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High thermal conductivity in cubic boron arsenide crystals

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Science  10 Aug 2018:
Vol. 361, Issue 6402, pp. 579-581
DOI: 10.1126/science.aat8982

Moving the heat aside with BAs

Thermal management becomes increasingly important as we decrease device size and increase computing power. Engineering materials with high thermal conductivity, such as boron arsenide (BAs), is hard because it is essential to avoid defects and impurities during synthesis, which would stop heat flow. Three different research groups have synthesized BAs with a thermal conductivity around 1000 watts per meter-kelvin: Kang et al., Li et al., and Tian et al. succeeded in synthesizing high-purity BAs with conductivities half that of diamond but more than double that of conventional metals (see the Perspective by Dames). The advance validates the search for high-thermal-conductivity materials and provides a new material that may be more easily integrated into semiconducting devices.

Science, this issue p. 575, p. 579, p. 582; see also p. 549

Abstract

The high density of heat generated in power electronics and optoelectronic devices is a critical bottleneck in their application. New materials with high thermal conductivity are needed to effectively dissipate heat and thereby enable enhanced performance of power controls, solid-state lighting, communication, and security systems. We report the experimental discovery of high thermal conductivity at room temperature in cubic boron arsenide (BAs) grown through a modified chemical vapor transport technique. The thermal conductivity of BAs, 1000 ± 90 watts per meter per kelvin meter-kelvin, is higher than that of silicon carbide by a factor of 3 and is surpassed only by diamond and the basal-plane value of graphite. This work shows that BAs represents a class of ultrahigh–thermal conductivity materials predicted by a recent theory, and that it may constitute a useful thermal management material for high–power density electronic devices.

Thermal management is a major challenge for a wide variety of engineering systems (13). In particular, effective thermal management often plays a determining role in the performance and reliability of high-power electronic and optoelectronic devices. A common component in a thermal management system is a high–thermal conductivity (Λ) material that can effectively conduct heat from a small high-power device to a larger heat exchanger that then dissipates heat to a working fluid. Diamond has the highest isotropic Λ of any bulk material (the room-temperature value is ~2200 W/m·K) (4) and is sometimes used in demanding heat dissipation applications. Heat spreaders constructed from single-crystal diamond, however, are costly and can be produced in only limited sizes. The thermal conductivity of more cost-effective diamond films produced by chemical vapor deposition (CVD) is often substantially compromised by microstructural defects. Another material with a predicted Λ = 940 W/m·K at room temperature, cubic boron nitride (c-BN) (5), requires high-pressure, high-temperature synthesis conditions of 10 GPa and >2000°C.

Cubic boron arsenide (BAs) is predicted to have ultrahigh thermal conductivity comparable to that of diamond (5). The main challenge in realizing the potential of this material is synthesizing high-quality crystals, as defects and impurities degrade the thermal properties. However, BAs is an appealing candidate for thermal management for high–power density devices. BAs is chemically inert, with a coefficient of thermal expansion (3.0 × 10−6 K–1) similar to that of Si (2.6 × 10−6 K–1) (6). BAs is also growth-compatible with GaN and GaAs (7), making it ideal for a variety of applications in the thermal management of high–power density devices.

BAs adopts the cubic zincblende structure and is a semiconductor with band gap of ~1.5 eV. We synthesized single crystals of BAs by a modified chemical vapor transport method using high-purity source materials (B and As powders) and transport agents (8). Among the different vapor transport agents we investigated (I2, H2, Br2, and NH4I), we found that NH4I yielded the highest–thermal conductivity crystals. We optimized the ratio of starting materials and temperature profiles for our synthesis [see (9) and figs. S1 to S4 for the details of the synthetic approach and characterization of microstructure]. Growth runs and individual specimens are labeled with Roman numerals and lower-case letters, respectively (e.g., Ia). This helped us track variations between and within growth runs.

