Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T17:58:04.688Z Has data issue: false hasContentIssue false
  • English
  • Français

Engineering thermal transport in SiGe-based nanostructures for thermoelectric applications

Published online by Cambridge University Press:  05 August 2015

Meenakshi Upadhyaya ,
Seyedeh Nazanin Khatami  and
Zlatan Aksamija
Meenakshi Upadhyaya
Affiliation:
Department of Electrical and Computer Engineering, University of Massachusetts–Amherst, Amherst, Massachusetts 01003-9292, USA
Seyedeh Nazanin Khatami
Affiliation:
Department of Electrical and Computer Engineering, University of Massachusetts–Amherst, Amherst, Massachusetts 01003-9292, USA
Zlatan Aksamija*
Affiliation:
Department of Electrical and Computer Engineering, University of Massachusetts–Amherst, Amherst, Massachusetts 01003-9292, USA
*
a)Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

Thermoelectric converters based on silicon nanostructures offer exciting opportunities for higher efficiency, lower cost, ease of manufacturing, and integration into circuits. This paper considers phonon transport in a broad range of nanostructured materials made from Si, Ge, and their alloys. Our model based on the phonon Boltzmann transport equation captures the lattice thermal transport in silicon–germanium (SiGe) nanostructures, including thin films, superlattices (SLs), and nanocomposites. In nanocomposites, the model captures the grain structure using a Voronoi tessellation to mimic the grains and their size distribution. Our results show thermal conductivity in SiGe nanostructures below their bulk counterparts and reaching almost to the amorphous limit of thermal conductivity. We also demonstrate that thermal transport in SiGe nanostructures is tuneable by sample size (thin films), period thickness (SLs), and grain size (nanocomposites) through boundary scattering. Our results are relevant to the design of nanostructured SiGe alloys for thermoelectric applications.

Keywords

thermoelectricthermal conductivitysimulation
Type
Articles
Information
Journal of Materials Research , Volume 30 , Issue 17: Focus Issue: Advances in Thermoelectric Materials II , 14 September 2015 , pp. 2649 - 2662
Copyright
Copyright © Materials Research Society 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Hochbaum, A.I., Chen, R., Delgado, R.D., Liang, W., Garnett, E.C., Najarian, M., Majumdar, A., and Yang, P.: Enhanced thermoelectric performance of rough silicon nanowires. Nature 451, 163 (2008).Google Scholar
DiSalvo, F.J.: Thermoelectric cooling and power generation. Science 285, 703–706 (1999).Google Scholar
Glassbrenner, C.J. and Slack, G.A.: Thermal conductivity of silicon and germanium from 3k to the melting point. Phys. Rev. 134, A1058–A1069 (1964).Google Scholar
Maycock, P.D.: Thermal conductivity of silicon, germanium, III–V compounds and III–V alloys. Solid-State Electron. 10, 161–168 (1967).Google Scholar
Liao, C.N., Chen, C., and Tu, K.N.: Thermoelectric characterization of Si thin films in silicon-on-insulator wafers. J. Appl. Phys. 86, 3204–3208 (1999).Google Scholar
Vining, C.B.: An inconvenient truth about thermoelectrics. Nat. Mater. 8, 83–85 (2009).Google Scholar
Bera, C., Soulier, M., Navone, C., Roux, G., Simon, J., Volz, S., and Mingo, N.: Thermoelectric properties of nanostructured Si1−xGex and potential for further improvement. J. Appl. Phys. 108, 124306 (2010).CrossRefGoogle Scholar
