Nano Materials Science 4 (2022) 10–17 Contents lists available at ScienceDirect Nano Materials Science journal homepage: www.keaipublishing.com/cn/journals/nano-materials-science/ Emerging properties of non-crystalline phases of graphene and boron nitride based materials Aleandro Antidormi a, Luigi Colombo b, Stephan Roche a, c, * a Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193, Barcelona, Spain b Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, TX, 75080, United States c ICREA–Institucio Catalana de Recerca i Estudis Avançats, 08010, Barcelona, Spain A R T I C L E I N F O A B S T R A C T Keywords: We review recent developments on the synthesis and properties of two-dimensional materials which, although amorphous graphene being mainly of an sp2 bonding character, exhibit highly disordered, non-uniform and structurally random amorphous boron nitride morphologies. The emergence of such class of amorphous materials, including amorphous graphene and boron thermal transport nitride, have shown superior properties compared to their crystalline counterparts when used as interfacial films. molecular dynamics amorphous materials In this paper we discuss their structural, vibrational and electronic properties and present a perspective of their electrical transport use for electronic applications. 1. Introduction was found to be an electrical (Anderson) insulator. Growing thin non-crystalline films eliminates the need for substrates of high crystalline In recent years, graphene and related materials have been evaluated quality, thus potentially enabling the deposition of an atomically flat in the ever-growing fields of energy harvesting, solar energy generation, dielectric film with sp2 bonding character [15]. In early 2020, an biosensors, reinforcement materials and heat dissipators to cite a few important milestone was achieved concerning the synthesis, via [1–4]. Today these materials are prepared using a variety of synthesis laser-assisted chemical vapour deposition of free-standing, centimetre methods, from mechanical and chemical exfoliation to catalytic vapour scale, continuous monolayer of amorphous graphene [16]. Amorphous deposition (CVD). The resulting structures show a multiplicity of atomic graphene, a-G, as an interfacial coating or seed for atomic layer deposi- morphologies which range from “ultraclean” nearly perfect crystalline tion processes presents many advantages for advancing the integration of films to strongly disordered reduced graphene oxides, polycrystalline 2D materials in electronic devices as well as their use for diffusion bar- graphene and h-BN thin films with varying grain sizes and grain riers in magnetic recording devices. However, the relation between the boundaries densities [5–8]. The latter forms of large-scale CVD graphene physical properties such as thermal transport and the degree of structural and h-BN are the most promising materials for emerging nanoelectronic imperfection remains to be fully established for these “new” materials. applications such as photodetectors, electrodes, brain implants, wearable Bulk hexagonal boron nitride (h-BN) is a layered material iso- devices for health monitoring, ultra-wide bandwidth and low power structural to graphite, alternating boron and nitrogen atoms in its atomic optical communications systems, and spintronics [9–13]. But current structure, is an excellent electrical insulator with a band gap of about 5.9 efforts to achieve large single-crystal graphene and h-BN are suffering eV. Hexagonal BN is one of the best dielectric substrates for two- from a low growth rate and unsuitable substrate materials making pro- dimensional (2D) material-based electronic devices due to its atomi- duction at the industrial scale extremely challenging [7,14]. cally smooth and charge-free interface, with an in-plane lattice constant Recent efforts have succeeded in growing wafer-scale forms of carbon that is nearly lattice matched to that of graphene, Δa=a of about 1.8%. As and boron-nitride based materials with a high degree of non-crystallinity, such, h-BN has shown to be a superior substrate for preserving graphene naming such structures as amorphous graphene [15,16] and amorphous properties from the invasive interaction with the substrate or interface boron-nitride (a-BN) respectively [17,18]. In Ref. [15], amorphous car- between graphene and substrate. Although h-BN has been extensively bon monolayers were grown on germanium substrates using conven- used to demonstrate nearly theoretical carrier mobilities in graphene, the tional CVD at high temperatures (> 900K), and the deposited material h-BN used for these experiments has been exfoliated from bulk grown * Corresponding author. Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193, Barcelona, Spain. E-mail address: stephan.roche@icn2.cat (S. Roche). https://doi.org/10.1016/j.nanoms.2021.03.003 Received 23 December 2020; Accepted 10 February 2021 Available online 27 March 2021 2589-9651/© 2021 Chongqing University. Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). A. Antidormi et al. Nano Materials Science 4 (2022) 10–17 crystals of very small area of hundreds of square microns [19–21]. Sig- and perhaps ideal material for practical electronic applications [17]. A nificant advances have been made in the area of h-BN thin film and bulk recent publication by Kim et al. [29] reported on potentially superior crystal growth; however, none of the reports have shown a material properties of graphene as an etch stop in comparison to traditional car- which would be simultaneously of high enough crystalline quality and bon based etch stops, such as diamond like amorphous carbon. Amor- sufficient size to be compatible with integration on wafers and device phous BN could also be used as an etch stop due its refractory nature, and flows of technological importance. expected high etch selectivity. Further, given its high sp2 character, as There has been some progress on the growth of bulk h-BN [22,23], will be shown later, it may be possible to use a-BN as an interfacial nearly a centimetre on the side, but these processes still face the difficulty dielectric to mitigate the deleterious properties of other dielectrics such of scaling single crystals to large volumes. Growth of large area h-BN thin as SiO2 to achieve higher mobility in graphene. films have also been reported on metals, polycrystalline as well as Lastly hybrid graphene-hBN heterostructures are worth mentioning textured metals on sapphire [24–26]. However, the issue of film transfer, since they provide a variety of properties which can be adjusted by layer number control, surface roughness and single crystallinity are still adjusting the relative ratio of carbon versus boron-nitride atoms, allow- major obstacles that have been difficult to overcome. Recently, atomic ing to tune the electronic transport as well as optical properties [30–32]. layer deposition of boron nitride (ALD-BN) using BCl3 and NH3 pre- In particular, the possibility of tuning the inert electronic property of cursors directly on thermal SiO2 substrates was achieved at a relatively h-BN via grain boundary engineering, with the experimental observation low temperature of 600 C [27], with dielectric properties comparable of local density of states variation near grain boundaries in poly- with that of SiO2 , while improving carrier mobility of graphene field crystalline hBN, has also been shown (see Fig. 1) [33]. The interesting effect transistors (G-FETs/ALD-BN/SiO2 ) by a factor of two, most likely electronic transport tunability of such hybrid structures was theoretically as a consequence of the lower surface charge density and inert surface of analyzed in Ref. [34]. Of particular interest are the in-plane hetero- ALD-BN in comparison to that of G-FETs fabricated on bare SiO2 . It is structures combining graphene and hexagonal boron nitride (h-BN) possible, therefore, that with further growth process improvements and which have been found to provide a new type of blue emission source tuning the quality ALD-BN could be improved. [35]. By exciting the interface with a laser, Kim and coworkers [35] In this context, the recent growth of amorphous boron-nitride (a-BN) observed a photoluminescence peak at 410 nm, absent in adjacent gra- with low dielectric constant has sparked a huge interest in the context of phene and h-BN areas. The intensity of the blue photoluminescence was microelectronics [17]. Indeed, some of the key requirements for inter- further increased by six-fold by increasing the “interface length” per unit connect isolation materials are that they should possess low relative area by preparing in-plane heterostructures of graphene quantum dots dielectric constants, serve as diffusion barriers against migration of (GQD) on a h-BN monolayer. These structures therefore offer an oppor- interconnect metals such as copper to prevent shorting and be thermally, tunity to fabricate new types of optoelectronic devices based on inherent chemically and mechanically stable [28]. Amorphous boron nitride, resonant defects at graphene/h-BN grain boundaries [35]. because of its inherent non-crystalline structure and refractory nature in The large variety of structural possibilities of graphene and boron comparison to Si-based low