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Modelling Technologies and Applications

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Nanopackaging

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Abstract

Modelling technologies are playing a key role in supporting new developments in nano-packaging for electronic systems. This chapter provides an overview of these technologies from continuum modelling using techniques such as finite elements, atomistic models based on molecular dynamics and optimisation under uncertainty, as well as homogenisation methods that link results across the length and timescales. Challenges for these techniques in terms of modelling nano-packaging applications are also discussed.

The chapter then goes onto providing a review of these technologies for key design stages in and electronic system such as fabrication, assembly and its performance/reliability. Examples include focused ion beam milling, nanoimprint lithography, electroforming, 3D printing and additive manufacturing, solder paste printing, microwave curing of polymers, impact of underfills on solder joint reliability, thermos-mechanical behaviour of conductive adhesives and performance thermal interface materials. These examples provide the reader with an overview of how these modelling technologies can be applied to real-world nano-packaging applications.

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References

  1. Alder BJ, Wainwright TE (1957) Phase transition for a hard sphere system. J Chem Phys 27:1208–1211

    Article  CAS  Google Scholar 

  2. Car R, Parrinello M (1985) Phys Rev Lett 55:2471

    Article  CAS  Google Scholar 

  3. Daw MS, Baskes MI (1983) Phys Rev Lett 50:1285

    Article  CAS  Google Scholar 

  4. Allen MP, Tildesley DJ (1987) Computer simulation of liquids. Clarendon, Oxford. 1987

    Google Scholar 

  5. Hawlow FH (1964) The particle in cell computing method for fluid dynamics. In: Alder BB, Fernbach S, Rotenberg M (eds) Methods in computational physics, Fundamental Methods in Hydrodynamics, vol 3. Academic, New York, pp 319–343

    Google Scholar 

  6. Lin CT, Chiang KN (2006) Investigation of nano-scale single crystal silicon using the atomistic-continuum mechanics with Stillinger-Weber potential function, IEEE Conference on Emerging Technologies – Nanoelectronics, Jan 10–13, pp 5–9

    Google Scholar 

  7. Wymyslowski A, Iwamoto N, Yuen M, Fan H (2015) Molecular modeling and multiscaling issues for electronic material applications, vol 2. Springer, Cham

    Google Scholar 

  8. Zhang GQ, Maessen P, Bisschop J, Janssen J, Kuper F, Ernst L (2001) Virtual thermo-mechanical prototyping of microelectronics – the challenges for mechanics professionals. In: Proceedings of EuroSIME, pp 21–24

    Google Scholar 

  9. Neubert H (2012) Uncertainty-based design optimisation of MEMS/NEMS. In: Gerlach G, Wolter K-J (eds) Bio and nano packaging techniques for electron devices. Springer, Berlin, pp 119–140

    Chapter  Google Scholar 

  10. Melchers RE (1999) Structural reliability analysis and prediction. Wiley, Chichister, United Kingdom

    Google Scholar 

  11. Haldar A, Mahadevan S (2000) Probability, reliability and statistical methods in engineering design. Wiley, New York, USA

    Google Scholar 

  12. Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton

    Google Scholar 

  13. Zadeh LA (1965) Fuzzy sets. Inf Control 81:338–353

    Article  Google Scholar 

  14. Thacker B, Huyse L (2003) Probabilistic assessment on the basis of interval data. AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Material Conference, AIAA-2003-1753, Norfolk, Virginia

    Google Scholar 

  15. Najm HN (2009) Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics. Annu Rev Fluid Mech 41:35–52

    Article  Google Scholar 

  16. Sepahvand K, Marburg S, Hardtke H-J (2010) Uncertainty quantification in stochastic systems using polynomial chaos expansion. Int J Appl Mech 02(2):305–353

    Article  Google Scholar 

  17. Vanderplaats GN (1999) Numerical optimisation techniques for engineering design: with applications. VR&D, Colorado Springs

    Google Scholar 

  18. Zhang J, Kosut R (2007) Robust design of quantum potential profile for electron transmission in semiconductor nanodevices. NSTI-Nanotech 2007 1:216–217

    CAS  Google Scholar 

  19. Putek P, Meuris P, Pulch R, ter Maten EJW, Schoenmaker W, Günther M (2016) Uncertainty quantification for robust topology optimization of power transistor devices. IEEE Trans Magn 52(3):1700104

