Lone-pair electrons induced anomalous

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May 21, 2018 - we establish a microscopic picture of the lone-pair electrons driving .... group III-nitrides, in comparison with graphene, are shown in Fig. ... In contrast, the κ of all the three monolayer group .... It is well known that in graphene the σ bonds are con- ..... include micro-/nano-scale thermal transport in novel en-.
Nano Energy 50 (2018) 425–430

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Lone-pair electrons induced anomalous enhancement of thermal transport in strained planar two-dimensional materials Guangzhao Qina, Zhenzhen Qinb, Huimin Wanga, Ming Hua,b,c,

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a

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 c Department of Mechanical Engineering, University of South Carolina, Columbia, SC 29208, USA b

A R T I C LE I N FO

A B S T R A C T

Keywords: Strain Two-dimensional Thermal transport First-principles Lone-pair electrons

Strain engineering is one of the most promising and effective routes towards continuously tuning thermal transport due to the flexibility and robustness. However, previous studies mainly focused on quantifying how the thermal conductivity (κ ) is modulated by strain, while the fundamental understanding on the electronic origin has yet to be explored. In this paper, we establish a microscopic picture of the lone-pair electrons driving strong phonon anharmonicity in two-dimensional (2D) materials beyond the traditional three-dimensional (3D) systems. We provide solid explanation for the unexpectedly up to one order of magnitude enlarged κ of a class of planar monolayers with bilateral tensile strain applied, which is in sharp contrast to the strain induced κ reduction in graphene despite their similar planar structures. The anomalous positive response of κ to tensile strain is attributed to the attenuated interaction between the lone-pair electrons and the bonding electrons of neighboring atoms, which reduces phonon anharmonicity and leads to the enlarged κ . Our study uncovers the electronic origin of the strain modulated thermal transport, which would have great impact on future investigations related to energy nanotechnologies and applications.

1. Introduction Effective manipulation of heat conduction plays a key role in high-performance thermal management for future nano energy technologies. Phonons play the dominant role in thermal transport in semiconductors [1–3]. Fundamental insight into phonon transport is of great significance to the efficient manipulation of heat flow, which is one of the appealing thermophysical problems with enormous practical implications related to energy, such as electronic cooling, thermoelectrics, phase change memories [3,4], thermal devices (diodes, transistors, logic gates) [5], etc. Thermal transport can be manipulated with rationally designed methods or engineered material process, as well as suitable geometry shape control and material composition, such as nanostructuring [6–8], doping [9], introducing porosity [10], applying external field [11], and physical/chemical processing [12–18]. Besides, efficient thermal modulation can also be realized by strain engineering [19–21]. Since it is flexible and robust, strain engineering has become one of the most promising and effective routes towards continuous tunability. Moreover, under realistic conditions in many systems, synthetic materials and nanoscale devices usually contain residual strain after fabrication [22]. However, previous studies mainly focused on quantifying how the thermal conductivity is modulated by mechanical strain [19,21,23–31], while the fundamental understanding of the electronic origin has yet to be explored.

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Two-dimensional (2D) materials with graphene as a representative have been intensively studied for many years for their promising applications in lots of fields [3]. Among these, monolayer hexagonal boron nitride (h-BN) with a wide band gap (∼ 5.0–6.0 eV) offers alternative solutions compensating to the gapless graphene, which establishes the key role of 2D nitrides in advancing the development of next generation nano-electronics [32]. Beyond h-BN, hexagonal aluminum and gallium nitrides (h-AlN and h-GaN) have been also successfully fabricated in experiments recently [33–36] and received extensive attention due to their fascinating properties [36–41]. Thus, the thermal transport properties of these 2D group III-nitrides (h-BN, h-AlN, hGaN), especially their response to the external mechanical strain, are of great interest for designing energy related novel devices with desirable thermal transport properties in terms of high performance thermal management. In this paper, we performed a comparative study of thermal transport in 2D group III-nitrides (h-BN, h-AlN, h-GaN) and graphene based on firstprinciples calculations. The lattice thermal conductivity (κ ) of 2D group IIInitrides is unexpectedly enlarged by one order of magnitude with bilateral tensile strain applied, which is in sharp contrast to the strain induced κ reduction in graphene. Considering that such enhancement was for a long time thought to be intrinsic and unique only for non-planar 2D materials, such as silicene and phosphorene, it is very intriguing to observe the anomalous positive response of κ to tensile strains regarding to the planar honeycomb

