Optical properties of cubic boron arsenide

Advanced electronic and optoelectronic technologies often demand higher carrier mobilities, wider energy bandgaps, and higher thermal conductivities, which are found in a range of unconventional materials beyond silicon. In particular, III–V semiconductors such as gallium arsenide (GaAs) and gallium nitride (GaN) are proven to be key to diverse applications from efficient solar cells and solid-state lighting to high-power and high-speed transistors. In the III–V family, cubic boron arsenide (BAs) remained largely unexplored for decades because of challenges in crystal growth. However, BAs has recently drawn considerable attention due to the theoretical prediction and experimental demonstration of an ultrahigh thermal conductivity (∼1200 W m⁻¹ K⁻¹).^1–4 Moreover, ab initio simulations predicted simultaneously high electron (∼1400 cm² V⁻¹ s⁻¹) and hole mobilities (∼2100 cm² V⁻¹ s⁻¹) in BAs⁵ that can be further increased by strain.⁶ These properties combined with an electronic bandgap^7–12 around 1.5 eV to 2 eV make BAs promising for future electronics and optoelectronics.

Despite progress in the study of heat and charge transport in BAs, its optical properties remain barely explored. Here, we grew high-quality millimeter-sized BAs crystals and systematically measured the complex dielectric function in the ultraviolet, visible, and near-infrared spectral range using spectroscopic ellipsometry combined with transmission and reflection spectroscopy. We further performed computations based on density functional theory (DFT) and many-body perturbation theory with quasiparticle and excitonic corrections. We obtained a refractive index around 3.0–3.5 in the visible range, comparable to other III-V semiconductors. We measured an indirect bandgap of 2.02 eV and a direct bandgap of 4.12 eV, which agreed well with our calculated values of 2.07 eV and 4.25 eV, respectively. We observed strong absorption for photon energies higher than the indirect gap. We also found that excitons have a sizeable effect on the direct absorption in BAs, in agreement with previous estimates of exciton binding energies around 40 meV.^7,13

We grew BAs crystals [Figs. 1(a) and 1(b)] using a seeded chemical vapor transport (CVT) technique.¹⁴ The samples were a few millimeters in size with thicknesses ranging from a few micrometers for thin transparent platelets to hundreds of micrometers for opaque bulk crystals. A clean, flat, and smooth surface is key to accurate optical characterizations. We sequentially treated the as-grown samples with hydrochloric acid, acetone, isopropanol, and oxygen and argon plasma cleaning. The high crystal quality of the samples was verified by Raman spectroscopy [Fig. 1(c), Horiba LabRAM] and single-crystal x-ray diffraction (XRD) [Fig. 1(d), Rigaku D/max-IIIB]. All the Raman and XRD peak positions agree well with literature values.^2–4 The Raman peak around 699.5 cm⁻¹ shows a full width at half maximum (FWHM) of 1.1 cm⁻¹, and the rocking curve around the (111) XRD peak shows a FWHM of 0.06°, indicating a relatively low level of crystal imperfections. Samples with flat, specularly reflecting surfaces were selected for further examination using atomic force microscopy (AFM, Veeco Dimension 3100). The root-mean-square (RMS) surface roughness was measured to be 2 nm over a 50 μm × 50 μm scanning area [inset of Fig. 1(b)], good for the intended optical studies.

To characterize the optical response of the BAs crystals, we began with spectroscopic ellipsometry.¹⁵ A variable-angle rotating compensator ellipsometer in the polarizer-compensator-sample-analyzer configuration (Woollam M-2000D) was employed to measure the ellipsometry angles $ψ$ and $Δ$ in the wavelength range of 190 nm to 1000 nm (1.2 eV–6.5 eV). More details and control experiments using a standard silicon wafer are provided in the supplementary material. We measured six opaque BAs samples, each at three random spots. Good agreement was observed among all samples. For each measurement, we collected data at a 20 Hz acquisition rate for over 60 s to achieve a good signal-to-noise ratio. In addition, we performed measurements at multiple incident angles (65°, 70°, and 75°) to further improve the reliability of our results. The ellipsometry angles and the corresponding dielectric functions (⁠$ε=ε1+iε2$⁠) measured from a representative BAs sample (#c4) are shown in Fig. 2. Although the ellipsometry angles at different incident angles largely differ, the extracted dielectric functions agree well.

