卒業論文

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1 Cu-Ru

2 () () Cu z <111> misfit misfit Cu z <011> Cu <001> Cu

3

4 Fig Fig Fig Fig Fig Fig.2.6 step Fig.2.7 fcchcp Fig.2.8 z <111> Cu Fig.2.9 z <011> Cu z <001> Cu Fig Cu z <111> Fig Cu z <111> Fig step Fig3.1.4 zeffective strain rate Fig Cu z <111> Fig Cu z <111> 24 Fig Cu z <111> σ step Fig Cu z <111> Fig Cu z <111> step Fig Cu z <111> Fig Custrain rate Fig Cu z <111> Fig Cu z <111> Fig Cu z <111> τ step Fig misfit Fig misfit Fig misfit σ step Fig misfit step z z - - 4

5 Fig misfit Fig misfit τ step Fig Cu z <111> misfit step Fig Cu z <111> misfit Fig Cu z <111> misfit step Fig Cu <111> Fig Cu z <011> Fig Cu z <011> 52 Fig Cu z <011> σ step Fig Cu z <011> 55 Fig Cu z <011> τ step Fig Cu z <001> Fig Cu z <001>. 61 Fig Cu z <111> σ step Fig Cu z <001>. 64 Fig Cu z <001> τ step Fig Cu z <111> <011> <001> σ step Fig Cu z <111> <011> <001> z z z τ σ τ z step

6 Table.2.1 GEAM Cu Ru 10 Table.3.1 Cu z <111> misfit..42 Table.3.2 Cu Ru γ sf γ us...46 Table.3.3 GEAM..47 Table.3.4 Cu z <111> <011> <001>

7 Cu-Ru 1.1. Cu-Ru Ru Cu [1] [2] Ru GEAM GEAM FEM BEM [3] - - 7

8 Cu-Ru

9 N N N 2~5 Book-keeping Verlet GEAM johnson FS - - 9

10 GeneralizedEAM GEAM [4] GEAM fcc bcc hcp Cu/Ru Table.2.1 GEAM 0 Cu Ru misfit Ru misfit a c E ev/atom B [GPa] [GPa] Table.2.1 GEAM Cu Ru AtomEye AtomEye JPEG PNG EPS

11 [5] Fig.2.1 Wad = + material-connected state material-separated state Wad Fig.2.1 Material-connected state material-separated state

12 GEAM 0[K] step 1.08[fs] Verlet x,y z () material-connected state z Fig.2.2 Fig.2.3 GEAM x,y z 1[K] 1step 1.08[fs] z 5000step 5.4[ps] 3 3 Fig

13 Fig () Fig.2.4 Fig y x y z y 6.0[nm] z 0.65[nm]

14 Fig.2.4 Fig GEAM 1[K] 1step 1.08[fs] 5000step 5.4[ps] step 25,000step 27ps step Fig step100step 0.1[ps] 100step 0.1[ps] = [m/s]

15 Fig.2.6 step 2.2. misfit Cu misfit Cu misfit misfit Cu z:<111>, x:<10-1>, y:<-12-1>ru z:<0001>, x:<11-20>, y:<-1100> Cu fcc Ru hcp fcc hcp Fig.2.7 Cu z <111> Cu z Fig.2.7 Ru z Fig.2.7 misfit

16 Fig.2.8 Cu Fig.2.7 fcc hcp Fig.2.8 z <111> Cu misfit Cu Ru Cu misfit misfit misfit

17 misfit Ru GEAM Cu Ru misfit Cu Cu z:<110>, x:<001>, y:<-110> z:<001>, x:<100>, y:<010> Cu Fig.2.9 Cu Fig.2.9 z <011> Cu z <001> Cu

