Outstanding Thermal Conductivity of Single Atomic Layer Isotope-Modified Boron Nitride

Materials with high thermal conductivities (k) is valuable to solve the challenge of waste heat dissipation in highly integrated and miniaturized modern devices. Herein, we report the first synthesis of atomically thin isotopically pure hexagonal boron nitride (BN) and its one of the highest k among all semiconductors and electric insulators. Single atomic layer (1L) BN enriched with 11B has a k up to 1009 W/mK at room temperature. We find that the isotope engineering mainly suppresses the out-of-plane optical (ZO) phonon scatterings in BN, which subsequently reduces acoustic-optical scatterings between ZO and transverse acoustic (TA) and longitudinal acoustic (LA) phonons. On the other hand, reducing the thickness to single atomic layer diminishes the interlayer interactions and hence Umklapp scatterings of the out-of-plane acoustic (ZA) phonons, though this thickness-induced k enhancement is not as dramatic as that in naturally occurring BN. With many of its unique properties, atomically thin monoisotopic BN is promising on heat management in van der Waals (vdW) devices and future flexible electronics. The isotope engineering of atomically thin BN may also open up other appealing applications and opportunities in 2D materials yet to be explored.

such as carbon nanotubes [1], graphene [2], and recently discovered cubic boron arsenide (cBAs) (~1000 W/mK) [3][4][5] are also excellent thermal conductors. However, electrically conductive carbon materials are not suitable in direct contact with electronic devices due to the potential for short circuiting. Although diamond and cBAs have the potential for high-power electronics, they are unsuitable for flexible electronic devices and new two-dimensional (2D) van der Waals (vdW) structures.
Distinct from their carbon counterparts, all boron nitride (BN) materials, including single-wall nanotubes and single atomic layer or monolayer (1L) BN are electric insulators and hence better candidates for waste heat dissipation, for example, in electronic devices. Bulk cubic (c) and hexagonal (h) BN crystals are good thermal conductors with κ of ~690 and 420 W/mK at room temperature, respectively [6]. Recently, we reported that high-quality and surface-clean 1L hBN had a κ of 751±340 W/mK [7]. This κ increase with reduced thickness down to the atomic level was due to a decrease in the number of phonon branches and states available for Umklapp scattering with less interlayer interaction. Defects, grain boundaries, and surface contaminations, nevertheless, could adversely affect the thermal conduction of atomically thin BN [8][9][10][11][12].
Isotope engineering affects many fundamental properties of a solid, e.g. lattice parameter, disordering, elastic constant, vibration, band structure and transition, exciton, polariton dispersion and scattering. It, in turn, gives rise to appealing phenomena and applications, including the elevation of superconducting transition temperature, improvement in the lifetime of organic lightemitting diodes (OLED), optical fibers with higher speed, precise and accurate quantification of PHYSICAL REVIEW LETTERS 125, 085902 (2020) proteomes, and ultra-trace environmental analysis [13][14][15]. Naturally occurring BN ( Nat BN) contains a relatively high percentage of two stable boron isotopes: 19.9% 10 B and 80.1% 11 B; while carbon (C) normally consists of 98.9% 12 C and only 1.1% 13 C. The phonon energy, electronic bandgap, and electron density distribution of hBN could be varied by isotope engineering [16].
Isotope enriched hBN greatly increased polariton lifetime [17]. In addition, 10 B is one of the best neutron absorbers and used widely in radiation shielding, nuclear reactivity control, and neutron capture therapy for tumor treatment [18,19]. Replacing 10 B by 11 B, on the other hand, prevents electronic devices from data loss or single-event upset caused by cosmic rays or their generation of ionizing particles.
Reducing isotopic disorder also increases thermal conductivity. The in-plane κ of isotopically pure 12 C graphene is 36% and ~100% higher than that of naturally occurring graphene and graphite, respectively [20]. The κ of 1L isotopically pure 100 MoS2 were 61.6 W/mK, larger than the 40.8 W/mK of 1L Nat MoS2 [21]. Note that chemical vapor deposition (CVD) was used to synthesize these monoisotopic graphene and MoS2. In terms of BN, the room temperature κ of bulk 10 BN crystals was 585 W/mK, ~39% higher than that of bulk Nat BN [22]. The effect of isotopic impurity on the κ of BN nanotubes was also studied: 310 W/mK for 11 BN nanotubes, much larger than the 200 W/mK of Nat BN nanotubes as a control [23]. Very recently, an ultrahigh κ of 1600 W/mK was achieved from isotopically enriched cBN, ~190% higher than that of natural occurring cBN [24].
However, there has been no report on the synthesis of atomically thin monoisotopic BN, let alone measurement of its κ, though a 25-36% enhancement in κ was theoretically predicted from 1L isotopically pure BN compared to that of 1L Nat BN [25][26][27][28].

