Dislocation depletion in thin films

Transcript

1. Dynamics of confined defects in metals:
   Mechanistic insights from atomistics
   Kedarnath Kolluri, Rauf Gungor, Dimitrios Maroudas
   Acknowledgments:
   Mayur Valipa, Miguel Amat
   

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2. Outline
   •Motivation
   • Confined interconnects in semiconductor materials
   • Confined defects in pillars and nanowires
   •Mechanical behavior of free-standing copper thin films
   • stress-strain behavior of pre-strained thin films
   • Mechanisms that lead to the observed behavior
   •Comparing with other FCC metals
   • Comparison motivated by mechanistic understanding of
   copper thin films
   

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3. Confined metallic systems in semiconductors
   3D view of interconnects after
   removal of the ILD layers (www.ibm.com)
   Cross-sectional view of the dual
   damascene structure (www.ibm.com)
   Schematic of the strained SiGe
   p-channel heterostructure MOSFET
   Silicon Nanowire Transistor
   (NIST Illustration)
   

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4. Line defects in metals: Edge dislocation
   

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5. on top of one another in a fashion illustrated in Fig. A.6. Given a layer A,
   can be extended by stacking the next layer so that its atoms occupy B or
   A, B, and C refer to the three possible layer positions in a projection norm
   packed layers. The stacking sequence corresponding to an fc
   …ABCABCABCABC…, while that for a hcp crystal is …ABABABABA
   partial dislocation is created in a fcc crystal, the fcc stacking sequence
   hcp stacking sequence; the stacking sequence in the crystal with a stackin
   …ABCABCACABCABC….
   6. Given a layer A, close packing
   atoms occupy B or C sites. Here
   a projection normal to the close-
   onding to an fcc crystal is
   is …ABABABABA…. When a
   tacking sequence changes to the
   ystal with a stacking fault can be
   Line defects in metals: Stacking faults
   Theory of Dislocations, Hirth & Lothe
   

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6. single crystal pillars were an
   remaining defects. Figure
   aforementioned samples a
   samples and a comparison t
   to the theoretical shear stren
   All data points represent the
   geneously during compressio
   2͑b͒.
   It is clear from the grap
   which were never subjected
   flow stresses higher than bul
   rise in strength as the diamet
   Ga+ removal and pretest-ann
   on the curve formed by the F
   believe that observed size e
   fabrication technique. Whil
   image of a compressed pillar after deformation. Slip lines in multiple orientations are clearly present
   change.
   Mechanical behavior of bulk
   J. Greer et al. Phys. Rev.
   B. 73, 245410 (2006)
   R. Madec et al., Phys. Rev. Lett. 89, 255508 (2002)
   http://www.geol.ucsb.edu
   Au
   

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7. Mechanical response is confined systems is different
   single crystal pillars were annealed at 300 °C to remo
   remaining defects. Figure 4 presents flow stresses
   aforementioned samples as well as the FIB-fab
   samples and a comparison to the axial stress corresp
   to the theoretical shear strength calculated by Ogata
   All data points represent the pillars which deformed
   geneously during compression testing, as can be seen
   2͑b͒.
   It is clear from the graph that the electroplated
   which were never subjected to the Ga+ ions, not onl
   flow stresses higher than bulk gold but also exhibit a
   rise in strength as the diameter is reduced. It is also cle
   Ga+ removal and pretest-annealing resulted in data th
   on the curve formed by the FIB pillars. This result lead
   believe that observed size effect is not linked to a s
   fabrication technique. While some minimal Ga+ mi
   image of a compressed pillar after deformation. Slip lines in multiple orientations are clearly present and indicate a homogeneou
   change.
   Au
   single crystal pillars were annealed at 300 °C to r
   remaining defects. Figure 4 presents flow stre
   aforementioned samples as well as the FIB
   samples and a comparison to the axial stress cor
   to the theoretical shear strength calculated by Og
   All data points represent the pillars which defor
   geneously during compression testing, as can be s
   2͑b͒.
   It is clear from the graph that the electropla
   which were never subjected to the Ga+ ions, no
   flow stresses higher than bulk gold but also exhib
   rise in strength as the diameter is reduced. It is als
   Ga+ removal and pretest-annealing resulted in da
   on the curve formed by the FIB pillars. This result
   believe that observed size effect is not linked to
   fabrication technique. While some minimal Ga
   formation. Stress-strain curves of FIB pillars whose diam-
   eters range between 290 nm and 7450 nm as well as the
   strength of bulk gold at 2% strain are presented in Fig. 2͑a͒.
   Uniaxial loading in the ͗001͘ direction, chosen for our ex-
   periments and corresponding to a high-symmetry orientation,
   ¯
   FIG. 1. ͑a͒ A representative ͗001͘-oriented gold pillar machined
   in the FIB. Pillar diameter=290 nm, pillar height=1.2 ␮m. ͑b͒ A
   large pillar ͑7.45 ␮m diameter͒ and a small pillar ͑250 nm
   diameter͒.
   J. Greer et al. Phys. Rev. B. 73, 245410 (2006)
   Au
   

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8. Mechanical behavior of a Ni nano-pillar
   ETTERS
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   Test 1
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   200 nm
   g = [111]
   ZA = [110]
   [111]
   200 nm 200 nm
   ure 1 Two consecutive in situ TEM compression tests on a FIB microfabricated 160-nm-top-diameter Ni pillar with 111⇥ orientation. a, Dark-field TEM image
   pillar before the tests; note the high initial dislocation density. b, Dark-field TEM image of the same pillar after the first test; the pillar is now free of dislocations.
   Z. Shan et al., Nature Materials 7, 115 (2007)
   

