Modeling of Joule Heating Induced Effects in Multiwall Carbon Nanotube Interconnects

Electrothermal performance of multiwall carbon nanotubes (MWCNT)-based interconnects has been studied under the influence of self-heating. The interlayer insulator is a low-k (<inline-formula> <tex-math notation="LaTeX">$\varepsilon _{r}\sim 2$ </tex-math></inline-formula>) dielectric. Various geometries have been studied for the normal operation and breakdown conditions. Electrothermal coupled equations have been solved iteratively by solving Fourier heat diffusion equation with a finite-element method. Within the relaxation time approximation, mean free path of the electron has been calculated under different scattering mechanisms. Landauer–Büttiker formalism resistance has been used for calculating electrical resistance. Breakdown voltages for varying MWCNT lengths have been calculated and found to be higher in MWCNT with a shorter length. Breakdown voltage varies from 8.2 to 12 V for inner diameters 10–40 nm of 5-<inline-formula> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> interconnect length and 50-nm outer diameter. Breakdown voltage decreases with the increase in the length of interconnect. For a 5-<inline-formula> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> long interconnect, the breakdown voltage is nearly 8 V whereas for the same diameter <inline-formula> <tex-math notation="LaTeX">$1~\mu \text{m}$ </tex-math></inline-formula> long interconnect it is nearly 22 V. Breakdown current density depends on the geometry<inline-formula> <tex-math notation="LaTeX">$\vphantom {_{\int }} $ </tex-math></inline-formula> of the MWCNT and is estimated on the order of <inline-formula> <tex-math notation="LaTeX">$10^{8}$ </tex-math></inline-formula> A <inline-formula> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula> cm<sup>−2</sup>.

[1]  E. Pop,et al.  Thermal conductance of an individual single-wall carbon nanotube above room temperature. , 2005, Nano letters.

[2]  Dmitri Golberg,et al.  Direct imaging of Joule heating dynamics and temperature profiling inside a carbon nanotube interconnect. , 2011, Nature communications.

[3]  S. Roche,et al.  Quantum dephasing in carbon nanotubes due to electron-phonon coupling. , 2005, Physical review letters.

[4]  Eric Pop,et al.  Electrical and thermal transport in metallic single-wall carbon nanotubes on insulating substrates , 2007 .

[5]  J. Meindl,et al.  Compact physical models for multiwall carbon-nanotube interconnects , 2006, IEEE Electron Device Letters.

[6]  G. Groeseneken,et al.  A study of Joule heating-induced breakdown of carbon nanotube interconnects , 2011, Nanotechnology.

[7]  Eric Pop,et al.  Molecular dynamics simulation of thermal boundary conductance between carbon nanotubes and SiO 2 , 2010 .

[8]  Supriyo Datta,et al.  Lessons from Nanoelectronics: A New Perspective on Transport , 2012 .

[9]  M. Dresselhaus,et al.  Atomic-scale imaging of wall-by-wall breakdown and concurrent transport measurements in multiwall carbon nanotubes. , 2005, Physical review letters.

[10]  P. Ajayan,et al.  Highly aligned scalable platinum-decorated single-wall carbon nanotube arrays for nanoscale electrical interconnects. , 2009, ACS nano.

[11]  R. Baughman,et al.  Thermal conductivity of multi-walled carbon nanotube sheets: radiation losses and quenching of phonon modes , 2010, Nanotechnology.

[12]  H. Wong,et al.  A Compact SPICE Model for Carbon-Nanotube Field-Effect Transistors Including Nonidealities and Its Application—Part I: Model of the Intrinsic Channel Region , 2007, IEEE Transactions on Electron Devices.

[13]  Dekker,et al.  High-field electrical transport in single-wall carbon nanotubes , 1999, Physical review letters.

[14]  Mitra Dutta,et al.  Thermal conductivity of carbon nanotubes , 2009 .

[15]  A. Maffucci,et al.  Electrothermal Analysis of Carbon Nanotubes Power Delivery Networks for Nanoscale Integrated Circuits , 2016, IEEE Transactions on Nanotechnology.

[16]  Jing Guo,et al.  High-field quasiballistic transport in short carbon nanotubes. , 2003, Physical review letters.

[17]  Christian Schönenberger,et al.  Physical Properties of Multi-wall Nanotubes , 2001 .

[18]  S. Mahapatra,et al.  Physics-Based Thermal Conductivity Model for Metallic Single-Walled Carbon Nanotube Interconnects , 2011, IEEE Electron Device Letters.

[19]  M. S. Sarto,et al.  Modelling of multiwall carbon nanotube transmission lines , 2007, 2007 International Conference on Electromagnetics in Advanced Applications.

[20]  Moon-Ho Jo,et al.  Preparation and characterization of porous silica xerogel film for low dielectric application , 1997 .

[21]  A. Balijepalli,et al.  Compact Model of Carbon Nanotube Transistor and Interconnect , 2009, IEEE Transactions on Electron Devices.

[22]  Contact characterization between multi-walled carbon nanotubes and metal electrodes , 2015, 2015 IEEE 15th International Conference on Nanotechnology (IEEE-NANO).

[23]  T. Saito,et al.  Electrothermal Analysis of Breakdown in Carbon Nanofiber Interconnects , 2009, IEEE Electron Device Letters.