18 3.1. Cu z <111> Cu z <111> misfit Fig material-connected state Cu-Ru x=10.5nm y=18.2nm z=10.6nm 161,700 material-separated state Cu Cu x=10.5nm y=18.2nm z=6.3nm 100,860 Ru Ru x=10.5nm y=18.2nm z=4.3nm 60,840 Fig Cu z <111> Cu-Ru -760,091[eV] Cu -353,477[eV] Ru -401,200[eV] material-connected state material-separated state 5,414[eV] 4.56[J/m ]

19 Fig3.1.2 x=10.5nm y=18.2nm z=12.8nm 190,545 Fig Cu z <111> step Fig Fig3.1.3 real strain rate 100step(0.1[ps]) 100step(0.1[ps]) Fig3.1.3 effective strain rate effective strain rate σ effective strain rate Fig3.1.4 z

20 Fig step 1 effective strain rate [ s ] Fig3.1.4 z effective strain rate

21 effective strain ratezeffective strain rate z effective strain 8 1 rate s s Fig fcc hcp fcc hcp σ 17,000[MPa] z -3,000[MPa] Fig Cu/Ru misfit Cu Ru Cu misfit z Fig σ σ σ σ z z z z

22 5.4[ps] 15[ps] 29[ps] [Mpa]

23 30[ps] 31[ps] 40[ps] [Mpa] Fig Cu z <111>

24 Fig Cu Cu Ru Cu-Ru 5.4[ps] 30[ps] 43[ps] 70[ps] Fig Cu z <111> Fig σ step z σ z = [MPa] =1.78[%] step 27,000 40,000[step] σ z Cu

25 Fig Cu z <111> σ step z Ru Cu Cu 6 Fig Fig ,330 Fig step 200[step] 26,800[step] [MPa] 27,000[step] 40,000[step] Fig ,000[MPa] 0[MPa]

26 Fig Cu z <111> Fig Cu z <111> step

27 25,400[step] 26,200[step] 27,000[step] 27,800[step] 28,600[step] 29,400[step] 0 3,000[MPa] Fig Cu z <111>

28 Fig Fig σ 27,000[step] z Cu Cu <111> Fig Fig Cu [MPa] Fig [MPa] Fig Fig Fig [MPa] Fig Cu strain rate

29 Fig x=10.5nm y=18.2nm z=12.8nm 188,196 A B Fig Cu z <111> Fig Fig AB fcc hcp y τ 6,000[MPa] -3000[MPa] misfit misfit τ τ [ps] misfit Fig misfit 16[ps] τ 19[ps] misfit

30 τ 0[ps] 5.4[ps] 12[ps] [Mpa]

31 16[ps] 19[ps] 27[ps] [Mpa] Fig Cu z <111>

32 misfit misfit τ misfit Fig τ step τ τ Fig misfit 4.86[%] misfit Fig Cu z <111> τ step

33 3.2. misfit misfit misfit Ru Cu GEAM Ru material-connected state Cu/Ru x=10.5nm y=18.2nm z=10.6nm 171,462 material-separated state Cu Cu x=10.5nm y=18.2nm z=5.6nm 90,774 Ru Ru x=10.5nm y=18.2nm z=5.0nm 80,688 Cu z <111> Cu-Ru -858,586[eV] Cu -317,773[eV] Ru -534,463[eV] material-connected state material-separated state 6,350[ev] 5.35[J/m ]

34 x=10.5nm y=18.2nm z=12.5nm 200,121 Cu z <111> Fig Cu z <111> σ Cu z <111> Fig Cu/Ru misfit Ru Cu 15[ps] Cu z <111> Cu z <111> z Fig Cu z <111> Cu z <111> σ z Cu z <111> Cu z <111>

35 5.4[ps] 15[ps] 24[ps] [Mpa]

36 25[ps] 45[ps] 52[ps] [Mpa] Fig misfit

37 Fig Cu z <111> y z Cu Cu z <111> misfit Cu/Ru 5.4[ps] 30[ps] 50[ps] 70[ps] Fig misfit Fig σ step z σ z = [MPa] =1.38[%] Cu z <111> 50,000[step] σ z Cu