PHYSICAL REVIEW LETTERS 125, 085902 (2020)
In this work, we successfully produced atomically thin isotopically pure 10 BN and 11 BN for the first time, and their intrinsic in-plane thermal conductivities could be determined due to their high quality and clean surface. Based on optothermal Raman measurements, the κ of 1L 11 BN and 10 BN were 1009±313 and 958±355 W/mK, respectively. These values were ~34% and ~140% larger than those of 1L and bulk Nat BN, respectively. Density functional theory (DFT) simulations were used to gain insights into the isotope effect. This study may also give rise to new possibilities in many other applications, e.g. multifunctional metal-matrix nanocomposites for radiation shielding and new cancer treatment [18,19].
High-quality and surface-clean atomically thin isotopically pure BN sheets were mechanically exfoliated from bulk crystals grown by the nickel-chromium solvent method [16,29]. According to secondary ion mass spectrometry (SIMS), these bulk crystals contained 99.2% and 99.9% 10 B and 11 B, respectively, close to the previously reported values [16]. Naturally occurring nitrogen has >99.6% 14 N, and thus can be considered as isotopically pure. The atomically thin 10  Information (FIG. S1). The chemical composition, crystal structure, and quality of the isotopically pure samples were probed by near-edge X-ray absorption fine structure (NEXAFS) spectroscopy, and compared with those of a single crystal Nat BN synthesized by the high pressure Ba-BN solvent method (FIG. 1c) [30]. Sharp π* resonances at 192.0 eV corresponding to 1s core electron transitions to the unoccupied antibonding orbitals of B atoms sp 2 -bond to three nitrogen atoms were observed from all samples, verifying their hexagonal crystal structure. No satellite peaks caused by other chemical environments were present, suggesting high chemical purities of the isotopically pure samples [31,32]. These results are in line with the previous finding that the 10 BN and 11 BN crystals were free of defects in the areas of tens of microns [22]. respectively. Reducing the thickness of suspended monoisotopic BN to the atomic scale barely changed their G band Raman frequencies but lowered the peak intensities. A similar phenomenon on atomically thin Nat BN was reported and explained by us before [33,34]. Due to mass disorder effects, the different isotope mass also affected the full width at half maximum (FWHM) of the G bands of bulk 10 BN, Nat BN, and 11 BN crystals, i.e. 5.9, 9.4, and 5.6 cm −1 , respectively [35]. The PHYSICAL REVIEW LETTERS 125, 085902 (2020) atomically thin sheets showed broader bandwidths, caused by stronger surface scattering influencing the vibrational excitation lifetime [33,34]. The κ of atomically thin 10 BN and 11 BN was measured by optothermal Raman technique [2,7,21,[36][37][38][39][40]. First, the Raman G band frequency of the suspended 1L 10 BN and 11 BN as a function of temperature was determined using a hot plate with accurate temperature control (±0.1 °C). In order to minimize laser heating, a small laser power of ~1.5 mW was chosen. FIG. 2b   PHYSICAL REVIEW LETTERS 125, 085902 (2020) summarizes the Raman G bands of a 1L 10  −0.0223±0.0012 cm −1 /K (black dashed line) [7]. Note that the volumetric thermal expansion of the Au/Si substrate during heating hardly affected these values due to the hanging down of suspended atomically thin BN, releasing the strain induced by thermal expansion coefficients mismatch between BN and the substrate, as we described before [7].
The suspended 1L 10  absorbed laser power [20,37]. The optical absorption of 1L 10 BN and 11 BN at 488 nm wavelength was determined by the difference in the measured laser power between empty and nearby BNcovered holes of SiNx grids (see Supporting Information, FIG. S6). That is, Q = Pempty−PBN. There was no noticeable difference in the absorbance of 1L 10 BN and 11 BN, and the averaged value was (0.32±0.13)%, close to that of 1L Nat BN [7]. is the heat loss in the air: where T is the temperature at radius r; h is the heat transfer coefficient of hBN. In the case of small temperature variation between an object and the ambient, the quadratic expression for radiation can be simplified to the linearized sum of convective (ℎ ) and radiative (ℎ ) components to obtain the total heat transfer coefficient. That is, ℎ = ℎ + ℎ , where ℎ =3475W/m 2 K for BN sheets; ℎ = 4 3 ; = 0.8 is the emissivity of hBN; and is the Stefan-Boltzmann constant with the value of 5.670373×10 −8 W/m 2 K 4 [41].