    Article  Google Scholar 

  20. Becker B, Hellebrand S, Polian I, Straube B, Vermeiren W, Wunderlich H-J (2010) Massive statistical process variations: a grand challenge for testing nanoelectronic circuits. In: International conference on Dependable Systems and Networks Workshops (DSN-W), Chicago, pp 95–100

    Google Scholar 

  21. Utke I, Moshkalev S, Russel P (eds) (2012) Nanofabrication using focused ion beam and electron beams: principles and applications. Oxford University Press

    Google Scholar 

  22. Zhou J, Yang G (2010) Focused ion-beam based nanohole modeling, simulation, fabrication, and application, J Manuf Sci Eng 132(1);Article 11005:1–8

    Article  Google Scholar 

  23. Ray V, Chang E, Toula K, Liou S-C, Chiou W-A (2015) Methodology for studying nanoscale details of focused ion beam gas-assisted etching and deposition by TEM and numerical modelling. Microsc Microanal 21(3):1843–1844

    Article  Google Scholar 

  24. Vasile M, Niu Z, Nassar R, Zhang W, Liu S (1997) Focussed ion beam milling: depth control for three-dimensional microfabrication. J Vac Sci Technol B 15(6):2350–2354

    Article  CAS  Google Scholar 

  25. Nassar R, Vasile M, Zhang W (1998) Mathematical modelling of focused ion beam microfabrication. J Vac Sci Technol B 16(1):109–115

    Article  CAS  Google Scholar 

  26. Yamamura Y, Itikawa Y, Itoh N (1983) Report IPPJ-AM-26. Nagoya University Institute of Plasma Physics

    Google Scholar 

  27. Tseng A, Leeladharan B, Li B, Insua I (2003) Fabrication and modelling of microchannel milling using focused ion beam. Int J Nanosci 2(4–5):375–379

    Article  CAS  Google Scholar 

  28. Munoz-Garcia J, Castro M, Cuerno R (2006) Nonlinear ripple dynamics on amorphous surfaces patterned by ion beam sputtering. Phys Rev Lett 96:086101

    Article  Google Scholar 

  29. Chou SY, Krauss PR, Zhang W, Guo L, Zhuang L (1997) Sub-10 nm imprint lithography and applications. J Vac Sci Technol B 15(6):2897–2904

    Article  CAS  Google Scholar 

  30. Patel BC, Jain A (2013) Thermal modeling of ultraviolet nanoimprint lithography. J Manuf Sci Eng 135(6):064501

    Article  Google Scholar 

  31. Gervasio M, Lu K, Davis R (2015) Experimental and modeling study of solvent diffusion in PDMS for nanoparticle–polymer cosuspension imprint lithography. Langmuir 31(36):9809–9816

    Article  CAS  Google Scholar 

  32. Kim S-K (2014) Modeling and simulation of patterning diblock copolymers through nanoimprint lithography. J Nanosci Nanotechnol 14(8):6065–6068

    Article  CAS  Google Scholar 

  33. Nguyen LP, Hao K-C, Su Y-H, Hung C (2015) Modeling the embossing stage of the ultrasonic-vibration-assisted hot glass embossing process. Spec Issue Gen Glas Sci 6(2):172–181

    CAS  Google Scholar 

  34. Hirai Y, Konishi T, Yoshikawa T, Yoshida S (2004) Simulation and experimental study of polymer deformation in nanoimprint lithography. J Vac Sci Technol B 22(6):3288–3293

    Article  CAS  Google Scholar 

  35. Mooney M (1940) A theory of large elastic deformation. J Appl Phys 11:582–582

    Article  Google Scholar 

  36. Rivlin RS (1948) Large elastic deformation of isotropic materials. Phil Trans Roy Soc Lond Ser A 241:379–397

    Article  Google Scholar 

  37. Hirai Y, Yoshida S, Takagi N (2003) Defect analysis in thermal nanoimprint lithography. J Vac Sci Technol B 21(6):2765–2770

    Article  CAS  Google Scholar 

  38. Hirai Y, Fujiwara M, Okuno T, Tanaka Y (2001) Study of the resist deformation in nanoimprint lithography. J Vac Sci Technol B 19(6):2811–2815

    Article  CAS  Google Scholar 

  39. Rowland H, King W, Sun A, Schunk P (2006) Impact of polymer film thickness and cavity size on polymer flow during embossing: towards process design rules for nanoimprint lithography. SANDIA Report SAND2006-4864

