Thermal transport properties of monolayer phosphorene: a mini-review of theoretical studies

doi:10.1007/s11708-018-0513-y

Front. Energy

2018, Vol. 12

Issue (1) : 87-96 https://doi.org/10.1007/s11708-018-0513-y

REVIEW ARTICLE

Thermal transport properties of monolayer phosphorene: a mini-review of theoretical studies

Guangzhao QIN¹, Ming HU²(

)

¹. Institute of Mineral Engineering, Division of Materials Science and Engineering, Faculty of Georesources and Materials Engineering, RWTH Aachen University, Aachen 52064, Germany
². Institute of Mineral Engineering, Division of Materials Science and Engineering, Faculty of Georesources and Materials Engineering, RWTH Aachen University, Aachen 52064, Germany; Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Aachen 52062, Germany

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Abstract

Phosphorene, a two-dimensional (2D) elemental semiconductor with a high carrier mobility and intrinsic direct band gap, possesses fascinating chemical and physical properties distinctively different from other 2D materials. Its rapidly growing applications in nano-/opto-electronics and thermoelectrics call for fundamental understanding of the thermal transport properties. Considering the fact that there have been so many studies on the thermal transport in phosphorene, it is on emerging demand to have a review on the progress of previous studies and give an outlook on future work. In this mini-review, the unique thermal transport properties of phosphorene induced by the hinge-like structure are examined. There exists a huge deviation in the reported thermal conductivity of phosphorene in literature. Besides, the mechanism underlying the deviation is discussed by reviewing the effect of different functionals and cutoff distance in calculating the thermal transport properties of phosphorene. It is found that the van der Waals (vdW) interactions play a key role in the formation of resonant bonding, which leads to long-ranged interactions. Taking into account of the vdW interactions and including the long-ranged interactions caused by the resonant bonding with large cutoff distance are important for getting the accurate and converged thermal conductivity of phosphorene. Moreover, a fundamental insight into the thermal transport is provided based on the review of resonant bonding in phosphorene. This mini-review summarizes the progress of the thermal transport in phosphorene and gives an outlook on future horizons, which would benefit the design of phosphorene based nano-electronics.

Keywords thermal transport phosphorene resonant bonding

Corresponding Author(s): Ming HU

Just Accepted Date: 27 December 2017 Online First Date: 30 January 2018 Issue Date: 08 March 2018

Cite this article:

Guangzhao QIN,Ming HU. Thermal transport properties of monolayer phosphorene: a mini-review of theoretical studies[J]. Front. Energy, 2018, 12(1): 87-96.

URL:

https://academic.hep.com.cn/fie/EN/10.1007/s11708-018-0513-y
https://academic.hep.com.cn/fie/EN/Y2018/V12/I1/87

Fig.1 Top and side views of phosphorene structure (The unit cell is marked with a dashed rectangle. The zigzag and armchair directions are indicated with arrows. Reproduced by permission of the PCCP Owner Societies [32].)

Fig.2 Comparison of thermal conductivity (k) of phosphorene calculated from different methods (such as analytical estimation [21,26], classical molecular dynamics (MD) simulation using optimized Stillinger-Weber (SW) potential [27–29], solving the phonon Boltzmann transport equation (BTE) based on an harmonic lattice dynamics (ALD) using the iterative method [22,31,38,42] or the single relaxation time approximation (RTA) [22,30–32], and spectral energy density (SED) coupled with the equilibrium ab-initio molecular dynamics (EAIMD) simulations [38]. The methods employed for calculations are labeled on site in five groups. The corresponding author for each reported k is indicated in the horizontal axis.

Fig.3 Thermal conductivity (k) of phosphorene and its anisotropy at room temperature (300 K) as a function of system size. The anisotropy is defined as the k_zigzag/k_armchair. The k along the armchair direction obtained by NEAIMD simulations is plotted for comparison, where the error bar is determined during the calculation of temperature gradient. Reprinted with permission from Ref. [38]. Copyright 2016 by the American Physical Society.

Fig.4 Lattice thermal conductivity of phosphorene at room temperature (300 K) with respect to the interaction cutoff distance (ALD/BTE). When doing first-principles calculations for the IFCs, the optB88 (including vdW interactions) and PBE (NOT including vdW interactions) functionals are adopted and the results are shown in (a) and (b), respectively. Reproduced with the permission from Ref. [38] and the Creative Commons Attribution 4.0 International License in Ref. [31]. Copyrights 2016 by the American Physical Society and 2015 by Nature Publishing Group.

Fig.5 (Color online) Lattice thermal conductivity (k) of phosphorene as a function of the size of Q-grid (N× N× 1). The PBE functional is adopted when doing first-principles calculations for the IFCs. The size dependence/independence of k shows different behavior for different cutoff distances of (a) 7.88 Å and (b) 4.4 Å. Reprinted with permissions from Ref. [38] and Ref. [30]. Copyright 2014/2016 by the American Physical Society.

Fig.6 (Color online) Insight into the resonant bonding and phonon anharmonicity in phosphorene

(a) Orbital-projected electronic band structure of phosphorene (The size of the circles represents the relative contribution from the corresponding orbitals. The s-orbital is mainly confined 9 eV below the valence band maximum, showing weak hybridization with p_x/p_y/p_z-orbital. Owing to the weak sp-hybridization, the three p-electrons are highly delocalized and form the resonant bonding, while the remaining two s-electrons are localized around P atom being lone-pair.); (b) phonon dispersion curves and density of states (DOS) of phosphorene (The soft out-of-plane TOz phonon branch and the three acoustic phonon branches are in different colors and labeled on site. Inset: The BZ with high-symmetry k-points indicated. Reprinted with permission from Ref. [38]. Copyright 2016 by the American Physical Society.)

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