dielectric constant materials, is expected to nitride-based materials have recently stimulated an intense theoretical have lower metal diffusion and thus acting as a better barrier than the effort aimed at exploring the relation between their morphological/ low-k counterpart. This non-crystalline material could, in principle, be chemical aspects and their physical properties. In this respect, atomistic used for several applications, i.e. integrated circuits where a stable low calculations performed via classical molecular dynamics (MD) and tight- dielectric constant barrier material is needed, and as a dielectric, below binding hamiltonians represent widely employed and successful the active 2D film as as well as above below the gate electrode, for the computational frameworks: they proved to be able to both elucidate integration of 2D materials to achieve higher carrier mobility. The newly features hardly deducible from experiments and to make predictions of synthesised a-BN as thin as 3 nm was deposited directly onto a silicon structural, thermal and electronic properties, respectively. In particular, substrate using inductively coupled plasma-CVD. The resulting material classical MD with the employment of empirical potentials has been showed a low dielectric constant of less than 2 [17]. Moreover, diffusion usefully exploited to explore the atomistic structure of disordered forms barrier tests for this new material demonstrated that it can prevent metal of Carbon and defective BN correlating them with their vibrational and atom migration from the interconnects into the insulator. Together with a thermal properties [36–49]. Such simulations have been also used to high breakdown voltage, these characteristics make a-BN an attractive perform thin-film depositions and cooling processes “in silico”, thus Fig. 1. Left panel: (main frame) evolution of the total density of states of hybrid graphene/hBN structures (% indicates hBN parts); (inset) typical local density of states (LDoS) at grain boundaries betwen graphene and hBN parts, pinpointing the emergence of impurity states. Right frame: Evolution of the charge mobility (main frame) and sheet resistance (inset) for the same structures. Adapted from Ref. [34]. 11 A. Antidormi et al. Nano Materials Science 4 (2022) 10–17 replicating the experimentally employed protocols on a computer [17, 50–53]. A fundamental feature of classical MD is given by the compu- tational efficiency of the calculations, allowing to study systems made of up to millions of atoms. This factor represents a clear advantage with respect to density-functional-based methods, which are strongly limited to systems of few hundred atoms. An extremely efficient methodology to describe electronic and transport properties of large-area, spatially complex disordered or nanostructured materials is offered by quasiparticle-based real-space tight-binding (TB) models. Combining this strategy with linear-scaling algorithms also called order-N or O(N) [54], i.e., with computational cost linearly increasing with the number of atoms, the transport properties of a large collection of disordered materials hase been investigated, from polycrystalline/defective graphene to hybrid graphene-hBN structures [6,34,55,56]. In this paper, we present the fundamental structural, electronic and thermal properties of amorphous graphene and boron-nitride obtained Fig. 2. (a) Total density of states of amorphous graphene samples with different using molecular dynamics simulations and model Hamiltonians. We degrees of disorder (different values of triatic order); (b) Semiclassical con- show that there exists a large variability of possible structures and degree ductivity of the corresponding samples; (inset) Elastic mean free path vs. energy. of disorder which can be obtained by tuning the growth conditions, and that the resulting structures will present tunable electronic and thermal The corresponding conductivity estimated via a Green-Kubo real- conductivities. These results provide some possible guidelines for further space order-N quantum wave packet evolution approach is shown in optimizing desired properties of large scale non-crystalline phases of Fig. 2(b). In the proximity of the charge neutrality point, the conductivity sp2 -carbon and boron-nitride membranes. of all the systems converges to the minimum value σ min ¼ 4e2 =π h, which corresponds to the theoretical limit in the diffusive regime [55]. In an 2. Structure, electronic and thermal properties of amorphous energy window of few eV around the charge neutrality point, σ generally graphene increases albeit to a weaker extent in the most disordered