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1.
Phys Chem Chem Phys ; 26(3): 1891-1903, 2024 Jan 17.
Artículo en Inglés | MEDLINE | ID: mdl-38053401

RESUMEN

The two-dimensional (2D) MA2Z4 family has received extensive attention in manipulating its electronic structure and achieving intriguing physical properties. However, engineering the electronic properties remains a challenge. Herein, based on first-principles calculations, we systematically investigate the effect of biaxial strains on the electronic structure of 2D Rashba MoSiGeN4 (MSGN), and further explore how the interlayer interactions affect the Rashba spin splitting (RSS) in such strained layered MSGN systems. After applying biaxial strains, the band gap decreases monotonically with increasing tensile strains but increases when the compressive strains are applied. An indirect-direct-indirect band gap transition is induced by applying a moderate compressive strain (<5%) in the MSGN systems. Due to the symmetry breaking and moderate spin-orbit coupling (SOC), the monolayer MSGN possesses an isolated RSS near the Fermi level, which could be effectively regulated to the Lifshitz-type spin splitting (LSS) by biaxial strain. For instance, the LSS ← RSS → LSS transformation of the Fermi surface is presented in the monolayer and a more complex and changeable LSS ← RSS → LSS → RSS evolution is observed in bilayer and trilayer MSGN systems as the biaxial strain varies from -8% to 12%, which actually depends on the appearance, variation, and vanish of the Mexican hat band in the absence of SOC under different strains. The contribution of the Mo-dz2 orbital hybridized with the N-pz orbital in the highest valence band plays a dominant role in band evolution under biaxial strains, where the RSS → LSS evolution corresponds to the decreased Mo-dz2 orbital contribution. Our study highlights the biaxial strain controllable RSS, in particular the introduction and even the evolution of LSS near the Fermi surface, which makes the strained MSGN systems promising candidates for future applications in spintronic devices.

2.
Phys Chem Chem Phys ; 26(8): 7010-7019, 2024 Feb 22.
Artículo en Inglés | MEDLINE | ID: mdl-38345334

RESUMEN

The negative Poisson's ratio (NPR) effect usually endows materials with promising ductility and shear resistance, facilitating a wider range of applications. It has been generally acknowledged that alloys show strong advantages in manipulating material properties. Thus, a thought-provoking question arises: how does alloying affect the NPR? In this paper, based on first-principles calculations, we systematically study the NPR in two-dimensional (2D) GaN and AlN, and their alloy of AlxGa1-xN. It is intriguing to find that the NPR in AlxGa1-xN is significantly enhanced compared to the parent materials of GaN and AlN. The underlying mechanism mainly originates from a counter-intuitive increase of the bond angle θ. We further study the microscopic origin of the anomalies by electron orbital analysis as well as electron localization functions. It is revealed that the distribution and movement of electrons change with the applied strain, providing a fundamental view on the effect of strain on lattice parameters and the NPR. The physical origin as revealed in this study deepens the understanding of the NPR and shed light on the future design of modern nanoscale electromechanical devices with fantastic functions based on the auxetic nanomaterials and nanostructures.

3.
Nanotechnology ; 34(17)2023 Feb 13.
Artículo en Inglés | MEDLINE | ID: mdl-36779917

RESUMEN

High thermal conductivity is of great interest due to the novel applications in high-performance heat dissipation for microelectronic devices. Two-dimensional (2D) materials with graphene as a representative have attracted tremendous interest due to the excellent properties, where C23is an emerging 2D allotrope of carbon with a large bandgap. In this paper, by solving the Boltzmann transport equation based onstate-of-the-artfirst-principles calculations, the C23is predicted to have an ultrahigh thermal conductivity of 2051.47 Wm-1K-1, which is on the same order of magnitude as graphene. Based on the comparative analysis among C23, graphene, and penta-graphene, it is shown that the unique spatial structure and the orbital hybridization of C23lead to weak anharmonicity, which results in the large relaxation time of phonons and finally results in ultrahigh thermal conductivity. Our study is expected to promote the comprehensive understanding of thermal transport in C23and shed light on future exploration of novel materials with high thermal conductivity.

