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Thermal Transport Mechanism of Amorphous HfO2: A Molecular Dynamics Based Study

  • Nano/Microscale Heat Conduction
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Abstract

Amorphous hafnium dioxide (a-HfO2) has attracted increasing interest in the application of semiconductor devices due to its high dielectric constant. However, the thermal transport properties of a-HfO2 are not well understood, which hinders its potential application in electronics. In this work, we systematically investigate the thermal transport property of a-HfO2 using the molecular dynamics method. The non-equilibrium molecular dynamics simulations reveal that the thermal conductivity of a-HfO2 is length-dependent below 100 nm. Spectrally decomposed heat current further proves that the thermal transport of propagons and diffusons is sensitive to the system length. The thermal conductivity is found to increase with temperature using Green-Kubo mode analysis. We also quantify the contribution of each carrier to the thermal conductivity at different temperatures. We find that propagons are more important than diffusons in thermal transport at low temperatures (<100 K). In comparison, diffusons dominate heat transport at high temperatures. Locons have negligible contribution to the total thermal conductivity.

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References

  1. Matthews J.N., Semiconductor industry switches to hafnium-based transistors. Physics Today, 2008, 61: 25.

    Article  Google Scholar 

  2. Schlom D.G., Guha S., Datta S., Gate oxides beyond SiO2. MRS Bulletin, 2008, 33: 1017–1025.

    Article  Google Scholar 

  3. Kang L., Lee B.H., Qi W.J., Jeon Y., Nieh R., Gopalan S., Onishi K., Lee J.C., Electrical characteristics of highly reliable ultrathin hafnium oxide gate dielectric. IEEE lectron Device Letters, 2000, 21: 181–183.

    Article  ADS  Google Scholar 

  4. Salaün A., Grampeix H., Buckley J., Mannequin C., Vallée C., Gonon P., Jeannot S., Gaumer C., Gros-Jean M., Jousseaume V., Investigation of HfO2 and ZrO2 for resistive random access memory applications. Thin Solid Films, 2012, 525, 20–27.

    Article  ADS  Google Scholar 

  5. Milo V., Zambelli C., Olivo P., Pérez E.K., Mahadevaiah M.G., Ossorio O., Wenger C., Ielmini D., Multilevel HfO2-based RRAM devices for low-power neuromorphic networks. APL Materials, 2019, 7: 081120.

    Article  ADS  Google Scholar 

  6. Mart C., Weinreich W., Czernohorsky M., Riedel S., Zybell S., Kuhnel K., CMOS compatible pyroelectric applications enabled by doped HfO2 films on deep-trench structures. 2018 48th European Solid-State Device Research Conference (ESSDERC), 2018, pp. 130–133.

  7. Park M.H., Lee Y.H., Kim H.J., Kim Y.J., Moon T., Kim K.D., Mueller J., Kersch A., Schroeder U., Mikolajick T., Hwang C.S., Ferroelectricity and antiferroelectricity of doped thin HfO2-based films. Advanced Materials, 2015, 27: 1811–1831.

    Article  Google Scholar 

  8. Wang T., Ekerdt J.G., Atomic layer deposition of lanthanum stabilized amorphous hafnium oxide thin films. Chemistry of Materials, 2009, 21: 3096–3101.

    Article  Google Scholar 

  9. Kim H., McIntyre P.C., Saraswat K.C., Effects of crystallization on the electrical properties of ultrathin HfO2 dielectrics grown by atomic layer deposition. Applied Physics Letters, 2003, 82: 106–108.

    Article  ADS  Google Scholar 

  10. Xu Z., Houssa M., Carter R., Naili M., De Gendt S., Heyns M., Constant voltage stress induced degradation in HfO2/SiO2 gate dielectric stacks. Journal of Applied Physics, 2002, 91: 10127–10129.

    Article  ADS  Google Scholar 

  11. Jiang R., Xie E., Wang Z., Interfacial chemical structure of HfO2/Si film fabricated by sputtering. Applied Physics Letters, 2006, 89: 142907.

    Article  ADS  Google Scholar 

  12. Renault O., Samour D., Rouchon D., Holliger P., Papon A.-M., Blin D., Marthon S., Interface properties of ultra-thin HfO2 films grown by atomic layer deposition on SiO2/Si. Thin Solid Films, 2003, 428: 190–194.

