Thermal transport properties of boron nitride based materials: A review

Renewable and Sustainable Energy Reviews 120 (2020) 109622

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Thermal transport properties of boron nitride based materials: A review b � Vaishali Sharma a, Hardik L. Kagdada a, Prafulla K. Jha a, *, Piotr Spiewak , b, c Krzysztof J. Kurzydłowski a

Department of Physics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara, 390002, India Materials Design Division, Faculty of Materials Science and Engineering, Warsaw University of Technology, 141 Wołoska Str., 02-507, Warsaw, Poland c Faculty of Mechanical Engineering, Bialystok University of Technology, 45C Wiejska Str., 15–351, Bialystok, Poland b

A R T I C L E I N F O

A B S T R A C T

Keywords: Boron nitride allotropes Electronic transport Thermal transport Power factor Figure of merit

The era of thermoelectric materials has begun in the search of clean, green and renewable anticipated energy resources. Thermoelectric materials are attracting a lot of spotlights by directly converting waste heat in elec­ tricity and could be a valuable part in world’s energy emergence. Present review provides an insight into the emerging boron nitride (BN) structures on the basis of their thermoelectric properties. In the recent years, ad­ vances in the synthesis of boron nitride based structures which are analogous to carbon, have attracted signif­ icant interest by the researchers. The electronic, optical and vibrational properties of boron nitride structures are widely studied, while the thermoelectric properties have not been thoroughly investigated. However, over the past years, a significant effort has been directed towards the enhancement of their thermoelectric properties. The higher the value of figure of merit (ZT), the greater is the production of electricity. Different technologies were adopted by researchers in developing the thermoelectric efficiency. Due to the interconnection between ther­ moelectric parameters it is difficult to achieve ZT up to 2 or 3. Commercially existing Pb–Te and Bi–Te based thermoelectric materials provide good thermoelectric efficiency but are toxic, denser and of high cost. Therefore, there is a need of environment friendly, reusable and low cost thermoelectric materials. An extensive review of the thermoelectric characteristics of bulk phases of BN (like a-BN, c-BN, and w-BN), hexagonal-BN (h-BN), boron nitride nanotube (BNNT), boron nitride nanoribbon (ABNNR and ZBNNR), boron nitride quantum dots and boron nitride composites is presented. This evolution in boron nitride based materials will elucidate their po­ tential for developing high-performance next-generation thermoelectric devices.

1. Introduction In the recent years, owing to the world’s need for managing energy crisis, thermoelectric materials play an important role in converting waste heat to the valuable electricity. Several methods are appropriate to recover waste heat including steam and organic Rankine cycle which are indirect power generation methods, absorption cooling, plant/dis­ trict water heating, direct power generation like piezoelectric and thermoelectric, biomass co-location, water desalination etc. [1]. Among all these technologies, thermoelectric begun a new realm in research field to recover waste heat as this technology directly converts the thermal energy to electrical energy, unlike others. Fig. 1(a–b) presents the arising need of energy demand, while ~90% of the total power supply still relies upon fossil fuels. Moreover, 70% of energy of these fuels is unused and wasted in heat form in factories which needs giant cooling systems. Therefore, an urgency in the sustainable alternative is

needed thinking the total energy consumption up to 13 billion tonnes of oil in 2015 [2]. Thermoelectricity and pyroelectricity are two main approaches to accumulate concerned heat energy. Temperature differ­ ence in materials generate an electric potential in two different semi­ conductors which accomplishes Seebeck effect for conversion in thermoelectricity, whereas in pyroelectricity the structure of a specific material changes when heat is enforced on them resulting in alteration of polarization developing electric potential [3]. The Seebeck effect like the Peltier effect is a predominant thermoelectric effect. The Seebeck effect is a phenomena that shows voltage difference (ΔV) is induced in proportion to applied temperature gradient (ΔT), expressed as: ∆V ¼ SΔT

(1)

where S is called the Seebeck coefficient and also known as thermo­ electric power or thermopower. The Seebeck effect can be used to

* Corresponding author. E-mail address: [email protected] (P.K. Jha). https://doi.org/10.1016/j.rser.2019.109622 Received 17 February 2019; Received in revised form 29 October 2019; Accepted 22 November 2019 Available online 11 December 2019 1364-0321/© 2019 Elsevier Ltd. All rights reserved.

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List of acronyms BN a-BN c-BN r-BN w-BN h-BN BNNT BNNR ZBNNR GNR ABNNR BCNNR BNND PGEC SLBN (ZT)eng (PF)eng NEGF MD

μ

PF T

HOVB LUCB ZT S

Boron nitride Amorphous boron nitride Cubic boron nitride Rhombohedral boron nitride Wurtzite boron nitride Hexagonal boron nitride Boron nitride nanotube Boron nitride nanoribbon Zigzag boron nitride nanoribbon Graphene nanoribbon Armchair boron nitride nanoribbon Hybrid graphene/boron nitride Boron nitride quantum dots Phonon Glass Electron Crystal Single layer boron nitride Engineering figure of merit Engineering power factor Nonequilibrium green function Molecular dynamics Chemical potential Power factor Temperature

σ

PGEC κ κe κl SLBN PHDOS (ZT)eng (PF)eng Tc Th NEGF MD DFT

Highest occupied valence band Lowest unoccupied conduction band Figure of merit Seebeck coefficient Electrical conductivity Phonon Glass Electron Crystal Thermal conductivity Electronic thermal conductivity Lattice thermal conductivity Single layer boron nitride Phonon density of states Engineering figure of merit Engineering power factor Cold side temperature Hot side temperature Non equilibrium Green’s function Molecular dynamics Density functional theory

Measurement Units W/mK Watt per meter kelvin eV Electron volt W/cmK Watt per centimetre kelvin nW/K Nanowatt per kelvin

convert thermal energy into electric energy which is called thermo­ electric power generation. Fig. 1 shows the schematic diagram of a thermoelectric power generation. It comprises n-type and p-type semi­ conducting materials linked by metal terminals. Thermoelectric devices are made of various such couples. These both semiconductors (n- and ptype) are joined electrically from one end placed in association with a heat source, at the same time the other one is kept at a lower

temperature. Due to the temperature difference formed at both ends, the carriers in both n-type and p-type semiconductors begin to diffuse from the hotter side to colder one. After connecting to a load resistor, the gradient in carrier type i.e. electrons in n-type and holes in p-type will produce an electric current. The potential fall in load resistor will then be used to design a suitable device. Thermoelectric materials provide low cost electricity, green energy mechanization with no moving parts

Fig. 1. (a) Worldwide energy consumption of 2005, 2015, and 2040 [2] (b) 2015 share of total energy [2] (c) Schematic diagram of a thermoelectric power generation. The applied temperature difference in the material stimulates charge carriers (electrons or holes) to spread from hot-region to the cold-region, causing flow of current over the circuit. Reprinted with permission from Ref. [2]. 2

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of solid state devices. However, they specifically depend on materials properties. The efficiency of thermoelectric materials is given by the well-known dimensionless quantity figure of merit (ZT) [4]: ZT ¼

S2 σ T κe þ κl

transformation from thermal energy to electrical energy equal to one at room temperature [35]. Thermoelectric and thermal transport study increases exponentially from 2010 which can be seen from Fig. 2. From this graph, after 2009, a sudden increase in number of studies on ther­ moelectric and thermal transport properties has been noticed. We have found two regions of drastic increase in number of paper published per year: (i) from 2010 to 2013, the frequency of studied publications were ~6557 and (ii) 2014 to 2017, the publications per year were ~10,610 much higher than previous region [36]. The star mark in Fig. 2 presents the published papers on thermoelectric in the months of 2019, which are almost equal to the research done in 2018. We can see in Fig. 2, the studies on thermoelectric materials are increasing day by day and highest in the last year (2018). Up to ~3000 publications were reported in the year of 2018 which is almost double the publication in 2010–2013. The development of thermoelectric ma­ terials has been started from the traditional semiconductors of groups IV-V (like SiGe), III-V (like InSb), IV and V chalcogenides (like PbTe, Bi2Te3, GeTe, Sb2Te3 etc.) to the recently developed skutterdites, clathrates, half-Huesler alloys, cobaltites [37–40] as mentioned above and so on. Bi2Te3 is a common member of V-group chalcogenides with ZT reaching to unity at room temperature (shown in Fig. 3.) [41–43]. In addition, an alloy from earth abundant elements and non-toxic material MgAsSb gives higher ZT around 1.1–1.4 at 500 K which can become promising material for the conversion of heat to electrical energy [44, 45]. In the medium temperature range (600–900K), PbTe alloys give the highest ZT with value 1.7 for n-type skutterudites at 850 K and 2.2 for p-type at 915 K [46,47]. In case of higher temperature range (>900 K) SiGe, ZrSiSn and alloys of FeNbSb, a member of half-Heusler alloys present a significant higher value of ZT near unity [48–51]. Hicks and Dresselhauss in year 1993, explained that one and two dimensional structures can have high figure of merit than their conventional bulk counterparts [9,15]. The quantum well structure of Bi2Te3 gives the enhanced figure of merit by the factor of thirteen as compared to their bulk counterpart. This huge enhancement depends significantly on anisotropic effective mass tensor of the material. To attain this enhancement, Hicks and Dresselhauss suggested the preparation of layer in a0-c0 plane, and direction of current flow should be along a0 axis exhibiting high mobility [9]. However, in the case of multilayers with thickness of ~10 Å, which are perpendicular to c0 axis in plane a0-b0, an enhancement by the factor of three compared to their bulk counterpart is expected. Further, in case of one-dimensional materials and quantum wires, the figure of merit greatly relies upon width of the wire. The

