6 Atomic Scale Kinetics of TSV Protrusion
155
21. M. Kawasaki, T.G. Langdon, The many facets of deformation mechanism mapping and the
application to nanostructured materials. J. Mater. Res. 28, 1827–1834 (2013)
22. Z. Huang, J. Liu, P. Conway et al., An atomistic study of copper extrusion in through-siliconvia using phase field crystal models, in Electronic System-Integration Technology Conference.
(IEEE, 2016), p. 7764700
23. W. Shen, K. Chen, Three-dimensional integrated circuit (3D IC) key technology: throughsilicon via (TSV). Nanoscale Res. Lett. 1, 56 (2017)
24. M. Ehsan, Z. Zhou, L. Liu et al., An analytical through silicon via (TSV) surface roughness
model applied to a millimeter wave 3-D IC. IEEE Trans. Electromagn. Compat. 57, 815–826
(2015)
25. T. Nakamura, H. Kitada, Y. Mizushima et al., Comparative study of side-wall roughness effects
on leakage currents in through-silicon via interconnects, in International 3D Systems Integration Conference (IEEE, 2011), pp. 1–4
26. L. Chan, M. MacDonald, D. Chung et al., A systematic investigation of roughness height
and wavelength in turbulent pipe flow in the transitionally rough regime. J. Fluid. Mech. 771,
743–777 (2015)
27. B. Wilshire, A.J. Battenbough, Creep and creep fracture of polycrystalline copper. Mater. Sci.
Eng. A 443, 156–166 (2007)
28. J. Berry, J. Rotter, C.W. Sinclair et al., Atomistic study of diffusion-mediated plasticity and
creep using phase field crystal methods. Phys. Rev. B 92, 134103 (2015)
29. S. Biswas, M. Grant, I. Samajdar et al., Micromechanics of emergent patterns in plastic flows.
Sci. Rep. 3, 2728 (2013)
30. T. Watanabe, Grain boundary engineering: historical perspective and future prospects. J. Mater.
Sci. 46, 4095–4115 (2011)
31. K. Lu, L. Lu, S. Suresh, Strengthening materials by engineering coherent internal boundaries
at the nanoscale. Science 324, 349–352 (2009)
32. K. Lu, Stabilizing nanostructures in metals using grain and twin boundary architectures. Nat.
Rev. Mater. 1, 16019 (2016)
33. G. Gottstein, L.S. Shvindlerman, Grain Boundary Migration in Metals: Thermodynamics,
Kinetics, Applications, 2nd edn. (CRC Press, Boca Raton, FL, 2009)
34. N. Goldenfeld, B.P. Athreya, J.A. Dantzig et al., Renormalization group approach to multiscale
simulation of polycrystalline materials using the phase field crystal model. Phys. Rev. E. 72,
020601 (2005)
35. B.P. Athreya, N. Goldenfeld, J.A. Dantzig, Renormalization-group theory for the phase-field
crystal equation. Phys. Rev. E 74, 011601 (2006)
36. S. Praetorius, M. Salvalaglio, A. Voigt, An efficient numerical framework for the amplitude
expansion of the phase-field crystal model. Modell. Simul. Mater. Sci. Eng. 27, 044004 (2019)
37. P.Y. Chan, N. Goldenfeld, Nonlinear elasticity of the phase-field crystal model from the renormalization group. Phys. Rev. E 80, 065105 (2009)
38. A. Skaugen, L. Angheluta, J. Vinals, Separation of elastic and plastic timescales in a phase
field crystal model. Phys. Rev. Lett. 121, 255501 (2018)
39. M. Greenwood, N. Ofori-Opoku, J. Rottler et al., Modeling structural transformations in binary
alloys with phase field crystals. Phys. Rev. B 84, 064104 (2011)
40. M. Sung, A. Lee, T. Kim et al., Sulfur-containing additives for mitigating Cu protrusion in
through silicon via (TSV). J. Electrochem. Soc. 166, D514–D520 (2019)
155
21. M. Kawasaki, T.G. Langdon, The many facets of deformation mechanism mapping and the
application to nanostructured materials. J. Mater. Res. 28, 1827–1834 (2013)
22. Z. Huang, J. Liu, P. Conway et al., An atomistic study of copper extrusion in through-siliconvia using phase field crystal models, in Electronic System-Integration Technology Conference.
