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Grüneisen parameters and thermal conductivity in the phase change compound GeTe

  • S.I.: Computational Electronics of Emerging Memory Elements
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Abstract

Thermal conductivity is one of the key properties for the application of phase change materials in nonvolatile memories. In this work we compute the mode Grüneisen parameters of the phase change compound GeTe by means of density-functional perturbation theory. The Grüneisen parameters are then used to estimate the bulk thermal conductivity with a phenomenological formula (Slack in Solid State Phys 34:1–71, 1979). This estimate is compared with the full solution of the Boltzmann Transport Equation we obtained in a previous work within the same theoretical framework. This comparison allowed us to validate the phenomenological formula also for the prototypical phase change compound GeTe.

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References

  1. Burr, G.W., Kurdi, B.N., Scott, J.C., Lam, C.H., Gopalakrishnan, K., Shenoy, R.S.: Overview of candidate device technologies for storage-class memory. IBM J. Res. Dev. 52, 449–464 (2008)

    Article  Google Scholar 

  2. Chen, A.: A review of emerging non-volatile memory (NVM) technologies and applications. Solid-State Electron. 125, 25–38 (2016)

    Article  Google Scholar 

  3. Pirovano, A., Lacaita, A.L., Benvenuti, A., Pellizzer, F., Bez, R.: Electronic switching in phase-change memories. IEEE Trans. Electron. Dev. 51, 452–459 (2004)

    Article  Google Scholar 

  4. Lacaita, A.L., Wouters, D.J.: Phase-change memories. Phys. Stat. Sol. A 205, 2281–2297 (2008)

    Article  Google Scholar 

  5. Wuttig, M., Yamada, N.: Phase-change materials for rewriteable data storage. Nat. Mater. 6, 824–832 (2007)

    Article  Google Scholar 

  6. Ghezzi, G.E., Raty, J.Y., Maitrejean, S., Roule, A., Elkaim, E., Hippert, F.: Effect of carbon doping on the structure of amorphous GeTe phase change material. Appl. Phys. Lett. 99, 151906–151908 (2011)

    Article  Google Scholar 

  7. Reifenberg, J.P., Kencke, D.L., Goodson, K.E.: The impact of thermal boundary resistance in phase-change memory devices. IEEE Electron Dev. Lett. 29, 1112–1114 (2008)

    Article  Google Scholar 

  8. Bozorg-Grayeli, E., Reifenberg, J.P., Asheghi, M., Wong, H.S.P., Goodson, K.E.: Thermal transport in phase change memory materials. Ann. Rev. Heat Transf. 16, 397–428 (2013)

    Article  Google Scholar 

  9. Baroni, S., de Gironcoli, S., Dal Corso, A., Giannozzi, P.: Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515–562 (2001)

    Article  Google Scholar 

  10. Debernardi, A., Baroni, S., Molinari, E.: Anharmonic phonon lifetimes in semiconductors from density-functional perturbation theory. Phys. Rev. Lett. 75, 1819–1822 (1995)

    Article  Google Scholar 

  11. Lazzeri, M., de Gironcoli, S.: First-principles study of the thermal expansion of Be(\(10\bar{1}0\)). Phys. Rev. B 65, 245402–245409 (2002)

    Article  Google Scholar 

  12. Deinzer, G., Birner, G., Strauch, D.: Ab initio calculation of the linewidth of various phonon modes in germanium and silicon. Phys. Rev. B 67, 144304–144309 (2003)

    Article  Google Scholar 

  13. Paulatto, L., Mauri, F., Lazzeri, M.: Anharmonic properties from a generalized third-order ab initio approach: theory and applications to graphite and graphene. Phys. Rev. B 87, 214303–214320 (2013)

    Article  Google Scholar 

  14. Fugallo, G., Lazzeri, M., Paulatto, L., Mauri, F.: Ab initio variational approach for evaluating lattice thermal conductivity. Phys. Rev. B 88, 045430–045438 (2013)

  15. Campi, D., Paulatto, L., Fugallo, G., Mauri, F., Bernasconi, M.: First-principles calculation of lattice thermal conductivity in crystalline phase change materials: GeTe, \(\text{ Sb }_2\text{ Te }_3\), and \(\text{ Ge }_2\text{ Sb }_2\text{ Te }_5\). Phys. Rev. B 95, 024311–024322 (2017)

    Article  Google Scholar 

  16. Slack, G.A.: The thermal conductivity of nonmetallic crystals. Solid State Phys. 34, 1–71 (1979)

    Article  Google Scholar 

  17. Morelli, D.T., Slack, G.A.: High lattice thermal conductivity solids. In: Shinde, S.L., Goela, J. (eds.) High Thermal Conductivity Materials, p. 36. Springer, Berlin (2016). ISBN-10: 0-387-22021-6

