## Introduction

Heat dissipation has been a critical technology challenge for modern electronics for decades1,2,3,4,5,6,7. With information technology ramping up in an increasingly digitalized world, electronics cooling is scaling up rapidly in its impact on global energy consumption8,9. For instance, current data centers consumes over 200 TWh (terawatt-hour) of electricity annually but more than 50% of the total electricity is used for cooling, i.e., removing waste heat rather than for data storage or computing10,11. In all hierarchical electronic systems ranging from nanoscale transistors, smart phones, laptops, vehicle electronics, to data server farms, waste heat dissipates from the hot spots to heat sink across a series of thermal resistance of multiple device layers and their interfaces. As a result, the device performance, reliability, and energy efficiency can be strongly degraded by a large thermal resistance and a rising hot spot temperature. To address this challenge, recent key research focus for thermal management aims to develop thermal interfaces that enhances thermal coupling and minimize thermal resistance between heterogeneous components10. In general, high-performance thermal interface requires both high thermal conductivity (κ) and low elastic modulus (E). When inserted between an electronics layer and a heat sink (Fig. 1a), high κ minimizes thermal resistance and enhance heat dissipation, and low E enables good surface compliance, thermal contact area, and thermomechanical stability. Current commercial thermal interfaces, however, are usually limited by low κ ~ 1 W/m ∙ K or high E ~ 1 GPa, which largely constrains the cooling performance. In addition, emerging applications like wearable electronics and soft robotics require their thermal interfaces to be soft and flexible, but has yet to be explored12,13,14.

## Results and discussion

To achieve high performance, we first carefully examine the structural design of BAs particles to achieve efficient heat-dissipation pathways. Based on literature experience16, it has been shown that structural optimization is critical to the thermal conductivity of thermal interfaces: Polymer matrixes are generally soft to enable mechanical compliance, but their intrinsic low thermal conductivity (~0.2 W/m ∙ K) could reduce the overall thermal conductivity. In particular, when high conductivity fillers are randomly distributed, the heat-transfer paths in polymer could be significantly elongated and thereby minimize the contribution from fillers16. In addition, the organic–inorganic interfaces could result in thermal boundary resistance due to mismatch in phonon spectra and density of states between heterogeneous components33,34,35. As a matter of fact, this explains why typical industrial thermal interfaces have a low conductivity around 1 W/m ∙ K or below. To quantitatively evaluate the effect from structural design on the overall thermal conductivity, we performed multiscale simulation to calculate the thermal conductivity of the composite materials with varying extents of alignment of BAs fillers (Fig. 2f)33. The alignment is quantified by the standard deviation of distance (σ) from the BAs particles to the centerline of the alignment pillar, with σ approaching 0 for perfect alignment and increased σ for disorders36. A temperature gradient is applied across the structure to compute the volume-averaged heat flux density over the whole domain using the finite element analysis (Methods and Supplementary Information). The effective thermal conductivities of self-assembled boron arsenide (s-BAs) with varied extents of alignment are determined and plotted in Fig. 2f (pink shadowed background). The thermal conductivity and specific heat used in this simulation are all measured from experiment. The simulation results indicate that an effective design to achieve aligned fillers could effectively enhance the overall thermal conductivity of s-BAs.

To achieve rational alignment of BAs structures in the thermal interface, we designed a self-assembly based manufacturing method using the ice-template process (Fig. 2a). First, BAs particles were dispersed to form an aqueous suspension. The BAs aqueous slurry was subsequently transferred into a tube mold. A directional temperature gradient (e.g., from dry ice bath at the cold side to room temperature at the high temperature side) was applied across the mold that led the slurry to freeze. At the cold side, the nucleation of the ice crystals started and led to the formation of a constitutionally super-cooled zone directly ahead of the growing ice front. Such an unstable region eventually resulted in perturbations, breaking the planar ice front into a columnar structure; consequently, ice crystals start to follow the temperature gradient direction to gradually grow into aligned lamellar pillars. In the meanwhile, as driven by the growth of ice template37,38, BAs crystals are expelled and enforced into assembled arrays to replicate the morphology and fill the interspacing between the ice pillars. After this self-assembly process is complete, we dehydrated the sample using a freeze-drying process so that the aligned BAs structures were maintained. Thermodynamically, the freeze-drying process uses a low pressure and a low temperature below the equilibrium triple points in the phase diagram of water (i.e., 273.16 K and a partial vapor pressure of 611.657 Pa) to achieve sublimation of solid ice directly to vapor without going through a liquid phase, so that the structural distortion is minimized37,38,39. Finally, polymer melt was infiltrated into the BAs assembly and solidifies to enhance the mechanical supporting and form composite s-BAs. The resulting structures were carefully verified by cross-section scanning electron microscopy (SEM) images before (Fig. 2b) and after the assembly process (Fig. 2c), indicating that the aligned lamellar network of BAs pillars can be formed and well maintained during the processing. Note that this manufacturing approach allows readily preparation of inch-size s-BAs samples and further scaling up (Fig. 2d).