(IEEE, 2016), p. 7764700
23. W. Shen, K. Chen, Three-dimensional integrated circuit (3D IC) key technology: throughsilicon via (TSV). Nanoscale Res. Lett. 1, 56 (2017)
24. M. Ehsan, Z. Zhou, L. Liu et al., An analytical through silicon via (TSV) surface roughness
model applied to a millimeter wave 3-D IC. IEEE Trans. Electromagn. Compat. 57, 815–826
(2015)
25. T. Nakamura, H. Kitada, Y. Mizushima et al., Comparative study of side-wall roughness effects
on leakage currents in through-silicon via interconnects, in International 3D Systems Integration Conference (IEEE, 2011), pp. 1–4
26. L. Chan, M. MacDonald, D. Chung et al., A systematic investigation of roughness height
and wavelength in turbulent pipe flow in the transitionally rough regime. J. Fluid. Mech. 771,
743–777 (2015)
27. B. Wilshire, A.J. Battenbough, Creep and creep fracture of polycrystalline copper. Mater. Sci.
Eng. A 443, 156–166 (2007)
28. J. Berry, J. Rotter, C.W. Sinclair et al., Atomistic study of diffusion-mediated plasticity and
creep using phase field crystal methods. Phys. Rev. B 92, 134103 (2015)
29. S. Biswas, M. Grant, I. Samajdar et al., Micromechanics of emergent patterns in plastic flows.
Sci. Rep. 3, 2728 (2013)
30. T. Watanabe, Grain boundary engineering: historical perspective and future prospects. J. Mater.
Sci. 46, 4095–4115 (2011)
31. K. Lu, L. Lu, S. Suresh, Strengthening materials by engineering coherent internal boundaries
at the nanoscale. Science 324, 349–352 (2009)
32. K. Lu, Stabilizing nanostructures in metals using grain and twin boundary architectures. Nat.
Rev. Mater. 1, 16019 (2016)
33. G. Gottstein, L.S. Shvindlerman, Grain Boundary Migration in Metals: Thermodynamics,
Kinetics, Applications, 2nd edn. (CRC Press, Boca Raton, FL, 2009)
34. N. Goldenfeld, B.P. Athreya, J.A. Dantzig et al., Renormalization group approach to multiscale
simulation of polycrystalline materials using the phase field crystal model. Phys. Rev. E. 72,
020601 (2005)
35. B.P. Athreya, N. Goldenfeld, J.A. Dantzig, Renormalization-group theory for the phase-field
crystal equation. Phys. Rev. E 74, 011601 (2006)
36. S. Praetorius, M. Salvalaglio, A. Voigt, An efficient numerical framework for the amplitude
expansion of the phase-field crystal model. Modell. Simul. Mater. Sci. Eng. 27, 044004 (2019)
37. P.Y. Chan, N. Goldenfeld, Nonlinear elasticity of the phase-field crystal model from the renormalization group. Phys. Rev. E 80, 065105 (2009)
38. A. Skaugen, L. Angheluta, J. Vinals, Separation of elastic and plastic timescales in a phase
field crystal model. Phys. Rev. Lett. 121, 255501 (2018)
39. M. Greenwood, N. Ofori-Opoku, J. Rottler et al., Modeling structural transformations in binary
alloys with phase field crystals. Phys. Rev. B 84, 064104 (2011)
40. M. Sung, A. Lee, T. Kim et al., Sulfur-containing additives for mitigating Cu protrusion in
through silicon via (TSV). J. Electrochem. Soc. 166, D514–D520 (2019)