0.805 0.801 rg 64.5 465.78 174 15.48 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 0.004 0.004 0.004 RG 0.75 w 8 M 1 J 238.5 481.26 -174 -15.48 re 64.5 481.26 m h S Q BT /TT1 1 Tf 0.0001 Tc 8.2487 0 0 8.2644 142.278 469.2192 Tm [(Normaliz)-8(ed )]TJ ET q 0.9700012 0 0 0.9700012 9 12 cm 1 0.801 0.801 rg 236.1 518.4 60.3 34.8 re f Q q 0.9700012 0 0 0.9700012 298.8363342 611.6352997 cm 0.004 0.004 0.004 RG 0.75 w 1 j 1 J 0 0 m 0 -157.8 l S Q q 0.9700012 0 0 0.9700012 9 12 cm 1 1 1 rg 330.48 459.48 237.18 209.88 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 0.801 1 1 rg 357.24 489.12 187.8 170.82 re f Q q 0.9700012 0 0 0.9700012 9 12 cm 0.504 0.504 0.504 RG 0.4 w 8 M 1 J 545.04 659.88 -187.8 -170.76 re 357.24 659.88 m h S Q q 0.9700012 0 0 0.9700012 355.5232086 652.1425476 cm 0.004 0.004 0.004 RG 0.06 w 1 j 1 J 0 0 m 0 -170.82 l -2.04 -170.82 m 0 -170.82 l -2.04 -146.52 m 0 -146.52 l -2.04 -121.8 m 0 -121.8 l -2.04 -97.56 m 0 -97.56 l -2.04 -73.26 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0.9700012 0 0 0.9700012 401.0938568 559.4880524 cm 0.004 0.004 1 rg 0 0 m 2.04 -2.04 l 0 -4.14 l -2.1 -2.04 l 0 0 l f* Q q 0.9700012 0 0 0.9700012 401.0938568 559.4880524 cm 0.004 0.004 1 RG 0.4 w 1 j 1 J 0 0 m 2.04 -2.04 l 0 -4.14 l -2.1 -2.04 l 0 0 l h S Q q 0.9700012 0 0 0.9700012 403.8874664 570.3132629 cm 0.004 0.004 1 rg 0 0 m 2.04 -2.1 l 0 -4.2 l -2.04 -2.1 l 0 0 l f* Q q 0.9700012 0 0 0.9700012 403.8874664 570.3132629 cm 0.004 0.004 1 RG 0.4 w 1 j 1 J 0 0 m 2.04 -2.1 l 0 -4.2 l -2.04 -2.1 l 0 0 l h S Q q 0.9700012 0 0 0.9700012 375.1366272 502.801178 cm 0.004 0.004 1 rg 0 0 m 2.04 -2.1 l 0 -4.14 l -2.04 -2.1 l 0 0 l f* Q q 0.9700012 0 0 0.9700012 375.1366272 502.801178 cm 0.004 0.004 1 RG 0.4 w 1 j 1 J 0 0 m 2.04 -2.1 l 0 -4.14 l -2.04 -2.1 l 0 0 l h S Q q 0.9700012 0 0 0.9700012 387.8824463 570.3132629 cm 0.004 0.004 1 rg 0 0 m 2.04 -2.1 l 0 -4.2 l -2.04 -2.1 l 0 0 l f* Q q 0.9700012 0 0 0.9700012 387.8824463 570.3132629 cm 0.004 0.004 1 RG 0.4 w 1 j 1 J 0 0 m 2.04 -2.1 l 0 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However, in term)12(s )6(of)]TJ 0.0012 Tc 0.2707 Tw 12.359 0 Td ( the acceleration factor \(AF\), )Tj -0.0004 Tc 