(2)

Where S, σ , T, are Seebeck coefficient, electrical conductivity and tem­ perature while κe and κl are electronic thermal conductivity and lattice thermal conductivity respectively. The ZT of a material is an achieve­ ment indicator for estimating their capabilities to generate electrical energy when exposed to heat. It demonstrates the fraction of the Carnot efficiency which can be accomplished through different thermoelectric materials. The product of Seebeck coefficient and electrical conductivity together is known as power factor (PF). The PF is a crucial parameter to attain high performance. The large power factor represents the pro­ duction of high current and voltage during power generation. The biggest challenge in enhancing the figure of merit is the highly inter­ dependency of these parameters. It is interesting to note from equation (1), that the absence of thermal conductivity causes figure of merit (ZT) to reach infinity, and the thermoelectric devices to approach Carnot cycle efficiency. The energy carrier electrons and holes contribute to the electrical conductivity (σ) and electronic thermal conductivity (κe ) whereas phonons contribute to lattice thermal conductivity (κl ). The commercially available thermoelectric materials with ZT ~1 operating at a relatively larger temperature lift or difference cannot compete with the traditional vapour compression systems [5]. However, decrease in temperature lift rapidly increases the thermoelectric efficiency. There­ fore, it is expected that for very small temperature lift the efficiency of thermoelectric modulus can surpass the efficiency of traditional vapour compression [6]. Furthermore, it is interesting to know that crossing a certain limit by ZT is difficult despite not having any restriction from the second law of thermodynamics [7]. The aim is to increase power factor which can be achieved through high charge carrier concentration and mobility and at the same time, the thermal conductivity must be decreased. Several strategies are acquired to enhance this figure of merit in order to increase the efficiency of thermoelectric materials like reducing only independent material parameter lattice (phonon) thermal conductivity, moving to low dimensions [8–16], quantum confinement [9–15], complexing crystal structures like Zintl compounds [17], skut­ terudites [18,19], clathrates [20,21], half-Heusler alloys [22,23], het­ erostructure of superlattice thin films [24], introducing dopants [25–30], edge disorders [31], creating defects [32,33] etc. in addition to the proper optimization of phonon drag which will enhance the Seebeck coefficient [34]. Furthermore, a basic aim is to increase the power factor (S2 σ) by optimizing the carrier concentration, and/or to reduce the thermal conductivity (κe ) by introducing the scattering centres. The interconnected thermoelectric parameters depend on the scattering factor r, carrier effective mass m* and carrier mobility μ [5]. The interconnectivity of thermoelectric parameters and their effect on the power factor (S2 σ), Seebeck coefficient S and figure of merit (ZT) is well discussed by Alam et al. [5]. Over the past decades, the ‘Phonon Glass Electron Crystal (PGEC)’ paradigm developed by Slack in 1995 became the main concept for the materials in thermoelectric applications which suggested that a good thermoelectric material should have the thermal properties of glass and electronic properties of crystalline material [4]. This PGEC material can be described as a material that takes cages or tunnels in their crystal structure. It further contains large atoms which are tiny corresponding to the cage or tunnel to “rattle”. These rattling frequencies are low and create damping in phonon which will further result in drastic reduction in lattice thermal conductivity. In PGEC paradigm, thermal conductivity analogues to glass can fundamentally exist together with high mobility charge carriers. This approach has accelerated substantial new research and has excelled enhancement of thermoelectric efficiency for various compounds [4]. It has been pre­ dicted that thermoelectric materials must have efficiency for

Fig. 2. Number of publications per year for thermoelectric materials from 1988 to 2019. Here star sign presents the research in thermoelectric materials in 2019 year (data obtained from the web of knowledge with search option of thermoelectric [36]). 3

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thermoelectric properties of 2D boron nitride nanostructures along with hybrid and heterostructures. Section 5, discusses one dimensional BN structures like BNNR and BNNT and their thermoelectric properties. Section 6 describes the thermal properties of boron nitride quantum dots. Section 7 presents the role of BN structures with different com­ posites along with their application in thermal management. Finally, ending with the conclusion and an outlook towards future exploration of boron nitride based thermoelectric materials presented in Section 8 and 9. 2. Boron nitride allotropes An intense effect in the structure of BN allotropes has been acquired due to the ionic nature of B–N bond. Boron nitride allotropes can form structures with either sp2 or sp3 bonds [77]. The different allotropes of boron nitride from bulk to zero-dimensional are cubic-BN (c-BN), wurtzite-BN (w-BN), hexagonal-BN (h-BN), rhombohedral-BN (r-BN), boron nitride nanotubes (BNNT) with single and multiwall, boron nitride nanoribbon (BNNR) with zigzag and armchair edges, boron nitride nanocages and quantum dots [76]. Fig. 4 shows the structures of boron nitride allotropes. The hexagonal boron nitride structures are extensively used in industry and scientific applications due to their low electrical conductivity and high thermal conductivity [78–80]. None­ theless, this low electrical conductivity and high thermal conductivity hinders the use in thermoelectric materials in bulk or original forms [78–80]. Fig. 5 shows the range of thermal conductivity in BN allotropes and variation from going bulk to low dimensions. The figure shows that the thermal conductivity values are in the range of 0.3–2000 W/mK [81–88]. Thermal conductivity depends on several parameters such as structure, atomic mass, acoustic mode frequency, strength of the bonds, anisotropy in structure etc. Heavy elements carry low thermal conduc­ tivity as the perturbation causes suppression of phonon mode fre­ quencies which results in reduction of group velocity and hence reduces the thermal conductivity. Here, the BN allotropes have significantly high thermal conductivity in case of cubic structure compared to its hexag­ onal counterpart. The reason behind is that the cubic structure of BN is highly symmetric and isotropic than the hexagonal one, which in turn results in higher lattice thermal conductivity of cubic BN than in bulk h-BN. Furthermore, the number of atoms in unit cell of cubic BN is lower than hexagonal structure which may favour low thermal conductivity in hexagonal structure. Moreover, the reduction in phonon-phonon scat­ tering in single layer boron nitride (SLBN) results in the higher thermal conductivity than its bulk analogue [82]. The reflection symmetry perpendicular to the layer vanishes the matrix elements of phase space for three phonon processes resulting in odd number of flexural phonon modes (ZA) [89,90]. This will limit the phonon-phonon scattering and increases the phonon lifetime of ZA modes and will be the dominating parameter for higher lattice thermal conductivity in SLBN. However, interaction between the layers of bulk h-BN lessens the reflection sym­ metry, which broke the symmetry rules and the phonon-phonon scat­ tering increases results in lower thermal conductivity of bulk h-BN [91]. The PF and thermal conductivity are main parameters which influence the efficiency of thermoelectric materials and figure of merit (ZT). The modification of crystal structure by making heterostructure [24], including defects and dopants [25–30,32,33] and moving to low dimension [8–15] reduces the thermal conductivity and enhances the Seebeck coefficient. Fortunately in this regard, BN nanostructures pre­ sent themselves as promising thermoelectric materials. In the next sec­ tions, the thermoelectric properties of boron nitride based materials are focused along with the discussion of certain approaches to improve thermoelectric properties of BN.

