Skip to main content
SpringerLink
Log in

Modeling heating effects in nanoscale devices: the present and the future

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

Abstract

In this review paper we give an overview on the present state of the art in modeling heat transport in nanoscale devices and what issues we need to address for better and more successful modeling of future devices. We begin with a brief overview of the heat transport in materials and explain why the simple Fourier law fails in nanoscale devices. Then we elaborate on attempts to model heat transport in nanostructures from both perspectives: nanomaterials (the work of Narumanchi and co-workers) and nanodevices (the work of Majumdar, Pop, Goodson and recently Vasileska, Raleva and Goodnick). We use our own simulation results which we have used to examine heat transport in nanoscaling devices to point out some important issues such as the fact that thermal degradation does not increase as we decrease feature size due to the more pronounced non-stationary transport and ballistic transport effects in nanoscale devices. We also point out that instead of using SOI, if one uses Silicon on Diamond technology there is much less heat degradation and better spread of the heat in the Diamond material. We also point out that tools for thermal modeling of nanoscale devices need to be improved from the present state of the art as 3D tools are needed, for example, to simulate heat transport and electrical transport in a FinFET device. Better models than the energy balance equations for the acoustic and optical phonons what we presently use in our simulators are also welcomed. The ultimate goal is to design the tool that can be efficient enough but at the same time can simulate most accurately both electrons and phonons within the particle pictures by solving their corresponding Boltzmann transport equations self-consistently. Investigations in integration of Peltier coolers with CMOS technology are also welcomed and much needed to reduce the problem of heat dissipation in nanoscale devices and interconnects.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Feynman, R.P.: In: Gilbert, H.D. (ed.) Miniaturization, pp. 282–296. Reinhold, New York (1961)

    Google Scholar 

  2. International Technology Roadmap for Semiconductors (ITRS). http://public.itrs.net/ (2003)

  3. Keyes, R.W.: Fundamental limits of silicon technology. Proc. IEEE 89, 227 (2001)

    Article  Google Scholar 

  4. Nalwa, H.S. (ed.): Nanostructured Materials and Nanotechnology. Academic Press, London (2002)

    Google Scholar 

  5. Dresselhaus, M.S., Thomas, I.L.: Alternative energy technologies. Nature 414, 332 (2001)

    Article  Google Scholar 

  6. Borkar, S.: Design challenges of technology scaling. IEEE Micro 19, 23–29 (1999)

    Article  Google Scholar 

  7. Geppert, L.: Solid state [semiconductors. 1999 technology analysis and forecast]. IEEE Spectrum 36, 52–56 (1999)

    Article  Google Scholar 

  8. Zeng, G., Fan, X., LaBounty, C., Croke, E., Zhang, Y., Christofferson, J., Vashaee, D., Shakouri, A., Bowers, J.E.: Cooling power density of SiGe/Si superlattice micro refrigerators. In: Materials Research Society Fall Meeting 2003, Boston. Proceedings vol. 793, paper S2.2 (2003)

  9. Majumdar, A.: Microscale heat conduction in dielectric thin films. J. Heat Transfer 115, 7–16 (1993)

    Article  Google Scholar 

  10. Chen, G.: Ballistic-diffusive heat-conduction equations. Phys. Rev. Lett. 86, 2297–2300 (2001)

    Article  Google Scholar 

  11. Reif, F.: Fundamentals of Statistical and Thermal Physics. McGraw-Hill, London (1985)

    Google Scholar 

  12. Asheghi, M., Touzelbaev, M.N., Goodson, K.E., Leung, Y.K., Wong, S.S.: Temperature dependent thermal conductivity of single-crystal silicon layers in SOI substrates. J. Heat Transfer 120, 30–33 (1998)

    Article  Google Scholar 

  13. Choi, S.-H., Maruyama, S.: Evaluation of the phonon mean free path in thin films by using classical molecular dynamics. J. Korean Phys. Soc. 43, 747–753 (2003)

    Google Scholar 

  14. Ju, Y.S., Goodson, K.E.: Phonon scattering in silicon films with thickness of order 100 nm. Appl. Phys. Lett. 74, 3005–3007 (1999)

    Article  Google Scholar 

  15. Liu, W., Asheghi, M.: Phonon-boundary scattering in ultra thin single-crystal silicon layers. Appl. Phys. Lett. 84, 3819–3821 (2004)

    Article  Google Scholar 

  16. Liu, W., Asheghi, M.: Thermal conductivity of ultra-thin single crystal silicon layers. J. Heat Transfer 128, 75–83 (2005)

    Article  Google Scholar 

  17. Ruxandra, M., Costescu, M., Wall, A., Cahill, D.G.: Thermal conductance of epitaxial interfaces. Phys. Rev. B 67, 054302 (2003)

    Article  Google Scholar 

  18. Chen, G., Shakouri, A.: Heat transfer in nanostructures for solid-state energy conversion. J. Heat Transfer 124, 242–252 (2002)

    Article  Google Scholar 

  19. Vashaee, D., Shakouri, A.: Electronic and thermoelectric transport in semiconductor and metallic superlattices. J. Appl. Phys. 95, 1233–1245 (2004)

