We have grown c-BAs single crystals up to 1000 μm size by the chemical vapor transport (CVT) technique using combined As and I2 transport agents with the As:I ratio of 1:3 under gas pressures of up to 35 atm. Raman spectroscopy revealed a very sharp (∼2.4 cm−1) P1 phonon mode and an interesting splitting behavior of P1 from detailed polarization studies. Electron paramagnetic resonance (EPR) experiments revealed no evidence for EPR active growth-related defects under the experimental resolution. Finally, a moderate thermal conductivity value of ∼132 W/m-K was obtained using a transient thermal grating technique. These results suggest that although the high As gas vapor pressure environment in CVT growth can increase the transport rate of c-BAs significantly, it may not be efficient in reducing the defects and enhancing the thermal conductivity in c-BAs significantly.

In the modern microelectronics industry, with devices characterized by decreasing dimensions and increasing output power densities, it is crucial that the electronic packaging can dissipate heat rapidly to avoid overheating. As a result, high thermal conductivity materials which can conduct heat to the ambient environment expeditiously are under intensive investigation. The record room-temperature thermal conductivity (κRT) is still held by diamond. Its value of about 2000 W/m-K is almost five times that of the widely used conventional heat conductor copper. However, the technical difficulty and the enormous cost in synthesizing diamond to large dimensions have hindered its massive commercial applications. Recently, it has been proposed that materials with a large acoustic-optic phonon energy gap and bunching of the acoustic phonon dispersion branches can significantly reduce phonon-phonon scattering, and thus enhance the thermal conductivity dramatically. Among the family of these materials, based on first principles calculations,1–3 c-BAs was predicted to have a κRT reaching ∼2000 W/m-K with only three-phonon scattering and ∼1400 W/m-K when four-phonon interactions are also included.4 Later on, the phonon dispersion of c-BAs single crystals measured by inelastic x-ray scattering confirmed a large acoustic-optical frequency gap and bunching of the acoustic branches, supporting the theoretical prediction that c-BAs is a potential superthermal conductor.5 

However, it is challenging to grow c-BAs single crystals into large sizes with favorable κRT. Although the binary phase diagram of boron and arsenic was constructed several years ago,6–10 due to the high melting point of B, the high vapor pressure of As and the low irreversible decomposition temperature of c-BAs (920 °C),11 it is difficult to grow sizable c-BAs single crystals with low concentrations of defects. The chemical vapor transport (CVT) method with I2 as the transport agent has been the only growth technique which was reported to produce bulk c-BAs single crystals. In 2015, Lv et al. reported that c-BAs single crystals up to ∼200 μm size could be grown by the CVT method with iodine as the transport agent.12 The κRT values of ∼200 W/m-K, obtained from the time-domain thermoreflectance (TDTR) technique, were one order of magnitude smaller than the theoretical prediction. A c-BAs rod with a diameter of 1.15 μm measured by the standard four point technique shows a κRT of ∼186 W/m-K.13 Recently, the TDTR technique performed on crystals up to 400–600 μm grown by a seeded CVT method reported a higher κRT of ∼351 W/m-K.14 

Although significant progress has been made in the last couple of years, the size of c-BAs crystals is still in the 500 μm range and the κRT is poorly enhanced. It remains a big challenge to make c-BAs larger and purer. Due to the high vapor pressure of As, it was postulated that As deficiency may be a major source of defects in c-BAs that act to reduce κRT.12 To suppress the As deficiency and increase the transport rate of the CVT process, with the hope that a higher density of As vapor may help lower the possible As deficiency, we optimized the CVT growth process using I2 and extra As as the transport agents under various pressures much higher than 1 atm. Sizable single crystals were grown using an As:I ratio of 1:3 under high gas pressures of up to 35 atm. Single crystal x-ray diffraction, Raman spectroscopy measurements, electron paramagnetic resonance (EPR) as well as transient thermal grating (TTG) measurements were performed to investigate the sample quality and the thermal conductivity of single crystals grown under gas pressure.

The high purity B chunks (99.9999%, Alfa Aesar), As chunks (99.9999%, Alfa Aesar), and I2 pieces (99.999%, Alfa Aesar) were used in the growth. First, the As chunks were further purified by the CVT method to remove the possible oxidized surface layers. They were sealed inside a quartz tube under vacuum. Then, the source end was set to 600 °C and the sink end was set to 400 °C. After several hours, shiny purified arsenic chunks were collected at the sink end. Secondly, B chunks, As chunks or small c-BAs single crystals with I2 were mixed according to various molar ratios shown in Table I. The mixture was then sealed in the quartz tube under vacuum. The tube length is around 15 cm. The sink and the source end were slowly heated up to 800 °C and 900 °C by 60 °C per hour, respectively. The whole handling process was performed inside a glovebox and the growth took place in a two-zone furnace inside a fume hood. During the CVT growth, the reaction can be described as

BAs(s)+3/2I2(g)BI3(g)+1/4As4(g).
(1)

After two to three weeks, three dimensional c-BAs single crystals could be found at the sink end.

