This paper (arXiv 2402.00248) by Songrui Hou, Fengjiao Pan and twelve co-authors reports cubic Boron Arsenide (BAs) crystals that conduct heat better than any previously measured, and then asks a sharper question than "how high?": how fast does that conductivity fall as the crystal warms up? The answer, a fall proportional to 1/T² between 300 K and 600 K, is a little steeper than current theory predicts. The crystals were grown in the group of Zhifeng Ren at the University of Houston; the thermal measurements were led from the University of California, Riverside, with collaborators at UCLA and the University of Illinois Urbana-Champaign. Chen Li, Ren and Richard B. Wilson are the corresponding authors.
What the paper reports
- A room-temperature thermal conductivity of about 1500 W m⁻¹ K⁻¹ in boron-11-enriched crystals. The authors contrast this with earlier experimental values of 1000 to 1300 W m⁻¹ K⁻¹ and with a first-principles prediction of about 1330 W m⁻¹ K⁻¹ for isotopically pure material.
- More than fifty crystals were measured; four of them exceeded 1400 W m⁻¹ K⁻¹.
- In the best crystals the conductivity scales as 1/T² from 300 to 600 K, against a predicted exponent between 1.7 and 1.8 for isotopically pure boron arsenide.
- Even the 1500 W m⁻¹ K⁻¹ crystals show optical signatures of defects.
Why the temperature exponent matters
The paper's logic rests on a simple contrast. Scattering of heat-carrying lattice vibrations (phonons) by defects does not depend on temperature; scattering of phonons by other phonons does. A defect-laden crystal should therefore have both a lower room-temperature conductivity and a flatter decline on heating. The authors note that earlier studies did not line up this way: one group reported 1300 W m⁻¹ K⁻¹ with an exponent of 1.3, another 1160 W m⁻¹ K⁻¹ with an exponent of 2. They read that mismatch as a sign of differing systematic errors between laboratories, and present their own work as a single consistent survey across crystals of varying purity.
The exponent also says something about which scattering process is in charge. Where three-phonon collisions dominate, as in most pure crystals, conductivity falls roughly as 1/T. Four-Phonon Scattering rates rise with the square of temperature, pushing the exponent towards 2. The paper cites boron phosphide (1.4) and indium phosphide (1.5) as rare examples above 1, and measured 1.2 for its own diamond control sample.
How the crystals were made and measured
The crystals were grown by chemical vapor transport, with three stated changes from the group's earlier recipe: the isotopically enriched boron, the arsenic and the iodine were given additional treatment to remove contaminants such as carbon, oxygen and sulfur; the arsenic-to-boron ratio was raised to reduce arsenic deficiency; and the crystals were removed mechanically instead of by a soak in aqua regia lasting over 24 hours, which the authors suspect had introduced point defects. The resulting samples are small: hundreds of microns across and tens of microns thick.
That size rules out conventional steady-state methods, so conductivity was measured by time-domain thermoreflectance (TDTR), a pump–probe laser technique, using a 783 nm laser modulated at 10.7 MHz. The authors describe several cross-checks: a separate beam-offset TDTR measurement of in-plane conductivity on the best sample (BAs-1500); a second 1500 W m⁻¹ K⁻¹ crystal (B7N2) showing the same temperature dependence; repeat runs on different dates; an atomic force microscopy roughness of 1.8 nm; and a test of laser spot size, where shrinking the spot from 15 to 1.7 μm lowered the apparent room-temperature value by about 20% and had no effect at 450 or 600 K.
Four further crystals, with room-temperature values of 1350, 1200, 1000 and 700 W m⁻¹ K⁻¹, showed progressively weaker temperature dependence, the trend expected if defects are responsible for the lower values.
The gap with theory
The authors describe the disagreement as minor. Measured and predicted conductivities differ by less than 15% at every temperature, but the measured exponent is 20% higher than predicted. They weigh three explanations:
- Four-phonon scattering may be stronger relative to three-phonon scattering than calculated. The paper notes that such calculations, though free of fitting parameters, are sensitive to computational choices.
- Processes of still higher order may contribute. The paper records that Ravichandran and David Broido expect these to be negligible, but adds that they "have not yet been carefully explored."
- The phonon spectrum itself might shift on heating. The authors consider this unlikely, since their Brillouin and Raman measurements show frequency changes below 1% from 300 to 600 K. They concede that those techniques do not probe the high-frequency acoustic phonons that carry most of the heat.
Four-phonon scattering acting alone is excluded: the paper says that limit would imply a conductivity around 1.5×10⁴ W m⁻¹ K⁻¹, an order of magnitude above what is observed.
Defects in the best crystals
To look for defects, the team shone 1.58 eV laser light, about 0.26 eV below the 1.84 eV band gap, on uncoated crystals. A perfect crystal should absorb almost nothing at that energy, so any transient reflectivity microscopy (TRM) signal points to impurity states. Most samples gave a signal, including the 1500 W m⁻¹ K⁻¹ ones, whose response was of the same order as gallium phosphide doped with roughly 10¹⁸ cm⁻³ zinc. Control crystals behaved as expected: large signals for silicon and gallium arsenide, negligible ones for gallium phosphide and gallium nitride.
The link between TRM signal and conductivity is described as rough. TRM maps varied by orders of magnitude across a crystal while conductivity stayed within ±20%, and one crystal near 800 W m⁻¹ K⁻¹ gave almost no signal. Photoluminescence showed no clear correlation either. The authors' interpretation is that some point defects alter optical absorption with little effect on heat flow, and the reverse. They cite earlier work identifying carbon, silicon, oxygen and iodine impurities, and calculations that a 10% conductivity loss would need on the order of 3×10¹⁷ to 3×10¹⁸ cm⁻³ of particular defects. The paper does not discuss the antisite pairs covered in Antisite Defects in Boron Arsenide.
What it does and does not establish
The paper documents a measured value and a temperature trend, corroborated by a second method and a second crystal within the same collaboration. It does not quantify defect concentrations: the authors call the TRM method "only qualitative" and state that whether the remaining defects impede heat flow is not known. They suggest that, if the concentration exceeds about 10¹⁸ cm⁻³, the intrinsic conductivity could be above 1500 W m⁻¹ K⁻¹ and the intrinsic temperature dependence steeper than 1/T². The underlying data are available from the authors on request, not publicly deposited.
For the wider dossier, the result complicates the tidy story in Ultrahigh Thermal Conductivity in Boron Arsenide and Boron Arsenide Claims vs. Evidence: Measured Values, Patent Claims and the Theory–Experiment Gap: here experiment sits slightly above the latest theory instead of below it. It also bears on Isotope Enrichment and Thermal Conductivity, since the crystals are both boron-11 enriched and grown by a cleaner process, and the paper does not separate the contribution of each.
Source notes & attribution
- https://arxiv.org/pdf/2402.00248