RESEARCH ◥ Criteria (i) and (ii) contribute to unusually weak REPORT phonon-phonon scattering (20) and a large intrin- sic thermal conductivity, whereas criteria (i) and (iii) cause relatively weak scattering of phonons THERMAL CONDUCTIVITY by isotopes (21, 22).Theabinitiotheoryidentified the III-V zinc-blende compound, defect-free boron arsenide (BAs), as having an exceptionally high Experimental observation of high thermal conductivity of more than 1000 W/m·K (8, 16–18). This predicted HTC exceeds that of most state-of-the-art HTC materials and more thermal conductivity in than triples that of the current industrial HTC standard, i.e., silicon carbide. BAs possesses an boron arsenide advantageous combination of properties that incorporates both conventional (light boron mass Joon Sang Kang, Man Li, Huan Wu, Huuduy Nguyen, Yongjie Hu* and stiff, almost pure, covalent bonding) and new criteria [large arsenic-to-boron mass ratio, bunch- Improving the thermal management of small-scale devices requires developing materials ing together of its acoustic phonon branches, and with high thermal conductivities. The semiconductor boron arsenide (BAs) is an attractive isotopically pure As (heavy) atom] (8, 16–18). target because of ab initio calculation indicating that single crystals have an ultrahigh Experimental efforts to synthesize and char- thermal conductivity. We synthesized BAs single crystals without detectable defects and acterize BAs have been scarce (17). Although the Downloaded from measured a room-temperature thermal conductivity of 1300 watts per meter-kelvin. Our growth of cubic BAs was reported in the 1950s, spectroscopy study, in conjunction with atomistic theory, reveals that the distinctive band its detailed structural characterization and prop- structure of BAs allows for very long phonon mean free paths and strong high-order erties were not reported (23–28). Generally, boron- anharmonicity through the four-phonon process. The single-crystal BAs has better thermal related materials are notably difficult to obtain conductivity than other metals and semiconductors. Our study establishes BAs as a in dense bulk form (29). The synthesis of BAs is benchmark material for thermal management applications and exemplifies the power of further complicated by the high volatility of ar- combining experiments and ab initio theory in new materials discovery. senic and the introduced vacancy defects, as http://science.sciencemag.org/ well as the possible formation of subphases he decreasing size of modern electronics assembled into practical sizes, owing to ambient (e.g., B12As2). In a collaborative effort, we reported makes heat dissipation one of the most crit- interactions and disorder scattering. Their intrinsic the earliest thermal measurements on cubic ical technological challenges. The worldwide anisotropy creates other challenges for applications. BAs using the time-domain thermoreflectance T semiconductor industry, which has powered Fundamentally, understanding the origins of technique (30). Our thermal conductivity value the information technology revolution since HTC remains a challenge. The conventionally ac- of 190 W/m·K measured in BAs samples with a the 1960s, acknowledged in 2016 that Moore’slaw cepted criteria for HTC materials are (i) small high density of defects is far below the theoret- is nearing its end (1). A major issue is the enor- average atomic mass (M ); (ii) strong interatomic ical expectation. Later study made improvement, mous amount of waste heat generated during bonding; (iii) simple crystal structure; and (iv) but the samples still show defects and grain electronic device operation (2, 3). For example, low anharmonicity (6–8). Criteria (i) and (ii) im- boundaries that degraded the crystal quality and a U.S. data center devotes about 50% of its total ply a large Debye temperature (QD)andprovide thermal properties (31). On the basis of subse- on September 12, 2018 electricity use to cooling (4). At the nanoscale, the the commonly used rule of thumb that thermal quent analysis and calculation, defect scattering power density of hot spots in current transistors is conductivity increases with decreasingM and plays a dominant role in those samples, which approaching that of the Sun’s surface (5). Low increasing QD. Diamond is the prototypical crys- makes probing the actual intrinsic thermal con- thermal conductivity and heat dissipation rates tal. Diamond’s two-atom primitive unit cell, light ductivity of BAs impossible in the absence of high- severely degrade the performance and energy effi- carbon mass, and stiff covalent bonding result in quality BAs crystals (32). ciency of electronic and photonic devices. Thermal an exceptionally high value for thermal conduc- Here, we synthesized