We synthesized single crystals of cubic BAs and characterized the crystals with scanning electron microscopy (SEM) (Fig. 1A), Raman spectroscopy (Fig. 1B), and single-crystal x-ray diffraction (Fig. 1C). SEM showed that specimen Ia has a lateral dimension of ~0.5 mm and a large crystal facet parallel to the {111} crystal planes. Raman spectroscopy and single-crystal x-ray diffraction confirmed the zincblende structure and high crystalline quality of the crystals. The strong Raman peak we labeled as P1 at 698 cm−1 (Fig. 1B, inset), with its overtone at 1398 cm–1, corresponds to the T2 longitudinal optical phonon. Because isotope disorder typically does not generate a localized phonon mode (10), we attributed the P2 peak at 717 cm−1 to scattering from the high phonon density of states at the L or W point in the Brillouin zone (11) that is induced by isotope disorder. In other words, isotope disorder partially relaxes the crystal momentum conservation rules and allows the peak corresponding to zone boundary phonons to appear in the one-phonon spectra. This assignment is consistent with prior studies of the Raman spectra of Si, Ge, and diamond (1214).

Fig. 1 Structural characterization of BAs crystals.

(A) SEM image of BAs specimen Ia. (B) Raman spectrum of BAs specimen Ia with the intensity normalized to the excitation laser power (cps, counts per second). The inset shows the details near the T2 longitudinal optical phonon at the Γ point. Assignment of the second-order peaks is discussed in (9). (C) Precession image of the hk0 layer integrated from complete sets of single-crystal x-ray diffraction frames, where all detected reflections are indexed as circled spots, suggests a high-quality single lattice in BAs specimen Ib. (D) ADF-STEM image of BAs specimen Ic along the [110] zone axis, showing the zincblende crystal structure. FIB-induced surface damage and carbon contamination during image acquisition are responsible for the low-frequency contrast modulation across the image. The image is a cross-correlated sum of several image frames; raw data are available in fig. S5. A cartoon of the BAs lattice (orange spheres, As; blue spheres, B) is overlaid on the STEM image (top right). Inset: Fast Fourier transform of the STEM image.

We found high-quality single-domain crystals by means of single-crystal x-ray diffraction (XRD) on the selected crystals. We reconstructed a pseudo-precession photograph for the a*-b* plane pixel-by-pixel from complete sets of single-crystal XRD images (2178 frames) that we measured with a scan width of Δω = 0.30° (Fig. 1C). We reconstructed precession photographs for other reciprocal lattice planes as well (fig. S2). The pseudo-precession photographs provide an undistorted image of layers of reciprocal space and a direct view of crystal quality (9). All of the detected reflections (circled spots) are derived from a single lattice; we did not observe any evidence for crystal twinning in samples grown using the conditions of specimen I. We observed twinning in crystals grown under different conditions (e.g., specimens IIb and IIIb) (figs. S3 and S4) (9). We further used selected-area electron diffraction, diffraction-filtered TEM, and annular dark-field scanning transmission electron microscopy (ADF-STEM) to look for large-scale structural defects (Fig. 1D and fig. S11). We did not detect grain boundaries or twinning in our high-quality single crystals, consistent with single-crystal XRD results. Because of damage caused by a focused ion beam (FIB) during sample preparation and electron beam damage during imaging, we cannot make any conclusions about the potential presence of point defects in our samples.

We measured the thermal conductivity of our crystals by time-domain thermoreflectance (TDTR) (1517) on smooth facets of ~100 μm. TDTR is a pump-probe optical metrology with a spatial resolution on the order of 10 μm, allowing for measurements on smooth-faceted crystals of less than 1 mm3 (15, 18). We determined the thermal conductivity of BAs by comparing the time dependence of the ratio of the in-phase (Vin) and out-of-phase (Vout) thermoreflectance signals from the lock-in amplifier with a thermal diffusion model (15). Determining Λ from TDTR data requires a model fit (9), for which we present the corresponding result for our highest-Λ samples (Fig. 2A). We used 1/e2 intensity radii of 10.4 μm for both the pump and probe laser beams to collect the data (Fig. 2, A and B). The thermal conductivity of BAs (Λ) and the thermal conductance of the interface between the transducer layer (~80 nm Al) and BAs (G) are the two free parameters in the fit. The best fit of our experimental data for sample Ia gives Λ = 1000 ± 90 W W/m·K and G = 130 ± 10 MW m–2 K–1 (see fig. S7). We show our measurement sensitivity by fixing Λ at either 890 or 1090 W/m·K, and allowing G to vary (Fig. 2A).

Fig. 2 Thermal conductivity measurement of BAs crystals.