0.0204 Tw -12.359 -1.168 Td [(w)-4(h)-4(ich)-4( is th)-4(e ratio)-4( o)-4(f)-3( th)-4(e lifetim)10(e in)-4( field)-4( an)-4(d)-4( )6(test, )6(th)-4(o)-4(s)-1(e )6(effects )]TJ 0.0011 Tc 0.0009 Tw T* (are cancelled out. )Tj -0.0003 Tc 0.0443 Tw 1.44 -1.27 Td [(Th)-4(e FEA)-4( b)-4(ased)-4( A)-4(F)-2( resu)-4(lts o)-4(f)-3(ten)-4( p)-4(r)-3(ed)-4(ict )6(th)-4(at )6(th)-4(e )6(g)-4(eo)-4(m)10(etry )]TJ 0.002 Tc 0.198 Tw -1.44 -1.168 Td [(or m)12(a)2(t)4(e)2(ri)4(al)4( propert)4(i)4(e)2(s effect)4(s are not)4( cancel)4(l)4(e)2(d out)4(. It)4( )6(has )]TJ 0.0022 Tc 0.0658 Tw T* [(been )-6(not)4(ed )-6(t)4(h)-2(at)4( t)4(h)-2(e current)4( FEA does not)4( t)4(a)2(ke consi)4(d)-2(erat)4(i)4(ons )]TJ -0.0003 Tc 0.1523 Tw T* [(o)-4(f)-3( )-6(th)-4(e )-6(so)-4(ld)-4(er )-6(so)-4(ften)-4(in)-4(g)-4( o)-4(r)-3( ag)-4(in)-4(g)-4( effect in)-4(to)-4( sim)10(u)-4(latio)-4(n)-4(.)-2( Th)-4(is )]TJ 0.0022 Tc 0.2937 Tw T* [(m)12(i)4(ght)4( be one of reasons t)4(h)-2(at)4( )6(t)4(h)-2(e )6(di)4(screpancy)4( )6(usi)4(n)-2(g )6(FEA )]TJ -0.0099 Tc 0.0119 Tw T* [(c)-10(o)-14(me)-10(s)-11( f)-13(r)-13(o)-14(m.)-12( )]TJ 0.0021 Tc 0.2578 Tw 1.44 -1.27 Td [(It)4( )-6(has )-6(been )-6(debat)4(e)2(d )-6(whet)4(her or not)4( a sat)4(u)-2(rat)4(i)4(o)-2(n effect)4( )]TJ 0.0016 Tc 0.1864 Tw -1.44 -1.168 Td (needs to be considered for th)Tj 0.0011 Tc 0.1869 Tw 12.509 0 Td [(e frequency term)11( since solder )]TJ -0.0009 Tc 0.1349 Tw -12.509 -1.168 Td [(j)-5(o)-5(in)-5(t d)-5(a)-1(m)9(a)-1(g)-5(e)-1( in)-5( a certain)-5( )6(th)-5(er)]TJ 0.0007 Tc 0.1273 Tw 12.371 0 Td [(m)11(a)1(l cycle \221saturates\222 when the )]TJ 0.0012 Tc 0.0728 Tw -12.371 -1.168 Td [(joint reaches a point where the )-4(m)11(a)1(jority of the )6(relaxation )6(has )]TJ 0.0022 Tc 0.0478 Tw T* [(occurred. )-6(In )-6(our t)4(e)2(st)4(, we have desi)4(gned a coupl)4(e of t)4(e)2(st)4(s wi)4(t)4(h)-2( )]TJ 0.0018 Tc 0.0842 Tw T* [(ext)4(e)2(nded )-6(cy)4(cl)4(e )-6(t)4(i)4(m)12(e t)4(o)-2( m)12(a)2(ke sure t)4(h)-2(at)4( t)4(h)-2(e proposed m)12(odel)4( i)4(s)1( )]TJ T* [(cal)4(i)4(b)-2(rat)4(e)2(d )-6(t)4(o)-2( )-6(i)4(n)-2(cl)4(ude )-6(t)4(h)-2(e )-6(l)4(ong cy)4(cl)4(e t)4(i)4(m)12(e effect)4(. It)4( has shown )]TJ -0.0003 Tc 0.1463 Tw T* [(th)-4(at, sim)10(ilar to)-4( th)-4(e Sn)-4(Pb)-4( assem)10(b)-4(ly, th)-4(e )6(SA)-4(C )6(w)-4(ill )6(ev)-4(en)-4(tu)-4(ally )]TJ 0.001 Tc 0.001 Tw T* [(reach to a point where the stress is com)11(p)-3(letely relaxed. )]TJ 0.0021 Tc 0.2578 Tw 1.44 -1.27 Td [(The paper al)4(so exam)12(i)4(n)-2(ed t)4(h)-2(e AF )6(predi)4(c)2(t)4(i)4(ons )6(based )6(on )]TJ 0.0025 Tc 0.4614 Tw -1.44 -1.168 Td [(fi)4(ni)4(t)4(e)2( el)4(em)12(ent)4( anal)4(y)5(s)2(i)4(s)2(. Al)4(t)4(hough vari)4(ous )6(exi)4(s)2(t)4(i)4(ng )6(fi)4(ni)4(t)4(e)2( )]TJ 0.0956 Tw T* [(el)4(em)12(ent)4( m)12(odel)4(s)2( were supposed t)4(o)-1( gi)4(ve )6(a )6(good )6(predi)4(c)2(t)4(i)4(o)-2(n )6(for )]TJ -0.0003 Tc 0.0383 Tw T* [(certain)-4( typ)-4(es o)-4(f)-3( p)-4(ack)-4(ag)-4(es an)-4(d)-4( certain)-4( test co)-4(n)-4(d)-4(itio)-4(n)-4(s)-1(, th)-4(e )6(FEA)-4( )]TJ 0.0026 Tc 0.1794 Tw T* [(resul)5(t)5(s)2( )-6(showed )-6(poor )-6(predi)5(c)3(t)5(i)5(on t)5(o)-1( ot)5(her dat)5(a)3( when package )]TJ 0.0014 Tc 0.0546 Tw T* [(form)11(at and accelerated )6(conditions)]TJ 0.0018 Tc 0.0482 Tw 13.709 0 Td ( change. One of the reasons )Tj -0.0006 Tc 0.0086 Tw -13.709 -1.168 Td [(th)-4(at FEA)-4( m)9(o)-4(d)-4(e)-1(ls d)-4(i)1(d)-4( n)-4(o)-4(t)1( p)-4(r)-4(ed)-4(ict w)-4(e)-1(ll is )6(th)-4(at )6(th)-4(e )6(m)9(a)-1(terial )6(ag)-4(in)-4(g)-4( )]TJ 0.0025 Tc 0.3114 Tw T* [(effect)4( i)4(s)2( not)4( t)4(a)2(ken i)4(n)-1(t)4(o)-1( cons)]TJ 0.0013 Tc 0.3066 Tw 12.623 0 Td [(ideration )-6(in current lead-free )]TJ -0.0003 Tc 0.2183 Tw -12.623 -1.168 Td [(m)10(o)-4(d)-4(els in)-4( FEA)-4( im)10(p)-4(l)2(em)10(en)-4(tatio)-4(n)-4(.)-2( H)-4(o)-4(w)-4(ev)-4(er, )6(FEA)-4( )6(an)-4(alysis )6(is )]TJ -0.0001 Tc 0.0561 Tw T* [(efficien)-4(t in)-4( p)-4(r)-3(ed)-4(ictin)-4(g)-4( th)-4(e w)-4(o)-4(rst-case an)-4(d)-4( q)-4(u)-4(alitativ)-4(e tren)-4(d)-4( )6(fo)-4(r )]TJ 0.0017 Tc 0.0243 Tw T* [(a given fam)12(ily of packages unde)]TJ 0.0013 Tc 0.0247 Tw 13.127 0 Td [(r sam)11(e)1( test conditions. Future )]TJ 0 Tc 0.038 Tw 13.367 66.174 Td [(effo)-4(rt )-6(w)-4(ill )-6(b)-4(e fo)-4(cu)-4(sed)-4( o)-4(n)-4( co)-4(m)10(b)-4(in)-4(in)-4(g)-4( th)-4(e FEA)-4( m)10(o)-4(d)-4(el