high-quality single-crystal management is arguably the biggest roadblock for tivity. Recent ab initio calculations show excellent BAs and measured an ultrahigh thermal conduc- next-generation devices, such as microprocessors agreement with the measured thermal conductiv- tivity of 1300 W/m·K in our BAs crystals. This andintegratedcircuits,light-emitting diodes, and ityofawiderangeofmaterials(8–16), including value exceeds that of most HTC materials and is high-power radio frequency devices, to name just silicon, diamond, graphene, and carbon nano- consistent with the ab initio prediction (8, 16–18). afew(1, 5). tubes. Such calculations provide new physical We characterized our samples with scanning elec- Discovering high thermal conductivity (HTC) insights into the nature of phonon thermal tron microscopy, Raman spectroscopy, powder materials is needed to enable efficient heat dissi- transport and the HTC mechanism. x-ray diffraction (P-XRD), single-crystal x-ray pation from hot spots and improve device per- Recent ab initio theoretical work indicates that diffraction (S-XRD), and high-resolution trans- formance. So far, much of the research has been the conventional criteria for HTC materials are missionelectronmicroscopy(HRTEM).BAshas focused on carbon-based crystals—diamond, gra- incomplete and points to new ones stemming a zinc-blende face-centered cubic (fcc) crystal phene, and carbon nanotubes. Although these from fundamental vibrational properties that can structure in the F43m space group, where boron materials can have exceptional heat transfer lead to HTC (8, 16–18). These new criteria applied and arsenic atoms are interpenetrating and co- properties, there are several drawbacks for to binary compounds are (i) a large mass ratio of valently bonded to form a tetrahedral geometry widespread use. Diamond, the most developed constituent atoms; (ii) bunching together of the (Fig. 1A). The Raman spectroscopy data (Fig. 1C) material for passive cooling of high-power elec- acoustic phonon branches; and (iii) an isotopi- clearly show two peaks, at 700 and 720 cm−1, tronics, suffers from high cost, slow synthesis cally pure heavy atom. The large mass ratio pro- corresponding to the separate vibrational be- rates, low quality, and challenging integration vides a large frequency gap between acoustic and haviors of two boron isotopes (10Band11B) in with semiconductors. Degradation of thermal con- optical phonons (a-o gap). According to materials their natural abundance, respectively. The P-XRD ductivity plagues graphene and nanotubes when examined thus far, bunching of the acoustic pho- peaks that we observed (Fig. 1D) are in agreement non dispersions tends to occur in crystals with with the zinc-blende fcc crystal structure. Our light constituent atoms, such as boron and car- S-XRD confirmed the F43mspacegroupandthe School of Engineering and Applied Science, University of California, Los Angeles (UCLA), Los Angeles, CA 90095, USA. bon, where it derives from an unusual inter- crystal quality, and was performed to unambig- *Corresponding author. Email: [email protected] atomic bonding that lacks core p electrons (19). uously verify the single domain, single-crystalline Kang et al., Science 361, 575–578 (2018) 10 August 2018 1of4 RESEARCH | REPORT nature over entire crystals (33). Each of the re- laser that creates a temperature rise at the materials, exceeded only by diamond. As a semi- flections in the x-ray diffraction pattern (Fig. 1E) sample surface (Fig. 2A). The transient temper- conductor, BAs has a high potential for manu- appears clearly as a single dot without distortion, ature decay, caused by the heat impulse, was facturing integration and holds promise for indicating that the sample has no grain bounda- monitored with another probe pulse that is thermal management applications. ries. To collect a complete dataset of all recipro- delayed in time with respect to the pump using Fundamentally, thermal transport in solids cal lattice points through the whole crystal, we a mechanical delay stage. The thermal conduc- can be described by the interactions of phonons, rotated BAs samples over 360° under x-ray ex- tivity was obtained by fitting the full transient i.e., the quantum-mechanical modes of lattice citation and collected diffraction data at every decay curve, acquired by varying the time delay, vibrations (6). Thermal conductivity results from 0.3° rotation. The reconstructed reciprocal lattice to a thermal model (Fig. 2B). We measured a phonon scattering processes that are closely rel- images from the S-XRD [see [100] plane in Fig. 1F room-temperature thermal conductivity of our ated to the structure of materials. Phonon scatter- and (34)] confirms the single-domain, single- high-quality BAs crystals of ~1300