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.
Similar content being viewed by others
References
A.I. Hochbaum, R. Chen, R.D. Delgado, W. Liang, E.C. Garnett, M. Najarian, A. Majumdar, and P. Yang: Enhanced thermoelectric performance of rough silicon nanowires. Nature 451, 163 (2008).
F.J. DiSalvo: Thermoelectric cooling and power generation. Science 285, 703–706 (1999).
C.J. Glassbrenner and G.A. Slack: Thermal conductivity of silicon and germanium from 3k to the melting point. Phys. Rev. 134, A1058–A1069 (1964).
P.D. Maycock: Thermal conductivity of silicon, germanium, III–V compounds and III–V alloys. Solid-State Electron. 10, 161–168 (1967).
C.N. Liao, C. Chen, and K.N. Tu: Thermoelectric characterization of Si thin films in silicon-on-insulator wafers. J. Appl. Phys. 86, 3204–3208 (1999).
C.B. Vining: An inconvenient truth about thermoelectrics. Nat. Mater. 8, 83–85 (2009).
C. Bera, M. Soulier, C. Navone, G. Roux, J. Simon, S. Volz, and N. Mingo: Thermoelectric properties of nanostructured Si1−xGex and potential for further improvement. J. Appl. Phys. 108, 124306 (2010).
G. Jeffrey Snyder and E.S. Toberer: Complex thermoelectric materials. Nat. Mater. 7, 105–114 (2008).
L.D. Hicks and M.S. Dresselhaus: Effect of quantum-well structures on the thermoelectric figure of merit. Phys. Rev. B 47, 12727 (1993a).
M.S. Dresselhaus, G. Chen, M.Y. Tang, R.G. Yang, H. Lee, D.Z. Wang, Z.F. Ren, J-P. Fleurial, and P. Gogna: New directions for low-dimensional thermoelectric materials. Adv. Mater. 19, 1043–1053 (2007).
K.L. Wang, G. Chen, A. Khitun, and A. Balandin: 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).
O.L. Lazarenkova and A.A. Balandin: Mechanisms for thermoelectric figure-of-merit enhancement in regimented quantom dot superlattices. Appl. Phys. Lett. 82, 415–417 (2003).
L.D. Hicks and M.S. Dresselhaus: Thermoelectric figure of merit of a one-dimensional conductor. Phys. Rev. B 47, 16631 (1993b).
G. Joshi, H. Lee, Y. Lan, X. Wang, G. Zhu, D. Wang, R.W. Gould, D.C. Cuff, M.Y. Tang, M.S. Dresselhaus, G. Chen, and Z. Ren: Enhanced thermoelectric figure-of-merit in nanostructured p-type silicon germanium bulk alloys. Nano Lett. 8, 4670–4674 (2008).
A.J. Minnich, H. Lee, X.W. Wang, G. Joshi, M.S. Dresselhaus, Z.F. Ren, G. Chen, and D. Vashaee: Modeling study of thermoelectric SiGe nanocomposites. Phys. Rev. B 80, 155327 (2009).
G.H. Zhu, H. Lee, Y.C. Lan, X.W. Wang, G. Joshi, D.Z. Wang, J. Yang, D. Vashaee, H. Guilbert, A. Pillitteri, M.S. Dresselhaus, G. Chen, and Z.F. Ren: Increased phonon scattering by nanograins and point defects in nanostructured silicon with a low concentration of germanium. Phys. Rev. Lett. 102, 196803 (2009).
H.J. Ryu, Z. Aksamija, D.M. Paskiewicz, S.A. Scott, M.G. Lagally, I. Knezevic, and M.A. Eriksson: Quantitative determination of contributions to the thermoelectric power factor in si nanostructures. Phys. Rev. Lett. 105, 256601 (2010).
Z. Aksamija and I. Knezevic: Anisotropy and boundary scattering in the lattice thermal conductivity of silicon nanomembranes. Phys. Rev. B 82, 045319 (2010).
Z. Aksamija and I. Knezevic: Thermal conductivity of Si1−xGex/Si1−yGey superlattices: Competition between interfacial and internal scattering. Phys. Rev. B 88, 155318 (2013).
Z. Aksamija: Lattice thermal transport in si-based nanocomposites for thermoelectric applications. J. Electron. Mater. 441–7 (2014).