Ellipsometry is highly sensitive to the sample surface. To better capture the bulk properties, we further performed transmittance (T) and reflectance (R) measurements on thin BAs platelets. A custom-built setup with an optical parametric amplifier (OPA, Light Conversion Orpheus) as the light source and a commercial UV-Vis-NIR spectrophotometer (Agilent Cary 5000) was used. Experimental details and control measurements using a 2 μm-thick silicon membrane are described in the supplementary material. Two BAs platelets (sample #c2 and #c10) were characterized using the custom-built setup [inset of Figs. 3(a) and S4]. In addition, a third BAs sample (#f1) was characterized using the commercial spectrophotometer (Fig. S4). Figure 3 summarizes all the measured complex refractive index (⁠$ñ=ε=n+ik$⁠) for BAs, along with results from our DFT simulations. At wavelengths longer than 300 nm, the measured refractive index n approaches the computed curve and converges to a constant refractive index n₀ (3.04 ± 0.02) in the near-infrared region. In the visible range, the extinction coefficient k from the T/R measurement and the DFT calculation are both very small (close to zero) [see detailed comparison in Fig. 4(b)]. The measured k values from ellipsometry are generally larger than the DFT calculation, but are closer to the computed result when excitonic effects are considered at wavelengths shorter than 300 nm. Some possible reasons are discussed later.

The procedure for calculating the quasiparticle bandgaps and band structure of BAs is detailed in previous work.⁷ We calculated the imaginary part of the dielectric function (ε₂$)$ due to direct interband optical transitions¹⁶ by interpolating the quasiparticle band structure and velocity matrix elements using the maximally localized Wannier function¹⁷ method and the wannier90 code.¹⁸ Details of our calculation setting and treatment can be found in the supplementary material. Due to the small overlap of wave functions at the band extrema in an indirect-gap material such as silicon or BAs, excitonic effects in the indirect-absorption regime are not expected to be significant¹⁹ and are not considered. This expectation is further supported by the overall good agreement between our calculated phonon-assisted absorption spectra with the experimental measurements in the visible range, where indirect absorption occurs.

In Fig. 4(a), we present our calculated optical constants $n$ and $k$ of BAs as a function of photon energy, where it is evident that excitonic effects appreciably modify these properties, especially at higher photon energies. The theoretical refractive index $n0$ at near-zero photon energy is 2.99 without excitons, and 3.05 with excitons, agreeing excellently with the measured $n0$ at long wavelength. We observe a steep increase in k value that coincides with the minimum direct bandgap, and a peak around 6.4 eV which we attribute to a large joint density of states at this energy.⁷ In Fig. 4(b), we plot the measured absorption coefficients as a function of photon energy together with our calculated values. We note that our calculations have good qualitative agreement with other reports in the literature;^20,21 however, these previous works underestimate the bandgap by about 0.5 eV, a point that Lyons et al.¹³ also noted in their recent work on BAs.

As mentioned above, the measured absorption was generally larger than calculated values. We propose that this disparity is mainly due to crystal imperfections. Recently, the characteristics of various imperfections in BAs crystals such as point defects and common impurities were studied both experimentally and theoretically.^13,22–24 Lyons et al. revealed that BAs crystals grown by the CVT method typically contain a considerable amount of carbon and silicon impurities which could lead to p-type conductivity.¹³ Chae et al. used DFT to find that the As_B antisites, the B_As-As_B antisite pairs, and a range of boron-related defects were the lowest energy native defects, while carbon impurities were also determined to be likely.²⁴ Such defects and impurities can form states within the bandgap of BAs, providing additional channels for optical transitions and hence increasing the absorption, especially at photon energies smaller than the indirect bandgap. While the native defects in BAs typically introduce deep states, many of the impurity levels are shallow.^13,24 The recombination across donor and acceptor impurity levels is considered responsible for the peaks around 1.4–1.6 eV observed in previous photoluminescence measurements of BAs.^13,22 Further, the thermal activation of shallow impurities generates free carriers which also enhance optical absorption.¹³ It is likely that the sub-bandgap absorption we observed is due to the combined effect of free carriers, impurities, and defects, although the precise mechanism will be the topic of a further study.