4.
Nanotechnology ; 33(27)2022 Apr 20.
Artículo en Inglés | MEDLINE | ID: mdl-35276687

RESUMEN

The negative Poisson's ratio (NPR) is a novel property of materials, which enhances the mechanical feature and creates a wide range of application prospects in lots of fields, such as aerospace, electronics, medicine, etc. Fundamental understanding on the mechanism underlying NPR plays an important role in designing advanced mechanical functional materials. However, with different methods used, the origin of NPR is found different and conflicting with each other, for instance, in the representative graphene. In this study, based on machine learning technique, we constructed a moment tensor potential for molecular dynamics (MD) simulations of graphene. By analyzing the evolution of key geometries, the increase of bond angle is found to be responsible for the NPR of graphene instead of bond length. The results on the origin of NPR are well consistent with the start-of-art first-principles, which amend the results from MD simulations using classic empirical potentials. Our study facilitates the understanding on the origin of NPR of graphene and paves the way to improve the accuracy of MD simulations being comparable to first-principle calculations. Our study would also promote the applications of machine learning interatomic potentials in multiscale simulations of functional materials.

5.
Phys Chem Chem Phys ; 24(29): 17479-17484, 2022 Jul 27.
Artículo en Inglés | MEDLINE | ID: mdl-35822513

RESUMEN

The two-dimensional (2D) materials, represented by graphene, stand out in the electrical industry applications of the future and have been widely studied. As commonly existing in electronic devices, the electric field has been extensively utilized to modulate the performance. However, how the electric field regulates thermal transport is rarely studied. Herein, we investigate the modulation of thermal transport properties by applying an external electric field ranging from 0 to 0.4 V Å-1, with bilayer graphene, monolayer silicene, and germanene as study cases. The monotonically decreasing trend of thermal conductivity in all three materials is revealed. A significant effect on the scattering rate is found to be responsible for the decreased thermal conductivity driven by the electric field. Further evidence shows that the reconstruction of internal electric field and generation of induced charges lead to increased scattering rate from strong phonon anharmonicity. Thus, the ultralow thermal conductivity emerges with the application of external electric fields. Applying an external electric field to regulate thermal conductivity illustrates a constructive idea for highly efficient thermal management.

6.
Phys Chem Chem Phys ; 24(18): 11268-11277, 2022 May 11.
Artículo en Inglés | MEDLINE | ID: mdl-35481990

RESUMEN

In recent years, the energy crisis and global warming have been urgent problems that need to be solved. As is known, thermoelectric (TE) materials can transfer heat energy to electrical energy without air pollution. High-throughput calculations as a novel approach are adopted by screening promising TE materials. In this paper, we use first-principles calculations combined with the semiclassical Boltzmann transport theory to estimate the TE performance of monolayer Ir2Cl2O2 according to the prediction that Ir2Cl2O2 has potential as a good TE material via high-throughput calculations. The low thermal conductivities of 1.73 and 4.68 W mK-1 of Ir2Cl2O2 along the x- and y-axes are calculated, respectively, which exhibits the strong anisotropy caused by the difference in group velocities of low-frequency phonon modes. Then, the electronic transport properties are explored, and the figure of merit ZT is eventually obtained. The maximum ZT value reaches 2.85 (0.40) along the x-axis (y-axis) at 700 K, revealing that the TE properties of the Ir2Cl2O2 monolayer are highly anisotropic. This work reveals that the anisotropic layer Ir2Cl2O2 exhibits high TE performance, which confirms that it is feasible to screen excellent TE materials via high-throughput calculations.

7.
Phys Chem Chem Phys ; 24(5): 3086-3093, 2022 Feb 02.
Artículo en Inglés | MEDLINE | ID: mdl-35040847

RESUMEN

With the miniaturization and integration of nanoelectronic devices, efficient heat removal becomes a key factor affecting their reliable operation. Two-dimensional (2D) materials, with high intrinsic thermal conductivity, good mechanical flexibility, and precisely controllable growth, are widely accepted as ideal candidates for thermal management materials. In this work, by solving the phonon Boltzmann transport equation (BTE) based on first-principles calculations, we investigated the thermal conductivity of novel 2D layered MSi2N4 (M = Mo, W). Our results point to a competitive thermal conductivity as large as 162 W m-1 K-1 of monolayer MoSi2N4, which is around two times larger than that of WSi2N4 and seven times larger than that of monolayer MoS2 despite their similar non-planar structures. It is revealed that the high thermal conductivity arises mainly from its large group velocity and low anharmonicity. Our result suggests that MoSi2N4 could be a potential candidate for 2D thermal management materials.