ap)-4(p)-4(r)-3(o)-4(ach)-4( )]TJ -0.0002 Tc 0.0022 Tw T* [(w)-4(ith)-4( th)-4(e em)10(p)-4(i)2(rical m)10(o)-4(d)-4(el ap)-4(p)-4(r)-3(o)-4(ach)-4( to)-4( assess LF reliab)-4(ility )]TJ /TT3 1 Tf 0.0022 Tc -0.0002 Tw 0 -1.886 TD [(7. Concl)4(usi)4(on )]TJ /TT2 1 Tf 0.0023 Tc 0.1317 Tw 1.44 -1.258 Td [(In t)4(h)-2(i)4(s)2( paper a new set)4( of )]TJ 0.0025 Tc 0.1315 Tw 11.273 0 Td [(AF m)12(odel)4( const)4(a)2(nt)4(s based on )]TJ 0.0023 Tc 0.4856 Tw -12.713 -1.168 Td [(t)4(h)-2(e )-6(Norri)4(s-Landzberg )-6(equat)4(i)4(on has been proposed. The )]TJ 0.0019 Tc 0.0721 Tw 0 -1.168 TD [(proposed )-6(m)12(odel)4( )-6(has been val)4(i)4(d)-2(at)4(ed usi)4(ng t)4(h)-2(erm)12(a)2(l)4( cy)4(cl)4(e t)4(e)2(st)4(s. )]TJ 0.0011 Tc 0.1389 Tw T* [(The therm)11(a)1(l cycling )6(experim)11(e)1(nt)]TJ 0.0016 Tc 0.1324 Tw 13.217 0 Td [(al data from)12( various sources )]TJ -0.0003 Tc 0.2662 Tw -13.217 -1.168 Td [(w)-4(ith)-4( v)-4(ario)-4(u)-4(s typ)-4(es o)-4(f)-3( p)-4(ack)-4(ag)]TJ 0.0015 Tc 0.2644 Tw 12.599 0 Td (es, such as FCBGA, CBGA, )Tj 0.0017 Tc 0.0423 Tw -12.599 -1.168 Td (CSP, QFP, socket, and die-side)Tj 0.0015 Tc 0.0425 Tw 12.743 0 Td [( capacitor packages have )6(been )]TJ 0 Tc 0.3379 Tw -12.743 -1.168 Td [(u)-4(s)-1(ed)-4( )-6(fo)-4(r d)-4(eterm)10(in)-4(in)-4(g)-4( th)-4(e m)10(o)-4(d)-4(el fit. Th)-4(e tem)10(p)-4( cycle test )]TJ 0.0022 Tc 0.2757 Tw T* [(condi)4(t)4(i)4(ons have a wi)4(de spread, wi)4(t)4(h)-2( di)4(fferent)4( t)4(e)2(m)12(p)-2(erat)4(ure )]TJ -0.0099 Tc 0.3118 Tw T* [(r)-13(a)-10(n)-14(g)-14(e)-10(,)-12( d)-14(i)-8(f)-13(f)-13(e)-10(r)-13(e)-10(n)-14(t)-8( ma)-10(x)-14(i)-8(mu)-14(m t)-8(e)-10(mp)]TJ 0.0011 Tc 0.2948 Tw 13.619 0 Td (erature and different cycle )Tj -0.0002 Tc 0.0622 Tw -13.619 -1.168 Td [(tim)10(e, in)-4( p)-4(articu)-4(l)2(ar, th)-4(e cycle tim)10(e ran)-4(g)-4(in)-4(g)-4( fro)-4(m)10( 1)-4(5)-4( )6(m)10(i)2(n)-4(u)-4(tes )6(to)-4( )]TJ 0.0026 Tc 0.0054 Tw T* [(480 )-6(m)13(i)5(nut)5(es. )-6(The )-6(m)13(odel)5( )-6(fi)5(t)5( t)5(o)-1( experi)5(m)13(e)3(nt)5(al)5( dat)5(a)3( was excel)5(l)5(e)3(nt)5( )]TJ 0.0006 Tc 0.0434 Tw T* [(an)-3(d)-3( )-6(th)-3(e )-6(erro)-3(r w)-3(a)1(s less th)-3(an)-3( 6)-3(%. Th)]TJ 0.0433 Tw 