Skip to main content
SpringerLink
Log in

An impact of multi-layered structures of modern optoelectronic devices on their thermal properties

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

Phonon scattering at layer boundaries reducing efficiency of heat extraction from volumes of modern multi-layered electronic devices is believed to be one of the most important obstacles to their further miniaturization. Therefore the main goal of this work is to examine theoretically thermal conductivities of thin semiconductor layers as a function of their thickness using, as a typical example, the GaAs layer between two AlAs or (AlGa)As layers. Applicability of various possible theoretical approaches to a heat transport in such a structure is discussed. However, theory of the nanoscale thermal transport has been found to be still at an immature stage. Nevertheless, following the phonon-radiative-transfer approach of Chen and Tien derived from the Boltzmann transport equation, the RT (=300 K) GaAs thermal conductivity has been found to be dramatically reduced from its bulk value of 44 W/mK, to only 1.05 W/mK for the 20-nm layer and even to 0.15 W/mK for 2-nm layer, which is in a general agreement with experimental results. However, this approach has happened to give distinctly incorrect results for relatively small composition changes of successive layers. Then reasonable values of effective thermal conductivities should be extracted from thermal conductivities determined experimentally for similar devices.

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

  • Amith A., Kudman I. and Steigmeier E.F. (1965). Electron and phonon scattering in GaAs at high temperatures. Phys. Rev. 138: A1270–A1276

    Article  ADS  Google Scholar 

  • Berman R., Foster E.L. and Ziman J.M. (1955). Thermal conduction in artificial sapphire crystals at low temperatures. Proc. Roy. Soc. A (London) 231: 130–144

    ADS  Google Scholar 

  • Bies W.E., Radtke R.J. and Ehrenreich H. (2000). Phonon dispersion effects and the thermal conductivity reduction in GaAs/AlAs superlattices. J. Appl. Phys. 88: 1498–1503

    Article  ADS  Google Scholar 

  • Borca-Tasciuc T., Song T.W., Meyer J.R., Vurgaftman I., Yang M.-J., Nosho B.Z., Whitman L.J., Lee H., Martinelli R.U., Turner G.W., Manfra M.J. and Chen G. (2002). Thermal conductivity of AlAs0.07Sb0.93 and Al0.9Ga0.1As0.07Sb0.93 alloys and (AlAs)1/(AlSb)11 digital-alloy superlattices. J. Appl. Phys. 92: 4994–4998

    Article  ADS  Google Scholar 

  • Cahill D.G., Ford W.K., Goodson K.E., Mahan G.D., Majumdar A., Maris H.J., Merlin R and Phillpot S.R. (2003). Nanoscale thermal transport. J. Appl. Phys. 93: 793–818

    Article  ADS  Google Scholar 

  • Callaway J. (1959). Model of lattice thermal conductivity at low temperature. Phys. Rev. 113: 1046–1051

    Article  MATH  ADS  Google Scholar 

  • Capinski W.S., Cardona M., Katzer D.S., Maris H.J., Ploog K. and Ruf T. (1999b). Thermal conductivity of GaAs/AlAs superlattices. Physica B 263–264: 530–532

    Article  Google Scholar 

  • Capinski W.S. and Maris H.J. (1996). Thermal conductivity of GaAs/AlAs superlattices. Physica B 219&220: 699–701

    Article  Google Scholar 

  • Capinski W.S., Maris H.J., Ruf T., Cardona M., Ploog K. and Katzer D.S. (1999a). Thermal-conductivity measurements of GaAs/AlAs superlattices using a picosecond optical pump-and-probe technique. Phys. Rev. B 59: 8105–8113

    Article  ADS  Google Scholar 

  • Casimir H.B.G. (1938). Note on the conduction of heat in crystals. Physica 5: 495–500