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9. Outline
   •Motivation
   • Confined interconnects in semiconductor materials
   • Confined defects in pillars and nanowires
   •Mechanical behavior of free-standing copper thin films
   • stress-strain behavior of pre-strained thin films
   • Mechanisms that lead to the observed behavior
   •Comparing with other FCC metals
   • Comparison motivated by mechanistic understanding of
   copper thin films
   

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10. Free-standing film as a model for confined metals
    x
    xx
    εxx
    εyy
    z
    y
    εyy
    

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11. How its done
    • Analysis based on constant strain and dynamic deformation
    molecular-dynamics (MD) simulations
    13
    ection of interacting atoms following classical mechanics. For a system
    g N atoms with positions {r
    i
    }
    i=1
    N and velocities {!
    i
    = dr
    i
    / dt}
    i=1
    N , the tot
    ian is given by
    H({r
    i
    }
    i=1
    N ) = T+ U = 1
    2
    m
    i
    !
    i
    2 + U({r
    i
    }
    i=1
    N )
    i=1
    n
    " (2.1)
    • Embedded-Atom-Method (EAM) potential
    • Supercell size: up to 1.54 million atoms
    • Film thickness varied from 4 nm to 10 nm
    • Applied equi-biaxial tensile strain through cell size expansion:
    – applied strain rate: 107 s-1 - 1011 s-1
    

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12. Deformation in Cu thinfilm: Prestraining
    rmation of Cu thinfilm: Prestraining
    

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13. Deformation in Cu thinfilm: Prestraining
    Top view:
    Light blue are in stacking faults
    Dark blue are fcc atoms
    others are at dislocations
    

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14. Deformation in Cu thinfilm: Prestraining
    Side view:
    dark blue are in stacking faults
    others are at dislocations
    FCC atoms are not shown
    

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15. Response of thin Cu film (∼ 4nm) to further strain
    Strain rate 4 orders of magnitute lower than that during prestraining
    Stage I : Near elastic response and depletion of 15% of dislocations
    Stage II : Easy-glide; dislocation annihilation
    Stage III : Insufficient plastic flow; stress increases
    Stage III+: Nucleation of additional dislocations; material failure
    

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16. Response of thin Cu film (∼ 4nm) to further strain
    Stage I : Near elastic response and depletion of 15% of dislocations
    Stage II : Easy-glide; dislocation annihilation
    Stage III : Insufficient plastic flow; stress increases
    Stage III+: Nucleation of additional dislocations; material failure
    

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17. Response of thin Cu film (∼ 10nm) to further strain
    Dislocation starvation and creation occurs in cycles
    Such cycles observed in experiments of fcc nanopillars
    

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18. Outline
    •Motivation
    • Confined interconnects in semiconductor materials
    • Confined defects in pillars and nanowires
    •Mechanical behavior of free-standing copper thin films
    • stress-strain behavior of pre-strained thin films
    • Mechanisms that lead to the observed behavior
    •Comparing with other FCC metals
    • Comparison motivated by mechanistic understanding of
    copper thin films
    

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19. Dislocation-stacking fault interactions cause
    annihilation
    

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20. Dislocation-stacking fault interactions cause
    annihilation
    

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21. Dislocation-stacking fault interactions cause
    annihilation
    

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22. Outline
    •Motivation
    • Confined interconnects in semiconductor materials
    • Confined defects in pillars and nanowires
    •Mechanical behavior of free-standing copper thin films
    • stress-strain behavior of pre-strained thin films
    • Mechanisms that lead to the observed behavior
    •Comparing with other FCC metals
    • Comparison motivated by mechanistic understanding of
    copper thin films
    

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23. Comparing behavior of metals with different
    propensity for formation of stacking faults
    Factors considered in choosing model materials
    • Stable stacking fault energy, ϒs
    • Ratio of unstable to stable stacking-fault
    energy, ϒs/ϒu
    • Ideal shear strength
    ϒ/ϒu
    x/bp
    0
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    0 0.2 0.4 0.6 0.8 1
    0
    0.2
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    1
    1.2
    0 0.2 0.4 0.6 0.8 1
    !/!
    u
    x/bp
    0.4 0.6 0.8 1
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    0 0.2 0.4 0.6 0.8 1
    !/!
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    x/bp
    0.8 1
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    0 0.2 0.4 0.6 0.8
    !/!
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    x/bp
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    !/!
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    x/b
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    !/!
    u
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    0
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    !/!
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    x/bp
    0
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    0
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    Al
    Cu
    Ni
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    Al
    Cu
    Ni
    

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24. Response of different prestrained films (∼ 4nm) to
    further strain
    In stage II:
    Ni and Cu Constant stress and dislocations annihilate
    Al Stress increases monotonically
    Al Dislocations annihilate at half the rate
    35% more annihilation in Ni and Cu than in Al
    

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25. Response of different prestrained films (∼ 4nm) to
    further strain
    In stage II:
    In Ni and Cu, plastic strain decreases monotonically
    In Al, plastic strain remains constant
    Critical plastic strain beyond which stress increases in every thinfilm
    In Al, plastic strain never exceeds critical plastic strain
    

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26. Dislocations annihilate by collinear interactions in Al
    Dislocations with same Burgers vector but in different glide plane
    Initial
    

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27. Dislocations annihilate by collinear interactions in Al
    Dislocations with same Burgers vector but in different glide plane
    3% strain
    

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28. Dislocations annihilate by collinear interactions in Al
    Dislocations with same Burgers vector but in different glide plane
    3% strain
    

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29. Summary:
    • Dislocation interactions with stacking faults (SF) play an important role
    • SF aid cross-slip and increase dislocation annihilation rate
    • Dislocation annihilation occurs without SF as well, only much less
    

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