TEMPERATURE DEPENDENCES OF THE AVERAGED GROUP VELOCITIES OF ACOUSTIC PHONONS IN FLAT NANOFILMS OF LEAD DIIODIDE
DOI:
https://doi.org/10.32782/pet-2024-2-6Keywords:
nanostructure, nanofilm, lead diiodide, phononAbstract
Unique properties of quasi-two-dimensional structures based on the layered semiconductor lead diiodide make them attractive for the creation of advanced nanoelectronic devices. Currently, a number of technologies have been developed for obtaining quasi-two-dimensional structures based on lead diiodide, and a large body of experimental research results on their properties has been accumulated. However, there are relatively few studies dedicated to the theoretical description of the phenomena and processes occurring in such structures. In particular, the role of acoustic phonons in shaping the characteristic properties of these structures remains largely unexplored. The purpose of this work was to investigate theoretically the temperature dependencies of the average group velocities of acoustic phonons in lead diiodide nanofilms of varying thickness. Using the methods of classical dynamics of atoms in a crystalline lattice within the approximation of an elastic continuum, the frequencies and group velocities of acoustic phonons in a hexagonal quasi-two-dimensional crystalline structure – lead diiodide nanofilm (polytype 2H-PbI2) – were calculated. The calculations were carried out using previously established analytical dependencies of the dispersion laws for these quantities for each mode of acoustic phonons with all possible polarizations: shear, flexural, and dilatational. Further averaging of the group velocities was performed using methods of statistical physics with the distribution function of phonon states by frequencies in the 2D-structure and the Bose-Einstein distribution. Thus, for the first time, a study was conducted on the temperature dependencies of the average phonon velocities for each of the mentioned polarizations for different sets of values of the parameter N – the number of layered 2H-PbI2 packets in the nanofilm, which determines its thickness. It has been shown that by changing the temperature and thickness of the nanofilm, the propagation speed of phonons for each polarization can be significantly altered. Particularly, by reducing the thickness of the lead diiodide nanofilm, the group velocity of shear-polarized phonons can be reduced by several times, and the velocities of SA- and AS-polarized phonons can be reduced by tens of times. The temperature changes in phonon propagation speeds are nonlinear: in the low-temperature range (below 150, 90, and 50 K for SA-, AS-, and shear-polarized phonons, respectively), their values increase rapidly with rising temperature, whereas at higher temperatures, they are almost independent of it. Results of this study can be used to create thermoelectric devices based on 2H-PbI2 nanofilms with the desired properties, since the speed of heat flows, determined by the speed of propagation of acoustic phonons, is regulated by the appropriate thickness selection.
References
Tsakalakos T. Nanostructures and Nanotechnology: Perspectives and New Trends. In: T. Tsakalakos, I. A. Ovid’ko, A. K. Vasudevan (eds) Nanostructures: Synthesis, Functional Properties and Applications. NATO Science Series (Series II: Mathematics, Physics and Chemistry), vol. 128. Dordrecht: Springer, 2003. P. 1–36.
Kovalenko M. V., Manna L., Cabot A., [et al.]. Prospects of Nanoscience with Nanocrystals. ACS Nano. 2015. Vol. 9. № 2. P. 1012–1057. https://doi.org/10.1021/nn506223h
Toulouse A. S., Isaacoff B. P., Shi G., [et al.]. Frenkel-like Wannier-Mott Excitons in Few-Layer PbI2. arXiv: 1408.1942v2 [cond-mat.mes-hall] (Submit. 18 Feb 2015). https://doi.org/10.48550/arXiv.1408.1942 (дата звернення: 12.06.2024).
Yamamoto A., Nakahara H., Yano S., [et al.]. Exciton dynamics in PbI2 ultra-thin microcrystallites. Phys. stat. sol. (b). 2001. Vol. 224. № 1. P. 301–305. https://doi.org/10.1002/1521-3951(200103)224:1<301::AID-PSSB301>3.0.CO;2-N
Savchuk A. I., Fediv V.I., Kandyba Ye.O., [et al.]. Platelet-shaped nanoparticles of PbI2 and PbMnI2 embedded in polymer matrix. Mat. Sci.&Engineering: C. 2002. Vol. 19. № 1–2. P. 59–62. DOI: 10.1016/S0928-4931(01)00439-8.
