Skip to main content
SpringerLink
Log in

First Principles Calculations

  • Chapter
  • First Online:
Thermal Transport in Semiconductors

Part of the book series: Springer Theses ((Springer Theses))

  • 686 Accesses

Abstract

Since the development of quantum mechanics, big efforts have been done in order to implement such knowledge for computational modeling. This has allowed predicting experimental results with an incredible accuracy.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Strictly speaking, umklapp collisions also conserve crystalline momentum, but a non-zero vector of the reciprocal lattice must be used to bring back the final momentum to the first Brillouin zone.

  2. 2.

    This assumption is only valid for isotropic systems.

  3. 3.

    We want to remark that N processes alone must not contribute to the thermal resistance as are momentum conserving collisions.

References

  1. M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias, J.D. Joannopoulos, Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 64, 1045 (1992)

    Article  ADS  Google Scholar 

  2. A. Debernardi, Anharmonic properties of semiconductors from density-functional perturbation theory, Thesis Dissertation, 1995

    Google Scholar 

  3. P. Hohenberg, W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136, 864 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  4. W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, (1965)

    Article  MathSciNet  ADS  Google Scholar 

  5. S. Baroni, P. Giannozzi, A. Testa, Green’s-function approach to linear response in solids. Phys. Rev. Lett. 58, 1861 (1987)

    Article  ADS  Google Scholar 

  6. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009)

    Article  Google Scholar 

  7. K. Esfarjani, H. Stokes, Method to extract anharmonic force constants from first principles calculations. Phys. Rev. B 77, 144112 (2008)

    Article  ADS  Google Scholar 

  8. G. Leibfried, W. Ludwig, Theory of anharmonic effects in crystals. Solid State Phys. 12, 275 (1961)

    Article  MathSciNet  Google Scholar 

  9. M.H.F. Sluiter, M. Weinert, Y. Kawazoe, Force constants for substitutional alloys. Phys. Rev. B 59, 4100 (1999)

    Article  ADS  Google Scholar 

  10. X. Gonze, Adiabatic density-functional. Phys. Rev. A 52, 1096 (1995)

    Article  ADS  Google Scholar 

  11. G. Deinzer, G. Birner, D. Strauch, Ab initio calculation of the linewidth of various phonon modes in germanium and silicon. Phys. Rev. B 67, 144304 (2003)

    Article  ADS  Google Scholar 

  12. K. Esfarjani, G. Chen, H.T. Stokes, Heat transport in silicon from first-principles calculations. Phys. Rev. B 84, 085204 (2011)

    Article  ADS  Google Scholar 

  13. P.E. Blöchl, O. Jepsen, O. Andersen, Improved tetrahedron method for Brillouin-zone integrations. Phys. Rev. B 49, 16223 (1994)

    Article  ADS  Google Scholar 

  14. J.A. Johnson, A.A. Maznev, J. Cuffe, J.K. Eliason, A.J. Minnich, T. Kehoe, C.M.S. Torres, G. Chen, K.A. Nelson, Direct measurement of room-temperature nondiffusive thermal transport over micron distances in a silicon membrane. Phys. Rev. Lett. 110, 025901 (2013)

    Article  ADS  Google Scholar 

  15. M.E. Siemens, Q. Li, R. Yang, K.K.A. Nelson, E.H. Anderson, M.M. Murnane, H.C. Kapteyn, Quasi-Ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams. Nat. Mater. 9, 26 (2010)

    Article  ADS  Google Scholar 

  16. A.J. Minnich, J.A. Johnson, A.J. Schmidt, K. Esfarjani, M.S. Dresselhaus, K.A. Nelson, G. Chen, Thermal conductivity spectroscopy technique to measure phonon mean free paths. Phys. Rev. Lett. 107, (2011)

    Google Scholar 

  17. K.T. Regner, D.P. Sellan, Z. Su, C.H. Amon, A.J.H. McGaughey, J. Malen, Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance. Nat. Commun. 4, 1640 (2013)