14.195 0 Td (is analysis showed that the )Tj 0.0013 Tc 0.5106 Tw -14.195 -1.168 Td [(LF acceleration factor )6(\(AF\) )]TJ 0.0006 Tc 0.5053 Tw 13.337 0 Td [(m)11(odel is not significantly )]TJ 0.0027 Tc 0.0533 Tw -13.337 -1.168 Td [(di)5(fferent)5( from)13( t)5(h)-1(e Sn/)5(P)1(b m)13(odel)5( and proposed )6(m)13(odel)5( )6(provi)5(d)-1(es )]TJ -0.0001 Tc 0.0021 Tw T* [(th)-4(e b)-4(est fit to)-4( th)-4(e ex)-4(p)-4(erim)10(en)-4(t)2(al resu)-4(lts. )]TJ /TT3 1 Tf 0.0013 Tc 0 Tw 0 -1.784 TD (Acknowledgments )Tj /TT2 1 Tf 0.0025 Tc 0.0055 Tw 1.44 -1.258 Td [(The aut)4(hors woul)4(d l)4(i)4(k)-1(e t)4(o)-1( )6(acknowl)4(edge )6(t)4(h)-1(e )6(fol)4(l)4(o)-1(wi)4(ng )6(Int)4(e)2(l)4( )]TJ 0.0027 Tc 0.0653 Tw -1.44 -1.168 Td [(peopl)5(e for t)5(h)-1(ei)5(r cont)5(ri)5(but)5(i)5(ons and support)5( )6(t)5(o)-1(wards )6(t)5(h)-1(i)5(s)2( )6(st)5(udy)5(:)5( )]TJ 0.0032 Tc 0.0048 Tw 0 -1.168 TD [(Dave Young, Eri)5(c)3( M)5(onroe, Al)5(an)]TJ 0.0028 Tc 0.0052 Tw 13.193 0 Td [( Lucero and )6(Ni)5(ck )6(M)4(e)3(nci)5(nger. )]TJ 0.0026 Tc 0.0774 Tw -13.193 -1.168 Td [(The aut)5(hors woul)5(d l)5(i)5(k)-1(e t)5(o)-1( t)5(h)-1(ank Gregory)5( Henshal)5(l)5( of HP for )]TJ 0.0016 Tc 0.0004 Tw T* [(his valuable feed back and com)12(m)12(e)2(nts)]TJ 1 0 0 rg 0 Tc 0 Tw 14.998 0 Td ( )Tj 0 0 0 rg /TT3 1 Tf 0.001 Tc -14.998 -1.886 Td (References )Tj /TT2 1 Tf 0.0039 Tc 0 -1.156 TD (1.)Tj /TT0 1 Tf 0 Tc 0.756 0 Td ( )Tj /TT2 1 Tf 0.0025 Tc 0.0835 Tw 1.044 0 Td (Vasudevan, Vasu, Fan, Xuejun;)Tj 0.0775 Tw 13.037 0 Td [( Li)4(u Tao, Young, Dave, )]TJ 0.0015 Tc 0.1445 Tw -13.037 -1.168 Td [(\223Slow cycle fatigue creep perform)11(ance of )6(Pb-Free )6(\(LF\) )]TJ 0.0017 Tc 0.5162 Tw 0 -1.168 TD (solders\224, Proceedings - El)Tj 0.0016 Tc 0.5163 Tw 11.975 0 Td [(ectronic Com)12(p)-2(onents and )]TJ 0.0019 Tc 0.24 Tw -11.975 -1.168 Td [(Technology Conference, )6(Pro)]TJ 0.0014 Tc 0.2345 Tw 12.047 0 Td (ceedings - 57th Electronic )Tj 0.0023 Tc 0.2456 Tw -12.047 -1.168 Td [(Com)12(ponent)4(s )-6(and Technol)4(ogy)4( Conference 2007, ECTC )]TJ 0.0035 Tc -0.0015 Tw T* [(')10(07, 2007, p 116-123 )]TJ 0.0039 Tc 0 Tw -1.8 -1.168 Td (2.)Tj /TT0 1 Tf 0 Tc 0.756 0 Td ( )Tj /TT2 1 Tf -0.0006 Tc 0.0326 Tw 1.044 0 Td [(Pard)-4(eep)-4( )-6(K)-4(.)