Fig. 3. Timeline presenting the maximum figure of merit for traditional ma­ terials. Reprinted with permission from Ref. [43].

thermoelectric ZT enhances substantially with reducing length con­ cerning the width of materials are narrower and in the order of thermal de Broglie wavelength for carriers [15]. It was predicted that the one dimensional form of Bi2Te3 presents figure of merit up to 14 for 5 Å width [15]. The work provoked the thorough investigation of nano­ structured low dimensional thermoelectric materials. Based on PGEC model [4] and exploration of low-dimensional materials, researchers illustrated the excellent development in thermoelectric materials with ZT values surpassing the hurdle of unity easily and even in the range of 2–3 [9,52]. The strategies for enhancing ZT are classified in two di­ visions. First is the reduction of lattice thermal conductivity and sec­ ondly the increase in the term power factor which is nothing but the product of Seebeck coefficient and electrical conductivity (PF ¼ S2σ) [53–55]. There are some excellent reviews focusing on the thermo­ electric materials and on the strategies to design thermoelectric mate­ rials in order to attain high efficiency [55–57]. Boron nitride based materials are the most rising inorganic systems being investigated so far. Boron nitrides (BN) are not found naturally and are produced synthetically, which consist of equal numbers of boron (B) and nitrogen (N) [58,59]. They have same crystal structure related to carbon and exist in various crystalline forms. It is first synthesized by Balmain in 1842 [58,59] with the help of boric acid (H3BO3) and po­ tassium cyanide (KCN). BN based materials are analogous to carbon and their counterparts like cubic boron nitride (c-BN) is related to diamond. It is the second hardest material after diamond [60]. Wurtzite boron nitride (w-BN) is analogous to lonsdaleite. Hexagonal boron nitride (h-BN) is similar to the graphite and is also known as white graphene [61]. Boron nitride structures have excellent physical properties, remarkable thermal and chemical stabilities like h-BN is stable at tem­ peratures up to 1000 � C in air, 1400 � C in vacuum and 2800 � C in an inert atmosphere [62]. Most of the experimental researches revolve around the mechanical [63], electrical [64–67] and optical [68–71] properties of BN materials including interaction, sensing properties and bio-conjugation etc. [72–75]. It is noteworthy that BN materials are nontoxic, chemically inert, have transparency to microwaves, hard and have high Young modulus [76]. These unique properties of BN based materials rise the interest in researchers putting them in the limelight. Here in this review, the thermoelectric properties of BN allotropes in order to improve the efficiency of these materials as thermoelectric materials are focused. This review is systematized as follows. In Section 2, the BN allotropes are discussed. In Section 3, the bulk BN with pos­ sibilities as thermoelectric properties is explored. Section 4 reviews

3. Bulk boron nitride The selection of thermoelectric materials relies upon the figure of merit, which further counts on the Seebeck coefficient and conductivity. 4

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Fig. 4. Structural models of boron nitride (a) Bulk BN with different crystal structures like hexagonal, rhombohedral, cubic and wurtzite, and (b) BN nanostructures with nanosheet, nanoribbon (zigzag and armchair configurations), nanotube and zero-dimensional fullerene.

Fig. 5. Schematic model for thermal conductivity of BN allotropes [ref. 81–88]. Boron nitride based materials like BNNR, c-BN and nanotube have high thermal conductivity which hinders them to be used in their pristine form. The thermal conductivity varies from ~2000 W/m-K to ~0.3 nW/K in which nanoengineering reduces thermal conductivity significantly.

The Seebeck coefficient depends on the electronic structures near Fermi level and it is perceptive to effective mass, carrier concentration and shape of bands [92]. Bulk boron nitride nanostructures are present in three forms: (i) amorphous BN (a-BN) (ii) cubic BN (c-BN) and (iii) wurtzite-BN (w-BN). The a-BN, c-BN and w-BN have large band gap with the values 5.04 eV, 6.4 eV and 4.9 eV respectively [93–96]. These wide band gap insulators have large Seebeck coefficient but very low elec­ trical conductivity resulting in poor power factor. The Seebeck coefficient (S) and carrier concentration (n) relation can

be given by Ref. [97]: S¼

2=3 8π2 k2B * � π � mT 2 3eh 3n

(3)

Where kB is the Boltzmann constant, e is the carrier charge, h is Planck’s constant, m* is the effective mass of the charge carrier and n is the carrier concentration. From the above, the Seebeck coefficient is inversely proportional to the carrier concentration. The electrical conductivity (σ ) 5

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and carrier concentration (n) can be expressed as [94]:

σ ¼ neμ

(4)

Where μ is the charge mobility. From equation (4), electrical conduc­ tivity is directly proportional to the carrier concentration. In wide band gap insulators, free charge carrier concentration is very low leading to the large Seebeck coefficient than semiconductors and metals. Further­ more, due to low carrier mobility in insulators, it shows smaller elec­ trical conductivity which in turn results in poor thermopower. Therefore, if one attempts to increase the figure of merit by enhancing carrier concentration and thus conductivity, one may lose the achieve­ ment by the abatement of Seebeck coefficient [97]. The c-BN is a semiconductor compound of group III-V with wide band gap. Further­ more, c-BN belongs to the group of thermoelectric materials having high thermal conductivity, making them useful in heat sink for semi­ conductor lasers, micro-wave devices etc. The thermal conductivity of c-BN was found experimentally in the range of 2–9 W/cmK [94,95] and theoretically 13 W/cmK [94]. The other consecutive bulk counterparts w-BN and a-BN [98] also have large thermal conductivity leading in the small figure of merit, which makes bulk boron nitride nanostructures unsuitable for thermoelectric applications. The large thermal conduc­ tivity of BN bulk structures are due to the fact that these structures are lightweight materials leading in the high frequency of acoustic modes in BN structures followed by higher group velocity attributed to large slope in acoustic modes [99]. However, these drawbacks may overcome by introducing defects, alloying, developing low dimensional systems and by making heterostructure with other materials. Fig. 6. Thermal conductivity of layered h-BN with 11 layer and 5 layer h-BN. The room temperature thermal conductivity for 11 layer h-BN reaches to basalplane value of its bulk counterpart. Thermal conductivities of its other family members like bulk h-BN, nanotube and single layer h-BN is also presented Reprinted with permission from Ref. [104].

4. Hexagonal boron nitride The hexagonal boron nitride (h-BN) is a white slippery powder, similar to graphite. The bond between boron and nitrogen atoms in h-BN is covalent with the bond length of 1.45 Å. The h-BN is a layered structure and inside each layer, the B and N atoms are strongly in-plane bounded with every layer grasped together through the van der Waals forces. From this layered structure of h-BN, a single layer is commonly indicated as boron nitride nanosheets (BNNS). The BNNS nomenclature is suitable only for small aspect ratio h-BN sheets. The high aspect ratio together with width less than 50 nm is considered as boron nitride nanoribbon (BNNR). The h-BN crystal structure is hexagonal with the space group P63/mmc. The lattice constants and bond angles of h-BN are a ¼ b ¼ 0.2504 nm, c ¼ 0.66 nm and α ¼ β ¼ 90� , γ ¼ 120� respectively. Hexagonal boron nitride (h-BN) and graphene belong to same category of hexagonal layered crystal structure, but electronic bandgap of these two materials differs from each other completely [100]. While graphene is a gapless two dimensional material, h-BN has a bandgap more than 4.0 eV. Another important quality which is of direct relevance to ther­ moelectric figure of merit or thermal transport, the thermal conductivity of single h-BN is quite lower than the graphene [82]. The reason behind this is the reduction in the frequency of acoustic phonon modes resulting into the strong phonon-phonon scattering rates in the h-BN [82, 101–103]. Very recently, it is reported that the thermal conductivity of suspended eleven layered h-BN has a thermal conductivity of 360 W/mK at room temperature close to the room temperature thermal conduc­ tivity value of bulk h-BN [83,104]. The temperature reduction results in the increased thermal conductivity arising due to reduction in Umklapp scattering [104]. At lower temperatures, the thermal conductivity of the 11-layered sample of h-BN becomes lower than the bulk values. Further, the thermal conductivity of a five layered h-BN is found lower than the eleven layered h-BN [104] (shown in Fig. 6.), which contradicts the general behaviour of layered dependent thermal con­ ductivity in two dimensional layered structures. This shows an increase in thermal conductivity as the number of layers decreases due to reduced interlayer phonon scattering rate [82]. Moreover, it is found that, at lower temperature, the thermal conductivity is more evident in thinner