Corresponding author at: Department of Mechanical Engineering, University of South Carolina, Columbia, SC 29208, USA. E-mail address: [email protected] (M. Hu).

https://doi.org/10.1016/j.nanoen.2018.05.040 Received 24 March 2018; Received in revised form 6 May 2018; Accepted 17 May 2018 Available online 21 May 2018 2211-2855/ © 2018 Elsevier Ltd. All rights reserved.

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Fig. 2. Comparison of the thermal transport properties among monolayer group IIInitrides (h-BN, h-AlN, h-GaN) and graphene. (a) Temperature dependent κ of h-BN and graphene calculated using the iterative and RTA methods. The case of graphene with artificial mass difference (mass of B and N) is also plotted. Comparison of (b) room temperature κ , (c) mode level scattering rates, and (d) Grüneisen parameter.

Fig. 1. (a) The anomalous strain enlarged κ of h-(B/Al/Ga)N, h-BAs, and C3 N, in sharp contrast to graphene. All the κ are normalized to their respective intrinsic κ without strain. (Inset) Schematic of the strain weakened interactions of lone-pair N-s electrons with the bonding electrons. (b-e) The comparison of phonon lifetime with (3%) and without strain applied for (b) h-GaN, (c) h-AlN, (d) h-BN, and (e) graphene.

must lie in the weakened phonon-phonon scattering strength and phonon anharmonicity, which is distinctly different from that in graphene. In the following, we will show that the underlying mechanism for the weakened phonon anharmonicity can be well understood based on the microscopic picture of the lone-pair electrons driving strong phonon anharmonicity.

structure of the 2D group III-nitrides. A microscopic picture connecting phonon anharmonicity to lone-pair electrons is established based on the analysis of orbital projected electronic structure. The anomalous positive response of κ to tensile strain is attributed to the attenuated interaction between the lone-pair s electrons around N atoms and the bonding electrons of neighboring (B/Al/Ga) atoms, which reduces phonon anharmonicity and leads to the enlarged κ . The deep understanding on the electronic origin of the strain modulated thermal transport would have great impact on future research in micro-/nano-scale thermal transport such as high efficient thermal management.

2.2. Comparative analysis of thermal transport properties We start with comparison of the intrinsic thermal transport properties between these planar monolayer group III-nitrides (taking h-BN as a representative) and graphene for the fundamental understanding of their difference. Considering the same average atom mass and similar planar honeycomb structure of h-BN as graphene, one would intuitively expect analogical phonon transport properties, such as high κ of h-BN like graphene. However, the room temperature κ of h-BN is obtained to be only 245.45 W/ mK in this study, which agrees well with previous experimental and theoretical reports (227–625 W/mK) [49–53]. The κ of h-BN is more than one order of magnitude lower than that of graphene (3094.98 W/mK) [Fig. 2(a,b)]. Previous studies concluded that phonon hydrodynamics is responsible for the ultra-high κ of graphene [54–56]. Despite the relatively low κ of h-BN, the RTA method also largely underestimates the accurate κ by 73.02%, which is comparable to that for graphene (83.18%) [Fig. 2(a)], suggesting large proportion of N-process and similar phonon hydrodynamics in h-BN [54]. Actually, further analysis shows that the major characteristics of phonon transport properties of h-BN and graphene have large overlap, despite the huge difference in the absolute value of κ . For example, flexural acoustic (FA) branch dominates the phonon transport in both h-BN (72.6%) and graphene (81.2%) at 300 K. Moreover, the scattering channels for the dominating FA are also identical (FA+FA → TA/LA) as revealed in our previous study [41]. Due to the inversion symmetry of the planar structures of h-BN and graphene, only the scattering channels with participation of even numbers of FA are allowed [57], leading to limited scattering rate of FA and its dominating role in phonon transport. Hence, different from silicene with buckled structure [19], the much lower κ of h-BN than graphene is attributed to the larger scattering rate [Fig. 2(c)] driven by the stronger phonon anharmonicity [Fig. 2(d)], not the larger scattering phase space (channels).