    Google Scholar 

  40. Ritter G, McHugh P, Wilson G, Ritzdorf T (2000) Three dimensional numerical modelling of copper electroplating for advanced ULSI metallisation. Solid State Electron 44:797–807

    Article  CAS  Google Scholar 

  41. Griffiths SK et al (1998) Modeling electrodeposition for LIGA microdevice fabrication. SAND98-8231, Distribution Category UC-411

    Google Scholar 

  42. Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79:12–49

    Article  Google Scholar 

  43. Hughes M, Strussevitch N, Bailey C, McManus K, Kaufmann J, Flynn D, Desmulliez M (2010) Numerical algorithms for modelling electrodeposition: tracking the deposition front under forced convection from megasonic agitation. Int J Numer Methods Fluids 64(3):237–268

    Article  CAS  Google Scholar 

  44. Lefebvre M, Allardyce G, Seita M, Tsuchida H, Kusaka M, Hayashi S (2003) Copper electroplating technology for microvia filling. Circ World 29(2):9–14

    Article  CAS  Google Scholar 

  45. Strusevich N, Desmulliez M, Abraham E, Flynn D, Jones T, Patel M, Bailey C (2013) Electroplating for high aspect ratio vias in PCB manufacturing: enhancement capabilities of acoustic streaming. Adv Manuf 1(3):211–217

    Article  Google Scholar 

  46. Costello S, Strusevich N, Flynn D, Kay R, Patel M, Bailey C, Price D, Bennet M, Jones A, Desmulliez M (2013) Electrodeposition of copper into PCB vias using megasonic agitation. Microsyst Technol 19(6):783–790

    Article  CAS  Google Scholar 

  47. Nyborg W (1965) Acoustic streaming. In: Mason WP (ed) Physical acoustics, 2B. Academic, New York, pp 265–331

    Google Scholar 

  48. Gale G, Busnaina A (1999) Roles of cavitation and acoustic streaming in megasonic cleaning. Part Sci Technol 17:229–238

    Article  CAS  Google Scholar 

  49. Liu G, Huang X, Xiong Y, Tian Y (2008) Fabrication HARMS by using megasonic assisted electroforming. Microsyst Technol 14:1223–1226

    Article  CAS  Google Scholar 

  50. Bidoki SM, Lewis DM, Clark M, Vakorov A, Millner P, McGorman D (2007) Ink-jet fabrication of electronic components. J Micromech Microeng 17(5):967–974

    Article  CAS  Google Scholar 

  51. Perelaer J, de Laat AWM, Hendriks C, Schubert U (2008) Inkjet-printed silver tracks: low temperature curing and thermal stability investigation. J Mater Chem 18:3209–3215

    Article  CAS  Google Scholar 

  52. NEXTFACTORY (http://www.nextfactory-project.eu)

  53. ASTM F2792 Standard, “Standard terminology for additive manufacturing technologies”. Available at: http://www.astm.org

  54. Derby B (2011) Inkjet printing ceramics: from drops to solid. J Eur Ceram Soc 31(14):2543–2550

    Article  CAS  Google Scholar 

  55. Xiong J, Zhang G, Hu J, Wu L (2012) Bead geometry prediction for robotic GMAW-based rapid manufacturing through a neural network and a second-order regression analysis. J Intell Manuf 25(1):157–163

    Article  Google Scholar 

  56. Stava O, Vanek J, Benes B, Carr N, Mech R (2012) Stress relief: improving structural strength of 3d printable objects. ACM Trans Graph 31(4):48

    Article  Google Scholar 

  57. Salmeron J et al (2014) Properties and printability of inkjet and screen-printed silver patterns for RFID antennas. J Electron Mater 43(2):604–617

    Article  CAS  Google Scholar 

  58. Niittynen J et al (2014) Alternative sintering methods compared to conventional thermal sintering for inkjet printed silver nanoparticle ink. Thin Solid Films 556:452–459

    Article  CAS  Google Scholar 

  59. Gomm J, Yu DL, Williams D (1996) A new model structure selection method for non-linear systems in neural modelling. Int Conf Comput Control (UKACC) 2(427):752–757

    Google Scholar 

  60. Tourloukis G, Stoyanov S, Tilfrod T, Bailey C (2015) Data driven approach to quality assessment of 3D printed electronic products, 38th International Spring Seminar on Electronics Technology (ISSE), 300–305. ISNN 2161–2528