sample with peak values emerging near room temperature. Jo et al. [104] theoretically studied the phonon dispersion and thermal con­ ductivity (κ) of bulk h-BN along with the phonon scattering by means of point defects (vacancies and impurities). It is observed that because of high concentration of isotope impurities in h-BN, other defects like va­ cancies play less significant role even with the 1020 cm 3 vacancy concentration. The change in the κ values acquired from the two systems ranges between 3 and 36% for the 11-layers and 1–7% for 5-layers [104]. Through equilibrium molecular dynamics (EMD) simulations, Mortazavi et al. [105] studied the effect of average grain size on the thermal conductivity of polycrystalline h-BN films at different temper­ atures. For larger grain size, thermal conductivity was obtained using finite element methods using EMD. The thermal conductivity of 300 � 30 W/mK, was obtained for monocrystalline and pristine h-BN. At high temperature, due to rise in phonon-phonon scattering, thermal con­ ductivity of h-BN decreases with temperature [105]. As a result, with the temperature hike, thermal conductivity converges at reduced correla­ tion times due to reduced phonon lifetimes. Further, thermal conduc­ tivity of 95 � 10 W/mK was achieved for h-BN sheets at 900K that is beneath the one third at room temperature [106]. Moreover, it is found that the low frequency phonon density of states (PDOS) contribute significantly in the thermal conductivity of h-BN. Finally, it is concluded that by decreasing the grain size there is a decrease in the thermal conductivity which is attributing to the rise in defects concentration with grain boundaries [105]. Similar kind of study was done by Vargas et al. [106] with graphene and h-BN heterostructures by varying size and distribution. Electronic and transport properties of polycrystalline graphene and h-BN were calculated through quantum transport and molecular dynamics (MD) simulations. By increasing the h-BN concen­ tration in the heterostructures, the electronic band gap broadens up but with a rapid decay on the electron part of the spectrum. The thermal conductivity for sixteen grain sizes were investigated between 1 and 6

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1000 nm by altering the concentration of h-BN represented in Fig. 7 (a). Fig. 7(a) shows that over 100 nm the effect of grain boundaries on thermal conductivity becomes trivial implying that heat carriers with mean free path over 100 nm cause low contribution in κ. Fig. 7(b) in­ dicates the grain density dependency of and thermal conductivity for various sizes of h-BN in which the lowest thermal conductivity appears around 70% for small grain size. The lowest value of κ can be attributed to the fact that the graphene and h-BN hetero-structures (G-hBN) have lower thermal conductance as compared to hBN hBN and graphene-graphene heterostructures [106]. Finally, ZT for 40 nm grain size and 20% h-BN is evaluated and a very low value of �1 � 10 4 (carrier concentration, n ¼ 5 � 1012 cm 2) is found. The highest value ZT reaches ~ 1 � 10 2 even where the Seebeck coefficient is very high [106]. It was concluded that the electronic and thermal properties depend on their structural properties and hence in all considered structures the polycrystalline heterostructure of graphene and h-BN does not match the criteria of good thermoelectric material. Sevincli et al. [107] theoretically investigated the phonon and thermal conductivity of hybrid graphene and h-BN sheet by varying size between 2 and 8 nm and concentrations, 0–100% through Kubo-computational transport scheme. The calculations found that the thermal conductivity changes drastically around 0 and 100% [107]. However, the change is gradual near 50%. The thermal conductivity shows minimum value along with nearly symmetric nature around 50% concentrations. Further, this symmetric nature can be modified with precise investigation of out-of-plane vibrations. An enhancement in the thermal conductivity can be seen by increasing the size of hybrid graphene and h-BN sheet. Moreover, the thermal conductivities rely up on length of hybrid gra­ phene and h-BN sheets [107]. The heterostructure of h-BN and graphene and other two dimen­ sional materials such as h-BN and MoS2 show the significant properties like electron tunnelling, tuning of band gap etc. [108–110]. Chen et al. [111] fabricated a device of graphene/h-BN/graphene heterostructure on Si/SiO2 substrate, schematically presented in Fig. 8 for the thermo­ electric transport. The thermoelectric temperature difference was determined through Raman spectroscopy by length scales of 1–2 nm. The Seebeck coefficient of 97.1 μV/K and 99.3 μV/K for 100 Hz and 200 Hz frequencies respectively was obtained for graphene/h-BN/graphene heterostructure on Si/SiO2 substrate, almost double than the single layer graphene [111,112]. The resulting Seebeck coefficient is negative in these devices, as the band offsets (and accordingly energy barriers) among graphene and BN are much lower for electrons than holes. However, wide band gap of h-BN reduces the

Fig. 8. Schematic presentation of graphene/h-BN/graphene/Al2O3 devices along with measurement setup [Reprinted with permission from Ref. [111]].

electrical conductivity which results into the lower power factor (1.51 � 10 15 W/K2) and figure of merit, ZT (1.05 � 10 6) in this device [111]. The small value of ZT is attributed to the large energy barrier of ~0.5 eV in the graphene/h-BN interface. The studies suggest that the enhance­ ment in ZT can be acquired by optimizing the energy barrier height and thickness of h-BN flakes, however, this low value of ZT will not be useful for thermoelectric devices [111,112]. The theoretical study of D’Souza et al. [113] on graphene/h-BN/graphene with five layers of h-BN con­ firms the above experimental study [111]. Density functional theory (DFT) and Boltzmann transport theory calculations were used to study electric and thermoelectric properties of graphene/h-BN/graphene sandwiched structure through three different positions (corresponding to three, four and five layers sandwiched between graphene sheets). The thermal conductance was evaluated through MD simulations. For every system, thermal conductivity increases with temperature while it con­ verges at 220 K. Furthermore, thermal conductivity is maximum in the temperature between 200 and 250 K. They have also calculated the thermal transport coefficient for graphene/h-BN/graphene with three and four layers of h-BN, but still there is not a significant change in power factor [113]. Such a low value of power factor and ZT is not applicable in thermoelectric devices for the production of electricity. However, Duan et al. [114] have found an enhancement in Seebeck coefficient and thermoelectric power factor when h-BN is used as sub­ strate instead of SiO2. The high power factor of 10.35 W m 1K 1 was achieved in the device at room temperature. It is double the power factor value of 5 W m 1K 1 achieved in YbAl3 [114]. An another similar study of h-BN as substrate for graphene shows that the h-BN is a better sub­ strate than SiO2 for single layer graphene as h-BN dissipates 77% of the thermal conductivity of the single layer suspended graphene [115]. This reveals that the SiO2 substrate is better for thermoelectric properties while for heat dissipation h-BN substrate is better for a single layer graphene. Currently, a new conclusion is drawn, that when the heat source is unlimited or free (like solar heat and waste heat from auto­ mobiles, industries etc.) [116] efficiency regulated by the figure of merit (ZT) is not only the considered parameter for practical applications. High output power resulting from the high power factor (PF) is in fact equitably as valuable in contrary to the efficiency. Two ways are well known to scrutinize the next generation thermoelectric materials: (1) lowering thermal conductivity (κ), and (2) enhanceing power factor (PF). However, lowering thermal conductivity results in the negative effect on thermo-mechanical stability, though altering power factor (PF) will not affect the bonding structure and influence the

Fig. 7. Thermal conductivity of (a) polycrystalline graphene (p – G) and polycrystalline h-BN (p-hBN) (b) thermal conductivity as a function of h-BN concentration with different grain size using finite element method [Reprinted with permission from Ref. [106]]. 7

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thermo-mechanical stability for both efficiency and output power. Liu et al. [117] proposed the engineering thermoelectric parameters, (ZT)eng and (PF)eng to represent efficiency and output power, given by: ðPFÞ eng ðZTÞ eng ¼ R Th ðTh KðTÞdT Tc �R ðPFÞ eng ¼

Th Tc

SðTÞdTÞ 2

Tc

ρðTÞdT

R Th

Tc Þ

[131–133]. The state-of-the-art density functional theory calculations presented that the Seebeck coefficient increases up to 6.3 times in ZBNNR/BNNR hybrid structure [130]. Similarly, the electronic and thermal properties of GNR with edge terminated BNNR are investigated by Nakamura et al. [134]. The model of hybrid structure of graphene boron nitride nanoribbon (GBNNRs) is made of graphene nanoribbon sandwiched between boron nitride nanoribbons with hydrogen atoms passivated edges. Fig. 9 shows Seebeck coefficient with respect to bandgap at various temperatures. It was found that the HOVB and LUCB become flat similar to pudding mold band (Fig. 9 (d)) [135]. The in­ ternal electric field generated between BNNRs and GNRs expands the bandgap. The presence of pudding mold band along with finite bandgap results in the increment of Seebeck coefficient with the maximum value of 947 μV/K for (2,4) ZGBNNRs. As the Seebeck coefficient strongly depends on the bandgap of a material, thus, for systems with narrow bandgap, the counter carriers of HOVB and LUCB nullify each other leading to the small effect on Seebeck coefficient. However, even for systems with wide bandgap the counter carrier nullification takes place if the temperature is high enough. Similarly, using nonequilibrium Green’s function (NEGF), Jiang et al. [126] investigated thermal conductance of graphene and h-BN superlattice as a function of supercell size (ds) (Fig. 10). A minimum thermal conductance is found with supercell size ds/L � 5% which is underneath the phonon mean free path than h-BN or graphene. The decrement in thermal conductance can be described through confined modes presented in graphene and h-BN superlattice. Thermal conductivity in hybrid boron nitride and graphene sheets have also been studied theoretically using real-space Kubo-computa­ tional transport scheme with different sizes and concentrations [107]. Fig. 11 presents the schematic of the structure of 2D graphene-BN het­ erostructures. Here, BN clusters with 2-nm diameters are embedded