systems. For sufficiently disordered samples the conductivity remains almost equal to Amorphous graphene has a 2-D structure consisting of 5-6-7 polygons its minium semiclassical value σ min in a wide energy range around the with predominant sp2 bonding, which can be simulated either using Fermi energy, indicating stronger localization effects. Monte Carlo bond switching algorithm that systematically transforms a The estimated mean free path ( le ) as a function of energy is derived crystalline graphene sheet into a disordered structure or through mo- from the diffusion coefficient calculations and is shown in the inset of lecular dynamics simulations and quenched from the high temperature Fig. 2(b). A reduction of le is observed when increasing disorder in the liquid state [52]. Kotakoski and coworkers [57] have also used electron energy range considered. Specifically, for large values of q3 , the mean irradiation of pristine graphene to create a sp2 -hybridized free path averaged over the energy range shown decreases linearly with one-atom-thick flat carbon membrane with a random arrangement of the triatic order (le ∝q3 ). For q3 < 0:6 the mean free path finally saturates polygons, including four-membered carbon rings. to a value of e 0.5 nm, corresponding to about 3 nearest-neighbour dis- The impact of the level of randomness induced by topological disorder tances, in agreement with the theoretical predictions of [56]. on the electronic properties of a-G has already been extensively investigated A lot of attention has been recently paid to the evolution of thermal [56,59]. In contrast to some prior misleading claims, predicting a transition properties of aG upon varying the degree of disorder of the structure. Prior to metallicity when a sufficient amount of disorder is induced in graphene theoretical studies employed classical molecular dynamics (MD) and found [60], scaling transport studies, using efficient linear scaling approaches a significant reduction of the thermal conductivity with increasing disorder [54], have confirmed that, despite the increase of the density of states at low [41] while others have explored localization effects of the vibrational energy compared to pristine graphene, disorder will induce a short mean modes induced by disorder for a limited number of disorder configurations free path and a charge mobility μe1  10cm2 V1 s1 , much lower than clean [43]. In a more recent work [58], a systematic investigation of amorphous graphene materials, and inappropriate for most electronic applications [56, graphene based on classical MD has been performed, yielding a 59]. With a localization length of the order of 10 nm, revealed by variable self-contained discussion of its structural, vibrational and thermal proper- range hopping in low temperature measurements [15], a-G stands as a ties as a function of the degree of disorder. A consistent view of the impli- prototype of Anderson insulating membranes. cations of non-crystallinity on the morphology of the material and on the The impact of disorder on the electronic properties of a-G is better peculiar vibrational modes that are responsible for heat transport in elucidated by considering samples with a varying degree of non- amorphous graphene has consequently emerged. crystallinity. To this aim, a useful measure of the amount of disorder is Analyzing several atomistic samples of amorphous graphene with expressed by the averaged triatic order parameter q3 , which captures the different amounts of disorder, the authors of [58] have shown how the sp2 character of a system (see Ref. [58] for its definition), where small presence of topological defects in graphene breaks the regularity of the values (q3 <1) represent disordered samples and q3 ¼ 1 denotes crys- plane determining a gradual loss of its short- and long-range orders. talline graphene. Following [58], we will hereafter show the main The radial distribution functions gðrÞ (RDFs) of the amorphous graphene quantities of interest as a function of such disorder parameter. samples (Fig. 3(a)) reveal peaks (corresponding to various interatomic The density of states (DOS) of five a-G systems with increasing dis- distances) broadening when increasing disorder and eventually dis- order (decreasing q3 ) is shown in Fig. 2 (a). The graphene DOS is appearing for distances larger than a few nearest-neighbour distances. Such observed in all cases, accompanied by a broadening of the van-Hove a modification in the spatial order of amorphous graphene is associated singularities as an effect of disorder. As a result, a strong accumulation with an increasing number of non-hexagonal carbon