    Google Scholar 

  61. Bailey C, Stoyanov S, Tilford T, Tourloukis G (2016) 3D-printing for electronics packaging. 2016 Pan Pacific Microelectronics Symposium, 1–7, Pub IEEE. https://doi.org/10.1109/PanPacific.2016.7428385

  62. Nguty TA, Ekere NN (1999) The rheological properties of solder and solder pastes and the effect on stencil printing. Rheol Acta 39:607–612

    Article  Google Scholar 

  63. Brady JF, Bossis G (1988) Stokesian dynamics. A. Rev Fluid Mech 20:111–157

    Article  Google Scholar 

  64. McNamara G, Zanetti G (1988) Use of the Boltzmann equation to simulate lattice-gas automata. Phys Rev Lett 61(20):2332–2335

    Article  CAS  Google Scholar 

  65. Hoogerbrugge PJ, Koelman JM (1992) Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys Lett 19(3):155–160

    Article  Google Scholar 

  66. Flekkoy EG, Wagner G, Feder J (2000) Hybrid model for combined particle and continuum dynamics. Europhys Lett 52(3):271–276

    Article  CAS  Google Scholar 

  67. Dong H, Fan L, Moon K, Wong CP (2005) Molecular dynamics simulation of lead free solder for low temperature reflow applications. In: Proceedings 55th electronic components & technology conference, 2005, pp 983–987

    Google Scholar 

  68. Wang T, Fu Y, Becker M, Zhou M, Liu J (2001) Microwave heating of metal-filled electrically conductive adhesive curing. In: Proceedings IEEE electronic components and technology conference 2001, pp 593–597

    Google Scholar 

  69. Pavuluri SK, Ferenets M, Goussetis G, Desmulliez MPY, Tilford T, Adamietz R, Muller G, Eicher F, Bailey C (2012) Encapsulation of microelectronic components using open-ended microwave oven. IEEE Trans Compon Packag Manuf Technol 2(5):799–806. ISSN 2156-3950

    Article  CAS  Google Scholar 

  70. Adamietz R, Tilford T, Ferenets M, Desmulliez MPY, Muller G, Othman N, Eicher F (2010) Modular microwave-based system for packaging applications. In: Proceedings of international conference on electronics packaging, Sapporo, pp 325–330

    Google Scholar 

  71. Sinclair KI, Desmulliez MPY, Sangster AJ (2006) A novel RF-curing technology for microelectronics and optoelectronics packaging. In: Proceedings of IEEE electronics systemintegration technology conference 2006, vol 2, p 1149

    Google Scholar 

  72. Sun Y, Zhang Z, Wong CP (2005) Study on mono-dispersed nano-size silica by surface modification for underfill applications. J Colloid Interface Sci 292:436–444

    Article  CAS  Google Scholar 

  73. Lu H, Hung KC, Stoyanov S, Bailey C, Chan YC (2002) No-flow underfill flip chip assembly – an experimental and modelling analysis. Microelectron Reliab 42:1205–1212

    Article  Google Scholar 

  74. Shi SH, Wong CP (1999) Recent advances in the development of no-flow underfill encapsulants – a practical approach towards the actual manufacturing application. IEEE Trans Electron Packag Manuf 22:331–339

    Article  CAS  Google Scholar 

  75. Liu J, Kraszewshi R, Lin X, Wong L, Goh SH, Allen J (2001) New developments in single pass reflow encapsulant for flip chip application. In: Proceedings of international symposium on advanced packaging materials, Atlanta, pp 74–79

    Google Scholar 

  76. Lall P, Islam S, Suhling J, Tian GY (2005) Nano-underfills for high-reliability applications in extreme environments. In: Proceedings 55th electronic components and technology conference, pp 212–222

    Google Scholar 

  77. Chhanda NJ, Suhling JC, Lall P (2012) Implementation of a viscoelastic model for the temperature dependent material behavior of underfill encapsulants, IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), San Diego, pp 269–281

    Google Scholar 

  78. Chhanda NJ, Suhling JC, Lall P (2014) Effects of moisture exposure on the mechanical behavior of flip chip underfills in microelectronic packaging. IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), Orlando, pp 333–345

    Google Scholar 

  79. Liu J (1999) Conductive adhesive for electronics packaging. Electrochemical Publications Ltd, pp 234–248

    Google Scholar 

  80. Li Y, Yim MJ, Moon KS, Wong CP (2009) Novel nano-scale conductive films with enhanced electrical performance and reliability for high performance fine pitch interconnect. IEEE Trans Adv Packag 32:123–129