2. Results and discussions 2.1. Strain enhanced thermal transport The effect of bilateral tensile strain on the κ of the planar monolayer group III-nitrides, in comparison with graphene, are shown in Fig. 1(a). The κ of graphene decreases with tensile strain applied, which agrees very well with previous reports [42–44]. In contrast, the κ of all the three monolayer group III-nitrides is tremendously enlarged, especially for h-AlN and h-GaN (up to one order of magnitude). Such enhancement would be very beneficial for the applications of 2D group III-nitrides in nano- and opto-electronics in terms of efficient heat dissipation due to the strain accelerated thermal transport. Previous studies on the strain-dependent κ of silicene reported similar large enhancement, which is attributed to the flattening of the buckled structure of silicene upon stretching [9,19,26]. The case is similar for phosphorene with puckered structure [45–48]. In fact, such enhancement was thought to be intrinsic and unique only for 2D materials with non-planar structure [19]. Considering the perfect planar honeycomb structure of the monolayer group III-nitrides (similar to graphene, with no buckling or puckering), it is very intriguing to observe the anomalous positive response of κ to tensile strains. We performed further study to achieve a though understanding on the anomalous phenomena, which would be of great significance to the effective manipulation of heat conduction with promising applications in high-performance thermal management for future nano energy technologies. Detailed analysis on the phonon-phonon scattering reveals that the strain enlarged κ is mainly due to the overall enlarged phonon lifetime [Fig. 1(b–d)], which compensates the reduced heat capacity and group velocities caused by the softened phonon dispersions (Note 3 in the Supplementary Information). The phase space for phonon-phonon scattering would be enlarged due to the softened phonon dispersions, which could have negative contribution to the phonon lifetime [19]. Thus, the reason for the strain enlarged phonon lifetime

2.3. Phonon Dirac cone and anharmonicity Since for the first glance the main difference between h-BN and graphene is the atom mass, it is intuitive to attribute the lower κ , larger scattering rate, and stronger phonon anharmonicity in h-BN to the mass difference [52]. Fig. 3 depicts the phonon dispersions and partial density of states (pDOS) of h426

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of h-BN into graphene, i.e. replacing the two C atoms in the primitive cell with B and N atoms (we call it pseudo-BN, see Note 2 in the Supplementary Information for details), respectively, we find that the phonon Dirac cone is opened only by 2.03 THz, which is much smaller than that for h-BN (8.58 THz) [left panel of Fig. 3]. Moreover, the phonon bandgap between FO and FA cannot be fully closed in h-BN (only decreases from 8.58 THz to 6.93 THz), even when the mass difference is eliminated, i.e. setting the mass of B and N atoms as C atom. In addition, by introducing the mass difference into graphene, the κ of the pseudo-BN is much lowered (1808.25 W/mK at 300 K compared to the original value of 3094.98 W/mK for graphene) [Fig. 2(a)] due to the additional scattering induced by the mass difference, but the κ is still several folders higher than that of h-BN (245.45 W/mK). Therefore, there must be some physical mechanism other than mass difference responsible for the remarkable phonon anharmonicity and low κ of hBN compared to graphene.

Fig. 3. Comparison of phonon dispersions and partial density of states (pDOS) between h-BN and graphene. Also plotted are the phonon dispersions by artificially introducing mass difference in graphene and eliminating mass difference in h-BN. The colored ellipse highlights the evolution of phonon Dirac cone in graphene and h-BN.