8.
Phys Chem Chem Phys ; 24(35): 21085-21093, 2022 Sep 14.
Artículo en Inglés | MEDLINE | ID: mdl-36017798

RESUMEN

Thermal transport plays a key role in the working stability of gallium nitride (GaN) based optoelectronic devices, where doping has been widely employed for practical applications. However, it remains unclear how doping affects thermal transport. In this study, based on first-principles calculations, we studied the doping effect on the thermal transport properties of GaN by substituting Ga with In/Al atoms. The thermal conductivities at 300 K along the in-plane(out-of-plane) directions of In- and Al-doped GaN are calculated to be 7.3(8.62) and 12.45(11.80) W m-1 K-1, respectively, which are more than one order of magnitude lower compared to that of GaN [242(239) W m-1 K-1]. From the analysis of phonon transport properties, we find that the low phonon group velocity and small phonon relaxation time dominate the degenerated thermal conductivity, which originated from the strong phonon anharmonicity of In/Al-doped GaN. Furthermore, by examining the crystal structure and electronic properties, the lowered thermal conductivity is revealed lying in the strong polarization of In-N and Al-N bonds, which is due to the large difference in electronegativity of In/Al and N atoms. The results achieved in this study have guiding significance to the thermal transport design of GaN-based optoelectronic devices.

9.
Nanotechnology ; 32(13): 135401, 2021 Mar 26.
Artículo en Inglés | MEDLINE | ID: mdl-33296877

RESUMEN

Alloying is a widely employed approach for tuning properties of materials, especially for thermal conductivity which plays a key role in the working liability of electronic devices and the energy conversion efficiency of thermoelectric devices. Commonly, the thermal conductivity of an alloy is acknowledged to be the smallest compared to the parent materials. However, the findings in this study bring some different points of view on the modulation of thermal transport by alloying. The thermal transport properties of monolayer GaN, AlN, and their alloys of Ga x Al1-x N are comparatively investigated by solving the Boltzmann transport equation (BTE) based on first-principles calculations. The thermal conductivity of Ga0.25Al0.75N alloy (29.57 Wm-1 K-1) and Ga0.5Al0.5N alloy (21.49 Wm-1 K-1) are found exceptionally high to be between AlN (74.42 Wm-1 K-1) and GaN (14.92 Wm-1 K-1), which violates the traditional knowledge that alloying usually lowers thermal conductivity. The mechanism resides in that, the existence of Al atoms reduces the difference in atomic radius and masses of the Ga0.25Al0.75N alloy, which also induces an isolated optical phonon branch around 18 THz. As a result, the scattering phase space of Ga0.25Al0.75N is largely suppressed compared to GaN. The microscopic analysis from the orbital projected electronic density of states and the electron localization function further provides insight that the alloying process weakens the polarization of bonding in Ga0.25Al0.75N alloy and leads to the increased thermal conductivity. The exceptionally high thermal conductivity of the Ga x Al1-x N alloys and the underlying mechanism as revealed in this study would bring valuable insight for the future research of materials with applications in high-performance thermal management.

10.
Phys Chem Chem Phys ; 23(43): 24550-24556, 2021 Nov 10.
Artículo en Inglés | MEDLINE | ID: mdl-34486003

RESUMEN

Pursuing high thermal conductivity is of great significance to enhance the performance and working stability of microelectronics in terms of efficient heat dissipation. Traditionally, ultra-high thermal conductivity is thought to exist only in simple crystals with few atoms in the primitive cell, such as diamond and boron arsenide, where the phonon-phonon scattering is weak. In this study, we report an innovation from conventional knowledge based on state-of-the-art first-principles calculations. It is found that the thermal conductivities of three carbon allotropes of C32, C36, and C94 with non-simple structures can be as high as 1152.75, 1075.70, and 860.07 W m-1 K-1, respectively, despite a large number of atoms in the primitive cell. Through comparative analysis, it is revealed that there exist certain competitive mechanisms, where the weak phonon anharmonicity is found to dominate the high thermal conductivity. Our study not only uncovers excellent carbon-based candidates with ultra-high thermal conductivity for enhancing heat dissipation with potential applications in electronics, but also provides insights into the thermal transport, which will shed light on future studies.