38 Fig misfit σ step z Ru Cu 6 Cu Cu z <111> 5,002 Fig step 200step 3 21,600[step] [MPa] 22,000[step]

39 Fig misfit step x=10.5nm y=18.2nm z=12.5nm 197,620 Cu z <111> misfit Cu z <111> Fig τ Cu z <111> Cu z <111> 27[ps] misfit τ

40 0[ps] 5.4[ps] 10[ps] 15[ps] 20[ps] 27[ps] [Mpa] Fig misfit

41 Fig τ step τ 5000step τ Fig Cu z <111> τ τ [MPa] 6 misfit τ Fig misfit τ step

42 3.2.4 misfit misfit Cu z <111> misfit Cu Ru Cu/Ru Cu z <111> 4.56[J/m ] misfit 5.35[J/m ] Cu z <111> misfit 15% Cu z <111> misfit Table.3.1 Cu z <111> σ 24% 29% misfit z Cu z <111> misfit σ z [MPa] [%] step , ,000 Table.3.1 Cu z <111> misfit Cu z <111> misfit Fig Cu z <111> misfit σ z step misfit

43 Fig Cu z <111> misfit step σ z misfit Cu z <111> Fig Cu z <111> misfit Cu z <111> 1.78[%] misfit 1.38[%] Fig misfit misfit misfit misfit

44 Fig Cu z <111> misfit Cu z <111> misfit τ step Fig step Model A B τ Cu z <111> τ Cu z <111> misfit 1/6 misfit

45 Fig Cu z <111> misfit τ step Ru Fig GEAM fcc γ sf γ us

46 Fig Cu <111> Table.3.2 GEAM Cu Ru [6] Cu Ru misfit Ru misfit <111> γ sf (mj/m ) 23 <111> γ us (mj/m ) 111 basal γ sf (mj/m ) basal γ us (mj/m ) prism prism γ sf (mj/m ) γ us (mj/m ) Table.3.2 Cu Ru γ sf γ us

47 Ru Cu misfit Table.4.2 Ru γ us misfit Cu Ru Cu Cu Table.3.3 GEAM [7] γ sf γ us γ sf GEAM γ us Table.3.3 GEAM GEAM γ sf γ us GEAM Cu Cu GEAM

48 3.3. Cu z <011> Cu Cu Cu z:<110>, x:<001>, y:<-110>cu material-connected state Cu/Ru x=10.5nm y=26.1nm z=12.7nm 273,024 material-separated state Cu Cu x=10.5nm y=26.1nm z=6.1nm 141,984 Ru Ru x=10.5nm y=26.1nm z=6.5nm 131,040 Cu z <111> Cu-Ru -1,373,094[eV] Cu -496,674[eV] Ru -870,486[eV] material-connected state material-separated state 5,394[ev] 3.48[J/m ] x=10.5nm y=26.1nm z=12.7nm 271,453 Cu z <111> Fig Cu z <111> σ 12,000[MPa] 0[MPa] z

49 5.4[ps] 15[ps] 41[ps] [Mpa]

50 42[ps] 43[ps] 45[ps] [Mpa] Fig Cu z <011>

51 Fig misfit Cu z <111> Cu z <111> misfit misfit misfit z Cu Cu z <111> misfit 43[ps] xz Cu Ru Cu z <111> misfit Cu z <111> misfit z

52 Fig Cu z <111> misfit Ru Cu Cu z <111> misfit y Cu 5.4[ps] 30[ps] 50[ps] 70[ps] Fig Cu z <011> Fig σ step z σ z 3 = [MPa] =1.85[%] Cu z <111> misfit σ z z

53 Fig Cu z <011> σ step z x=10.5nm y=21.6nm z=12.7nm 269,227 Cu z <111> misfit Fig Cu z <111> Fig AB fcc hcp y τ Cu z <111> misfit