(5)

(6)

ðZTÞ eng and ðPFÞeng are the engineering figure of merit and engineering

power factor [118] which gives a cumulative results over a whole temperature range from Tc to Th (cold and hot side temperature). ðZTÞ eng and ðPFÞeng are much better to present efficiency and output power in comparison with traditional ZT and PF due to the fact that ZT and PF only give local temperature performance while ðZTÞeng and ðPFÞeng give

global temperature range from Tc to Th. The development in these techniques leads us to explore experi­ mentally the electronic properties of hybrid structures, superlattices and composites with BN. Recently, the electronic properties of h-BN/gra­ phene interface have been investigated both experimentally [119,120] and theoretically [121–125]. Theoretically, it was predicted that in graphene/h-BN superlattice and hybrid structures, the phonon thermal conductivity is substantially reduced due to the lateral strain effect on transmission of phonons at the interface [107,126–128]. For the reason of these reduced phonon transmission, Yang et al. theoretically pre­ dicted the enhancement of figure of merit in graphene/h-BN hybrid structure [129]. Moreover, a giant Seebeck coefficient has been observed in hybrid superlattice of ZGNR and ZBNNRs [130] due to the creation of finite bandgap and existence of flat band at the band edge

Fig. 9. Seebeck coefficient as a function of energy gap with temperature (a) 100 K (b) 200 K and (c) 300 K (d) Schematic of band range that participates in the Seebeck coefficient [Reprinted with permission from Ref. [134]]. 8

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Fig. 10. The geometry of graphene and h-BN superlattice with supercell size ds ¼ 2 unit cells and thickness L ¼ 10 considered in work done by Jiang et al. [126].

inside the graphene. Around 65% decrement of thermal conductivity is found at room-temperature with diameter 2 nm and concentration 50% [107]. Diverse thermal conductivities are also investigated for various hybrid h-BN/graphene structures like stripe superlattices and BN (gra­ phene) dots in graphene (BN) (Fig. 12). In case of stripe superlattices, it is found that the zigzag configuration shows higher thermal conduc­ tivity in parallel direction compared to armchair configuration. How­ ever, thermal conductivity in perpendicular direction is much less sensitive to the configuration and is restricted by the thermal conduc­ tivity of h-BN only. In addition, thermal transport properties are strongly influenced in case of dot structures than superlattices with both zigzag and armchair configurations [127]. The addition of h-BN as fillers in polymer-derived SiOC ceramics presents the enhancement in electrical conductivity and Seebeck coefficient [136]. Further, the SiOC ceramics consisting 1 wt % of h-BN presents highest Seebeck coefficient of 33 μV/K as compared to other polymer derived ceramics [136].

frequency of phonon branches are different leading to the different phonon transmission coefficients. At frequencies between 0 and 700 cm 1, the transmission coefficient is higher than Z-GNR. However, it is lesser in frequency range of 700–1600 cm 1. It was observed that with the increase in width the amount of phonon branches also increases while the bandwidth becomes narrower. It is also noteworthy that in the region between 0 and 700 cm 1, with increasing width, threshold fre­ quency decreases promptly. The study of Ouyang et al. [87] shows that phonon contributes in thermal transport in wider Z-BNNRs. The thermal conductance changes gradually with increasing temperature in the narrow BNNRs with less than 4 Å as the count of phonon modes is confined. There is a large improvement in thermal transport in wider BNNRs due to the appearance of several phonon modes in spectrum. After studying the nature of thermal conductance, they acquired an appropriate formula through fittings which shows T1.5 playing signifi­ cant role in thermal conductance of 2D hexagonal lattice structure rather than T and T2 [87]. Through NEGF method, the thermal conductance below 300K is higher as compared to GNRs, while at higher temperature it is vice-versa. Finally, through the studies the linear dependence of thermal conductance and width was found in both ABNNR and ZBNNR [87]. Also, one can find that the thermal conduc­ tance of ZBNNR is significantly higher (20%) than the armchair BNNR (ABNNR) indicating the anisotropic behaviour of thermal transport in nanoribbons [87]. The length and defect concentration dependent thermal conductivity of hexagonal BNNR (h-BNNR) have also been investigated using equilibrium molecular dynamics (MD) simulations [143]. The point vacancy, bi-vacancy and edge vacancy were considered in h-BNNR. The thermal conductivity of h-BNNR (10 � 3 nm) at 300 K and 400 K is 649 W/m-K and 368 W/m-K respectively. The low peaks in PDOS confirm its low thermal conductivity than GNR [143]. Phonon group velocity provides understanding of thermal conductivity. The calculated phonon group velocities are ~1.06, ~10.9 and ~19 km/s for acoustic out-of-plane (ZA), transverse acoustic (TA) and longitudinal acoustic (LA) modes respectively. These low phonon group velocities are attributed to the low Debye temperature of 410 K which is lower than

5. Boron nitride nanoribbons and nanotube Since graphene nanoribbons (GNRs) are weak in thermoelectric properties due to high thermal conductivity [137], boron nitride nanoribbons (BNNRs) have received much attention due to the simi­ larity in structure and useful physical properties such as high chemical, thermal stability, electronic, phonon, adsorption etc. [74,138–140]. Further, BNNRs exhibit semiconducting nature with wide bandgap which varies with the size and chirality [141,142]. Thermal conduc­ tivity depends on the phonon spectrum which can be calculated using the force constants. The phonon spectrum of honeycomb structure of BNNRs is similar to the phonon spectrum of GNRs in terms of number of phonon branches and trend [87]. This indicates a comparable thermal conductance between them. However, there are some dissimilarities among BNNRs and GNRs due to the variation in force constants. The frequency of Z-BNNR (1400 cm 1) is beneath the frequency of Z-GNR (1600 cm 1) [87]. Additionally, their bandwidth and threshold

Fig. 11. A pictorial representation of 2D graphene-BN heterostructures with BN 2 nm diagram enclosed in graphene [Reprinted with permission from Ref. [107]]. 9

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Fig. 12. Hybrid structure of h-BN and graphene nanostructure considered in work done by Kinaci et al. [127] presenting stripe superlattices and dots placed in sheet.

graphene. The low thermal conductivity of BNNRs is caused by high phonon scattering rates which are the result of low phonon group ve­ locity and Debye temperature. Additionally, the difference between thermal conductivities in BNNR and GNR is due to dissimilar masses of boron and nitrogen atoms resulting in high amplitude heat current and phonon-phonon scattering. The thermal conductivity of h-BNNR is length dependent [143]. The thermal conductivity of h-BNNR (10 � 3nm) with the vacancy percentage of 0.5% is ~80 W/m-K, ~65 W/m- K and ~85 W/m-K in case of point, edge and bi vacancies respectively. Further, the vacancy percentage was increased and resulted in the reduction in thermal conductivity (lowest at 1%) in edge vacancy. In the defect concentration around 0.2–0.3%, the

thermal conductivity is reduced by 80–85%, while about 90% reduced thermal conductivity was found with 0.5% defect percentage. A similar study was reported by Felix et al. [144] using non-equilibrium MD sim­ ulations in order to find the nature of thermal conductivity in graphene-hBN superlattice ribbons. The domain size and ribbon length dependent thermal conductivity has also been investigated. The zigzag structure of graphene-hBN interface was taken into consideration due to the fact that they are preferred in growth. Ballistic-diffusive transition regime (T) was observed in the vicinity which results in the similar sys­ tem length and phonon mean free path (MFP), further, leading to the reduction in dependency of thermal conductivity with length (Fig. 13 (a)). From the investigation, about 98% reduction in the thermal

Fig. 13. (a) Thermal conductivity of graphene-h-BN superlattice ribbon as a function of length (b) Scheme of both coherent (wave interference) and incoherent (diffuse scattering) phonon transport [Reprinted with permission from Ref. [144]]. 10