In the presence of defects and impurities, the absorption coefficient measured from T/R can be considered as the sum of two parts: α_T/R = α_crystal + α_imperfection. In Fig. 4(c), we plot the square root of α_T/R for three samples and compare with the computed absorption curve which assumes a perfect crystal and therefore only captures the α_crystal component. From 1.1 eV to ∼1.8 eV, instead of zero absorption suggested by the calculation, all α_T/R show a non-zero background which we attribute to the imperfection absorption. In addition to revealing this background absorption, a plot of the square root of α vs the photon energy allows us to determine the indirect bandgap. The absorption coefficient associated with the indirect bandgap transition can be expressed as:²⁵ $α≈Ahν−Egi2$⁠, where $hν$ and $Egi$ are the photon energy and the indirect bandgap, respectively. This indicates that the square root of $α$ should be linear with photon energy and the intersection with the x-axis would yield the indirect bandgap (⁠$Egi$⁠). In our case with additional imperfection absorption, the intersection is taken as the crossing point of the background and the increasing slope (which matches well with the slope of the calculated absorption), as indicated by the dashed lines shown in Fig. 4(c). The $Egi$ values determined for our BAs samples were 1.98 eV (#f1), 2.03 eV (#c2), and 2.05 eV (#c10), which are close to the calculated value of 2.07 eV. No $Egi$ value was extracted from the absorption coefficient measured using ellipsometry (α_ellips), since α_imperfection overwhelms the intrinsic absorption α_crystal for low energy photons [Fig. 4(b)].

In addition to the absorption by crystal imperfections, we note that including excitonic effects is important for direct absorption. As shown in Fig. 3(b), the calculated extinction coefficient for direct transitions shows better agreement with experiment once excitonic effects are included. Furthermore, the fact that the slope of our calculated indirect absorption matches well with the measured absorption indicates that indirect excitons are weak [Fig. 4(c)], as discussed earlier. We found that in the UV regime k_ellips is very close to k_calc [see $k$ in Fig. 3(b)], which indicates that α_ellips is dominated by the α_crystal contribution and enables the extraction of reliable intrinsic absorption information for short wavelengths. In Fig. 4(d), we plot the square of α_ellips, which is measured over a range extending up to photon energies of ∼6.5 eV, with the aim to determine the direct bandgap of BAs. The absorption associated with the direct bandgap transition can be expressed as:²⁶ $α≈Bhν−Egd$⁠, where $Egd$ is the direct bandgap. The square of $α$ should be linear with the photon energy, and the intersection with the x-axis is just the energy of the direct bandgap (⁠$Egd$⁠). In this way, we measured $Egd$ of 4.09 eV (#c4) and 4.15 eV (#c5), close to the calculated value of 4.25 eV. Since the calculation was performed at 0 K, we do expect the measured values for both $Egi$ and $Egd$ to be smaller at room temperature due to both zero-point effects and the temperature dependence of the bandgap.²⁷ 

In summary, we studied the optical properties of single crystal BAs experimentally with spectroscopic ellipsometry and transmission/reflection spectroscopy and theoretically using DFT and many-body perturbation theory considering quasiparticle and excitonic corrections. In the visible range, the measured refractive index showed good agreement with the calculated results, with values varying from 3.0 to 3.5. The measured extinction (absorption) coefficients were in good agreement with calculated values, with the discrepancy in the sub-bandgap regime attributed to optical absorption induced by bulk and surface imperfections. The measured indirect (∼2.02 eV) and direct bandgaps (∼4.12 eV) were consistent with the calculated values of 2.07 eV and 4.25 eV, respectively. Our results provide a useful reference for the design of BAs-based photonics and optoelectronics.

See the supplementary material for the basic principle of ellipsometry and control experiments on a silicon wafer, a description of the custom-built transmission and reflection spectroscopy setup and control measurements on a silicon membrane, and details of the DFT calculations.