(A) TDTR ratio data [the ratio of the in-phase (Vin) and out-of-phase (Vout) signals from the lock-in amplifier] measured using a laser spot size with 1/e2 intensity radius of 10.4 μm (circles) and model fitting (solid line) for BAs specimen Ia. Model curves using thermal conductivities 10% larger and 10% smaller than the best-fit thermal conductivity (dashed lines) are included to illustrate the measurement sensitivity. (B) Temperature-dependent Λ of the BAs specimen Ia (solid circles), Ig (triangles), IIa (open circles), and IIIa (open squares) from 300 to 600 K using the same laser spot size as (A) and comparison with the predictions of first-principles calculations based on only three-phonon scattering (blue solid line) (5) and both three- and four-phonon process (red solid line) (27). (C) Spot size radius–dependent (apparent) thermal conductivity from TDTR for specimen Ia at 300 K.

We measured the temperature-dependent thermal conductivity of BAs crystal specimens Ia, IIa, and IIIa between 300 and 600 K (Fig. 2B). The 300 K Λ values are ~1000 W/m·K for Ia, ~870 W/m·K for Ig, ~850 W/m·K for IIa, and ~500 W/m·K for IIIa, respectively, which are much higher than the previously reported Λ values of ~350 and ~200 W/m·K (8, 19, 20) (see table S1 for other specimens). The high Λ value of the best BAs crystal (Ia) also exceeds that of c-BN (~900 W/m·K), copper (~400 W/m·K) and 4H SiC (~320 W/m·K along the c axis). The thermal conductivity of BAs specimen Ia is lower than that of diamond by a factor of 2 (~2200 W/m·K) and graphite (in-plane direction, ~2000 W/m·K) (fig. S8) (4, 2124). BAs has the second highest measured isotropic thermal conductivity among the known single-phase bulk metal and semiconducting materials.

We need to consider deviations from Fourier’s law (25, 26) in TDTR measurements of high–thermal conductivity crystals. Such deviations result from ballistic phonon transport in the sample and from a mismatch in the distribution of phonons that carry heat across the metal transducer–sample interface and the distribution of phonons that carry heat in the sample. A reduction in the characteristic length scales of the temperature gradient by decreasing the laser spot size (w0) or increasing the pump modulation frequency (f) increases the percentage of low-frequency phonons with long mean free paths that are not in local equilibrium with high-frequency phonons. Such effects cause the apparent thermal conductivity (ΛA) derived from the thermal model using a small characteristic length scale to be less than the apparent thermal conductivity derived from the thermal model using a larger characteristic length scale (25).

We measured ΛA as a function of spot sizes w0 in TDTR for specimen Ia (Fig. 2C). As a result of ballistic phonon transport, ΛA drops by approximately 30% as w0 decreases from 26.5 to 2.7 μm at 300 K. The difference between ΛA measured with w0 = 10.4 μm and with w0 = 26.5 μm is ~7%, comparable to the typical uncertainty of TDTR measurements of thermal conductivity. We did not observe modulation frequency dependence in ΛA as we varied f from 1.1 to 9.3 MHz. This suggested negligible interfacial non-equilibrium effects (25). We used w0 = 10.4 μm and f = 9.3 MHz in the measurements plotted in Fig. 2B to maintain an improved signal-to-noise ratio. We expect the spot size dependence of ΛA to be smaller at elevated temperatures where phonon-phonon scattering becomes stronger and phonon mean free paths decrease.

We compared our measurements to the theoretical prediction from first-principles calculations based on three-phonon (3ph) scattering (5) and both three- and four-phonon (3ph + 4ph) scattering (Fig. 2B). Previous studies attributed the potential for high thermal conductivity of BAs to a large frequency gap between acoustic and optic phonons, in combination with the bunching of the acoustic phonon dispersions. The large acoustic-optic gap greatly limits the three-phonon scattering rate involving one optical and two acoustic phonons (5). However, such a gap does not forbid four-phonon scattering processes between the acoustic and optical phonons, and a calculation found that four-phonon processes substantially reduced the predicted Λ at room temperature from 2200 to 1400 W/m·K (27). At elevated temperatures when intrinsic phonon-phonon scattering becomes important (28), our measured values of Λ for Ia are comparable to the prediction based on 3ph + 4ph scattering. The measured thermal conductivity of Ia scales as Λ ~ T–1.4 in the temperature range 300 to 600 K, close to the calculation including four-phonon scattering (approximately Λ ~ T–1.6) and much stronger than the original calculation based on only three phonon processes (approximately Λ ~ T–0.8).