D.G. Cahill, P.V. Braun, G. Chen, D.R. Clarke, S. Fan, K.E. Goodson, P. Keblinski, W.P. King, G.D. Mahan, A. Majumdar, H.J. Maris, S.R. Phillpot, E. Pop, and L. Shi: Nanoscale thermal transport. II. 2003–2012. Appl. Phys. Rev. 1, 011305 (2014).
D.G. Cahill, W.K. Ford, K.E. Goodson, G.D. Mahan, A. Majumdar, H.J. Maris, R. Merlin, and S.R. Phillipot: Nanoscale thermal transport. J. Appl. Phys. 93, 793–818 (2003).
P. Carruthers: Theory of thermal conductivity of solids at low temperatures. Rev. Mod. Phys. 33, 92 (1961).
D.T. Morelli, J.P. Heremans, and G.A. Slack: Estimation of the isotope effect on the lattice thermal conductivity of group IV and group III-V semiconductors. Phys. Rev. B 66, 195304 (2002).
A. Ward and D.A. Broido: Intrinsic phonon relaxation times from first-principles studies of the thermal conductivities of Si and Ge. Phys. Rev. B 81, 085205 (2010).
K. Esfarjani, G. Chen, and H.T. Stokes: Heat transport in silicon from first-principles calculations. Phys. Rev. B 84, 085204 (2011).
S-I. Tamura: Isotope scattering of dispersive phonons in Ge. Phys. Rev. B 27, 858–866 (1983).
H.J. Maris: Phonon propagation with isotope scattering and spontaneous anharmonic decay. Phys. Rev. B 41, 9736–9743 (1990).
J. Garg, N. Bonini, B. Kozinsky, and N. Marzari: Role of disorder and anharmonicity in the thermal conductivity of silicon-germanium alloys: A first-principles study. Phys. Rev. Lett. 106, 045901 (2011).
G. Gilat and L.J. Raubenheimer: Accurate numerical method for calculating frequency-distribution functions in solids. Phys. Rev. 144, 390–395 (1966).
B. Abeles, D.S. Beers, G.D. Cody, and J.P. Dismukes: Thermal conductivity of Ge-Si alloys at high temperatures. Phys. Rev. 125, 44–46 (1962).
M.M. Rieger and P. Vogl: Electronic-band parameters in strained Si1−xGex and Si1−yGey substrates. Phys. Rev. B 48, 14276–14287 (1993).
B. Abeles: Lattice thermal conductivity of disordered semiconductor alloys at high temperatures. Phys. Rev. 131, 1906–1911 (1963).
P.G. Klemens: Thermal resistance due to point defects at high temperatures. Phys. Rev. 119, 507–509 (1960).
G. Slack: Solid State Physics, Vol. 34, F. Seitz, H. Ehrenreich, and D. Turnbull eds.; Academic Press: New York, NY, 1979.
J.E. Turney, A.J.H. McGaughey, and C.H. Amon: In-plane phonon transport in thin films. J. Appl. Phys. 107, 024317 (2010).
E.H. Sondheimer: The mean free path of electrons in metals. Adv. Phys. 1, 1–42 (1952).
R. Cheaito, J.C. Duda, T.E. Beechem, K. Hattar, J.F. Ihlefeld, D.L. Medlin, M.A. Rodriguez, M.J. Campion, E.S. Piekos, and P.E. Hopkins: Experimental investigation of size effects on the thermal conductivity of silicon-germanium alloy thin films. Phys. Rev. Lett. 109, 195901 (2012).
W. Liu and A.A. Balandin: Thermal conduction in AlxGa1−xN alloys and thin films. J. Appl. Phys. 97, 073710 (2005).
D.G. Cahill, S.K. Watson, and R.O. Pohl: Lower limit to the thermal conductivity of disordered crystals. Phys. Rev. B 46, 6131–6140 (1992).
J.P. Feser, E.M. Chan, A. Majumdar, R.A. Segalman, and J.J. Urban: Ultralow thermal conductivity in polycrystalline cdse thin films with controlled grain size. Nano Lett. 13, 2122–2127 (2013).
R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O’Quinn: Thin-film thermoelectric devices with high room-temperature figures of merit. Nature 413, 597 (2001).