rings and a conse- of states at the charge neutrality point emerges in the more disordered quently wider distribution of both the C–C bond lengths and angles samples together with an electron-hole asymmetry of the band structure. (Fig. 3(d)); their mean values are centered at 1.42 Å and 120 , respectively, As recognized in Refs. [55,56], such a feature is due to the presence of with a broadening increasing with disorder. These features have also been odd-membered rings, which are responsible for the creation of experimentally probed in real samples of amorphous graphene [16,61]. quasi-bound states at resonant energies. A remarkable modification in the structure of amorphous graphene induced by disorder is observed in terms of deviation from planarity. 12 A. Antidormi et al. Nano Materials Science 4 (2022) 10–17 Fig. 3. (a) Radial Distribution functions of amorphous graphene systems for different degrees of disorder (small q3 values denote more amorphous samples); (b) Structural models of three samples with the color map showing the out-of-plane component of the C–C bonds; (c) Ring statistical distribution as a function of q3 ; (d) Statistical distribution of the C–C bond lengths and bond angles. Adapted from Ref. [58]. Non-hexagonal rings are spatial loci where wrinkles are localized in the approximately 0.6 nm; this value is almost twice as large of that of gra- structure. This can be appreciated by looking at the Fig. 3(b) where the phene, in agreement with the disorder-induced roughness predicted out-of-plane component of the C–C bonds is depicted for three a-G theoretically. As also discussed in Ref. [58] and shown in Fig. 3(b), the samples. This feature has been also verified both theoretically in Refs. resulting roughness of amorphous graphene is strongly related to the [62,63] and experimentally. Specifically, the authors of [16] extracted a disorder of the material, with more disordered samples having a stronger value of interlayer spacing in multilayer amorphous graphene of deviation from planarity. Fig. 4. (a) Vibrational density of states (VDOS) of amorphous graphene systems for different degrees of disorder; (b)Participation Ratio (PR) of the vibrons in the various samples as a function of frequency. (c) Thermal conductivity of the a-G systems at T ¼ 300K vs. q3 normalized wrt to the corresponding value of crystalline system κ 0 ; (d) Atomic displacements for two vibrons in the sample with q3 ¼ 0.55: a diffuson on the left and a locon on the right. The (properly scaled) displacements are depicted as red vectors superimposed on blue dots representing atoms. Adapted from Ref. [58]. 13 A. Antidormi et al. Nano Materials Science 4 (2022) 10–17 The specific structural features of amorphous graphene are clearly the relationship between its morphological/chemical properties and the expected to play a major role in the determination of the vibrational resulting electrical/thermal performance is urgently needed. properties of the material, eventually affecting the thermal conductivity. The unveiling of the fundamental features of a-BN through atomistic In this respect, it has been shown [16,58] that the presence of disorder in simulations has already greatly helped elucidate the main properties of a-G is ultimately responsible for a substantial change in both the spatial its structural features. In particular, simulation of the chemical vapour character of the vibrations and their effect on thermal transport. deposition process has allowed the authors of [17] to explore the disor- The consequences of non-crystallinity on the vibrational properties of dered nature of a-BN films. Fig. 5(a) shows an image taken during the the material can be observed from the vibrational density of states deposition of Boron and Nitrogen atoms on a Si substrate simulated via (VDOS) shown in Fig. 4(a) as a function of the triatic order parameter. classical molecular dynamics. The simulation was used to grow a 3 nm While the VDOS of the more crystalline systems present peaks reminis- thick BN film under similar conditions as for experimentally fabricated cent of the phonon bands of crystalline graphene, the band separation is samples. For the simulation details we refer the reader to the Methods’ lost when increasing disorder and no bands can be identified in the most section. It is clear by visual inspection of Fig. 5(a) that both short- and disordered sample. long-range order is absent in the deposited BN film. The radial distri- More remarkably, the amount of disorder in amorphous graphene bution functions shown in Fig. 5(b) numerically confirm this evidence: no determines a substantial modification of