The thermal conductivity of s-BAs was measured using the standard laser flash method40. Figure 2e shows typical temperature rise curves for s-BAs with varied BAs volumetric loadings of 5%, 10%, 20%, 30%, and 40%, respectively. We have included detailed measurement results in Supplementary Table S1. The measurement verifies the high thermal conductivity of s-BAs (Fig. 2f): For example, a record-high thermal conductivity of 21 W/m·K has been measured for 40 vol% s-BAs, which represents ~20 times enhancement over typical thermal epoxies and greases as current industrial thermal interface standard. Consistent with our modeling design, the experimental results also show that the thermal conductivity of s-BAs was enhanced by over 400% through the self-assembled alignment versus random distribution. We also found that the overall thermal conductivity of the assembled s-BAs is dominated by that of BAs fillers, regardless of typical polymer matrix (elastomer, epoxy, etc.). Taking a typical thermal interface thickness of 100 μm, this leads to a total thermal resistance of 0.05 K·cm2/W, which is below most of the literature reports. For example, traditional materials based on greases, adhesive, gels, and phase change materials typically yield a higher resistance in the ranges of about 0.2–1, 0.15–1, 0.4–0.8, and 0.3–0.7 K·cm2/W, respectively24. Elastomic pad, silicone sheet, and thermal tapes typically have the total resistance range of about 1–4 K·cm2/W. The demonstrated performance of s-BAs is also record-high among other composites with various fillers including metals, ceramics, semiconductors, oxides, and nanomaterials16.

Further, we demonstrate the high flexibility of the s-BAs. A highly flexible thermal interface with both high thermal conductivity and high flexibility is required for thermal management applications in flexible electronics, soft robotics, and other emerging areas, which however remains to be demonstrated12,13,14. As shown in Fig. 3d, the s-BAs can be highly deformable to support uniaxial strains more than 500% stretching over its original size. In addition, the s-BAs can be compressed to random geometries such as a heart-shape circle (right, Fig. 3d) without leading to a mechanical breakdown, which is impossible for standard thermal interface materials. To further explore the potential application in flexible devices, we have performed thermal measurement of the s-BAs under cyclic mechanical bending of the sample (Fig. 3e), verifying the preserved high thermal conductivity. The thermal conductivity of our s-BAs sample maintains stability over at least 500 bending cycles with a maximum fluctuation within 7%. The persistent high thermal conductivity actually indicates the robust structures during bending tests, as verified by the cross-section SEM images taken after bending cycles (Supplementary Figure 1). The retention of highly efficient heat dissipation after mechanical bending underscores the promise of using s-BAs for thermal management of flexible devices.

As a further step, we demonstrated a proof of concept experiment to verify the superior device-cooling performance of the s-BAs, through the integration and in situ characterizations of a LED during its operation (Fig. 4). To make direct comparison, three types of thermal interfaces, i.e., the commercial thermal epoxy, silicone sheet, and our s-BAs (Methods) are integrated as sandwiched between a 10 W LED chip and a copper heat sink (Fig. 4a, b). Note that all thermal interfaces were chosen to be with the comparable size, thickness, etc. settings. An infrared camera was used to record the surface temperature of the LED chips, with the Cu heat sink maintained at the room temperature (23 °C). Figure 4c shows a series of infrared images after lighting up the LED chips, measuring the transient temperature dependence. With thermal epoxy and commercial silicone sheet, the chip surface temperature increased up to ~110 and 95 °C, respectively. In contrast, the stable temperature is much lower (~65 °C) when the BAs composite was used as the thermal interface. Quantitatively, the time-dependent surface temperature of the LED chip was measured based on the infrared images and plotted in Fig. 4d, showing a dramatic increase for the devices integrated with thermal epoxy and silicone sheet comparing to that with s-BAs. The large contrast in hot spot temperature difference clearly demonstrates the superior cooling capability of the developed s-BAs for future thermal management applications.

In conclusion, we developed a high-performance thermal interface material fabricated through a scalable self-assembly based manufacturing of the recently developed high-thermal-conductivity BAs for advanced thermal management. The s-BAs exhibits an unprecedented combination of high thermal conductivity (21 W/m · K) and an excellent elastic compliance similar to that of soft biological tissues (elastic modulus ~100 kPa). Our thermal and mechanical experiments together with multiphysics modeling show that, upon the designed alignment of BAs crystals, the thermal interface preserves efficient heat-transfer paths while maintaining the high mechanical compliance of polymer matrix. Moreover, the s-BAs shows high flexibility that could be applied to emerging applications such as efficient thermal management of flexible electronics and soft robotics.