TABLE I.

CVT growth conditions: ID and OD refer to the inner and outer diameters, respectively, of the quartz tubes used in various growths.

BatchAs/IID (mm)OD (mm)P (atm)Maximum size (μm)
JX089 1/3 14 16 10 ∼500 
JX092 14 16 10 ∼300 
JX093 14 16 10 ∼300 
JX120 1/3 14 18 25 ∼800 
JX158 1/3 19 23 35 ∼1000 
BatchAs/IID (mm)OD (mm)P (atm)Maximum size (μm)
JX089 1/3 14 16 10 ∼500 
JX092 14 16 10 ∼300 
JX093 14 16 10 ∼300 
JX120 1/3 14 18 25 ∼800 
JX158 1/3 19 23 35 ∼1000 

To optimize the CVT growth, we varied the pressure and the As/I ratio inside the quartz tube as listed in Table I. We used Avogadro's ideal gas law to roughly estimate the pressure inside the quartz tube

P=PAs4+PI2=(nAs4+nI2)RT/V,
(2)

where V is the volume of the quartz tube, T is set to 1173 K, nAs4 is one quarter of the molar amount of As inside the tube, while nI2 is the molar amount of I2.

With gas pressures up to 35 atm, the maximum size of crystals that can be reached is ∼1000 μm, which is almost double the maximum size reported in the literature.12,14 From Table I, we can conclude the following: First, under the same pressure, the largest single crystals were grown at the As/I = 1:3 ratio. This ratio, coincidentally, equals the stoichiometric ratio of AsI3, implying that AsI3 may play an important role in this transport process. A previous Raman spectroscopy study indeed suggested this possibility.15,16 Second, larger c-BAs crystals were obtained with increasing gas pressures. Apparently, the higher pressure increases the transport rate such that larger single crystals were grown during the same growth period.

A piece of c-BAs from batch JX120 is shown against a 1 mm scale in the left inset of Fig. 1. A well-defined triangular flat surface of around 800 μm can be observed. An X-ray diffraction pattern was made on this surface, as shown in Fig. 1. The index of these two peaks suggests that this triangular surface is the (111) plane. The right inset of Fig. 1 shows the reciprocal map of the (0kl) plane obtained by single crystal X-ray diffraction. Based on the structural refinement, one can say that the space group and the lattice parameter are similar with previous experimental measurements. Unlike the previous study with multiple twin domains in the crystals,12 multiple 30 μm-sized pieces we measured using single crystal X-ray diffraction all show a single domain.

FIG. 1.

The X-ray diffraction pattern obtained on the triangular surface of a single crystal shown in the left inset. Left inset: A c-BAs single crystal against a 1-mm scale. Right inset: The reciprocal single crystal X-ray diffraction patterns for the (0kl) plane.

FIG. 1.

The X-ray diffraction pattern obtained on the triangular surface of a single crystal shown in the left inset. Left inset: A c-BAs single crystal against a 1-mm scale. Right inset: The reciprocal single crystal X-ray diffraction patterns for the (0kl) plane.

Close modal

Although it remains a challenge to unambiguously identify the various defects in c-BAs and give a direct quantitative measure of the B/As ratios, Raman spectroscopy at room temperature was performed in order to obtain an additional measure of the crystalline quality of these c-BAs bulk samples. The Raman experiments were done using 488 nm laser light excitation with 2 mW power focused to a diameter of approx. 0.7 μm. The spectra were obtained in the typical backscattering geometry with incident and scattered light propagating normal to the sample surface. The Raman spectrum observed for sample JX089 with parallel incident and scattered light polarizations (eies) is shown in the right inset of Fig. 2(a). The two peaks labeled P1 and P2 at 698 cm−1 and 718 cm−1, respectively, are very similar to those reported previously for CVT-grown single crystalline c-BAs by another group.17 The features were assigned to 11B-like (P1) and 10B-like (P2) T2 phonon vibrational modes, respectively. Two main differences in the present samples are noted. First, a much larger P1/P2 intensity ratio is seen. Second, the FWHM value (∼2.4 cm−1) of the P1 phonon mode from JX089 is about half that observed for the c-BAs crystals reported in Ref. 17. The reduced linewidth suggests an improvement in the crystalline quality on employing this CVT growth method under elevated gas pressures. The weak intensity of the P2 phonon mode observed for sample JX089 is also reflected by its absence in the two-phonon Raman spectral region around 1400 cm−1.

FIG. 2.