the spatial extension of the peak can be identified for distances larger than 4 Å. In addition, the first vibrational modes, inducing a strong localization of the modes. The peak, found at a distance of about 1:43  A, is mostly due to the B–N bond participation ratio (PR) of the vibrons in the various systems as a function length, ruling out the possibility of homopolar bonds in the material. of frequency is shown in Fig. 4(b) (PRe1 for extended modes and PRe The corresponding statistical distribution of the bond angles in 0 for localized ones, respectively). The atomic displament field of an Fig. 5(c) shows an average value at about 120 , also pointing to a locally extended mode and of a locon is shown in Fig. 4(d) for the same sample. well-defined chemical environment for both boron and nitrogen atoms. Vibrational modes in amorphous samples are more spatially localized, Remarkably, among all of the atoms in the sample, more than 58% are involving a smaller number of atoms sizeably vibrating around their sp2 -hybridized, i.e. have coordination number equal to 3, whereas 40% equilibrium position. Furthermore, such a localization effect is depen- present coordination number 4, all of the remaining atoms being dent on the amount of disorder and is observed across the frequency undercoordinated. A visual insight of this finding can be gained from spectrum. Fig. 5(d) where a section of the a-BN sample is shown with atoms A more extensive numerical analysis of the vibrational modes in depicted in different colors depending on their coordination number nc : amorphous graphene reveals that the spatial localization of the vibrons in in red we show atoms with coordination number 3, in cyan those with the material is also accompanied by a disorder-induced change of the nc ¼ 4, yellow nc ¼ 2 and blue nc ¼ 1. It is also important to acknowl- fundamental mechanism of heat transport of the single modes [43,58]. edge that the chemical bonding state of a-BN, i.e. sp2 =sp3 has been When disorder is present in the system, extended vibrons called diffusons already observed experimentally via XPS [17]. appear in the higher frequency range of the spectrum: they are charac- Concerning the electronic properties, the disruption of the structural terized by a random field of atomic displacements and dynamically ordering in a-BN affects the electronic properties by slightly reducing the contribute to heat transfer by scattering diffusively along the sample. energy bandgap by e0.2 eV due to defect-induced gap states (see Fig. 6). They differ from propagons, which are mainly found at low frequency and Those states, even if forming an impurity band close to the bulk band are able to propagate without scattering across the material for more than edges, are however not conducting and a-BN remains a strong insulator. a few interatomic distances. The frequency range dominated by diffusons The thermal properties of a-BN are also governed by the topologically increases with disorder, with a consequently lower value of the so-called disordered morphology, leading to a comparatively small value of ther- Ioffe-Regel limit [64]. mal conductivity. Fig. 7 shows the value of in-plane κ of a-BN films with Both the localization of the modes and the emergence of diffusive different thickness. A bulk value of κe4:0W=ðmKÞ1 is obtained for modes along with propagons contribute to our understanding of the thicknesses larger than 1 nm. Such distance is consequently larger than reduction of the thermal conductivity experimentally observed in the phonon mean free path of the material. A slightly smaller value of the amorphous graphene. In this respect, modal analysis based on the Green- thermal conductivity is found for thinner films, reaching the minimum Kubo formalism [65] has proved that a) the most effective modes in for an a-BN monolayer: in this case, a value of κ two orders of magnitude carrying heat in such structures are the low-frequency propagons and b) smaller than the conductivity of a monolayer of h-BN is observed. the localized modes are less effective for heat transport with respect to extended modes. These findings offer a clear explanation of the strong 4. Summary and conclusions reduction of thermal conductivity in amorphous graphene with respect to crystalline graphene: the κ of amorphous graphene decreases with dis- The structural, vibrational, and electronic properties of amorphous order by up to more than two orders of magnitude (Fig. 4(c)). graphene and boron nitride were presented. This new class of materials exhibits a highly disordered structural state with some properties supe- 3. Structure, electronic and thermal