    Article  ADS  Google Scholar 

  • Cattaneo C. (1958). C. R. Acad. Sci. 247: 431

    MathSciNet  Google Scholar 

  • Chen G. (1997). Size and interface effects on thermal conductivity of superlattices and periodic thin-film structures. J. Heat Transfer 119: 220–229

    Article  Google Scholar 

  • Chen G. (1998). Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices. Phys. Rev. B 57: 14958–14973

    Article  ADS  Google Scholar 

  • Chen G. (2000). Particularities of heat conduction in nanostractures. J. Nanoparticle Res. 2: 199–204

    Article  Google Scholar 

  • Chen G. (2001). Ballistic-diffusive heat conduction equation. Phys. Rev. Lett. 86: 2297–2300

    Article  ADS  Google Scholar 

  • Chen G. (2002). Ballistic-diffusive equations for transient heat conduction from nano to macroscales. J. Heat Transfer 124: 320–328

    Article  Google Scholar 

  • Chen G. and Neagu M. (1997). Thermal conductivity and heat transfer in superlattices. Appl. Phys. Lett. 71: 2761–2763

    Article  ADS  Google Scholar 

  • Chen G. and Tien C.L. (1993). Thermal conductivities of quantum well structures. J. Thermophys. Heat Transfer 7: 311–318

    Article  ADS  Google Scholar 

  • Daly B.C. and Maris H.J. (2002). Calculation of the thermal conductivity of superlattices by molecular dynamics simulation. Physica B 316–317: 247–249

    Article  Google Scholar 

  • Escobar R.A., Ghai S.S., Jhon M.S. and Amon C.H. (2006). Multi-length and time scale thermal transport using the lattice Boltzmann method with application to electronics cooling. Int. J. Heat Mass Transfer 49: 97–107

    Article  Google Scholar 

  • Flik M.I., Choi B.I. and Goodson K.E. (1992). Heat transfer regimes in microstructures. J. Heat Transfer 114: 666–674

    Article  Google Scholar 

  • Flik M.I. and Tien C.L. (1990). Size effect on the thermal conductivity of high-Tc thin film superconductors. J. Heat Transfer 112: 872–881

    Article  Google Scholar 

  • Holland M.G. (1963). Analysis of lattice thermal conductivity. Phys. Rev. 132: 2461–2471

    Article  ADS  Google Scholar 

  • Holland M.G. (1964). Phonon scattering in semiconductors from thermal conductivity studies. Phys. Rev. 134: A471–A480

    Article  ADS  Google Scholar 

  • Joseph D.D. and Preziosi L. (1989). Heat waves. Rev. Mod. Phys. 61: 41–53

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Joseph D.D. and Preziosi L. (1990). Heat waves. Rev. Mod. Phys. 62: 375–391

    Article  ADS  MathSciNet  Google Scholar 

  • Joshi A.A. and Majumdar A. (1993). Transient ballistic and diffusive phonon heat transport in thin films. J. Appl. Phys. 74: 31–39

    Article  ADS  Google Scholar 

  • Ju Y.S. and Goodson K.E. (1999). Phononscattering in silicon films with thickness of order 100 nm. Appl. Phys. Lett. 74: 3005–3007

    Article  ADS  Google Scholar 

  • Klitsner T., VanCleve J.E., Fisher H.E. and Pohl R.O. (1988). Phonon radiative heat transfer and surface scattering. Phys. Rev. B 38: 7576–7594

    Article  ADS  Google Scholar 

  • Lambropoulos J.C., Jolly M.R., Amsden C.A., Gilman S.E., Sinisropi M.J., Diakomihalis D. and Jacobs S.D. (1989). Thermal conductivity of dielectric thin films. J. Appl. Phys. 66: 4230–4242

    Article  ADS  Google Scholar 

  • Lee S.-M., Cahill D.G. and Venkatasubramanian R. (1997). Thermal conductivity of Si–Ge superlattices. Appl. Phys. Lett. 70: 2957–2959