The κ of 1L 10 BN and 11 BN as a function of temperature was calculated based on Equation 1, and compared with that of 1L Nat BN from our previous study (FIG. 2c) [7]. The errors were calculated through the root sum square error propagation approach, where the temperature calibration by Raman, temperature resolution of the Raman measurements, and the uncertainty of the measured laser absorbance were considered. Due to the small temperature range and the uncertainty of the optothermal technique, we averaged the κ values: 958±355 and 1009±313 W/mK for 1L 10 BN and to diffusive phonons of higher frequency than ballistic phonons, and the temperature measured by the Raman method was the anharmonic scattering temperature between the zone-center or zoneboundary optical phonons and diffusive acoustic phonons [38,42,43]. In addition, the local nonequilibrium of phonon polarizations was ignored [44]. As a result, these Raman-deduced κ values should be underestimated. Our results showed that the κ of 1L monoisotopic BN was about 34% and 140% higher than those of 1L Nat BN and bulk Nat BN, respectively [6,7], though the Nat BN had

PHYSICAL REVIEW LETTERS 125, 085902 (2020)
Theoretical calculations were used to comprehensively understand the isotope effects. In the ab initio calculations of the κ of 1L 10 BN (99.2% 10 B), Nat BN, and 11 BN (99.9% 11 B), phonon-phonon, isotope, and boundary scatterings were taken into account. The boundary scattering rate was calculated as vg/L, where vg is the group velocity of the phonons, and L is the boundary length.
Isotope mixing caused isotope scattering and shortened phonon mean free path (λ). In excellent agreement with our experimental results, the 99.9% 11 BN had a slightly higher κ than the 99.2% 10 BN at 4 μm length close to the experimental sample size (FIG. 3a), revealing that the higher isotope purity in 11 BN was the main cause of the slightly higher κ. FIG. 3b shows the theoretical accumulative κ as a function of phonon frequency, and for comparison purpose, the phonon dispersions of 1L 10 BN and 11 BN are displayed in FIG. 3c. Apparently, the out-of-plane acoustic phonons (ZA) contributed to most of κ in all BN sheets, consistent with our previous study [7].
Interestingly, 1L 10 BN, Nat BN, and 11 BN showed almost no difference in the accumulative κ at phonon frequency lower than 320 cm -1 , indicating that the isotope mixing had a small influence on the ZA phonons (FIG. 3c). In the region of 320−600 cm -1 (highlighted in light grey in FIG. 3bc), the accumulative κ started to split between 1L naturally occurring and monoisotopic BN. This means that the isotopic purification decreased the scattering of transverse acoustic (TA) and longitudinal acoustic (LA) phonons. Nevertheless, the most significant deviation in κ happened at ~600−800 cm -1 , corresponding well to the contribution of the out-of-plane optical phonons (ZO) (highlighted in dark grey in FIG. 3b-c). This suggests that the ZO phonon-isotope scatterings play an important role in the thermal conductivity of Nat BN. Optical phonons barely contribute by themselves to thermal conductivity in bulk materials [45,46]; however as dimensionality is reduced, an important scattering channel for acoustic phonons is mediated through their optical counterparts. We observed that the majority of the difference in κ between 1L naturally occurring PHYSICAL REVIEW LETTERS 125, 085902 (2020) and monoisotopic BN was caused by a strong acoustic-optical phonon scattering between ZO and TA/LA phonons due to isotope mixing [46].  Table S1), and this could be due to the local density approximation (LDA). LDA is well known to over bind systems, leading to overestimations of phonon frequencies and consequently thermal conductivity [47].
We also measured the κ of few-layer monoisotopic BN using the same procedure.  (FIG. 3b). The additional layers in 2-3L BN have a much larger influence on the ZA phonon scatterings than TA and LA phonons (FIG. S8). As a result, the increased Umklapp PHYSICAL REVIEW LETTERS 125, 085902 (2020) scatterings of ZA phonons due to the additional layers give rise to more prominent decreases in the thermal conductivity of few-layer Nat BN than monoisotopic BN.
In summary, high-quality and suspended atomically thin isotopically pure BN sheets were produced by mechanical exfoliation, and their intrinsic in-plane thermal conductivities were measured by the optothermal Raman technique: 958±355 and 1009±313 W/mK for 1L 10 BN and 11 BN at close-to room temperature, respectively. These values were about 34% and 140% larger than those of 1L and bulk Nat BN, respectively, attributed to 1) the longer mean free path of phonons mainly due to less ZO phonon-isotope scattering and subsequent reduced acoustic-optical scatterings between ZO and TA/LA phonons; 2) decreased phonon Umklapp scatterings in atomically thin samples caused by less interlayer interactions and hence reduced phonon branches.
With its layered structure, low density, wide bandgap, excellent mechanical flexibility and strength, good chemical and thermal stability, atomically thin monoisotopic BN is promising on heat management in vdW devices and flexible electronics. This study not only deepens the fundamental understanding of isotope effect on 2D thermal conductivity but also forms the basis for further research and applications of isotopically engineered 2D materials.