## Methods

### Synthesis of cubic BAs crystals

BAs crystals were prepared through chemical vapor transport. High-purity boron and arsenic coarse powders (Alfa Aesar) were ground by using mortar and pestle, prior to introduction into a quartz tube at a stoichiometric ratio of 1:2. After we loaded our reaction sources, the quartz tube was evacuated and flame sealed under high vacuum (10−5 Torr) before placement into a customized three-zone furnace for synthesis around 1033~1058 K. More details regarding the synthesis can be found in our recent publication3. The particle sizes of BAs crystals can be well controlled using growth conditions and, for this work the size range of BAs crystals is mainly distributed around 5~10 μm (inset, Fig. 2b).

### Fabrication of BAs polymetric composites

BAs aqueous slurry was prepared through the mixture of BAs powders and the solution, followed by sonication for 1 h and degasification in vacuum. Next, the BAs aqueous slurry was transferred into a sealed mold and frozen directionally using liquid nitrogen. Further, the sample was dehydrated using the freeze-drying process for 48 h in a freeze-dryer (Labconco, USA) to form the BAs assembly. The epoxy resin monomer (EPIKOTE Resin 862) was mixed with the curing agents (EPIKURE Curing Agent W) at a weight ratio of 100/20, and then infiltrated into the BAs assembly. After that, the sample was cured at 80 °C and 120 °C each for 2 h to form a composite structure of s-BAs. In addition, s-BAs samples were prepared and measured using different polymer matrixes, including epoxy, polydimethylsiloxane (PDMS), and elastomer (Ecoflex), and they show consistent thermal measurement results.

### Structural characterization of materials

SEM images were obtained with a field-emission SEM instrument (SU-3500, Hitachi). Transmission electron microscope (TEM) samples were prepared by using a focused ion beam (FIB) machine (Nova 600, FEI). After cleaning, we took the high-angle annular dark-field (HAADF) image by using aberration-corrected high-resolution scanning TEM (Grand ARM, JEOL, 300 kV).

### Thermal measurements

Specific heat is measured using a differential scanning calorimeter (TA Instruments, 2920) with a temperature increase rate of 5 °C/min from room temperature to 100 °C. Thermal diffusivity were measured using a standard laser flash setup, where a pulse laser irradiation was used to heat the composites from one side, and time-dependent temperature was recorded at the back end. For laser flash measurement, experimental conditions are carefully designed to ensure reliable analysis. Cross-validation on both thick and thin samples are performed and show consistent measurement results. For thick samples, a large laser-heating size and insulated sample boundary are applied, so that the whole sample is uniformly heated up and heat conduction is through the whole cross-section making a one-dimensional temperature profile. Meanwhile, the samples were placed in vacuum to avoid the heat loss to the environment. By recording the temperature rise at the rear side, the thermal diffusivity α can be calculated by the following Eq. (1):

$$\alpha = \frac{{1.38d^2}}{{\pi ^2t_{0.5}}}$$

where d is the sample thickness and t0.5 is the characteristic time for the sample to heat up to the half of the maximum temperature on its rear surface. The thermal conductivity (κ) can be determined after the measurement of mass density ρ, specific heat cp, and the thermal diffusivity α, following Eq. (2): κ = αρcp.

### Thermal images of device temperatures

Transient temperature distributions near the hot spot of LED devices were taken by a calibrated infrared camera (FLIR A655sc). For comparison, three thermal interfaces including commercial thermal epoxy, silicone pad, and s-BAs were used. All samples were prepared in the same size and the LED chips were operating under the same conditions. The surface temperatures were calculated directly from the obtained videos and images by using the FLIR Tools+ (FLIR) and ImageJ (NIH) software packages. All variants of the experiments were performed for at least three different videos, verified with consistent results obtained in each instance.

### Thermal modeling

The effective thermal conductivity of the composite materials with varying extents of alignment is modeled by solving the heat conduction equation using the finite element method. The positions of BAs particles are distributed using random functions. The extent of alignment is quantified by the standard deviation of BAs particles to the averaged centerline upon alignment. Normal distribution function is used in the direction perpendicular to the alignment. The volume-averaged heat flux density over the whole domain was calculated under a given temperature gradient, and was consequently used to determine the effective thermal conductivity. The input thermal conductivity and specific heat used in this modeling are all measured from the experiment.

### Mechanical measurements

Mechanical properties were measured in the tensile mode with an Instron 5542 mechanical tester (Instron Corp., Norwood, MA) with a gauge length of 10 mm at a loading rate of 1 mm/min. All the samples were cut into 30 mm long segments. At least three samples were tested for each experimental condition to obtain statistically reliable values.

### Mechanical simulation

The Young’s modulus and shear modulus were modeled using the finite element method36, and under the same geometric model as the thermal model. For simulation, one end of the structure is fixed and the other end is applied with force to give the deformation. For the simulation of Young’s modulus, a normal force is applied and the axial deformation of the structure is computed. For simulation of the shear modulus, a shear force is applied and the shear deformation of the structure is computed. The effect of alignment of BAs particles on the mechanical properties were examined in the same setting as the thermal modeling, where the extent of alignment is quantified by the standard deviation of BAs particles.