    Article  ADS  Google Scholar 

  13. Shen W., Kumari N., Gibson G., Jeon Y., Henze D., Silverthorn S., Bash C., Kumar S., Effect of annealing on structural changes and oxygen diffusion in amorphous HfO2 using classical molecular dynamics. Journal of Applied Physics, 2018, 123: 085113.

    Article  ADS  Google Scholar 

  14. Wang Y., Zahid F., Wang J., Guo H., Structure and dielectric properties of amorphous high-κ oxides: HfO2, ZrO2, and their alloys. Physical Review B, 2012, 85: 224110.

    Article  ADS  Google Scholar 

  15. Pop E., Goodson K.E., Thermal phenomena in nanoscale transistors. Journal of Electronic Packaging, 2006, 128: 102–108.

    Article  Google Scholar 

  16. Pop E., Sinha S., Goodson K.E., Heat generation and transport in nanometer-scaletransistors. Proceedings of the IEEE, 2006, 94: 1587–1601.

    Article  Google Scholar 

  17. Luo X., Demkov A.A., Structure, thermodynamics, and crystallization of amorphous hafnia. Journal of Applied Physics, 2015, 118: 124105.

    Article  ADS  Google Scholar 

  18. Lee S.M., Cahill D.G., Allen T.H., Thermal conductivity of sputtered oxide films. Physical Review B, 1995, 52: 253.

    Article  ADS  Google Scholar 

  19. Ramana C., Noor-A-Alam M., Gengler J.J., Jones J.G., Growth, structure, and thermal conductivity of yttria-stabilized hafnia thin films. ACS Applied Materials & Interfaces, 2012, 4: 200–204.

    Article  Google Scholar 

  20. Scott E.A., Gaskins J.T., King S.W., Hopkins P.E., Thermal conductivity and thermal boundary resistance of atomic layer deposited high-k dielectric aluminum oxide, hafnium oxide, and titanium oxide thin films on silicon. APL Materials, 2018, 6: 058302.

    Article  ADS  Google Scholar 

  21. Song Y., Xu R., He J., Siontas S., Zaslavsky A., Paine D. C., Top-gated indium-zinc-oxide thin-film transistors with in situ Al2O3/HfO2 gate oxide. IEEE Electron Device Letters, 2014, 35: 1251–1253.

    Article  ADS  Google Scholar 

  22. Braun J.L., Baker C.H., Giri A., Elahi M., Artyushkova K., Beechem T.E., Norris P.M., Leseman Z.C., Gaskins J.T., Hopkins P.E., Size effects on the thermal conductivity of amorphous silicon thin films. Physical Review B, 2016, 93: 140201.

    Article  ADS  Google Scholar 

  23. Larkin J.M., McGaughey A.J., Thermal conductivity accumulation in amorphous silica and amorphous silicon. Physical Review B, 2014, 89: 144303.

    Article  ADS  Google Scholar 

  24. Lv W., Henry A., Non-negligible contributions to thermal conductivity from localized modes in amorphous silicon dioxide. Scientific Reports, 2016, 6: 1–8.

    Article  Google Scholar 

  25. Sultan R., Avery A., Underwood J., Mason S., Bassett D., Zink B., Heat transport by long mean free path vibrations in amorphous silicon nitride near room temperature. Physical Review B, 2013, 87: 214305.

    Article  ADS  Google Scholar 

  26. Allen P.B., Feldman J.L., Thermal conductivity of disordered harmonic solids. Physical Review B, 1993, 48: 12581.

    Article  ADS  Google Scholar 

  27. Sääskilahti K., Oksanen J., Tulkki J., McGaughey A., Volz S., Vibrational mean free paths and thermal conductivity of amorphous silicon from non-equilibrium molecular dynamics simulations. AIP Advances, 2016, 6: 121904.

    Article  ADS  Google Scholar 

  28. Lv W., Henry A., Direct calculation of modal contributions to thermal conductivity via Green-Kubo modal analysis. New Journal of Physics, 2016, 18: 013028.

    Article  ADS  Google Scholar 

  29. Simoncelli M., Marzari N., Mauri F., Unified theory of thermal transport in crystals and glasses. Nature Physics, 2019, 15: 809–813.

    Article  ADS  Google Scholar 

  30. Isaeva L., Barbalinardo G., Donadio D., Baroni S., Modeling heat transport in crystals and glasses from a unified lattice-dynamical approach. Nature Communications, 2019, 10: 1–6.