11.
Phys Chem Chem Phys ; 23(36): 20725-20726, 2021 Sep 22.
Artículo en Inglés | MEDLINE | ID: mdl-34518850

RESUMEN

Correction for 'Ultra-high thermal conductivities of tetrahedral carbon allotropes with non-simple structures' by Qiang Chen et al., Phys. Chem. Chem. Phys., 2021, DOI: 10.1039/d1cp02347k.

12.
Phys Chem Chem Phys ; 23(24): 13633-13646, 2021 Jun 23.
Artículo en Inglés | MEDLINE | ID: mdl-34116567

RESUMEN

With the ability to alter the inherent interatomic electrostatic interactions, modulating external electric field strength is a promising approach to tune the phonon transport behavior and enhance the thermoelectric performance of two-dimensional (2D) materials. Here, by applying an electric field (Ez = 0.1 V Å-1), it is predicted that an ultralow value of the lattice thermal conductivity (0.016 W m-1 K-1) at 300 K of 2D indium selenide (InSe) is nearly three orders of magnitude lower than that under an electric field of 0 V Å-1 (27.49 W m-1 K-1). Meanwhile, we calculated the variations in the electrical conductivities, electronic thermal conductivities, Seebeck coefficients, and figure of merit (ZT) of 2D InSe along with the carrier (hole and electron doping) concentrations under some representative electric fields. Owing to the smaller total thermal conductivity along the armchair and zigzag directions, p-type doped 2D InSe at Ez = 0.1 V Å-1 exhibits a larger ZT value (∼1.6) compared to the ZT value (∼0.1) without an electric field at room temperature. The peak ZT value (∼0.53) of the n-type 2D InSe at Ez = 0.1 V Å-1 is much higher than that without an electric field (∼0.02) at the same temperature. Our results pave the way for applying an external electric field to modulate the phonon transport properties and greatly promote the thermoelectric performance of some specific 2D semiconductor materials without altering their crystal structure.

13.
Nanotechnology ; 31(9): 095704, 2020 Feb 21.
Artículo en Inglés | MEDLINE | ID: mdl-31726437

RESUMEN

Thermal anisotropy/isotropy is one of the fundamental characteristics of the thermal properties of a material, playing a significant role in the high-performance thermal management in micro-/nanoelectronics. It has been well documented in the literature that the symmetry of geometric structures governs the anisotropy/isotropy of thermal transport. However, the fundamental correlation and the underlying mechanism remain unclear. In this paper, using a new two-dimensional (2D) van der Waals (vdW) phosphorus nanotube array as a case study, we show that the lattice thermal conductivity can be abnormally almost isotropic although the geometric structure presents remarkable anisotropy, which contradicts the previous consensus. The key factor for the abnormal isotropic thermal conductivity is mainly the essentially analogous group velocities along the intratube and intertube directions. Compared with a carbon-nanotube array, a traditional vdW system, a microscopic picture is established to underpin the underlying mechanism. The quasi-bond (non-covalent bonding, but far stronger than the vdW interatomic interaction) between the phosphorus nanotubes is found to be responsible for such diverse isotropic transport phenomena. The findings in this paper are expected to deepen our understanding of the anisotropy/isotropy thermal transport of materials and are also helpful for future thermal management technology.

14.
Phys Chem Chem Phys ; 21(28): 15647-15655, 2019 Jul 17.
Artículo en Inglés | MEDLINE | ID: mdl-31268444

RESUMEN

In this study, strain modulation of the lattice thermal conductivity of monolayer and bilayer penta-graphene (PG) at room temperature was investigated using first-principles calculations combined with the phonon Boltzmann transport equation. The thermal conductivities of both the monolayer and the bilayer PG exhibit a robust nonmonotonic up-and-down behavior under strain despite the effect of van der Waals (vdW) interactions, and the thermal conductivities of bilayer PG under strain are significantly reduced by up to 87%. Using phonon-level systematic analysis, the variation of thermal conductivity with the increasing strain was determined by increasing the phonon lifetime in specific phonon modes, and that with the reduction of strain was determined by the decrease of both phonon group velocity and phonon lifetime. Moreover, bilayer PG shows an unexpectedly different response to strain when compared with monolayer PG, and a significantly larger reduction (>60%) in the thermal conductivity of bilayer PG is achieved when the strain reaches 10% because the interlayer interactions enhance the phonon anharmonicity of the phonon modes of ultra-low frequency. Our study shows that bilayer PG will have tremendous opportunities for application in thermal management and two-dimensional nanoscale electronic devices owing to its largely tunable thermal conductivity.