    Article  ADS  Google Scholar 

  • Liang L.H. and Li B. (2006). Size-dependent thermal conductivity of nanoscale semiconducting systems. Phys. Rev. B 73: 153303

    Article  ADS  Google Scholar 

  • Majumdar A. (1991a). Microscale heat conduction in dielectric thin films. ASME HTD 184: 34–41

    Google Scholar 

  • Majumdar A. (1991b). Effect of interfacial roughness on phonon radiative heat conduction. J. Heat Transfer 113: 797–805

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Murthy J.Y., Narumanchi S.V.J., Pascual-Gutierrez J.A., Wang T., Ni Ch. and Mathur S.R. (2005). Review of multi-scale simulation in sub-micron heat transfer. Int. J. Multiscale Comput. Eng. 3: 5–32

    Article  Google Scholar 

  • Narayanamuri V., Störmer H.L., Chin M.A., Gossard A.C. and Wiegmann W. (1979). Selective transmission of high-frequency phonons by a superlattice: the ‘dielectric phonon filter. Phys. Rev. Lett. 43: 2012–2016

    Article  ADS  Google Scholar 

  • Norris P.M., Chen G. and Tien Ch.-L. (1994). Size effects on the temperature rise in vertical-cavity surface-emitting laser diodes. Int. J. Heat Mass Transfer 37(Suppl. 1): 9–17

    Article  Google Scholar 

  • Piprek J., Tröger T., Schröter B., Kolodzey J. and Ih C.S. (1998). Thermal conductivity reduction in GaAs–AlAs distributed Bragg reflectors. IEEE Photon. Technol. Lett. 10: 81–83

    Article  ADS  Google Scholar 

  • Ren S.Y. and Dow J.D. (1982). Thermal conductivity of superlattice. Phys. Rev. B 25: 3750–3755

    Article  ADS  Google Scholar 

  • Ridley B.K. (1997). Electrons and Phonons in Semiconductor Multilayers. Cambridge University Press, Cambridge

    Google Scholar 

  • Shelling P.K. and Phillpot S.R. (2003). Multiscale simulation of phonon transport in superlattices. J. Appl. Phys. 93: 5377–5387

    Article  ADS  Google Scholar 

  • Simkin M.V. and Mahan G.D. (2000). Minimum thermal conductivity of superlattices. Phys. Rev. Lett. 84: 927–930

    Article  ADS  Google Scholar 

  • Swartz E.T. and Pohl R.O. (1989). Thermal boundary resistance. Rev. Modern Phys. 61: 605–668

    Article  ADS  Google Scholar 

  • Touzelbaev M.N., Zhou P., Venkatasubramanian R. and Goodson K.E. (2001). Thermal characterization of Bi2Te3/Sb2Te3 superlattices. J. Appl. Phys. 90: 763–767

    Article  ADS  Google Scholar 

  • Yao T. (1987). Thermal properties of AlAs/GaAs superlattices. Appl. Phys. Lett. 51: 1798–1800

    Article  ADS  Google Scholar 

  • Yu X.Y., Chen G., Verma A. and Smith J.S. (1995). Temperature dependence of thermophysical properties of GaAs/AlAs periodic structure. Appl. Phys. Lett. 67: 3554–3556

    Article  ADS  Google Scholar 

  • Ziman J.M. (1960). Electrons and Phonons. Clarendon, Oxford

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Computer Physics, Institute of Physics, Technical University of Łódź, ul. Wólczańska 219, 93-005, Łódź, Poland

    Elżbieta Gęsikowska & Włodzimierz Nakwaski

Authors
  1. Elżbieta Gęsikowska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Włodzimierz Nakwaski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Włodzimierz Nakwaski.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gęsikowska, E., Nakwaski, W. An impact of multi-layered structures of modern optoelectronic devices on their thermal properties. Opt Quant Electron 40, 205–216 (2008). https://doi.org/10.1007/s11082-007-9151-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11082-007-9151-z

Keywords

Search

Navigation