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conductivity is found as compared to graphene, however, it is decreased by 78% in h-BN. Due to increment in super lattice period (ℓp), there is a reduction in κ∞ until it acquires a minimum value of 89 W/mK at ℓp ¼ 3.43 nm (Fig. 13), but finally it increases. This blend of wave interference affects and diffuse interface scattering results in lower thermal conduc­ tivity. The appearance of zone folding and flat bands in phonon disper­ sion curves due to increased lattice period results into the lower phonon group velocities and reduced thermal conductivity. To understand the relationship between thermal conductivity and superlattice period, the phonon dispersion curves were calculated using general utility lattice program (GULP). Through analysis of phonon dispersion curves and vibrational density of states (VDOS), it is observed that the minimum thermal conductivity (89 W/mK) for super lattice period length of 3.43 nm is due to decrement in number of flexural phonons. This reduction of thermal conductivity through heterostructures and superlattices will open up the gates for boron nitride based thermoelectric devices. Xie et al. [145] calculated thermoelectric properties of BNNRs using NEGF and found that the thermal conductance of ZBNNR is larger than ABNNR demonstrating the anisotropy in thermal conductance. Power factor was evaluated as a function of chemical potential in zigzag chains NZ (8) BNNR, and dimer lines NA (10) over the ribbon width of ABNNR at 300K. The maximum power factor is achieved when the chemical potential exists near first conductance band (FCB) that further dominates ZT. A comparison with GNR clearly suggests that the BNNR presents better thermoelectric properties. The maximum ZT calculated for 8-ABNNR and 8-ZBNNR is 0.2 and 0.08 respectively, whereas the ZT for equivalent GNR is 0.03 and 0.04 respectively. The site dependent study clearly shows that the lattice defect sites affect ZT [145]. A DFT study of Zberecki et al. [146] on BNNRs with hydrogen passivation at symmetrical and asymmetrical edges shows promising thermoelectric properties. The selected systems were nanoribbons with di-hydrogenated boron edges (2HB–1HN), nanoribbons with mono-hydrogenated boron edge and di-hydrogenated nitrogen edge (1HB–2HN) and lastly, nanoribbons passivated with two hydrogen atoms at both edges (2HB–2HN). The nanoribbons with bare edges (0HB–0HN) were also taken for investigation. It is seen that BNNR shows spin dependent thermoelectric properties. The inclusion of hydrogen atoms at the edge of nanoribbons greatly affects their electronic prop­ erties along with transmission function. Dimensionless thermoelectric figure of merit for conventional (ZTc) and spin (ZTs) configuration as a function of chemical potential (μ) is calculated and ZTs is found ~50 at low temperature of 90K due to the sudden decrease in the thermal transmission and increase in Seebeck coefficient, while for the same temperature ZTc is ~30 and it decreases with increasing the width of the tube [146]. These results show that BNNRs with B- and N-edges which are di-hydrogenated and mono hydrogenated respectively are promi­ nent materials for the thermoelectric devices at lower and room tem­ perature. In addition, the researchers have tried to make the compositions of GNRs and BNNRs in a search of better thermoelectric properties. Yang et al. [147] have theoretically studied the thermo­ electric properties of hybrid graphene/boron nitride nanoribbons (BCNNR) through NEGF. The addition of h-BN in GNR periodically improves the ZT. It was found that the ZT of BCNNR increases 10–20 times for the width 3pþ2 (p is positive number), while it increases 1.5–2 times for other widths due to the enhancement in Seebeck coefficient and reduction of thermal conductance. The reduced ratio of thermal conductance is ascribed to the destructive channels that hinder the carrier transmission. The calculations present the dependency of peri­ odic number N, to the figure of merit, which increases evenly up to certain level and then becomes constant which is an interesting aspect that should be considered [147]. Another graphene-hBN nanoribbon hybrid system was considered by Visan [148] who investigated the role of transition metals Cr, Mn, Fe, Co and Ni considering them as impu­ rities. These transition metals (Cr, Mn, Fe, Co and Ni) are doped sub­ stitutionally on boron and nitrogen atoms. Using ballistic transport model, followed by spin-dependent transmission functions,

thermopower and ZT were evaluated for considered transition metals doped hybrid G-hBN systems. It was found that Co doped at boron site (Co–B) gives highest spin polarization whereas doping on nitrogen site depicts low spin polari­ zation. Linear response functions (L0 and L1) were calculated in order to study the thermoelectric parameters like temperature dependent See­ beck coefficient. The Co–N gives the maximum Seebeck coefficient. Apart from that, at lower temperatures (up to 150 K), doping on boron site comprises of higher Seebeck coefficient as compared to nitrogen site. The presence of transition metal (TM) impurities significantly in­ creases the thermopower and figure of merit as compared to their pristine counterpart. The thermopower of hybrid graphene-hBN is ~10 μV/K, which increases on inclusion of transition metal impurities i.e. 40 μV/K, 50 μV/K and 85 μV/K for Mn–B, Cr–N and Co–N respectively. The calculated figure of merit shows large value of about 0.32 for cobalt substitution on nitrogen site (N-site) presented in Fig. 14. It was found that with temperature rise, maximum values for Seebeck and figure of merit were attained on N-site substitution. However, at lower temper­ atures, the thermopower and ZT comprises of high values as compared to the pristine form in B-site substitution. Recently, Algharagholy et al. [149] tuned the thermoelectric properties of heterostructures of boron nitride and graphene nanoribbons with doping of electron donor tetra­ thiafulvalene (TTF) and electron acceptor tetracyanoethylene (TCNE) molecules. In case of heterostructure of graphene and boron nitride, boron nitride behaves as a tunnel barrier resulting in the feebly couple states in graphene to create mini-bands. The delta-function-like char­ acteristic is obtained in transmission function due to interplay between localized states of TCNE or TTF and extended states on graphene-boron nitride heterostructure surface. It was observed that through nano­ structuring the system, roughness of surface and boundary scattering, thermal conductance is reduced. The phonon thermal conductance of 0.2 nWK 1 results in high ZT of 0.9 at room temperature in TTF doping [149]. This section concludes that there is a need of further study on the functionalization of boron nitride nanoribbons. More recently Mohammed [150] studied the effect of one hexagonal carbon ring naming it “hexagonal carbon island” in both zigzag and armchair single walled boron nitride nanotube (SWBNNT) using DFT calculations. The band gap of both armchair and zigzag SWBNNT re­ duces with one hexagonal carbon ring. The addition of carbon atoms alters the electronic properties of SWBNNT resulting in the reduction of band gap. This can be attributed to the fact that carbon atoms contribute to occupied energy levels that further aids the process of transmission of electrons from valence band to conduction band. In this study [150], six different structures were considered i.e. for zigzag-SWBNNT, n,0; n ¼ 4, 5,6 and for armchair SWBNNT, n, m; n ¼ m ¼ 4,5,6 respectively. Their electronic and thermoelectric properties are changed after the incor­ poration of C island as the insulating nature of armchair SWBNNT changes to semiconductor with band gap ranging between 2.7 and 3.1 eV (for n, m; 4,5,6). However, for zigzag SWBNNT band gap ranges from 0.119 to 1.83 eV (for n, m; 4, 5, 6). This shows that the nature of armchair SWBNNT is modified from insulator to semiconductor while the nature of zigzag BNNT continued to be semiconducting. The substitution of carbon atom at both B and N sites generate the donor and acceptor levels. The former leads to the charge transfer of 0.63e from carbon atoms to the tube and the latter leads to 2.7e charge transfer from tube to carbon atoms respectively. Further, the thermoelectric parameters are calculated in the range of 300–2000 K (Fig. 15). The Seebeck coefficient of zigzag SWBNNT is positive making them p-type material while for armchair SWBNNT, Seebeck coefficient is negative in the temperature range of 300–900 K and 300–1200 K for (5,5) and (6,6) respectively. After the incorporation of one hexagonal carbon island, Seebeck coefficient of zigzag SWBNNT (4, 0) decreases with increasing temperature. However, for (5, 0) and (6, 0) Seebeck coefficient becomes constant with temperature mostly after 1200 K. This depicts the independency of zigzag SWBNNT towards temperature, particularly for (6, 0) zigzag SWBNNT. In case of armchair 11

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Fig. 14. (a, b) Thermopower and (c, d) figure of merit as a function of temperature for h-BN nanoribbon incorporated in TM impurities [Reprinted with permission from Ref. [148]].