    Article  Google Scholar 

  31. Moon J., Latour B., Minnich A.J., Propagating elastic vibrations dominate thermal conduction in amorphous silicon. Physical Review B, 2018, 97: 024201.

    Article  ADS  Google Scholar 

  32. Zhou Y., Quantifying modal thermal conductivity in amorphous silicon. arXiv preprint arXiv: 2007.14031 2020.

  33. Allen P.B., Feldman J.L., Fabian J., Wooten F., Diffusons, locons and propagons: Character of atomie yibrations in amorphous Si. Philosophical Magazine B, 1999, 79: 1715–1731.

    Article  ADS  Google Scholar 

  34. Seyf H.R., Henry A., A method for distinguishing between propagons, diffusions, and locons. Journal of Applied Physics, 2016, 120: 025101.

    Article  ADS  Google Scholar 

  35. Nose S., A unified formulation of the constant temperature molecular dynamics methods. The Journal of Chemical Physics, 1984, 81: 511.

    Article  ADS  Google Scholar 

  36. Hoover W.G., Canonical dynamics: Equilibrium phase-space distributions. Physical Review A, 1985, 31: 1695.

    Article  ADS  Google Scholar 

  37. Scopel W.L., da Silva A.J., Fazzio A., Amorphous HfO2 and Hf1−xSixO via a melt-and-quench scheme using ab initio molecular dynamics. Physical Review B, 2008, 77: 172101.

    Article  ADS  Google Scholar 

  38. Gallington L.C., Ghadar Y., Skinner L.B., Weber J.K., Ushakov S.V., Navrotsky A., Vazquez-Mayagoitia A., Neuefeind J.C., Stan M., Low J.J., Benmore C.J., The structure of liquid and amorphous hafnia. Materials, 2017, 10(11): 1290.

    Article  ADS  Google Scholar 

  39. Zhao H., Freund J., Lattice-dynamical calculation of phonon scattering at ideal Si-Ge interfaces. Journal of Applied Physics, 2005, 97: 024903.

    Article  ADS  Google Scholar 

  40. Ni Y., Zhang H., Hu S., Wang H., Volz S., Xiong S., Interface diffusion-induced phonon localization in two-dimensional lateral heterostructures. International Journal of Heat and Mass Transfer, 2019, 144: 118608.

    Article  Google Scholar 

  41. Hu Y., Feng T., Gu X., Fan Z., Wang X., Lundstrom M., Shrestha S.S., Bao H., Unification of nonequilibrium molecular dynamics and the mode-resolved phonon Boltzmann equation for thermal transport simulations. Physical Review B, 2020, 101(15): 155308.

    Article  ADS  Google Scholar 

  42. Zhou Y., Hu M., Full quantification of frequency-dependent interfacial thermal conductance contributed by two-and three-phonon scattering processes from nonequilibrium molecular dynamics simulations. Physical Review B, 2017, 95: 115313.

    Article  ADS  Google Scholar 

  43. Seyf H.R., Gordiz K., DeAngelis F., Henry A., Using Green-Kubo modal analysis (GKMA) and interface conductance modal analysis (ICMA) to study phonon transport with molecular dynamics. Journal of Applied Physics, 2019, 125(8): 081101.

    Article  ADS  Google Scholar 

  44. Liao Y., Shiomi J., Akhiezer mechanism dominates relaxation of propagons in amorphous material at room temperature. Journal of Applied Physics, 2021, 130(3): 035101.

    Article  ADS  Google Scholar 

  45. Lukes J.R., Zhong H., Thermal conductivity of individual single-wall carbon nanotubes. Journal of Heat Transfer, 2007, 129(6): 705–716.

    Article  Google Scholar 

  46. Low J.J., Paulson N.H., D’Mello M., Marius S., Thermodynamics of monoclinic and tetragonal hafnium dioxide (HfO2) at ambient pressure. Calphad, 2021, 72: 102210.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (NSFC) (No. 12104291) and (No. 51676121). The computations are carried out on the π 2.0 cluster supported by the Center for High Performance Computing at Shanghai Jiao Tong University. The authors thank Dr. FAN Zheyong from Aalto University for useful discussions.

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Correspondence to Hua Bao.

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Zhang, H., Wei, H. & Bao, H. Thermal Transport Mechanism of Amorphous HfO2: A Molecular Dynamics Based Study. J. Therm. Sci. 31, 1052–1060 (2022). https://doi.org/10.1007/s11630-022-1626-5

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  • DOI: https://doi.org/10.1007/s11630-022-1626-5

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