    Article  Google Scholar 

  81. Kumbhat N, Choudhury A, Raine M, et al (2009) Highly-reliability, 30 um pitch copper interconnects using nano-ACF/NCF. 59th Electronic Components & Technology Conference, 2009, Proceedings. pp 1479–1485

    Google Scholar 

  82. Mercodo LL, White J, Sarihan V, Lee TYT (2003) Failure mechanism study of Anisotropic Conductive Film (ACF) packages. IEEE Trans Components Packag Technol 26(3):509–516

    Article  Google Scholar 

  83. Wei Z, Waf LS, Loo NY, Koon EM, Huang M (2002) Studies on moisture-induced failures in ACF interconnection. The 7th Electronics Packaging Technology Conference (EPTC), Singapore, pp 133–138

    Google Scholar 

  84. Kim JW, Jung SB (2006) Effects of bonding pressure on the thermo-mechanical reliability of ACF interconnection. J Microelectron Eng 83(11–12):2335–2340

    Article  CAS  Google Scholar 

  85. Rizvi MJ, Chan YC, Bailey C, Lu H (2005) Study of anisotropic conductive adhesive joint behaviour under 3-point bending. J Microelectron Reliab 45(3–4):589–596

    Article  CAS  Google Scholar 

  86. Wu CML, Liu J, Yeung NH (2001) The effects of bump height on the reliability of ACF in flip-chip. J Soldering Surface Mount Technol 13(1):25–30

    Article  Google Scholar 

  87. Yin CY, Lu H, Bailey C, Chan YC (2005) Moisture effects on the reliability of anisotropic conductive films. The 6th International Conference on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro- Electronics and Micro-Systems, Berlin, pp 162–167

    Google Scholar 

  88. Yin CY, Lu H, Bailey C, Chan YC (2006) Macro-micro modeling analysis for an ACF flip chip. J Soldering Surface Mounting Technol 18(2):27–32

    Article  Google Scholar 

  89. Tu KN (2003) Recent advances on electromigration in very large scale integration of interconnects. J Appl Phys 94(9):5451–5473

    Article  CAS  Google Scholar 

  90. Lloyd JR (1999) Electromigration and mechanical stress. Microelectron Eng 49(1–2):51–64

    Article  CAS  Google Scholar 

  91. Ye H, Basaran C, Hopkins D (2003) Thermomigration in Pb-Sn solder joints under joule heating during electric current stressing. Appl Phys Lett 82(7):1045–1047

    Article  CAS  Google Scholar 

  92. Alam MO, Wu BY, Chan YC, Tu KN (2006) High electric current density-induced interfacial reactions in micro ball grid array solder joints. Acta Mater 54(3):613–621

    Article  CAS  Google Scholar 

  93. Dan Y, Alam MO, Wu BY, Chan YC, Tu KN (2006) Thermomigration and electromigration in solder joint. In: Proceedings of 8th Electronics Packaging Technology Conference (EPTC 2006), Singapore, pp 565–569

    Google Scholar 

  94. Alam MO, Bailey C, Wu BY, Yang D, Chan YC (2007) High current density induced damage mechanisms in electronic solder joints – a state-of-art-review. In: The Proceedings of High Density Packaging Conference, Shanghai, pp 93–99

    Google Scholar 

  95. Zhu X, Kotadia H, Xu S, Lu H, Mannan S, Bailey C, Chan YC (2013) Modelling electromigration for microelectronics design. J Comput Sci Technol 7(2):251–264. ISSN 1881-6894

    Article  Google Scholar 

  96. Hong J, Yoon S, Hwang T, Oh J, Hong S, Lee Y, Nam J (2012) High thermal conductivity epoxy composites with bimodal distribution of aluminum nitride and boron nitride fillers. Thermochim Acta 537:70–75

    Article  CAS  Google Scholar 

  97. Agrawal A, Satapathy A (2013) Development of a heat conduction model and investigation on thermal conductivity enhancement of AlN/epoxy composites. Proc Eng 51:573–578

    Article  CAS  Google Scholar 

  98. Agrawal A, Satapathy A (2014) Effect of aluminum nitride inclusions on thermal and electrical properties of epoxy and polypropylene: an experimental investigation. Compos Part A 63:51–58

