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Phonon confinement effect in two-dimensional nanocrystals of black phosphorus with anisotropic phonon dispersions

Abstract

The RWL model for the phonon confinement effect in nanocrystals (NCs) had been found to result in deviations and limitations for crystals exhibiting obvious anisotropic phonon dispersions and modified models have been proposed to overcome these deficiencies. Here, we examine this issue in black phosphorus (BP), a typical anisotropic two-dimensional crystal exhibiting pronounced anisotropy in phonon dispersions. A detailed study is performed on the Raman spectra of BP NCs prepared by ion implantation technique. With decreasing the NC size, the peak positions of the three characteristic Raman modes, $A_{g}^{1}$, $B_{2g}$ and $A_{g}^{2}$ modes, keep almost unchanged, while the $A_{g}^{1}$ and $A_{g}^{2}$ modes show significant asymmetrical broadening tails towards higher- and lower-frequency sides, respectively. It is found that the RWL model based on one-dimensional phonon dispersion along $\Gamma$-Y and $\Gamma$-X axes in Brillouin zone (BZ) cannot interpret the unusual frequency invariance and inhomogeneous lineshape broadening of these three modes. However, after considering the contribution of two-dimensional anisotropic phonon dispersions from the whole BZ, the frequency and asymmetrical broadening of the $A_{g}^{1}$ and $A_{g}^{2}$ modes can be well reproduced. This study demonstrates that the RWL model can be applicable for crystals with anisotropic phonon dispersions once the phonons in the whole two-dimensional or three-dimensional BZ are properly taken into account, and provides a physically sound route into understanding the phonon confinement effect for anisotropic systems.

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Publication details

The article was received on 22 Feb 2018, accepted on 29 Mar 2018 and first published on 02 Apr 2018


Article type: Paper
DOI: 10.1039/C8NR01531G
Citation: Nanoscale, 2018, Accepted Manuscript
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    Phonon confinement effect in two-dimensional nanocrystals of black phosphorus with anisotropic phonon dispersions

    T. Lin, X. Cong, M. Lin, X. Liu and P. TAN, Nanoscale, 2018, Accepted Manuscript , DOI: 10.1039/C8NR01531G

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