Jeffrey Snyder, G. and Toberer, E.S.: Complex thermoelectric materials. Nat. Mater. 7, 105–114 (2008).Google Scholar
Hicks, L.D. and Dresselhaus, M.S.: Effect of quantum-well structures on the thermoelectric figure of merit. Phys. Rev. B 47, 12727 (1993a).Google Scholar
Dresselhaus, M.S., Chen, G., Tang, M.Y., Yang, R.G., Lee, H., Wang, D.Z., Ren, Z.F., Fleurial, J-P., and Gogna, P.: New directions for low-dimensional thermoelectric materials. Adv. Mater. 19, 1043–1053 (2007).Google Scholar
Wang, K.L., Chen, G., Khitun, A., and Balandin, A.: Enhancement of the thermoelectric figure of merit of Si1−xGex quantum wires due to spatial confinement of acoustic phonons. Phys. E 8, 13–18 (2000).Google Scholar
Lazarenkova, O.L. and Balandin, A.A.: Mechanisms for thermoelectric figure-of-merit enhancement in regimented quantom dot superlattices. Appl. Phys. Lett. 82, 415–417 (2003).Google Scholar
Hicks, L.D. and Dresselhaus, M.S.: Thermoelectric figure of merit of a one-dimensional conductor. Phys. Rev. B 47, 16631 (1993b).Google Scholar
Joshi, G., Lee, H., Lan, Y., Wang, X., Zhu, G., Wang, D., Gould, R.W., Cuff, D.C., Tang, M.Y., Dresselhaus, M.S., Chen, G., and Ren, Z.: Enhanced thermoelectric figure-of-merit in nanostructured p-type silicon germanium bulk alloys. Nano Lett. 8, 4670–4674 (2008).Google Scholar
Minnich, A.J., Lee, H., Wang, X.W., Joshi, G., Dresselhaus, M.S., Ren, Z.F., Chen, G., and Vashaee, D.: Modeling study of thermoelectric SiGe nanocomposites. Phys. Rev. B 80, 155327 (2009).Google Scholar
Zhu, G.H., Lee, H., Lan, Y.C., Wang, X.W., Joshi, G., Wang, D.Z., Yang, J., Vashaee, D., Guilbert, H., Pillitteri, A., Dresselhaus, M.S., Chen, G., and Ren, Z.F.: Increased phonon scattering by nanograins and point defects in nanostructured silicon with a low concentration of germanium. Phys. Rev. Lett. 102, 196803 (2009).Google Scholar
Ryu, H.J., Aksamija, Z., Paskiewicz, D.M., Scott, S.A., Lagally, M.G., Knezevic, I., and Eriksson, M.A.: Quantitative determination of contributions to the thermoelectric power factor in si nanostructures. Phys. Rev. Lett. 105, 256601 (2010).Google Scholar
Aksamija, Z. and Knezevic, I.: Anisotropy and boundary scattering in the lattice thermal conductivity of silicon nanomembranes. Phys. Rev. B 82, 045319 (2010).Google Scholar
Aksamija, Z. and Knezevic, I.: Thermal conductivity of Si1−xGex/Si1−yGey superlattices: Competition between interfacial and internal scattering. Phys. Rev. B 88, 155318 (2013).Google Scholar
Aksamija, Z.: Lattice thermal transport in si-based nanocomposites for thermoelectric applications. J. Electron. Mater. 44 1–7 (2014).Google Scholar
Cahill, D.G., Braun, P.V., Chen, G., Clarke, D.R., Fan, S., Goodson, K.E., Keblinski, P., King, W.P., Mahan, G.D., Majumdar, A., Maris, H.J., Phillpot, S.R., Pop, E., and Shi, L.: Nanoscale thermal transport. II. 2003–2012. Appl. Phys. Rev. 1, 011305 (2014).Google Scholar
Cahill, D.G., Ford, W.K., Goodson, K.E., Mahan, G.D., Majumdar, A., Maris, H.J., Merlin, R., and Phillipot, S.R.: Nanoscale thermal transport. J. Appl. Phys. 93, 793–818 (2003).Google Scholar
Carruthers, P.: Theory of thermal conductivity of solids at low temperatures. Rev. Mod. Phys. 33, 92 (1961).Google Scholar