Crystal imperfections and free carriers could both affect phonon thermal transport in semiconductors (28). Because the grain size determined by single-crystal XRD is much larger than the TDTR characteristic temperature length scale (9), and because we do not observe a high density of stacking faults in TEM, phonon scattering by boundaries should be negligible. On the other hand, we found that specimens with high hole concentrations of 1.9 × 1019 cm–3 (Ie) and 1.1 × 1020 cm–3 (Id) according to Hall measurements (fig. S10) have low Λ values of 130 and 110 W/m·K, respectively, much smaller than our best sample.

Relative to the Raman spectra of the best specimen of Ia, specimens with high hole concentration such as Id (Fig. 3A) show asymmetric one-phonon P1 and P2 phonon peaks and stronger background intensity resulting from Fano interference (i.e., the coherent interaction between a continuum of electronic excitations and a discrete optical phonon) (29, 30). To study the relation between the Raman spectra and Λ, and to avoid fitting for overlapping P1 and P2 peaks, we chose to use the integrated Raman intensity from 1050 to 1150 cm–1 (ARaman) where the main contribution is from electronic Raman scattering (31). The Λ values of BAs samples grown from several batches show clear correlation with the corresponding ARaman values (Fig. 3B), and samples with high carrier concentration (Id and Ie) indeed give large integrated Raman intensity and low Λ. In a single specimen with smooth facets, Λ and Raman spectra intensity are relatively uniform, with variations around 10% (see Λ and ARaman map in figs. S9 and S11). Free carriers, presumably resulting from impurities or vacancies, thus may reduce the thermal conductivity in each BAs sample even in our best specimens (32). We cannot, however, rule out the contribution from other crystal defects (e.g., point defects and clusters of point defects) in lowering Λ. In a high-Λ specimen such as Ia, however, theoretical predictions that relate defect density to Λ indicate that the point defect concentration should be low (33). Further improving the controllability of the carrier concentration in the growth of BAs could be an important path for enhancing the yield of BAs with high Λ. Future development of large-scale fabrication of BAs films by CVD using gas precursors may facilitate its widespread application in thermal management of high–power density electronic and optoelectronic devices.

Fig. 3 Raman spectra and thermal conductivity of BAs.

(A) Raman spectra of three representative BAs specimens, Ia, Id, and If. Specimen Id is measured to have a carrier concentration of 1.1 × 1020 cm–3 and a low thermal conductivity of 110 W/m·K. The black dashed squares indicate the range of the frequency between 1050 and 1150 cm–1 where the integration of the electronic Raman scattering intensity in (B), ARaman, is performed. The inset shows the magnified Raman spectra of the samples in (A) near the one-phonon peaks. (B) Thermal conductivity of BAs crystals from several growth batches versus integrated Raman spectra intensity ARaman. The data points for specimens in (A), the specimen on which we mapped Λ and ARaman (Ig; see figs. S9 and S11), and the specimens with measured hole concentrations (Id and Ie) are highlighted.

Supplementary Materials

www.sciencemag.org/content/361/6402/579/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S11

Table S1

References (3456)

References and Notes

  1. See supplementary materials.
Acknowledgments: We thank B. Janicek for help with STEM imaging measurement. Funding: Supported by Office of Naval Research (ONR) MURI grant N00014-16-1-2436. Thermal conductivity, Raman, and STEM research was carried out in part in Frederick Seitz Materials Research Laboratory (MRL) at the University of Illinois at Urbana-Champaign. S.L., X.L., and B.L. acknowledge support from U.S. Air Force Office of Scientific Research (AFOSR) grant FA9550-15-1-0236, and UT Dallas start-up funds. Author contributions: D.C. and B.L. conceived the project; S.L., X.L., and B.L. synthesized the materials; Q. Z, and D.C. performed TDTR and Raman measurements; Y.L. and P.H. performed STEM studies; X.W. and B.L. performed single-crystal analysis; D.C., B.L., S.L., and Q.Z. analyzed the results and co-edited the manuscript with input from all authors. Competing interests: Authors declare no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are available in the main text or the supplementary materials.
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