S.T. Huxtable, A.R. Abramson, C-L. Tien, A. Majumdar, C. LaBounty, X. Fan, G. Zeng, J.E. Bowers, A. Shakouri, and E.T. Croke: Thermal conductivity of Si/SiGe and SiGe/SiGe superlattices. Appl. Phys. Lett. 80, 1737–1739 (2002).
P. Hyldgaard and G.D. Mahan: Phonon superlattice transport. Phys. Rev. B 56, 10754–10757 (1997).
G. Chen: Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices. Phys. Rev. B 57, 14958–14973 (1998).
M.V. Simkin and G.D. Mahan: Minimum thermal conductivity of superlattices. Phys. Rev. Lett. 84, 927–930 (2000).
B. Yang and G. Chen: Lattice dynamics study of anisotropic heat conduction in superlattices. Microscale Thermophys. Eng. 5, 107–116 (2001).
P. Martin, Z. Aksamija, E. Pop, and U. Ravaioli: Impact of phonon-surface roughness scattering on thermal conductivity of thin Si nanowires. Phys. Rev. Lett. 102, 125503 (2009).
J.P. Dismukes, L. Ekstrom, E.F. Steigmeier, I. Kudman, and D.S. Beers: Thermal and electrical properties of heavily doped Ge-Si alloys up to 1300[degree]k. J. Appl. Phys. 35, 2899–2907 (1964).
P.G. Klemens: Solid State Physics (Academic Press, NY, 1958).
M-H. Bae, Z. Li, Z. Aksamija, P.N. Martin, F. Xiong, Z-Y. Ong, I. Knezevic, and E. Pop: Ballistic to diffusive crossover of heat flow in graphene ribbons. Nat. Commun. 4, 1734 (2013).
W. Weber: Adiabatic bond charge model for the phonons in diamond, Si, Ge, and α−Sn. Phys. Rev. B 15, 4789 (1977).
K.C. Rustagi and W. Weber: Adiabatic bond charge model for the phonons in A3B5 semiconductors. Solid State Commun. 18, 673–675 (1976).
D. Strauch and B. Dorner: Phonon dispersion in GaAs. J. Phys.: Condens. Matter 2, 1457–1474 (1990).
B.D. Rajput and D.A. Browne: Lattice dynamics of II-VI materials using the adiabatic bond-charge model. Phys. Rev. B 53, 9052–9058 (1996).
A. Khitun, A. Balandin, J.L. Liu, and K.L. Wang: In-plane lattice thermal conductivity of a quantum-dot superlattice. J. Appl. Phys. 88, 13–18 (2000).
J.L. Liu, K.L. Wang, A. Khitun, and A. Balandin: 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).
Z. Aksamija and U. Ravaioli: Anharmonic decay of g-process longitudinal optical phonons in silicon. Appl. Phys. Lett. 96, 091911 (2010).
M. Shamsa, W. Liu, A.A. Balandin, and J. Liu: Phonon-hopping thermal conduction in quantum dot superlattices. Appl. Phys. Lett. 87, 202105 (2005).
M. Shamsa, K. Alim, A.A. Balandin, Y. Bao, W.L. Liu, and J.L. Liub: Electrical and thermal conductivity of Ge/Si quantum dot superlattices. J. Electrochem. Soc. 152, 6432–6435 (2005).
Y. Lan, A. Jerome Minnich, G. Chen, and Z. Ren: Enhancement of thermoelectric figure-of-merit by a bulk nanostructuring approach. Adv. Funct. Mater. 20, 357–376 (2010).
Z. Wang and N. Mingo: Absence of casimir regime in two-dimensional nanoribbon phonon conduction. Appl. Phys. Lett. 99, 101903 (2011).
L. Braginsky, N. Lukzen, V. Shklover, and H. Hofmann: High-temperature phonon thermal conductivity of nanostructures. Phys. Rev. B 66, 134203 (2002).
M. Zebarjadi, K. Esfarjani, Z. Bian, and A. Shakouri: Low-temperature thermoelectric power factor enhancement by controlling nanoparticle size distribution. Nano Lett. 11, 225–230 (2011).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Upadhyaya, M., Khatami, S.N. & Aksamija, Z. Engineering thermal transport in SiGe-based nanostructures for thermoelectric applications. Journal of Materials Research 30, 2649–2662 (2015). https://doi.org/10.1557/jmr.2015.202
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/jmr.2015.202