-3( )-6(Bh)-4(atti; )-6(Min)-4( Pei; an)-4(d)-4( X)-4(u)-4(ej)-5(u)-4(n)-4( Fan)-4(,)-3( \223Reliab)-5(ility )]TJ 0 Tc 0.128 Tw T* [(an)-4(alysis o)-4(f)-3( Sn)-4(Pb)-4( an)-4(d)-4( Sn)-4(A)-4(g)-4(Cu)-4( so)-4(ld)-4(er j)-4(o)-4(in)-4(ts )6(in)-4( )6(FC-BG)-4(A)-4( )]TJ 0.001 Tc 0.8349 Tw T* [(packages with therm)11(a)1(l )]TJ 0.0017 Tc 0.8282 Tw 11.759 0 Td (enabling preload\224, IEEE )Tj 0.0021 Tc 0.5518 Tw -11.759 -1.168 Td [(El)4(ect)4(roni)4(c Com)12(ponent)4(s and )6(Technol)4(o)-2(gy)4( )6(Conference )]TJ 0.0024 Tc -0.0004 Tw T* [(\(ECTC\), 2006, M)4(a)2(y)5( 30 - June 2, San Di)4(ego, CA )]TJ 0.0039 Tc 0 Tw -1.8 -1.168 Td (3.)Tj /TT0 1 Tf 0 Tc 0.756 0 Td ( )Tj /TT2 1 Tf 0.0021 Tc 0.2578 Tw 1.044 0 Td [(Xuejun Fan;)4( G. Rasi)4(er;)4( V. S. Vasudevan, \223Effect)4(s )6(of )]TJ -0.0001 Tc 0.0921 Tw T* [(D)-4(w)-4(ell Tim)10(e an)-4(d)-4( Ram)10(p)-4( Rate o)-4(n)-4( Lead)-4(\254Free )6(So)-4(ld)-4(er )6(Jo)-4(in)-4(ts )]TJ 0.0015 Tc 0.0665 Tw T* [(in FCBGA Packages\224, IEEE Electronic Com)11(ponents )6(and )]TJ 0.0021 Tc 0.2339 Tw T* (Technology Conference, 2005.)Tj 0.0018 Tc 0.2281 Tw 12.911 0 Td [( )-6(ECTC ')8(05 Proceedings, )]TJ 0.003 Tc -0.001 Tw -12.911 -1.168 Td [(M)4(a)3(y)5( 31-June 3, 2005 Page\(s\):)5(901 - 906 )]TJ 0.0039 Tc 0 Tw -1.8 -1.168 Td (4.)Tj /TT0 1 Tf 0 Tc 0.756 0 Td ( )Tj /TT2 1 Tf 0.0002 Tc 0.5237 Tw 1.044 0 Td [(Min)-4( Pei, X)-4(u)-4(ej)-4(u)-4(n)-4(,)-2( Fan)-4(;)2( Bh)-4(atti, )6(Pard)-4(eep)-4( )6(K)-4(., )6(\223Field)-4( )]TJ 0.0001 Tc 0.2358 Tw T* [(co)-4(n)-4(d)-4(itio)-4(n)-4( )-6(reliab)-4(ility )-6(assessm)10(en)-4(t fo)-4(r Sn)-4(Pb)-4( an)-4(d)-4( Sn)-4(A)-4(g)-4(Cu)-4( )]TJ -0.0006 Tc 0.2545 Tw T* [(so)-4(ld)-4(er j)-5(o)-4(in)-4(ts in)-4( p)-4(o)-4(w)-4(er cyclin)]TJ 0.0013 Tc 0.2526 Tw 12.437 0 Td [(g including m)11(i)3(ni )6(cycles\224, )252( )]TJ 0.2647 Tw -12.437 -1.168 Td [(Proceedings )-6(- Electronic Co)]TJ 0.002 Tc 0.2639 Tw [(m)12(ponents and Technology )]TJ 0.0018 Tc 0.0722 Tw T* [(Conference, )-6(v )-6(2006, )-6(Proceedings - IEEE 56th Electronic )]TJ 0.0027 Tc 0.1553 Tw T* [(Com)13(ponent)5(s and Technol)5(ogy)5( Conference, 2006, p 899-)]TJ 