    Article  CAS  Google Scholar 

  99. Lee G, Park M, Lee J, Yoon H Enhanced thermal conductivity of polymer composites filled with hybrid filler. Compos Part A 37:727–734

    Article  Google Scholar 

  100. Wang J, Carson J, North M, Cleland D (2008) A new structural model of effective thermal conductivity for heterogeneous materials with co-continuous phases. Int J Heat Mass Transf 51:2389–2397

    Article  CAS  Google Scholar 

  101. Zhou Y, Wang H, Wang L, Yu K, Lin Z, He L, Bai Y (2012) A fabrication and characterization of aluminum polymer matrix composites with high thermal conductivity and low dielectric constant for electronic packaging. Mat Sci Eng B 177:892–296

    Article  CAS  Google Scholar 

  102. Yang R, Chen G (2004) Thermal conductivity modeling of periodic two-dimensional nanocomposites. Phys Rev B 69:195316

    Article  Google Scholar 

  103. Tian W, Yang R (2008) Phonon transport and thermal conductivity percolation in random nanoparticle composites. Comput Model Eng Sci 24(2):123–141

    Google Scholar 

  104. Chuang P, Huang M (2013) Model and simulation predictions of the thermal conductivity of compact random nanoparticle composites. Int J Heat Mass Transf 61:490–498

    Article  CAS  Google Scholar 

  105. Hida S, Hori T, Shiga T, Elliott J, Shiomi J (2013) Thermal resistance and phonon scattering at the interface between carbon nanotubes and amorphous polyethylene. Int J Heat Mass Transf 67:1024–1029

    Article  CAS  Google Scholar 

  106. Qiu B, Bao H, Zhang G, Wu Y, Ruan X (2012) Molecular dynamics simulations for lattice thermal conductivity and spectral phonon mean free path of PbTe: bulk and nanostructures. Comput Mater Sci 53:278–285

    Article  CAS  Google Scholar 

  107. Termentzidis K, Merabia S (2012) Molecular dynamics simulations and thermal transport at the nano-scale, molecular dynamics – theoretical developments and applications in nanotechnology and energy. In: Prof. Wang L (ed). pp 73–104

    Google Scholar 

  108. Tian Z, Hu H, Sun Y (2013) A molecular dynamics study of effective thermal conductivity in nanocomposites. Int J Heat Mass Transf 61:557–582

    Article  Google Scholar 

  109. Li Z, Wu W, Chen H, Zhu Z, Wang Y, Zhang Y (2013) Thermal conductivity of micro/nano filler filled polymeric composites. RSC Adv 3:6417–6428

    Article  CAS  Google Scholar 

  110. Yue C, Zhang Y, Hu Z, Liu J (2010) Modeling of the effective thermal conductivity of composite materials with FEM based on resistor networks approach. Microsyst Technol 16:633–639

    Article  CAS  Google Scholar 

  111. Hill R, Strader J (2007) Rudimentary finite element thermal modeling of platelet-filled polymer-ceramic composites. IEEE Trans Compon Packag Technol 30(2):235–224

    Article  CAS  Google Scholar 

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Acknowledgements

The authors would like to acknowledge the financial support from the Engineering and Physical Sciences Research Council (EPSRC) that has supported some of the modelling development work at Greenwich as detailed in the illustrations above. We also acknowledge the 3D integration consortium (supported under ESPRC fund EP/C534212/) and the EU-funded programme NextFactory (http://www.nextfactory-project.eu, under grant agreement No. 608985) and the Centre for Power Electronics (funded by EPSRC under grant number EP/K034804/1).

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Authors and Affiliations

  1. Computational Mechanics and Reliability Group, Department of Mathematical Sciences, University of Greenwich, London, UK

    Chris Bailey, Stoyan Stoyanov, Hua Lu, Tim Tilford, Chunyan Yin & Nadia Strusevich

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  1. Chris Bailey
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  2. Stoyan Stoyanov
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Correspondence to Chris Bailey .

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  1. Department of Electrical and Computer Engineering, Portland State University, Portland, OR, USA

    James E. Morris

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Bailey, C., Stoyanov, S., Lu, H., Tilford, T., Yin, C., Strusevich, N. (2018). Modelling Technologies and Applications. In: Morris, J. (eds) Nanopackaging. Springer, Cham. https://doi.org/10.1007/978-3-319-90362-0_2

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