Session: 11-09-01: Thermal Transport Across Interfaces I

Paper Number: 77262

Start Time: Wednesday, 11:05 AM

77262 - Modeling Anisotropic Thermal Transport in Black-Phosphorus-Like Materials 

Recently, black phosphorus and other materials with biaxial symmetry, namely, the orthorhombic, monoclinic, or triclinic symmetries, have attracted significant attentions [1, 2].  On fundamental side, the thermal conductivity tensor of these materials has three distinct diagonal elements (principal components), referred to its principal axes.  On application side, black phosphorus has been widely seen as a promising candidate for electronic, optoelectronic, and thermoelectric applications, due to its unique properties , including high hole mobility, tunable direct bandgap, and its opposite anisotropy in thermal and electrical conductivities.

Though there are existing detailed first principle calculations [3, 4] on the anisotropic thermal properties of black phosphorus, a general Debye-type model with compact algebraic expressions, at least in limiting cases, is still lack.  This general model should be easily applied to other materials with biaxial symmetry, and more importantly the simple algebraic expressions should offer more physical insights in a more straightforward manner.

Building upon our anisotropic Debye model for materials with uniaxial symmetry [5, 6], namely, the tetragonal, trigonal, or hexagonal symmetries, we develop a general framework to model heat transfer in materials with biaxial symmetry.  Here we generalize both the first Brillouin zone (FBZ) and the isoenergy surfaces from standard ellipsoids, in which only one of the three principal directions is anisotropic, to index ellipsoids, , in which all three principal directions are anisotropic.  We obtain compact algebraic expressions in limiting temperature regimes for specific heat (C), phonon irradiation (H_s) and thermal conductivity (k_s) along different principal direction, s.  The temperature dependent specific heat shows power law transitions from T³ – T² – T¹ – T⁰, which indicates dimensionality crossovers from 3D – 2D – 1D and finally recovers the Dulong and Petit limit.  These dimensionality crossovers originate from the anisotropy of the phonon velocities along the principal axes and the FBZ truncation effect.  The analytical expressions of H_s, and k_s explicitly re-iterate the phonon focusing effect: in many cases the heat transfer along one specific principal direction can be increased by reducing a phonon velocity component in either of the other two principal directions.  This model is checked by comparison with the experimental results of C of black phosphorus, thermal boundary conductance (G_s) between aluminum and black phosphorus, and k_s of black phosphorus oriented in every principal direction.

 

References:

[1] S. Lee, F. Yang, J. Suh, S. Yang, Y. Lee, G. Li, H. Sung Choe, A. Suslu, Y. Chen, C. Ko, J. Park, K. Liu, J. Li, K. Hippalgaonkar, J. J. Urban, S. Tongay and J. Wu, Nature Communications 6 (1), 8573 (2015).

[2] Z. Luo, J. Maassen, Y. Deng, Y. Du, R. P. Garrelts, M. S. Lundstrom, P. D. Ye and X. Xu, Nature Communications 6 (1), 8572 (2015).

[3] L. Zhu, G. Zhang and B. Li, Physical Review B 90 (21), 214302 (2014).

[4]  M. Li, J. S. Kang, H. D. Nguyen, H. Wu, T. Aoki and Y. Hu, Advanced Materials 31 (33), 1901021 (2019).

[5] Z. Chen, Z. Wei, Y. Chen and C. Dames, Physical Review B 87 (12) (2013).

[6] Z. Chen and C. Dames, Applied Physics Letters 107 (19), 193104 (2015).

Presenting Author: Hengrui Chen Southeast University

Authors:

Hengrui Chen Southeast University
Zhen Chen Southeast University