    Google Scholar 

  18. Morelli, D.T., Jovovic, V., Heremans, J.P.: Intrinsically minimal thermal conductivity in cubic I–V–VI2 semiconductors. Phys. Rev. Lett. 101, 035901–035904 (2008)

    Article  Google Scholar 

  19. Siegert, K.S., Lange, F.R.L., Sittner, E.R., Volker, H., Schlockermann, C., Siegrist, T., Wuttig, M.: Impact of vacancy ordering on thermal transport in crystalline phase-change materials. Rep. Prog. Phys. 78, 013001–013012 (2015)

    Article  Google Scholar 

  20. Giannozzi, P., et al.: QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 21, 395502–395520 (2009). www.quantum-espresso.org

  21. Shaltaf, R., Gonze, X., Cardona, M., Kremer, R.K., Siegle, G.: Lattice dynamics and specific heat of \(\alpha \)-GeTe: theoretical and experimental study. Phys. Rev. B 79, 075204–075210 (2009)

    Article  Google Scholar 

  22. Monkhorst, H., Pack, J.D.: Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976)

    Article  MathSciNet  Google Scholar 

  23. Goldak, J., Barrett, C.S., Innes, D., Youdelis, W.: Structure of \(\alpha \)-GeTe. J. Chem. Phys. 44, 3323–3325 (1966)

    Article  Google Scholar 

  24. Chattopadhyay, T., Boucherle, J., Von Schnering, H.: Neutron diffraction study on the structural phase transition in GeTe. J. Phys. C 20, 1431–1440 (1987)

    Article  Google Scholar 

  25. Lucovsky, G., White, R.M.: Effects of resonance bonding on the properties of crystalline and amorphous semiconductors. Phys. Rev. B 8, 660–667 (1973)

    Article  Google Scholar 

  26. Shportko, K., Kremers, S., Woda, M., Lencer, D., Robertson, J., Wuttig, M.: Resonant bonding in crystalline phase-change materials. Nat. Mater. 7, 653–658 (2008)

    Article  Google Scholar 

  27. Lencer, D., Salinga, M., Grabowski, B., Hickel, T., Neugebauer, J., Wuttig, M.: A map for phase-change materials. Ibid. Nat. Mater. 7, 972–977 (2008)

    Article  Google Scholar 

  28. Perdew, J.P., Burke, K., Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996)

    Article  Google Scholar 

  29. Edwards, A.H., Pineda, A.C., Schultz, P.A., Martin, M.G., Thompson, A.P., Hjalmarson, H.P., Umrigar, C.J.: Electronic structure of intrinsic defects in crystalline germanium telluride. Phys. Rev. B 73, 045210–045222 (2006)

    Article  Google Scholar 

  30. Bevolo, A.J., Shanks, H.R., Eckels, D.E.: Molar heat capacity of GeTe, SnTe, and PbTe from 0.9 to 60 K. Phys. Rev. B 13, 3523–3533 (1976)

    Article  Google Scholar 

  31. Campi, D., Donadio, D., Sosso, G.C., Behler, J., Bernasconi, M.: Electron-phonon interaction and thermal boundary resistance at the crystal-amorphous interface of the phase change compound GeTe. J. Appl. Phys. 117, 015304–015312 (2015)

    Article  Google Scholar 

  32. Voc̆adlo, N.L., Price, G.D.: The Grüneisen parameter—computer calculations via lattice dynamics. Phys. Earth Planet. Inter. 82, 261 (1994)

    Article  Google Scholar 

  33. Domb, C., Salter, L.: CIX. The zero point energy and \(\Theta \) crystals. Philos. Mag. 43, 1083–1089 (1952)

    Article  Google Scholar 

  34. Fallica, R., Varesi, E., Fumagalli, L., Spadoni, S., Longo, M.: Effect of nitrogen doping on the thermal conductivity of GeTe thin films. Phys. Status Solidi RRL 7, 1107–1111 (2013)

    Article  Google Scholar 

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Acknowledgements

MB acknowledges funding from the European Union Seventh Framework Programme FP7/2007-2013 under Grant agreement No. 310339 and computational resources provided by Cineca (Casalecchio di Reno, Italy) through the ISCRA initiative.

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Correspondence to Marco Bernasconi.

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Bosoni, E., Sosso, G.C. & Bernasconi, M. Grüneisen parameters and thermal conductivity in the phase change compound GeTe. J Comput Electron 16, 997–1002 (2017). https://doi.org/10.1007/s10825-017-1040-5

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  • DOI: https://doi.org/10.1007/s10825-017-1040-5

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