2.4. Electronic origin of phonon anharmonicity To this end, we conduct detailed study based on the deep analysis of orbital projected electronic structure. We will show that the strong phonon anharmonicity in h-BN is fundamentally driven by the stereochemically active lone-pair electrons due to the special orbital hybridization. It is well known that in graphene the σ bonds are contributed from the C-s / px / py orbital, and the solo C- pz orbital forms the π bonds and the electronic Dirac cone [3]. However, the bonding states in h-BN are totally different with an intrinsic electronic bandgap. As shown in Fig. 4(a), the s orbital of B atom strongly hybridizes with px and py , contributing to the valence band, while B- pz contributes to the conduction band. As for N atom, the s orbital is largely (∼ 15 eV) confined below the valence band, forming an isolated band. Consequently, the σ bonds between B and N atoms are jointly contributed by the B-s / px / py and N- px / py / pz , and the s 2 electrons in the s 2p3 valence configuration of N atom do not participate in the bonding. Thus, the non-bonding lone-pair s electrons arise around N atoms in h-BN, leading to strong phonon anharmonicity by interacting with the bonding electrons of adjacent atoms (B) as revealed by the pDOS and electron localization function (ELF) [Fig. 4(a,b,h–j)].

BN and graphene. Despite the same average atom mass, an overall softness of phonon branches is clearly observed in h-BN compared with graphene, which could be caused by the weaker bonding strength of B-N than C-C (Supplemental Figure S4). In particular, the phonon Dirac cone at the K point formed by FO and FA in graphene is opened in h-BN with a gap of 8.58 THz, which largely softens the FA phonon branch. The softness of FA phonon branch in hBN is consistent with the strong phonon anharmonicity quantified by the Grüneisen parameter [Fig. 2(d)]. As revealed by the pDOS (right panel of Fig. 3), for h-BN the upper part of the opened phonon Dirac cone is mainly contributed by B atom, while the lower part is mainly contributed by N atom. Thus, it presents a consistent picture with the intuitive idea that the mass difference in h-BN leads to the opening of the phonon Dirac cone and the softness of FA phonon branch, which is closely associated with the strong phonon anharmonicity. However, only the mass difference cannot induce so large opening of the phonon Dirac cone. By artificially introducing the mass difference

Fig. 4. (a) The orbital projected electronic band structures of h-BN. (Inset) The schematic plot of the configuration of the lone-pair non-bonding N-s electrons and their interactions with the covalently bonding electrons. (b) The orbital projected electronic density of states (pDOS) of pristine h-BN. The lone-pair s-electrons are highlighted in color. (c, d) The asymmetric response of pDOS to the displacement of N atom. The positive and negative moves mean the two opposite directions of N atom as shown in the Inset of (a). (e, f) Top and (g-j) side views of the electron localization function (ELF).

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anharmonicity and reduces phonon-phonon scattering. Consequently, the κ of planar monolayer group III-nitrides is enlarged by the tensile strain. Note that the effect would be much stronger for h-AlN and h-GaN due to the larger difference in the electronegativity as discussed above. As a result, the κ of h-AlN and h-GaN is enlarged with larger magnitude by the external tensile strain [Fig. 1(a)]. As for graphene, there is no lone-pair electrons as analyzed above. Therefore, the tensile mechanical strain does not lead to the similar κ enlargement in graphene as 2D group III-nitrides despite their similar planar honeycomb structure. In order to soundly prove the above statements, we further studied two additional 2D planar systems (C3 N and h-BAs) with lone-pair electrons. All these systems share the common trend of enhanced thermal transport upon stretching [Fig. 1(a)], which is due to the attenuated interaction between the lone-pair electrons and the bonding electrons of neighboring atoms as analyzed above. It is anticipated that the thermal transport in other systems possessing lone-pair electrons could also be generally enhanced by weakening the interaction strength, such as by increasing the bond length with tensile strain.