[24]  Ashok Srivastava,et al.  Characterization of MWCNT VLSI Interconnect with Self-Heating Induced Scatterings , 2014, 2014 IEEE Computer Society Annual Symposium on VLSI.

[25]  A. Kawabata,et al.  Low-resistance multi-walled carbon nanotube vias with parallel channel conduction of inner shells [IC interconnect applications] , 2005, Proceedings of the IEEE 2005 International Interconnect Technology Conference, 2005..

[26]  Hai Lin,et al.  Modeling of Crosstalk Effects in Multiwall Carbon Nanotube Interconnects , 2012, IEEE Transactions on Electromagnetic Compatibility.

[27]  J. Meindl,et al.  Performance comparison between carbon nanotube and copper interconnects for gigascale integration (GSI) , 2005, IEEE Electron Device Letters.

[28]  S. Iijima.  Helical microtubules of graphitic carbon , 1991, Nature.

[29]  James D. Meindl,et al.  Carbon nanotube interconnects , 2007, ISPD '07.

[30]  P. McEuen,et al.  Thermal transport measurements of individual multiwalled nanotubes. , 2001, Physical Review Letters.

[31]  Ashok Srivastava,et al.  A Thermal Model for Carbon Nanotube Interconnects , 2013, Nanomaterials.

[32]  Kaustav Banerjee,et al.  Performance analysis of carbon nanotube interconnects for VLSI applications , 2005, ICCAD-2005. IEEE/ACM International Conference on Computer-Aided Design, 2005..

[33]  Masahiro Horibe,et al.  Electrical Properties of Carbon Nanotube Bundles for Future Via Interconnects , 2005 .

[34]  Jie Jiang,et al.  Charge transport in carbon nanotubes: quantum effects of electron–phonon coupling , 2007, Journal of physics. Condensed matter : an Institute of Physics journal.

[35]  R. Ishihara,et al.  Size-Dependent Effects on the Temperature Coefficient of Resistance of Carbon Nanotube Vias , 2013, IEEE Transactions on Electron Devices.

[36]  Gaofeng Wang,et al.  Modelling of self-heating effects in multi-wall carbon nanotube interconnects , 2011 .

[37]  Koji Takahashi,et al.  Enhanced anisotropic heat conduction in multi-walled carbon nanotubes , 2013 .

[38]  Ashok Srivastava,et al.  Characterization of SWCNT Bundle Based VLSI Interconnect with Self-heating Induced Scatterings , 2015, ACM Great Lakes Symposium on VLSI.

[39]  M. S. Sarto,et al.  Single-Conductor Transmission-Line Model of Multiwall Carbon Nanotubes , 2010, IEEE Transactions on Nanotechnology.

[40]  A. Maffucci,et al.  On the Evaluation of the Number of Conducting Channels in Multiwall Carbon Nanotubes , 2011, IEEE Transactions on Nanotechnology.

[41]  Ting-Yen Chiang,et al.  Impact of Joule heating on scaling of deep sub-micron Cu/low-k interconnects , 2002, 2002 Symposium on VLSI Technology. Digest of Technical Papers (Cat. No.01CH37303).

[42]  A. Srivastava,et al.  Carbon nanotubes for next generation very large scale integration interconnects , 2010 .

[43]  Kaustav Banerjee,et al.  Carbon Nanomaterials: The Ideal Interconnect Technology for Next-Generation ICs , 2010, IEEE Design & Test of Computers.

[44]  Toshishige Yamada,et al.  Length dependence of current-induced breakdown in carbon nanofiber interconnects , 2008 .

[45]  S. Mahapatra,et al.  Analytical Solution of Joule-Heating Equation for Metallic Single-Walled Carbon Nanotube Interconnects , 2011, IEEE Transactions on Electron Devices.

[46]  Anurag Jain,et al.  Thermal conductivity study of porous low K dielectric materials , 1999 .

[47]  Jesse Maassen,et al.  Steady-state heat transport: Ballistic-to-diffusive with Fourier's law , 2014, 1408.1631.

[48]  Marcello D'Amore,et al.  SPICE-model of multiwall carbon nanotube through-hole vias , 2010, 2010 Asia-Pacific International Symposium on Electromagnetic Compatibility.

[49]  Alvin Leng Sun Loke,et al.  Microstructure and reliability of copper interconnects , 1998 .

[50]  H J Li,et al.  Multichannel ballistic transport in multiwall carbon nanotubes. , 2005, Physical review letters.

[51]  Ashok Srivastava,et al.  A model of multi-walled carbon nanotube interconnects , 2009, 2009 52nd IEEE International Midwest Symposium on Circuits and Systems.

[52]  Kwon,et al.  Unusually high thermal conductivity of carbon nanotubes , 2000, Physical review letters.

[53]  P. Kapur,et al.  Compact Performance Models and Comparisons for Gigascale On-Chip Global Interconnect Technologies , 2009, IEEE Transactions on Electron Devices.

[54]  A. G. S. Filho,et al.  Improvement of the electrical contact between carbon nanotubes and metallic electrodes by laser irradiation , 2013, 28th Symposium on Microelectronics Technology and Devices (SBMicro 2013).

[55]  Yaser M. Banadaki,et al.  Metallic single-walled, carbon nanotube temperature sensor with self heating , 2014, Smart Structures.