54 0[ps] 5.4[ps] 15[ps] [Mpa]

55 27[ps] [Mpa] Fig Cu z <011> misfit τ Cu z <111> misfit Fig τ step τ τ [MPa] Cu z <111> 165[%] misfit 32[%] misfit

56 Fig Cu z <011> τ step

57 3.4. Cu <001> Cu Cu z:<001>, x:<100>, y:<010> material-connected state Cu/Ru x=10.5nm y=27.5nm z=12.7nm 287,932 material-separated state Cu Cu x=10.5nm y=27.5nm z=6.1nm 149,872 Ru Ru x=10.5nm y=26.1nm z=6.5nm 138,060 Cu <111> Cu-Ru -1,449,252[eV] Cu -524,924[eV] Ru -917,119[eV] material-connected state material-separated state 7,209[ev] 4.01[J/m ] x=10.5nm y=27.5nm z=12.7nm 286,362 Fig σ 17,000[MPa] -3,000[MPa] z

58 5.4[ps] 50[ps] 63[ps] [Mpa]

59 65[ps] 66[ps] 67[ps] [Mpa] Fig Cu z <001>

60 Fig misfit Cu <011> misfit misfit misfit z 65[ps] Cu <011> Cu Ru σ Cu <011> z Cu <011> z Fig Ru Cu Cu y Cu <011> Cu <001>

61 5.4[ps] 30[ps] 50[ps] 70[ps] Fig Cu z <001> Fig σ step z σ z 3 = [MPa] =3.81[%] 63[ps] step 60,000[step] Fig ,000[step]

62 Fig Cu z <111> σ step z x=10.5nm y=21.6nm z=12.7nm 269,227 Fig Cu z <111> Fig AB fcc hcp y τ Cu z <111> misfit Fig misfit misfit τ τ Fig [ps] misfit

63 0[ps] 5.4[ps] 15[ps] [Mpa]

64 27[ps] [Mpa] Fig Cu z <001> Fig τ step τ τ [MPa] Cu z <111> 118[%] misfit 23[%] misfit

65 Fig Cu z <001> τ step

66 Cu Cu Cu z <111> <011> <001> misfit Cu z <011> <001> 3 Cu z <111> 4.56[J/m ] Cu z <011> 3.48[J/m ] Cu z <001> 4.01[J/m ] <111><011> 24% <001> 12% <111><001><011> Table.3.3 σ z <111><011> 15% <001> 35%<111><011> 46% <001> 114% σ z [MPa] [%] step <111> ³ ,000 <011> ³ ,000 <001> ³ ,000 Table.3.4 Cu z <111> <011> <001> Fig Cu z <111> <011> <001> σ step <111><011><001> z

67 Fig Cu z <111> <011> <001> σ step z misfit Fig Fig Fig <111> misfit <011><001> misfit Fig Cu z <111> <011> <001> step <111> <011> <001> misfit 3,000[MPa] τ τ misfit

68 Fig Cu z <111> <011> <001> τ step misfit Cu misfit

69 Cu-Ru Cu-Ru Ru Cu Ru Ru 5 Cu Ru misfit Cu misfit misfit misfit misfit Cu

70 [1] Adhesion-Strength Calculation and Measurement Techniques for Interfaces between Nano-scale Thin Films Vol.14, No.4 ( ) pp [2] M&M2005 No ,20 [3] 1993 [4] X.W.ZHOU, H.N.G.WADLEY, R.A.JOHNSON ATOMIC SCALE STRUCTURE OF SPUTTERED METAL MULTILAYERS Acta mater. 49 (2001) p [5] T.Iwasaki Molecular dynamics study of adhesion strength and diffusion at interface between interconnect materials and underlay materials Computational Mechanics 25 (2000) p [6] The 19 th Computational Mechanics Conference No.06-9 p [7] N.Bernstein E.B.tadmor Tight-binding calculations of stacking energies and twinnability in fcc metals (2004)

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