    Google Scholar 

  18. R.B. Wilson, D.G. Cahill, Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments. Nat. Commun. 5, 5075 (2014)

    Article  ADS  Google Scholar 

  19. Y. Hu, L. Zeng, A.J. Minnich, M.S. Dresselhaus, G. Chen, Spectral mapping of thermal conductivity through nanoscale ballistic transport. Nat. Nanotechnol. 10, 701 (2015)

    Article  ADS  Google Scholar 

  20. K.M. Hoogeboom-Pot, J.N. Hernandez-Charpak, X. Gu, T.D. Frazer, E.H. Anderson, W. Chao, R.W. Falcone, R. Yang, M.M. Murnane, H.C. Kapteyn, D. Nardi, A new regime of nanoscale thermal transport: collective diffusion increases dissipation efficiency. Proc. Natl. Acad. Sci. 112, 201503449 (2015)

    Article  Google Scholar 

  21. P.G. Klemens, The scattering of low-frequency lattice waves by static imperfections. Proc. Phys. Soc. A 68, 1113 (1955)

    Article  ADS  Google Scholar 

  22. P. Klemens, Thermal resistance due to point defects at high temperatures. Phys. Rev. 119, 507 (1960)

    Article  ADS  Google Scholar 

  23. S.I. Tamura, Isotope scattering of dispersive phonons in Ge. Phys. Rev. B 27, 858 (1983)

    Article  ADS  Google Scholar 

  24. W. Capinski, H. Maris, S. Tamura, Analysis of the effect of isotope scattering on the thermal conductivity of crystalline silicon. Phys. Rev. B 59, 10105 (1999)

    Article  ADS  Google Scholar 

  25. H. Casimir, Note on the conduction of heat in crystals. Physica 5, 495 (1938)

    Article  ADS  Google Scholar 

  26. C. De Tomas, A. Cantarero, A.F. Lopeandia, F.X. Alvarez, From kinetic to collective behavior in thermal transport on semiconductors and semiconductor nanostructures. J. Appl. Phys. 115, (2014)

    Article  ADS  Google Scholar 

  27. A.V. Inyushkin, A.N. Taldenkov, A.M. Gibin, A.V. Gusev, H.-J. Pohl, On the isotope effect in thermal conductivity of silicon. Phys. Status Solidi (C) 1, 2995 (2004)

    Article  ADS  Google Scholar 

  28. Z.M. Zhang, in Nano/microscale Heat Transfer (McGraw-Hill Nanoscience and Technology, New York, 2007)

    Google Scholar 

  29. B. Liao, B. Qiu, J. Zhou, S. Huberman, K. Esfarjani, G. Chen, Significant reduction of lattice thermal conductivity by the electron-phonon interaction in silicon with high carrier concentrations: a first-principles study. Phys. Rev. Lett. 114, 1 (2015)

    Google Scholar 

  30. J. Ziman, in Electrons and Phonons: The Theory of Transport Phenomena in Solids (Oxford University Press, Oxford, 2001)

    Google Scholar 

  31. B.-L. Huang, M. Kaviany, Ab initio and molecular dynamics predictions for electron and phonon transport in bismuth telluride. Phys. Rev. B 77, 125209 (2008)

    Article  ADS  Google Scholar 

  32. R.A. Guyer, J.A. Krumhansl, Solution of the linearized phonon boltzmann equation. Phys. Rev. 148, 766 (1966)

    Article  ADS  Google Scholar 

  33. C. De Tomas, A. Cantarero, A.F. Lopeandia, F.X. Alvarez, Enhancing of optic phonon contribution in hydrodynamic phonon transport. J. Appl. Phys. 118, (2015)

    Google Scholar 

  34. A. Cepellotti, N. Marzari, Thermal transport in crystals as a kinetic theory of relaxons. Phys. Rev. X 6, 041013 (2016)