properties of amorphous BN rior to their crystalline counterparts when used as interfacial materials. In particular, the bonding state of a-BN was found to be predominantly of an Amorphous Boron Nitride (a-BN) has been recently shown to be very sp2 character by molecular dynamics and supported by recent experi- promising as a low dielectric constant material, with a dielectric constant mental data. The data presented and reviewed in this paper is of great smaller than 2 [17]. Among all, future electronics could largely benefit significance for both the 2D materials community as well as the elec- from the use of a-BN, opening the way to efficient low dielectric constant tronics industry. Because of the difficulty in growing large area single barrier materials that could benefit current device technology scaling as crystal h-BN, a-BN with its predominantly sp2 bonding character could be well as the integration of two-dimensional materials. In this respect, the particularly useful as an interfacial dielectric to screen impurity and comparatively high density of the material (e2:1g=cm3 ) also plays a defect charges from traditional dielectric substrates. Amorphous gra- fundamental role, making it an effective barrier against metal diffusion, phene on the other hand could be a good diffusion barrier without grain which is also a key requirement for next-generation insulating materials. boundaries for many electronic applications especially as the electronics The exceptional properties of a-BN clearly depend on its intrinsically industry scales transistors to the sub 5 nm range. disordered nature. Consequently, the formidable task of understanding 14 A. Antidormi et al. Nano Materials Science 4 (2022) 10–17 Fig. 5. (a) Image of a film of a-BN deposited on a Silicon substrate extracted from a computer-simulated process; (b) Radial distribution functions (total and chemically resolved) of a-BN: functions are rigidly shifted for the sake of clarity; (c) Statistical distribution of the chemically-resolved bond angles; (d) Section of the a-BN atomistic sample from (a) with 5 thickness; atoms are shown with different colors depending on their coordination number (cyan, 4; red, 3, yellow, 2; blue, 1); e) Statistical distribution of the chemically-resolved bond lengths. cooling rates determine more crystalline samples (larger q3 ). The final systems considered in this work use a number of atoms as large as 10032 atoms, with a linear dimension of e160. Classical molecular dynamics has been adopted to carry out all the calculations, as implemented in the open source LAMMPS package [67]. To extract the vibrational properties of the resulting systems, we computed and diagonalized the dynamical matrix. From the knowledge of the eigenvectors es and eigenvalues ω2s with s ¼ 1; …; 3N where N is the number of atoms in the sample, the vibrational density of states and the participation ratio (PR) are even- tually computed. The PR is given by P 2 N 2 i¼1 ei;s Fig. 6. Total density of states computed via tight-binding approach of a-BN and 1 bulk h-BN systems with 5000 atoms. The tight-binding parameters used in the PRs  PN (1) calculation are presented in Ref. [66]. N 4 i¼1 ei;s with ei;s being the i-th component of the s-th eigenmode. Equilibrium molecular dynamics runs have been employed for the calculation of thermal conductivity at T ¼ 300K via the Green-Kubo formula. Heat flux correlations have been extracted from evolutions of the systems as long as 10ns with a timestep of 0.25 fs. The final value of thermal conductivity of each sample has been averaged over six independent trajectories. The details on the computational protocol used, the study of the reliability of the force-field and a comparison of the simulated samples with experi- ments can be found in Ref. [58]. The electronic and transport properties of amorphous graphene have been studied with a π  π * orthogonal tight-binding (TB) model with Fig. 7. In-plane thermal conductivity of a-BN films as a function of the film nearest neighbour hopping γ 0 ¼ 2.8 eV [56] and zero onsite energies. No thickness at T ¼ 300K. Values for monolayer hBN are also shown. [*] data are modification of these parameters has been introduced as a function of the taken from Ref. [34]. interatomic distances, since the topological disorder is the main factor affecting the electronic properties of such systems. The corresponding 5. Methods quantum transport features have been analyzed using a real-space order-N quantum wave packet evolution approach allowing to derive 5.1. Amorphous graphene the Kubo-Greenwood conductivity [54]. 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