15.
Small ; 14(12): e1702465, 2018 03.
Artículo en Inglés | MEDLINE | ID: mdl-29392875

RESUMEN

Phosphorene, a novel elemental 2D semiconductor, possesses fascinating chemical and physical properties which are distinctively different from other 2D materials. The rapidly growing applications of phosphorene in nano/optoelectronics and thermoelectrics call for comprehensive studies of thermal transport properties. In this Review, based on the theoretical and experimental progresses, the thermal transport properties of single-layer phosphorene, multilayer phosphorene (nanofilms), and bulk black phosphorus are summarized to give a general view of the overall thermal conductivity trend from single-layer to bulk form. The mechanism underlying the discrepancy in the reported thermal conductivity of phosphorene is discussed by reviewing the effect of different functionals and cutoff distances on the thermal transport evaluations. This Review then provides fundamental insight into the thermal transport in phosphorene by reviewing the role of resonant bonding in driving giant phonon anharmonicity and long-range interactions. In addition, the extrinsic thermal conductivity of phosphorene is reviewed by discussing the effects of strain and substrate, together with phosphorene based heterostructures and nanoribbons. This Review summarizes the progress of thermal transport in phosphorene from both theoretical calculations and experimental measurements, which would be of significance to the design and development of efficient phosphorene based nanoelectronics.

16.
Phys Chem Chem Phys ; 19(20): 12882-12889, 2017 May 24.
Artículo en Inglés | MEDLINE | ID: mdl-28474040

RESUMEN

Two-dimensional (2D) materials have attracted tremendous interest due to their fascinating physical and chemical properties and promising applications in nano-electronics, where thermal transport plays a vital role in determining the performance of devices. In this paper, we present a first-principles study of the thermal transport properties of monolayer zinc oxide (ZnO), which has potential applications in nano-electronics and thermoelectrics. The thermal conductivity of monolayer ZnO is found to be as low as 4.5 W m-1 K-1 at 300 K, which is dramatically lower than those of bulk ZnO and lots of other 2D materials. A detailed analysis is performed in the framework of Boltzmann transport theory and electronic structure to understand low thermal conductivity. Most surprisingly, the thermal conductivity of monolayer ZnO slowly decreases with temperature and does not follow the conventional 1/T law. This unusual phonon transport behavior arises from the dominant contribution of optical phonon modes to the overall thermal transport in monolayer ZnO, which has been rarely reported in the literature, and the significantly increased specific heat of the high frequency (optical) phonon modes with increasing temperature, both of which compensate the decrease in the phonon relaxation time. Our study highlights the abnormal thermal transport properties of the new 2D material and we anticipate that this research will motivate the experimentalists to further study other physical and chemical properties of monolayer ZnO for its emerging applications in thermoelectrics, thermal circuits, and nano-/opto-electronics.

17.
Nano Lett ; 16(6): 3831-42, 2016 06 08.
Artículo en Inglés | MEDLINE | ID: mdl-27228130

RESUMEN

Two-dimensional (2D) carbon allotrope called penta-graphene was recently proposed from first-principles calculations and various similar penta-structures emerged. Despite significant effort having been dedicated to electronic structures and mechanical properties, little research has been focused on thermal transport in penta-structures. Motivated by this, we performed a comparative study of thermal transport properties of three representative pentagonal structures, namely penta-graphene, penta-SiC2, and penta-SiN2, by solving the phonon Boltzmann transport equation with interatomic force constants extracted from first-principles calculations. Unexpectedly, the thermal conductivity of the three penta-structures exhibits diverse strain dependence, despite their very similar geometry structures. While the thermal conductivity of penta-graphene exhibits standard monotonic reduction by stretching, penta-SiC2 possesses an unusual nonmonotonic up-and-down behavior. More interestingly, the thermal conductivity of penta-SiN2 has 1 order of magnitude enhancement due to the strain induced buckled to planar structure transition. The mechanism governing the diverse strain dependence is identified as the competition between the change of phonon group velocity and phonon lifetime of acoustic phonon modes with combined effect from the unique structure transition for penta-SiN2. The disparate thermal transport behavior is further correlated to the fundamentally different bonding nature in the atomic structures with solid evidence from the distribution of deformation charge density and more in-depth molecular orbital analysis. The reported giant and robust tunability of thermal conductivity may inspire intensive research on other derivatives of penta-structures as potential materials for emerging nanoelectronic devices. The fundamental physics understood from this study also solidifies the strategy to engineer thermal transport properties of broad 2D materials by simple mechanical strain.