Finlayson C. E. and Sazio P. J. A. Highly efficient blue photoluminescence from colloidal lead-iodide nanoparticles. J. Phys. D: Appl. Phys. 2006. Vol. 39. № 8. P. 1477–1480. DOI: 10.1088/0022-3727/39/8/003.
Peng B., Mei H., Zhang H., Shao H., Xu K., Jin Q., Soukoulis C. M., Zhu H. High thermoelectric efficiency in monolayer PbI2 from 300 K to 900 K. Inorg. Chem. Front. 2019. Vol. 6. P. 920–928. https://doi.org/10.1039/C8QI01297K
Dou L, Wong A. B., Yu Y., Lai M., Kornienko N., Eaton S. W., Fu A., Bischak C. G., Ma J., Ding T., Ginsberg N. S., Wang L. W., Alivisatos A. P., Yang P. Atomically thin two-dimensional organic-inorganic hybrid perovskites. Science. 2015. Vol. 349. № 6255. P. 1518–1521. DOI: 10.1126/science.aac7660
Zhang W., Eperon G., Snaith H. Metal halide perovskites for energy applications. Nature Energy. 2016. Vol. 1. № 16048. P. 1–8. doi: 10.1038/nenergy.2016.48.
Lutsiuk Yu. V., Kramar V. M. Analytical calculation of frequency spectrum and group velocities of acoustic phonons in quasi-two-dimensional nanostructures. Journal of Nano- and Electronic Physics. 2020. Vol. 12. №5. P. 05033(5pp). DOI: 10.21272/jnep.
Lutsiuk Yu., Kramar V., Petryk I. Frequency spectrum and group velocities of acoustic phonons in PbI2 nanofilms. Physics and Chemistry of Solid State. 2022. Vol. 23. № 3. P. 478–483. https://doi.org/10.15330/pcss.23.3.478-483
Balandin A. A. and Wang K. L. Significant decrease of the lattice thermal conductivity due to phonon confinement in a free-standing semiconductor quantum well. Phys. Rev. B. 1998. Vol. 58. № 3. P. 1544–1549. https://link.aps.org/doi/10.1103/PhysRevB.58.1544
Zhong M., Zhang S., Huang L., You J., Wei Z., Liu X., Li J. Large-scale 2D PbI2 monolayers: experimental realization and their band-gap related properties. Nanoscale. 2017. Vol. 9. № 11. P. 3736–3741. DOI:10.1039/c6nr07924e
Wangyang P., Sun H., Zhu X., Yang D., Gao X. Mechanical exfoliation and Raman spectra of ultrathin PbI2 single crystal. Mater. Lett. 2016. Vol. 168. P. 68–71. DOI:10.1016/j.matlet.2016.01.034
Zheng W., Zhang Z., Lin R., Xu K., He J., Huang F. High-crystalline 2D layered PbI2 with ultrasmooth surface: liquid-phase synthesis and application of high-speed photon detection. Adv. Electron. Mater. 2016. Vol. 2. № 11. P. 1600291. https://doi.org/10.1002/aelm.201600291.
Bannov N., Mitin V., Stroscio M. Confined acoustic phonons in a free-standing quantum well and their interaction with electrons. Phys. Stat. Sol.(b). 1994. Vol. 183. P. 131–142. 10.1107/S0567739475001787.
Pokatilov E. P., Nika D. L., Balandin A. A. Phonon spectrum and group velocities in AlN/GaN/AlN and related heterostructures. Superlattices and Microstructures. 2003. Vol. 33. № 3. P. 155–171. doi: 10.1016/S0749-6036(03)/00069-7.
Minagava T. Common polytypes of PnI2 at low and high temperatures and the 2H-12R transformation. Acta Cryst. A, 1975. Vol. 31. № 6. P. 823–824. URL: https://www.ee.buffalo.edu/faculty/mitin/old/Papers/074
Lead diiodide (PbI2): Sound velocities, elastic moduli; Grüneisen parameters, effective charge, force constants. In: O. Madelung, U. Rössler, M. Schulz (Eds.). Springer Materials. Landolt-Börnstein - Group III Condensed Matter 41C : Non-Tetrahedrally Bonded Elements and Binary Compounds. Berlin, Heidelberg : Springer-Verlag, 1998. 923 p. DOI: 10.1007/b71138.
Schlüter I. Ch., Schlüter M. Electronic structure and optical properties of PbI2. Phys. Rev. B. 1974. Vol. 9, № 4. P. 1652–1663. URL: https://escholarship.org/uc/item/4hj3r1bt.