Morelli, D.T., Heremans, J.P., and Slack, G.A.: Estimation of the isotope effect on the lattice thermal conductivity of group IV and group III-V semiconductors. Phys. Rev. B 66, 195304 (2002).Google Scholar
Ward, A. and Broido, D.A.: Intrinsic phonon relaxation times from first-principles studies of the thermal conductivities of Si and Ge. Phys. Rev. B 81, 085205 (2010).Google Scholar
Esfarjani, K., Chen, G., and Stokes, H.T.: Heat transport in silicon from first-principles calculations. Phys. Rev. B 84, 085204 (2011).Google Scholar
Tamura, S-I.: Isotope scattering of dispersive phonons in Ge. Phys. Rev. B 27, 858–866 (1983).Google Scholar
Maris, H.J.: Phonon propagation with isotope scattering and spontaneous anharmonic decay. Phys. Rev. B 41, 9736–9743 (1990).Google Scholar
Garg, J., Bonini, N., Kozinsky, B., and Marzari, N.: Role of disorder and anharmonicity in the thermal conductivity of silicon-germanium alloys: A first-principles study. Phys. Rev. Lett. 106, 045901 (2011).Google Scholar
Gilat, G. and Raubenheimer, L.J.: Accurate numerical method for calculating frequency-distribution functions in solids. Phys. Rev. 144, 390–395 (1966).CrossRefGoogle Scholar
Abeles, B., Beers, D.S., Cody, G.D., and Dismukes, J.P.: Thermal conductivity of Ge-Si alloys at high temperatures. Phys. Rev. 125, 44–46 (1962).Google Scholar
Rieger, M.M. and Vogl, P.: Electronic-band parameters in strained Si1−xGex and Si1−yGey substrates. Phys. Rev. B 48, 14276–14287 (1993).Google Scholar
Abeles, B.: Lattice thermal conductivity of disordered semiconductor alloys at high temperatures. Phys. Rev. 131, 1906–1911 (1963).Google Scholar
Klemens, P.G.: Thermal resistance due to point defects at high temperatures. Phys. Rev. 119, 507–509 (1960).Google Scholar
Slack, G.: Solid State Physics, Vol. 34, Seitz, F., Ehrenreich, H., and Turnbull, D. eds.; Academic Press: New York, NY, 1979.Google Scholar
Turney, J.E., McGaughey, A.J.H., and Amon, C.H.: In-plane phonon transport in thin films. J. Appl. Phys. 107, 024317 (2010).Google Scholar
Sondheimer, E.H.: The mean free path of electrons in metals. Adv. Phys. 1, 1–42 (1952).CrossRefGoogle Scholar
Cheaito, R., Duda, J.C., Beechem, T.E., Hattar, K., Ihlefeld, J.F., Medlin, D.L., Rodriguez, M.A., Campion, M.J., Piekos, E.S., and Hopkins, P.E.: Experimental investigation of size effects on the thermal conductivity of silicon-germanium alloy thin films. Phys. Rev. Lett. 109, 195901 (2012).Google Scholar
Liu, W. and Balandin, A.A.: Thermal conduction in AlxGa1−xN alloys and thin films. J. Appl. Phys. 97, 073710 (2005).Google Scholar
Cahill, D.G., Watson, S.K., and Pohl, R.O.: Lower limit to the thermal conductivity of disordered crystals. Phys. Rev. B 46, 6131–6140 (1992).Google Scholar
Feser, J.P., Chan, E.M., Majumdar, A., Segalman, R.A., and Urban, J.J.: Ultralow thermal conductivity in polycrystalline cdse thin films with controlled grain size. Nano Lett. 13, 2122–2127 (2013).Google Scholar
Venkatasubramanian, R., Siivola, E., Colpitts, T., and O'Quinn, B.: Thin-film thermoelectric devices with high room-temperature figures of merit. Nature 413, 597 (2001).Google Scholar
Huxtable, S.T., Abramson, A.R., Tien, C-L., Majumdar, A., LaBounty, C., Fan, X., Zeng, G., Bowers, J.E., Shakouri, A., and Croke, E.T.: Thermal conductivity of Si/SiGe and SiGe/SiGe superlattices. Appl. Phys. Lett. 80, 1737–1739 (2002).Google Scholar