We further establish a microscopic picture of direct connection between phonon anharmonicity and the lone-pair electrons, by showing how the nonlinear restoring forces arise from the asymmetric change of the electronic structure induced by the atoms' motion. As analyzed above, the N-s electrons interact with the bonding electrons of adjacent atoms (B) due to the overlap of wave functions, which induces nonlinear electrostatic force among atoms when they thermally vibrate around the equilibrium position. The nonlinear electrostatic force originates from the asymmetric change of the hybridization between N-s and B-s / px / py for the atomic motion, as revealed by the pDOS in Fig. 4(b–d). A more asymmetric potential energy well would be induced together with the additional nonlinear electrostatic force due to the lone-pair s-electrons (Supplemental Figures S2 and S4), which leads to the strong phonon anharmonicity in h-BN and significantly reduces κ . It was claimed in previous studies that the interaction between lone-pair electrons and bonding electrons of adjacent atoms would lead to phonon anharmonicity [58–65]. However, no explicit evidence has been provided for the direct connection. Here, by analyzing the evolution of orbital hybridizations, we provide direct evidence in Figs. 4(a,b,e,h–j) for the interactions and further establish the microscopic picture of how the phonon anharmonicity arises from a fundamental level of electronic structure [Figs. 4(b–d)]. Besides, the concept of lone-pair electrons driving strong phonon anharmonicity is successfully expanded to 2D materials beyond the traditional three-dimensional (3D) [65,66] materials. Note that there exists difference in the electronegativity between B and N atoms, which leads to polarization for the B-N bonds as revealed by the ELF [Figs. 4(e,h)], in contrast to the nonpolarization in graphene [Figs. 4(f,g)]. Thus, the bonding electrons would be relatively closer to N atom, contributing positively to the stronger interaction with the nonbonding N-s electrons and stronger phonon anharmonicity. Considering the larger difference in the electronegativity between N and Al/Ga atoms, the phonon anharmonicity in h-AlN and h-GaN is expected to be much stronger. In addition, the larger difference in atom mass and radius for h-AlN and h-GaN compared to h-BN may also have some influence on the thermal transport properties [40,41]. As shown in Fig. 2(d), the magnitude of the Grüneisen parameter of the representative FA phonon branch increases monotonically for h-BN, hAlN, and h-GaN, all of which are larger than graphene. Consistently, from graphene to h-GaN, the scattering rate [Fig. 2(c)] increases and the κ decreases [Fig. 2(b)]. Based on the insight into the lone-pair electrons induced strong phonon anharmonicity and polarization effect, a coherent understanding is achieved for the diverse thermal transport properties of monolayer group III-nitrides and graphene.

3. Conclusions In summary, we have performed a comparative study of thermal transport in graphene and monolayer group III-nitrides combining with other similar representative 2D compounds. All these 2D materials share similar planar honeycomb structure. However, the κ of all monolayer compounds is unexpectedly enlarged by up to one order of magnitude with bilateral tensile strain applied, which is in sharp contrast to the strain induced κ reduction in graphene. Considering that the enhancement of κ by stretching is proprietary for 2D materials with non-planar structure, the observed anomalous positive response of κ of 2D planar group III-nitrides to tensile strains is counter-intuitive. By deeply analyzing the orbital projected electronic structure, we establish a microscopic picture of the lone-pair electrons driving strong phonon anharmonicity in 2D materials. Explicit evidence is provided for the interaction between stereochemically active lone-pair electrons and bonding electrons of adjacent atoms. We show how the nonlinear restoring forces directly arise from the asymmetric change of the electronic structure induced by the atom motion, leading to strong phonon anharmonicity and thus low κ . The insight into the relationship between lone-pair electrons and strong phonon anharmonicity provides coherent understanding on the diverse thermal transport properties of monolayer group III-nitrides and graphene. Furthermore, the underlying mechanism for the anomalous positive response of κ to tensile strain can be well understood based on the established microscopic picture of the lone-pair electrons driving strong phonon anharmonicity. Upon stretching, the interaction between the lone-pair s electrons around N atoms and the bonding electrons of neighboring (B/Al/Ga) atoms is attenuated, which reduces phonon anharmonicity and leads to the enlarged κ . Our study deepens the understanding of phonon transport in 2D materials and uncovers the electronic origin of the strain modulated thermal transport, which would have great impact on future research in micro-/nano-scale thermal transport such as high efficient thermal management.