0.0039 Tc 0 Tw T* (905 )Tj -1.8 -1.168 Td (5.)Tj /TT0 1 Tf 0 Tc 0.756 0 Td ( )Tj /TT2 1 Tf 0.0023 Tc 0.1137 Tw 1.044 0 Td [(G.Q. Zhang, W)-8(.D. van Dri)4(e)2(l)4(, and X.J. Fan, )6(\223M)4(echani)4(c)2(s )]TJ 0.0014 Tc 0.0006 Tw T* (of Microelectronics\224, Springer, May 2006 )Tj 0.0039 Tc 0 Tw -1.8 -1.168 Td (6.)Tj /TT0 1 Tf 0 Tc 0.756 0 Td ( )Tj /TT2 1 Tf 0.0017 Tc 0.2942 Tw 1.044 0 Td [(N. Pan et al, \223An Acceleration Model for )6(Sn-Ag-Cu )]TJ 0.0008 Tc 0.0012 Tw T* (Solder Joint Reliability unde)Tj 0.001 Tc 0.001 Tw 11.495 0 Td [(r Various Therm)11(a)1(l Cycle )]TJ 0.0027 Tc -0.0007 Tw -7.895 -1.168 Td [(Condi)5(t)5(i)5(ons\224, Proc. SM)4(TA, 2005, pp. 876-883 )]TJ 0.0039 Tc 0 Tw -5.399 -1.27 Td (7.)Tj /TT0 1 Tf 0 Tc 0.756 0 Td ( )Tj /TT2 1 Tf -0.0001 Tc 0.0081 Tw 1.044 0 Td [(Ro)-4(n)-4( Zh)-4(an)-4(g)-4(,)-2( Jean)-4(-Pau)-4(l Clech)-4(, A)-4(p)-4(p)-4(licab)-4(ility o)-4(f)-3( v)-4(ario)-4(u)-4(s )6(Pb)-4(-)]TJ 0.0011 Tc 0.0009 Tw T* (free solder joint acceleration )Tj 0.002 Tc 0 Tw 11.699 0 Td [(factor m)12(odels, SMTA, 2006 )]TJ ET Q BT /GS1 gs /TT4 1 Tf 10 0 0 10 298.5 40.29 Tm (144)Tj /TT5 1 Tf 2.704 0 Td (2008 Electronic Components and Technology Conference)Tj ET endstream endobj 973 0 obj <>stream HB)P-]dd-=W2Bvt:wvl6kZ-b1gt:L&x4 `{^t:vj5FQkZRx/bP(l6dt*J$x<Ep8 z///nt>??vfZfd2A=>>jZZRJ\.dRT,D"@\.ùcXL&`t*JPd2D"`X FQ(D p8APA ,J\.LF"P(-ӓ^h4D(lժq\CPx<؟,I endstream endobj 974 0 obj <>stream HZjQPR:*](```w`a"*]ٱ6[857g|<O\P$T*˓JJhEJJuU:C}Ccdtvu  [GFmvsl5195{}+k[;{G@0xv~ ዋ >ƖƦ@ol`5n:"vg};It=-F؀Bَ([e#Dlb&m*V@J5ikߑ iHȵ!16&Ho6&l516K붇 ߍ`s6w3 ~KI al/6aMj+'lzՁl-`3![_|}ml^-m;[036^Fynil:]+p )\A L -BNRxbIc%d(SY!lf* M[2&d L%q&wʤ-Ld,[olTM*4a*R!Oc4SZņEZFmmY˴ LKFԴ LJKlJ%.Vʑ-ᐩBDziqikƲ饡RmfPi[ailu`S6L2mkmi666N35گv68Z87L2XXzV \gsܘMm`384}1 R%>d3LwCB06:bz#.:{d{#S#S#e|G6 2H0ld~LP d:;!m.9춤L`sOOM&$lxd[=i̷ yy'HLWWb϶˴deyFA;/@[l `%ݝm)`c[R"Sw63=9ai pJ؎6,2= 퐶i&md4O^dz~ endstream endobj 975 0 obj [722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 250 333 408 500 500 833 778 180 333 333 500 564 250 333 250 278 500 500 500 500 500 500 500 500 500 500 278 278 564 564 564 444 921 722 667 667 722 611 556 722 722 333 389 722 611 889 722 722 556 722 667 556 611 722 722 