18.
Nano Lett ; 16(10): 6364-6370, 2016 10 12.
Artículo en Inglés | MEDLINE | ID: mdl-27580070

RESUMEN

We report electronic and phononic transport measurements of monocrystalline batch-fabricated silicon nanowire (SiNW) arrays functionalized with different surface chemistries. We find that hydrogen-terminated SiNWs prepared by vapor HF etching of native-oxide-covered devices show increased electrical conductivity but decreased thermal conductivity. We used the kinetic Monte Carlo method to solve the Boltzmann transport equation and also numerically examine the effect of phonon boundary scattering. Surface transfer doping of the SiNWs by cobaltocene or decamethylcobaltocene drastically improves the electrical conductivity by 2 to 4 orders of magnitude without affecting the thermal conductivity. The results showcase surface chemical control of nanomaterials as a potent pathway that can complement device miniaturization efforts in the quest for more efficient thermoelectric materials and devices.

19.
Nanotechnology ; 27(26): 265706, 2016 Jul 01.
Artículo en Inglés | MEDLINE | ID: mdl-27199352

RESUMEN

Silica is one of the most abundant materials in the Earth's crust and is a remarkably versatile and important engineering material in various modern science and technology. Recently, freestanding and well-ordered two-dimensional (2D) silica monolayers with octahedral (O-silica) building blocks were found to be theoretically stable by (Wang G et al 2015 J. Phys. Chem. C 119 15654-60). In this paper, by performing first-principles calculations, we systematically investigated the electronic and thermal transport properties of 2D O-silica and also studied how these properties can be tuned by simple mechanical stretching. Unstrained 2D O-silica is an insulator with an indirect band gap of 6.536 eV. The band gap decreases considerably with bilateral strain up to 29%, at which point a semiconductor-metal transition occurs. More importantly, the in-plane thermal conductivity of freestanding 2D O-silica is found to be unusually high, which is around 40 to 50 times higher than that of bulk α-quartz and more than two orders of magnitude higher than that of amorphous silica. The thermal conductivity of O-silica decreases by almost two orders of magnitude when the bilateral stretching strain reaches 10%. By analyzing the mode-dependent phonon properties and phonon-scattering channel, the phonon lifetime is found to be the dominant factor that leads to the dramatic decrease of the lattice thermal conductivity under strain. The very sensitive response of both band gap and phonon transport properties to the external mechanical strain will enable 2D O-silica to easily adapt to the different environment of realistic applications. Our study is expected to stimulate experimental exploration of further physical and chemical properties of 2D silica systems, and offers perspectives on modulating the electronic and thermal properties of related low-dimensional structures for applications such as thermoelectric, photovoltaic, and optoelectronic devices.

20.
Phys Chem Chem Phys ; 17(7): 4854-8, 2015 Feb 21.
Artículo en Inglés | MEDLINE | ID: mdl-25594447

RESUMEN

Phosphorene, the single layer counterpart of black phosphorus, is a novel two-dimensional semiconductor with high carrier mobility and a large fundamental direct band gap, which has attracted tremendous interest recently. Its potential applications in nano-electronics and thermoelectrics call for fundamental study of the phonon transport. Here, we calculate the intrinsic lattice thermal conductivity of phosphorene by solving the phonon Boltzmann transport equation (BTE) based on first-principles calculations. The thermal conductivity of phosphorene at 300 K is 30.15 W m(-1) K(-1) (zigzag) and 13.65 W m(-1) K(-1) (armchair), showing an obvious anisotropy along different directions. The calculated thermal conductivity fits perfectly to the inverse relationship with temperature when the temperature is higher than Debye temperature (ΘD = 278.66 K). In comparison to graphene, the minor contribution around 5% of the ZA mode is responsible for the low thermal conductivity of phosphorene. In addition, the representative mean free path (MFP), a critical size for phonon transport, is also obtained.

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