SWBNNT, Seebeck coefficient of (4, 4) armchair SWBNNT increases with temperature up to 800 K and then abruptly decreases with temperature with inclusion of one hexagonal carbon island. Moreover, in (5, 5) and (6, 6), Seebeck coefficient rises in range of 300–600 K, and reduces after 600 K. The electronic thermal conductance (κe), thermal conductivity (κl) and figure of merit (ZT) were also calculated and found that inclu­ sion of one hexagonal carbon island positively affects its thermoelectric properties [150]. The ZT shows the constant value at 300–800 K for (4, 0) and (6, 0) zigzag SWBNNT with value around zero. The study con­ cludes the increase in ZT with temperature for all considered systems. The ZT reaches up to ~0.8 with one hexagonal carbon island in (4, 0) zigzag SWBNNT.

6. Boron nitride quantum dots Owing to development in the field of nanotechnology, exploring and regulating electrical transport using zero-dimensional quantum dots (QD) have been one of the major breakthrough in nanoscale systems [151]. Quantum dots are often known as “artificial atom” due to the confinement of electrons in three-dimensional (3D) space leading to the discreteness in energy levels of electrons [152]. They are considered as a potential candidate for examining the phase coherence of transportation of electrons in nanoscale confluence. Till date, due to the restricted ef­ ficiency of QDs, they have less utilization in thermoelectric devices. However, after the experimental studies which show the ability of 12

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Fig. 15. (a, b) Thermopower and (c, d) figure of merit, as a function of temperature for h-BN nanoribbon incorporated in TM impurities [Reprinted with permission from Ref. [150]].

Fig. 16. (i) BN-quantum dots (ii) The thermoelectric parameters for 4-BNNR (soild line), 4/8-BNND (dashed line) and 4/12-BNND (dotted line): (a) Electron transmission functions Te, (b) Electrical conductance Ge, (c) Seebeck coefficient S and (d) Thermoelectric figure of merit ZT vs chemical potential l at temperature T ¼ 300 K [Reprinted with permission from Ref. [88]]. 13

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calculating Seebeck coefficient at atomic and molecular junctions [153, 154], there is a rapid advancement in the theoretical investigations of QDs for thermoelectricity [155,156]. With the aim to study the enhancement in thermoelectric properties in boron nitride quantum dots, Pan et al. [88] studied their thermoelectric properties and compared it with graphene quantum dots (GNRD). The introduction of zero-dimensional boron nitride quantum dots (BNND) with sizes equivalent to or smaller than the mean free path would lead into quantum confinement effects to embellish the thermoelectric perfor­ mance. Pan et al. [88] theoretically studied the thermoelectric proper­ ties of boron nitride quantum dots using non-equilibrium Green’s function and the Landauer transport theory. The enlarged Seebeck co­ efficient due to numerical fluctuation of electron transmission and the enormously decreased thermal conductance due to strong boundary scatterings on phonons is found. The size of the boron nitride quantum dot was defined by the width of scattering region. For example if left (Nl) and right (Nr) width of scattering region of the whole system is four and longitudinal width of the central scattering region (Nc) is 8, then the BNND is defined as 4/8-BNND. Fig. 16 shows the schematic model for 4/8-boron nitride quantum dots (4/8-BNND). Pan et al. [88] considered two quantum dots of sizes 4/8-BNND and 4/12-BNND and found that in lower region of frequency (<150 cm 1), 4/12-BNND has more com­ pressed phonon spectrum than 4/12-BNND [88]. In higher frequency region, phonon spectrum was almost identical for both 4/8-BNND and 4/12-BNND attributed to the no effect of structural parameters. The thermal conductance of 0.3 nW/K and 0.5 nW/K for 4/12-BNND and 4/8-BNND is found at room temperature 300K, which is quite lower than the thermal conductance of 4-BNNR [88]. Maximum value of ZT obtained in 4-BNNR is 0.16 near the conduction band edge while in the case of BNNDs maximum ZT values are 0.78 and 0.63 for 4/12-BNND and 4/8-BNND respectively. This result reveals that increasing phonon scattering region lowers thermal conductance and furthermore en­ hances the figure of merit. On comparing with GNRD the ZT of BNNDs is also higher in comparison with the same size and parameters of gra­ phene quantum dots [88] mainly in high and low temperature region. At low temperature of 100 K, the ZT of 4/8 size GNRD and 4/12 size GNRD is 0.1 and 0.29 respectively, which is less than both 4/8 and 4/14 – BNND. Also at high temperature of 800 K, both GNRD have 0.29 and 0.35 ZT which are still lower than both BNND. The parameters affecting ZT are well known i.e. thermal conductivity and power factor. The power factor of graphene quantum dot (4/8 GNRD) is low as compared to boron nitride quantum dot (4/8 BNND) in the temperature range 100–500 K and becomes a little high at higher temperature. Nonetheless, between 4/12 GNRD and 4/12 BNND, the power factor of 4/12 GNRD seems to be always less than 4/12 BNND in all studied temperature range. The phonon thermal conductance of BNND was also compared with GNRD. The κph of graphene quantum dot is higher than that of boron nitride quantum dot, similar to their two dimensional counter­ parts, mainly in lower and higher temperatures. For instance, at 100 K temperature the thermal conductance κph, of 4/8 GNRD (4/12 GNRD) and 4/8 BNND (4/12 BNND) is 0.26 nW/k (0.24 nW/k) and 0.09 nW/k (0.06 nW/k) respectively. However, for high temperature of 800 K, the thermal conductance κph, of 4/8 GNRD (4/12 GNRD) and 4/8 BNND (4/12 BNND) is 1.40 nW/k (1.24 nW/k) and 0.88 nW/k (0.53 nW/k) respectively. This low thermal conductance and higher power factor make them a good candidate for thermoelectric devices.

consisting of 1L, 2L and 9L shows the first-order temperature coefficients of –(3.41 � 0.12) � 10 2, –(3.15 � 0.14) � 10 2 and –(3.78 � 0.16) � 10 2 cm 1K 1 respectively. The thermal conductivity of few-layer h-BN was found to be in the range of 227–280 W/mK at room temperature, greater than silicon oxides. It surpasses silicon oxides to be used in dielectric materials with significant heat conduction. Similarly, composites of copper encapsulated within h-BN (Cu@hBN) and h-BN/alumina were developed [158,159]. Cu@h-BN has shown great thermal conductivity with the value of 253.7 Wm 1K 1 suggesting their utilization for electrical packaging and thermal management [158]. The thermal conductivity (κ) was calculated through the following equation: 8:0 κ ¼ Cp ​ � ​ α ​ � ​ ρ

(7)

Where Cp is the specific heat capacity in Jkg 1K 1, α represents thermal diffusivity in mm2s 1 and ρ is the density in kgm 3. It was found that the thermal conductivity of Cu@h-BN alters with the increased tempera­ ture. At 200 � C and 300 � C, the calculated thermal conductivities are 1.57 and 6.49 W/mK respectively. The schematic of Cu@h-BN is pre­ sented in Fig. 17. Being thermally stable in air, h-BN is of significant attraction for thermal management. The in-plane and through-plane thermal conductivities were found to be 157 W/mK and 14.4 W/mK respectively at 25 � C. However, with increasing temperature, thermal conductivity decreases with the values of 11.4, 7 and 4.7 W/mK for temperature 100, 500 and 1000 � C respectively in through-plane. Moreover, in-plane thermal conductivity values are 122, 58.6 and 21.9 W/mK respectively for 100, 500 and 1000 � C. The change clearly determines the flexibility of h-BN for its use in thermal management to lessen overheating in high power devices like generators, computer servers, motors etc [116]. Recently Ribeiro et al. [160] studied the hybrid composite of MoS2/h-BN with high mechanical and thermal performances shown in Fig. 18. The thermal conductivity increases up to 752% compared to its pristine counterpart for the utilization in designing thermoplastics, elastomeric and thermoset systems. Flash laser study was used to investigate thermal conductivities at room temperature with laser voltage power 1520 V and 100% transmission filter. The study observed the enhancement in thermal conductivity with increasing nanofiller concentration up to 0.5 wt % as presented in Fig. 18. For the electrical insulation or grounding applications, hybrid epoxy composites with graphene and BN fillers were explored experi­ mentally [161]. It is observed that electrically insulated BN fillers significantly affect the electrical and thermal conductivities of the composites. The thermal conductivity of ~6.5 W/mK was attained with equal proportions of graphene and h-BN fillers which is higher than those feasible in contemporary commercial [161]. In order to design materials based on composites for heat transfer, MD simulations were presented for h-BN-organic molecules composites [162]. The study shows thermal properties of single layer h-BN as filler with four organic molecules such as hexane (C6H12), hexanamine (C6H13NH2), hexanol (C6H13OH), and hexanoic acid (C5H11COOH). The high thermal conductance is obtained for hexane ¼ 90.47 � 14.49 MW/m2 K, hexanamine ¼ 113.38 � 17.72 MW/m2K, hexanol ¼ 136.16 � 25.12 MW/m2K, and hexanoic acid ¼ 155.17 � 24.89 MW/m2K due to enhanced density of interface in polar matrix [162]. In developing electronic devices, high thermally conductive polymer composites along with high thermally conductive fillers have gained much attention. Boron nitride nanosheets being highly thermal conductive were used as fillers with silver nanoparticle deposition to increase the thermal con­ ductivity of polymer [163]. The κl of composite increases from 1.63 W/mK to 3.06 W/mK with BNNS loading of 25.1 vol% as shown in Fig. 19 (a). Similarly, composite papers with 50 wt % of 2D BN shows thermal conductivity of 145.7 W/mK comparable to aluminium alloys [164]. Due to high thermal conductivity and aspect ratio of h-BN nanosheet, 113% of thermal enhancement factor is found for exfoliated h-BN nanosheet [165]. However, because of high thermal boundary