944 722 722 611 333 278 333 469 500 333 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 480 200 480 541 350 744 350 333 500 444 1000 500 500 333 1000 556 333 889 350 611 350 350 333 333 444 444 350 500 1000 333 980 389 333 722 350 444 722 250 333 500 500 744 500 200 500 333 760 276 500 564 333 760 333 400 549 300 300 333 576 453 250 333 300 310 500 750 750 750 444 722 722 722 722 722 722 889 667 611 611 611 611 333 333 333 333 722 722 722 722 722 722 722 564 722 722 722 722 722 722 556 500 444 444 444 444 444 444 667 444 444 444 444 444 278 278 278 278 500 500 500 500 500 500 500 549 500 500 500 500 500 500 500 500] endobj 976 0 obj [722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 722 250 333 408 500 500 833 778 180 333 333 500 564 250 333 250 278 500 500 500 500 500 500 500 500 500 500 278 278 564 564 564 444 921 722 667 667 722 611 556 722 722 333 389 722 611 889 722 722 556 722 667 556 611 722 722 944 722 722 611 333 278 333 469 500 333 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 480 200 480 541 350 744 350 333 500 444 1000 500 500 333 1000 556 333 889 350 611 350 350 333 333 444 444 350 500 1000 333 980 389 333 722 350 444 722 250 333 500 500 744 500 200 500 333 760 276 500 564 333 760 333 400 549 300 300 333 576 453 250 333 300 310 500 750 750 750 444 722 722 722 722 722 722 889 667 611 611 611 611 333 333 333 333 722 722 722 722 722 722 722 564 722 722 722 722 722 722 556 500 444 444 444 444 444 444 667 444 444 444 444 444 278 278 278 278 500 500 500 500 500 500 500 549 500 500 500 500 500 500 500 500] endobj 977 0 obj <>/ProcSet[/PDF/Text]/ExtGState<>>>/Type/Page>> endobj 978 0 obj <>stream q 0.9700012 0 0 0.9700012 9 12 cm 0 0 m 612 0 l 612 792 l 0 792 l 0 0 l W n 1.0309265 0 0 1.0309265 -9.2783388 -12.3711185 cm BT 0 0 0 rg /GS0 gs /TT0 1 Tf 0.0039 Tc 9.701 0 0 9.7194 55.7928 725.0083 Tm (8.)Tj /TT1 1 Tf 0 Tc 0.756 0 Td ( )Tj /TT0 1 Tf -0.0004 Tc 0.0924 Tw 1.044 0 Td [(O)-4(.)-2( Salm)10(ela et al, \223Reliab)-4(ility A)-4(n)-4(alysis o)-4(f)-3( )6(So)-4(m)10(e )6(Ceram)10(i)2(c )]TJ 0.0016 Tc 0.3303 Tw 0 -1.168 TD [(Lead-free Solder Attachm)12(e)2(nt)7(s\224, Proc. 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