Raman spectra obtained on batch JX089 for (a) parallel incident and scattered light polarizations (eies) and (b) crossed incident and scattered light polarizations (eies). Starting with the left most spectrum observed with θ = 0°, each of the subsequent spectra measured at 10° increments is shifted by 7 cm−1 to a higher energy to best illustrate the changes with the polarization angle (θ). Left inset of (a): The 35 μm × 40 μm optical image of the sample. θ = 0° refers to ei parallel to a vertical edge outlined by the red rectangular box. The arrow indicates the spot where the Raman spectrum was measured. Right inset: The Raman spectra of eies with θ=90° in an extended Raman shift region.

FIG. 2.

Raman spectra obtained on batch JX089 for (a) parallel incident and scattered light polarizations (eies) and (b) crossed incident and scattered light polarizations (eies). Starting with the left most spectrum observed with θ = 0°, each of the subsequent spectra measured at 10° increments is shifted by 7 cm−1 to a higher energy to best illustrate the changes with the polarization angle (θ). Left inset of (a): The 35 μm × 40 μm optical image of the sample. θ = 0° refers to ei parallel to a vertical edge outlined by the red rectangular box. The arrow indicates the spot where the Raman spectrum was measured. Right inset: The Raman spectra of eies with θ=90° in an extended Raman shift region.

Close modal

To further investigate the P1 peak, a detailed Raman polarization study was carried out on the c-BAs sample JX089 by simultaneous rotation of the incident light and analyzer light polarizers by 200° in 10° increments. The series of spectra obtained for both eies and eies are shown in Figs. 2(a) and 2(b), respectively. Most notably, as shown in Fig. 2(a), with eies, a clearly resolved splitting of ∼2–4 cm−1 for the P1 peak near 700 cm−1 is found for θ between 0° (130°) and 50° (180°). Such splitting behavior was not observed for the Raman spectra obtained with eies as shown in Fig. 2(b). (We believe that the spectrum with θ = 80° was performed with a misalignment error such that ei was not perpendicular to es.) In addition, similar behavior was observed for several spots probed in this region of the sample. The exact cause of the 2–4 cm−1 splitting behavior of P1 peak is not known. We note that a LO-TO splitting of the T2 phonon mode of no more than 4 cm−1 was predicted by density-functional perturbation theory (DFPT) lattice dynamic simulations as discussed in Ref. 16. However, it is puzzling that such splitting was not observed for all polarization angles. Thus, we suggest that the splitting of the P1 peak may be caused by growth-derived local strain fields.

The nature of the defects possibly present in these c-BAs crystals was also investigated by electron paramagnetic resonance (EPR). In principle, a defect with an unpaired electron spin is EPR-active. These could be impurities, lattice point defects (such as anti-sites, vacancies, interstitials), or even a complex consisting of an impurity paired with a lattice defect. Therefore, EPR was carried out for the B source, samples JX089 and JX120 at 6 K, on a commercial (E-300) Bruker 9.5 GHz spectrometer. A large signal with a Zeeman splitting g-value of 2.003 and a concentration of 2 × 1018 cm−3 estimated using a P-doped Si standard was found for the B source material as shown in Fig. 3. This defect was reported several years ago for undoped and C-doped β-rhombohedral boron and was assigned to carbon-related centers.18–21 However, EPR-active signals were not found for both c-BAs crystals. Based on the usual EPR detection limit of ∼5 × 1011 spins and the measured c-BAs masses of ∼2 mg, we estimate an upper (EPR-active) defect concentration limit of 1.2 × 1015 cm−3. An alternative explanation for the missing EPR signal could be that the lattice defects are EPR-inactive under dark conditions when other charges are around (from residual n- or p-type impurities) and get trapped in those lattice defects, leaving the defects in an EPR-inactive charge state. Thus, we plan to perform photo-EPR experiments in the future on the c-BAs crystals to see if any defects can be made EPR-active through a possible change in their charge state after light excitation.

FIG. 3.

EPR spectrum obtained at 6 K for the boron source material used in the synthesis of c-BAs crystals.

FIG. 3.

EPR spectrum obtained at 6 K for the boron source material used in the synthesis of c-BAs crystals.

Close modal

To measure the thermal conductivity of the c-BAs samples, we employed an optical pump-probe technique called transient thermal grating (TTG), in a reflection geometry (inset of Fig. 4).22 Briefly, two pulsed pump laser beams (515 nm, 60 ps pulse duration, 1 kHz repetition rate) with pulse energies of up to 3 μJ are crossed at the surface of the sample, whereby beam interference and subsequent absorption create a sinusoidal temperature profile in the material. This sinusoidal temperature profile results in a corresponding sinusoidal surface displacement profile due to thermal expansion of the heated regions, yielding a transient optical grating. The time evolution of this thermal grating is then monitored by diffraction of a quasi-continuous 532 nm probe laser beam. The diffracted signal is detected in a heterodyne scheme by an avalanche photodiode and recorded. TTG typically measures the heat flow parallel to the sample surface and is sensitive over a cross-plane depth of approximately L/π, where L is the grating period. A grating period of 4.25 μm was used for our measurements. The thermal conductivity accumulation in BAs essentially saturates at a phonon mean free path of this value.2 Given the small absorption coefficient and a large penetration depth of 515 nm light in c-BAs,23 the measured thermal transport was assumed to be 1-dimensional, in which case the TTG signal follows the relation:

I(t)eαq2t,
(3)

where α is the thermal diffusivity and q=2π/L is the wavenumber of the grating. As a result, fitting the measured decay of the TTG signal to an exponential function directly yields the thermal diffusivity, which further leads to thermal conductivity as κ=Cα, where C is the computed volumetric specific heat.

FIG. 4.

Thermal conductivity measurements using transient thermal grating technique. The inset is an illustration showing how the thermal grating is formed. The pump and probe beams are about 100 μm in diameter on the sample surface. The oscillation in the gray line is due to surface acoustic waves that are also generated by the pump beams which is well understood.22 The decay curve corresponding to the best fit thermal conductivity is shown, as well as curves with 12% deviations from the best fit.

FIG. 4.

Thermal conductivity measurements using transient thermal grating technique. The inset is an illustration showing how the thermal grating is formed. The pump and probe beams are about 100 μm in diameter on the sample surface. The oscillation in the gray line is due to surface acoustic waves that are also generated by the pump beams which is well understood.22 The decay curve corresponding to the best fit thermal conductivity is shown, as well as curves with 12% deviations from the best fit.

Close modal

The as-grown crystals were finely polished before the TTG measurement and the room-mean-square roughness was measured to be about 7 nm over 30 μm × 30 μm areas. The measured area is ∼100 μm, which is the size of the probe beam on the sample. Due to the large laser spot, we only measured the thermal conductivity on one region with the best surface condition in one crystal. Figure 4 shows a TTG measurement of a JX120 sample, from which we obtained a thermal conductivity of 132 W/m-K. We considered the statistical error, the power error, and the error associated with assuming one-dimensional heat transport, and obtained a total error of about 12% in the thermal conductivity. The computed decay curves corresponding to a plus or minus 12% deviation from the best-fitted thermal conductivity are also presented in Fig. 4. Similar or smaller values were measured from a few other pieces, indicating that our c-BAs crystals, although large, feature moderate thermal conductivities compared to the crystals in Refs. 12 and 14 grown at ambient gas pressure. Under high As vapor pressure, it is reasonable to suppose that As deficiencies in c-BAs will be reduced and thermal conductivity will be enhanced if they are indeed the major defects here. However, from our experiment, although the high As gas vapor pressure environment in CVT growth can enhance the transport rate of c-BAs significantly, it has little effect in increasing the thermal conductivity. This suggests that As deficiencies may not be the dominant defects to reduce the thermal conductivity in c-BAs as it was proposed.12 Furthermore, we should also keep in mind that at high gas pressures, diffusion is no longer the major growth mechanism in the CVT growth process. Instead, convection dominates. Even if As deficiency was significantly decreased in the As-rich environment, the convection growth mechanism may lead to higher concentrations of other types of defects in the as-grown samples; thus, as a compromise, reduced thermal conductivity can be obtained. Further systematic investigation, such as STEM, may be needed to help understand the defect mechanisms. Besides defects, the other possible reason for the reduced thermal conductivity may arise from the formation of multiple grains in the measurement area of the sample. On some of the samples, we have indeed observed grain boundaries using back-scattered electron microscopy.

In conclusion, c-BAs single crystals up to ∼1000 μm size were grown by CVT technique under elevated gas pressures of up to 35 atm using an As:I ratio of 1:3 as the transport agent. Raman spectroscopy revealed a sharp P1 peak originating from the 11B T2 phonon mode, suggesting good crystalline quality. A unique splitting behavior of the P1 peak was revealed by the Raman polarization study, which may be caused by growth-derived local strain fields. EPR did not reveal evidence for any measurable EPR active defect-related signals under the current experimental conditions and detection limits. Finally, a moderate thermal conductivity value at room temperature of 132 W/m-K was found, suggesting that the As-rich environment may not be effective in reducing the defects in c-BAs. As a result, alternative growth routes are required to approach the recent predictions of ultra-high κRT values for c-BAs.

See supplementary material for sample surface conditions measured by atomic force microscopy and the grain boundaries in some c-BAs crystals imaged by scanning electron microscopy.

The work at UCLA and MIT was funded by the Office of Naval Research under a MURI Grant No. N00014-16-1-2436. The work at NRL was supported by the Office of Naval Research. The authors thank Alexei Maznev for many helpful discussions about using TTG to measure the BAs samples.

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Supplementary Material