7. Boron nitride composites The h-BN and functionalized h-BN are well studied for their appli­ cation in thermal management to solve heat dissipation problems. Zhou et al. [157] experimentally studied the thermal conductivity of mono­ layer (1L), bilayer (2L) and nine-layers (9L) hexagonal boron nitride. The experimental micro-Raman spectroscopy method was used to study the thermal conduction. It is a non-destructive and unconventional way for the analysis of thermal conductivity of h-BN sheets. The h-BN 14

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Fig. 17. Schematic representation of synthesis process of Cu@h-BN composite [Reprinted with permission from Ref. [115]].

solving the energy crisis. To fulfil the utilization of thermoelectric conversion approach, complications concerning the design proper ma­ terial and assembly fabrication of thermoelectric devices have to be addressed. With the exponentially increasing research on thermoelectric materials in past decades, the thermal transport properties in boron nitride and its allotropes with graphene composition is reviewed. Pre­ sent review reflects that thermal conductivity of bulk BN is very high which results into smaller value of ZT. The bulk BN which consists of amorphous, cubic and wurtzite structures are wide bandgap insulators resulting in large Seebeck coefficient and low electrical conductivity leading to unsatisfactory power factor. These drawbacks of thermo­ electric parameters were conquered including defects, making alloys, moving from bulk to low dimensional systems and development of heterostructure of material. Further, the thermal conductivity of h-BN layered structure decreases as the number of layers increases. By reducing grain size, the thermal conductivity of h-BN sheets also de­ creases due to increase in defects concentration with grain boundaries. Overall it is found that the thermoelectric efficiency can be enhanced by appropriate engineering of BN nanostructures with graphene and with other two dimensional materials like MoS2, SiO2 etc. Besides, h-BN is a famous quasi-ideal insulating material to be used in heterostructure with different 2D materials as it shows identical crystal configuration and nearly same lattice parameter. Taking benefit to the matter of fact that heterostructures in nowadays can be synthesized, it will be easy to design different heterostructures to attain high thermoelectric perfor­ mance. In some cases for example for heat dissipation h-BN can be used as better substrate for graphene, while in thermoelectric conversion it cannot be applicable as substrate for graphene. For nanoribbons one can tune the electronic bandgap as well as thermal conductance of BNNRs with chirality and width of the ribbons which results into the flexibility of thermal transport properties. Further, enhancement in thermoelectric performance carried by composition with GNRs results into reduction of thermal conductivity and improvement in ZT. The creation of defects reduces thermal conductivity up to 80–85%. The passivation of BNNRs with hydrogen presents promising thermoelectric properties. The sub­ stitutional inclusion of transition metals considered as impurities en­ hances thermopower and figure of merit of hybrid graphene-hBN nanoribbon in comparison with their pristine form. Boron nitride nanostructures with different electron donor and acceptor molecules present significant thermoelectric properties and can be explored widely. Addition of carbon atoms in boron nitride nanotube diminishes its wide band gap which further improves their thermoelectric

Fig. 18. Thermal conductivity of hybrid MoS2/h-BN along with their pristine counterparts [Reprinted with permission from Ref. [160]].

resistance, h-BN nanosheet becomes less effective for high filler loading. A noteworthy increment of κl (220%) is found in epoxy resin with sin­ gle/few layer BN making them a potential candidate for the advance­ ment of novel underfill in 3D packaging [166]. Therefore, boron nitride is emerging as an omnipotent material due to its high thermal conduc­ tivity, structural stability, good mechanical and anti-oxidant properties making them promising functional filler for polymers for thermal management in electronic devices. 8. Conclusions In the scenario of recent days, difficulties on large-scale are affecting our planet earth and inhabitants like energy resources limitation, global warming, air pollution etc. Almost 70% of valuable energy entering in the atmosphere is loss through hazardous and non-essential gases resulting in the waste of fuel in production, industries and transportation sectors. Therefore, there is a requirement of clean, green, sustainable and efficient energy resources. Adoption of energy converters and re­ covery of advantageous energy from waste heat supports in somewhat 15

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Fig. 19. (a) κL of the epoxy composite with respect to BNNSs loading. (b) Thermal conductivity enhancement (TCE) of the composite with BNNSs loading in comparison with pristine epoxy. (c) Calculated TCE of the composite per 1 vol% filler loading. (d) Experimentally evaluated dependence of κl of composites on temperature with the BNNSs 17.7 vol% loading [Reprinted with permission from Ref.[163]].

properties (ZT 0.8). To improve thermoelectric performance, zero dimensional boron nitride nanoribbon dots shows that the phonon thermal conductance and power factors are higher than the graphene nanoribbon dots. In present review, it is observed that most of the theoretical works were based on NEGF and DFT method. So there is a need of experimental evidences for thermoelectric properties. Also thermoelectric performance can be enhanced by application of doping of chalcogenides in boron nitride nanomaterials. Several research papers are published, mostly theoretical regarding the thermoelectric proper­ ties derived from NEGF of these novel BN allotropes. Regardless of huge progress in the past decades, there lasts ample room for advancement in the areas of functionalization, doping, adsorption etc. in boron allo­ tropes. The concerns addressed in present review of boron nitride will be advantageous for better construction of thermoelectric materials with high efficiency conversion. However, detail experiments are yet to be done for their utilization in thermoelectric devices.

reviewed. Boron nitride structures present unique properties including electrically insulating, high thermal stability, high mechanical strength especially high thermal conductivity and are analogous to the carbon counterparts. However, for its application in thermoelectric devices, the high thermal conductivity is major limitation. Apparently, the bulk boron nitride allotropes are not applicable for either due to their low Seebeck coefficient or too high thermal conductivity to generate sub­ stantial amount of thermoelectric power. Accordingly, various chal­ lenges have to be employed to make its utilization for physical applications. The blend of hexagonal boron nitride and other two dimensional materials with vibrational frequency range lower than hBN in a heterostructure will result in strong decrement of phonon conductance which in turn lead to attain high efficiency in boron nitride heterostructures. Moreover, low dimensional boron nitride show sig­ nificant reduction in thermal conductivity. By means of functionaliza­ tion resulting in the chemical modification, several strategies have found major achievement in enhancing the thermoelectric properties. Nevertheless, from the studies, it is found that the power factor and figure of merit of boron nitride family are still far from the ideal ther­ moelectric materials. The major challenge to enhance the thermal pa­ rameters is to reduce its too high thermal conductivity and low power factor. Therefore, thorough research attempts with inclusion of density functional theory based first principles calculations, molecular dy­ namics simulations and materials modelling, experiments are yet needed for developing novel high-performance boron nitride based thermoelectric materials. There is an acceptable logic to await

9. Future scope The thermoelectricity being a “Green Technology” to generate electricity without any harmful effect became most important in solving today’s energy challenges. Evolution of thermoelectric materials with high efficiency has become the urgency to cope bad environmental sit­ uations like global warming, change in climate and also for preserving our natural resources of energy essentially minerals and oils. Current advances in thermoelectric materials based on boron nitride family are 16

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substantial advancement in the thermoelectric efficiency with figure of merit higher than one and higher power factor in the coming two-three decades as more researchers are participating in this inspiring world of thermoelectric materials.

[21] [22] [23]

Declaration of competing interest

[24]

The authors declare no conflict of interest. Acknowledgements

[25]

Authors acknowledge the financial assistance from the Department of Science & Technology under the Indo – Poland program of coopera­ tion on science and technology through project DST/INT/POL/P-33/ 2016. We are thankful to Elsevier, ACS, RSC, APS, Springer publishers for providing copyrights for related Figures.

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