    Article  Google Scholar 

  20. Vashaee, D., Shakouri, A.: Nonequilibrium electrons and phonons in thin film thermionic coolers. Microscale Thermophys. Eng. 8, 91–100 (2004)

    Article  Google Scholar 

  21. Pop, E., Sinha, S., Goodson, K.E.: Heat genareation and transport in nanometer-scale transistors. Proc. IEEE 94, 1587–1601 (2006)

    Article  Google Scholar 

  22. Lai, J., Majumdar, A.: Concurent thermal and electrical modeling of submicrometer silicon devices. J. Appl. Phys. 79, 7353 (1996)

    Article  Google Scholar 

  23. Majumdar, A., Fushinobu, K., Hijikata, K.: Effect of hate voltage on hot electron and hot phonon interaction and transport in a submicrometer transistor. J. Appl. Phys. 77, 6686 (1995)

    Article  Google Scholar 

  24. Wachutka, G.K.: Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling. IEEE Trans. Comput. Aided Des. 11, 1141–1149 (1990)

    Article  Google Scholar 

  25. Gaur, S.P., Navon, D.H.: Two-dimensional carrier flow in a transistor structure under non-isothermal conditions. IEEE Trans. Electron Devices 23, 50–57 (1976)

    Article  Google Scholar 

  26. Leung, Y.K., Paul, A.K., Goodson, K.E., Plummer, J.D., Wong, S.S.: Heating mechanisms of LDMOS and LIGBT in ultrathin SOI. IEEE Electron Device Lett. 18, 414 (1997)

    Article  Google Scholar 

  27. Sadi, T., Kelsall, R.W., Pilgrim, N.J.: Electrothermal Monte Carlo simulation of submicrometer Si/SiGe MODFETs. IEEE Trans. Electron Devices 54(2), 332–339 (2007)

    Article  Google Scholar 

  28. Narumanchi, S.V.J., Murthy, J.Y., Amon, C.H.: Submicron heat transport model in silicon accounting for phonon dispersion and polarization. J. Heat Transfer 126, 946–955 (2004)

    Article  Google Scholar 

  29. Cercignani, C.: The Boltzmann Equation and its Applications. Applied Mathematical Sciences, vol. 67. Springer, Berlin (1988)

    MATH  Google Scholar 

  30. Sinha, S., Pop, E., Dutton, R.W., Goodson, K.E.: Non-equilibrium phonon distributions in sub-100 nm silicon transistors. Trans. ASME 128, 638–647 (2006)

    Article  Google Scholar 

  31. Raleva, K., Vasileska, D., Goodnick, S.M.: J. Appl. Phys. (2008, submitted)

  32. Tien, C.L., Majumdar, A., Gerner, F.M. (eds.): Microscale Energy Transport. Taylor & Francis, London (1998)

    Google Scholar 

  33. Raman, A., Walker, D.G., Fisher, T.S.: Non-equilibrium thermal effects in SOI power transistors. Solid-State Electron. 47, 1265–1273 (2003)

    Article  Google Scholar 

  34. He, X.: M.S. Thesis, Arizona State University (1999). Advisor: Prof. D. Vasileska

  35. Ahmed, S.S.: Ph.D. Thesis, Arizona State University (2005). Advisor: Prof. D. Vasileska

  36. http://www.silvaco.com/

  37. Ferry, D.K.: Semiconductor Transport. Taylor & Francis, London (2000)

    Google Scholar 

  38. Artaki, M., Price, P.J.: Hot phonon effects in silicon field-effect-transistors. J. Appl. Phys. 65, 1317–1320 (1989)

    Article  Google Scholar 

  39. Raman, A., Walker, D.G., Fisher, T.S.: Non-equilibrium thermal effects in SOI power transistors. Solid-State Electron. 47, 1265–1273 (2003)

    Article  Google Scholar 

  40. http://www.sp3inc.com/dimd_sil.htm

  41. Li, J., Ma, T.-P.: Scattering of silicon inversion layer electrons by metal/oxide interface roughness. J. Appl. Phys. 62, 4212–4215 (1987)

    Article  Google Scholar 

  42. Chu, P.K.: Novel silicon-on-insulator structures for reduced self-heating effects, IEEE Circuits Syst. Mag. (2005)

  43. Sverdrup, P.G., Sinha, S., Uma, S., Asheghi, M., Goodson, K.E.: Appl. Phys. Lett. 78, 3331 (2001)

    Article  Google Scholar 

  44. Goshal, U., et al.: Appl. Phys. Lett. 80, 3006 (2002)

    Article  Google Scholar 

  45. Chen, G.: J. Heat Transfer 118, 539 (1996)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Arizona State University, Tempe, AZ, 85287-5706, USA

    D. Vasileska & S. M. Goodnick

  2. FEIT-UKIM, Skopje, Republic of Macedonia

    K. Raleva

Authors
  1. D. Vasileska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Raleva
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. M. Goodnick
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Vasileska.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vasileska, D., Raleva, K. & Goodnick, S.M. Modeling heating effects in nanoscale devices: the present and the future. J Comput Electron 7, 66–93 (2008). https://doi.org/10.1007/s10825-008-0254-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10825-008-0254-y

Keywords

Search

Navigation