Hyldgaard, P. and Mahan, G.D.: Phonon superlattice transport. Phys. Rev. B 56, 10754–10757 (1997).CrossRefGoogle Scholar
Chen, G.: Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices. Phys. Rev. B 57, 14958–14973 (1998).Google Scholar
Simkin, M.V. and Mahan, G.D.: Minimum thermal conductivity of superlattices. Phys. Rev. Lett. 84, 927–930 (2000).Google Scholar
Yang, B. and Chen, G.: Lattice dynamics study of anisotropic heat conduction in superlattices. Microscale Thermophys. Eng. 5, 107–116 (2001).Google Scholar
Martin, P., Aksamija, Z., Pop, E., and Ravaioli, U.: Impact of phonon-surface roughness scattering on thermal conductivity of thin Si nanowires. Phys. Rev. Lett. 102, 125503 (2009).Google Scholar
Dismukes, J.P., Ekstrom, L., Steigmeier, E.F., Kudman, I., and Beers, D.S.: Thermal and electrical properties of heavily doped Ge-Si alloys up to 1300[degree]k. J. Appl. Phys. 35, 2899–2907 (1964).Google Scholar
Klemens, P.G.: Solid State Physics (Academic Press, NY, 1958).Google Scholar
Bae, M-H., Li, Z., Aksamija, Z., Martin, P.N., Xiong, F., Ong, Z-Y., Knezevic, I., and Pop, E.: Ballistic to diffusive crossover of heat flow in graphene ribbons. Nat. Commun. 4, 1734 (2013).Google Scholar
Weber, W.: Adiabatic bond charge model for the phonons in diamond, Si, Ge, and α−Sn. Phys. Rev. B 15, 4789 (1977).Google Scholar
Rustagi, K.C. and Weber, W.: Adiabatic bond charge model for the phonons in A3B5 semiconductors. Solid State Commun. 18, 673–675 (1976).Google Scholar
Strauch, D. and Dorner, B.: Phonon dispersion in GaAs. J. Phys.: Condens. Matter 2, 1457–1474 (1990).Google Scholar
Rajput, B.D. and Browne, D.A.: Lattice dynamics of II-VI materials using the adiabatic bond-charge model. Phys. Rev. B 53, 9052–9058 (1996).Google Scholar
Khitun, A., Balandin, A., Liu, J.L., and Wang, K.L.: In-plane lattice thermal conductivity of a quantum-dot superlattice. J. Appl. Phys. 88, 13–18 (2000).CrossRefGoogle Scholar
Liu, J.L., Wang, K.L., Khitun, A., and Balandin, A.: The effect of the long-range order in a quantum dot array on the in-plane lattice thermal conductivity. Superlattices Microstruct. 30, 415–417 (2001).Google Scholar
Aksamija, Z. and Ravaioli, U.: Anharmonic decay of g-process longitudinal optical phonons in silicon. Appl. Phys. Lett. 96, 091911 (2010).Google Scholar
Shamsa, M., Liu, W., Balandin, A.A., and Liu, J.: Phonon-hopping thermal conduction in quantum dot superlattices. Appl. Phys. Lett. 87, 202105 (2005).Google Scholar
Shamsa, M., Alim, K., Balandin, A.A., Bao, Y., Liu, W.L., and Liub, J.L.: Electrical and thermal conductivity of Ge/Si quantum dot superlattices. J. Electrochem. Soc. 152, 6432–6435 (2005).Google Scholar
Lan, Y., Jerome Minnich, A., Chen, G., and Ren, Z.: Enhancement of thermoelectric figure-of-merit by a bulk nanostructuring approach. Adv. Funct. Mater. 20, 357–376 (2010).Google Scholar
Wang, Z. and Mingo, N.: Absence of casimir regime in two-dimensional nanoribbon phonon conduction. Appl. Phys. Lett. 99, 101903 (2011).Google Scholar
Braginsky, L., Lukzen, N., Shklover, V., and Hofmann, H.: High-temperature phonon thermal conductivity of nanostructures. Phys. Rev. B 66, 134203 (2002).Google Scholar
Zebarjadi, M., Esfarjani, K., Bian, Z., and Shakouri, A.: Low-temperature thermoelectric power factor enhancement by controlling nanoparticle size distribution. Nano Lett. 11, 225–230 (2011).Google Scholar