    Google Scholar 

  35. X. Cartoixà, R. Dettori, C. Melis, L. Colombo, R. Rurali, Thermal transport in porous Si nanowires from approach-to-equilibrium molecular dynamics calculations. Appl. Phys. Lett. 109, 013107 (2016)

    Article  ADS  Google Scholar 

  36. J.E. Turney, A.J.H. McGaughey, C.H. Amon, In-plane phonon transport in thin films. J. Appl. Phys. 107, 024317 (2010)

    Article  ADS  Google Scholar 

  37. M. Luisier, Thermal transport and Matthiessen’s rule in ultra-scaled Si nanowires. Appl. Phys. Lett. 103, 113103 (2013)

    Article  ADS  Google Scholar 

  38. P. Torres, A. Torello, J. Bafaluy, J. Camacho, X. Cartoixà, F.X. Alvarez, First principles kinetic-collective thermal conductivity of semiconductors. Phys. Rev. B 95, 165407 (2017)

    Article  ADS  Google Scholar 

  39. W. Li, N. Mingo, L. Lindsay, D.A. Broido, D.A. Stewart, N.A. Katcho, Thermal conductivity of diamond nanowires from first principles. Phys. Rev. B 85, 195436 (2012)

    Google Scholar 

  40. A. Ward, D.A. Broido, D.A. Stewart, G. Deinzer, Ab initio theory of the lattice thermal conductivity in diamond. Phys. Rev. B 80, 125203 (2009)

    Google Scholar 

  41. G. Fugallo, M. Lazzeri, L. Paulatto, F. Mauri, Ab initio variational approach for evaluating lattice thermal conductivity. Phys. Rev. B 88, 045430 (2013)

    Article  ADS  Google Scholar 

  42. L. Bellaiche, D. Vanderbilt, Virtual crystal approximation revisited: application to dielectric and piezoelectric properties of perovskites. Phys. Rev. B 61, 7877 (2000)

    Article  ADS  Google Scholar 

  43. J. Garg, N. Bonini, B. Kozinsky, N. Marzari, Role of disorder and anharmonicity in the thermal conductivity of silicon-germanium alloys: a first-principles study. Phys. Rev. Lett. 106, 1 (2011)

    Article  Google Scholar 

  44. A. Zunger, S. Wei, L.G. Ferreira, J.E. Bernard, Special quasirandom structures. Phys. Rev. Lett. 65, 353 (1990)

    Article  ADS  Google Scholar 

  45. J. Sanchez, F. Ducastelle, D. Gratias, Generalized cluster description of multicomponent systems. Phys. A 128, 334 (1984)

    Article  MathSciNet  Google Scholar 

  46. G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15 (1996)

    Article  Google Scholar 

  47. G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996)

    Article  ADS  Google Scholar 

  48. G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558 (1993)

    Article  ADS  Google Scholar 

  49. G. Kresse, J. Hafner, Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 14251 (1994)

    Article  ADS  Google Scholar 

  50. T. Tadano, Y. Gohda, S. Tsuneyuki, Anharmonic force constants extracted from first-principles molecular dynamics: applications to heat transfer simulations. J. Phys. Condens. Matter 26, 225402 (2014)

    Article  Google Scholar 

  51. A. Togo, L. Chaput, I. Tanaka, Distributions of phonon lifetimes in Brillouin zones, Phys. Rev. B 91, (2015)

    Google Scholar 

  52. P. Torres, Kinetic collective model: BTE-based hydrodynamic model for thermal transport (2017), https://physta.github.io/. Accessed 20 Aug 2017

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain

    Pol Torres Alvarez

Authors
  1. Pol Torres Alvarez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pol Torres Alvarez .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Torres Alvarez, P. (2018). First Principles Calculations. In: Thermal Transport in Semiconductors. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-94983-3_3

Download citation

Publish with us

Policies and ethics

Search

Navigation