2.5. Strain attenuated interactions and phonon anharmonicity Finally, we would like to bring back the attention to the anomalous strain enlarged κ of planar monolayer group III-nitrides as presented at the very beginning, which was analyzed due to the weakened phononphonon scattering strength and phonon anharmonicity. The fundamental understanding on the strain weakened phonon anharmonicity can be achieved based on the above established microscopic picture of the lone-pair electrons driving strong phonon anharmonicity. Upon stretching, the separation distance between the atoms becomes larger and the lone-pair electrons become more localized. For instance, the energy span of N-s states in h-BN decreases from 3.62 to 3.07 eV with 5% strain applied (Supplemental Figure S3), revealing the more localized N-s states. Thus, the interaction between the lone-pair s electrons around N atoms and the bonding electrons of adjacent atoms (s / px / py of B/Al/Ga atoms) are weakened due to the reduced overlap of wave functions. The inset of Fig. 1(a) shows the schematic of the strain enlarged distance and weakened interaction, which attenuates phonon

4. Methods All the first-principles calculations are performed based on the density functional theory (DFT) using the projector augmented wave (PAW) method [67] as implemented in the Vienna ab initio simulation package (vasp) [68]. The κ is obtained by iteratively solving the phonon Boltzmann transport equation (BTE) with the ShengBTE package, which is equivalent to the solution of relaxation time approximation (RTA) if the iteration stops at the first step [69,70]. Detailed information can be

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found in Note 1 in the Supplementary Information. The κ of graphene is calculated to be 3094.98 W/mK by using the iterative method. The good agreement with previous results confirms the reliability of our calculations [3,71,72].

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Notes The authors declare no competing financial interest. Acknowledgments This work is supported by the Deutsche Forschungsgemeinschaft (DFG) (Project number: HU 2269/2-1). G.Q. gratefully acknowledges Dr. Jia-Yue Yang, Dr. Sheng-Ying Yue, and Mr. Li-Chuan Zhang (RWTH Aachen University) for their fruitful discussions. Simulations were performed with computing resources granted by RWTH Aachen University under projects jara0168 and rwth0223. Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.nanoen.2018.05.040. Supplementary Information: 1. Detailed information on computational methods; 2. Pseudo systems; 3. Strain modulated thermal conductivity; 4. Figures for the strain modulated thermal conductivity of hBN, orbital projected electronic structures, the effect of strain on the pDOS of h-BN, and the comparison of the potential energy well between graphene and h-BN. References [1] [2] [3] [4]

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Guangzhao Qin received his B.S. degree (2011) in Zhengzhou University and M.Sc. degree (2015) in the University of Chinese Academy of Sciences, China, and is currently a Ph.D. candidate at RWTH Aachen University, Germany, supervised by Prof. Ming Hu. He is the winer of “National Award for Outstanding Self-Financed Oversea Students” and the director of the 26th council of the Annual Conference of Gesellschaft Chinesischer Physiker in Deutschland (GCPD). His research interests are mainly in micro-/nano-scale energy transport and conversion, together with the mechanical and electronic properties of materials.

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G. Qin et al. Dr. Zhenzhen Qin received her Ph.D. degree in Electronics Science and Technology from Nankai University (NKU) in 2017. Then she started to work as a postdoctoral fellow in Aachen Institute for Advanced Study in Computational Engineering Science (AICES) of RWTH Aachen University, Germany. Her research mainly focuses on magnetism, thermal transport and mechanical properties of low-dimensional materials.

Dr. Ming Hu received the B.S. degree from Department of Mechanical Engineering, University of Science and Technology of China in 2001 and the Ph.D. degree in solid mechanics from Institute of Mechanics, Chinese Academy of Sciences in 2006. After 5 years of faculty at RWTH Aachen University in Germany, he recently joined Department of Mechanical Engineering at the University of South Carolina as an Associate Professor. His current research interests include micro-/nano-scale thermal transport in novel energy systems, in particular low-dimensional materials and nanostructures, interfacial heat transfer for advanced thermal management, and multiphysics modeling of complex energy transport process.

Huimin Wang received her M.Sc. degree in the Northeastern University of China, and is currently a joint Ph.D. candidate in the key laboratory of electromagnetic processing of materials at the same university and RWTH Aachen University. Her research interests focus on nanoscale thermal transport and the control processes of materials by high magnetic field.

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