Strain stiffening, high load-invariant hardness, and electronic anomalies of boron phosphide under pressure

New refractory hard materials with a favorable band gap are in high demand for the next-generation semiconductors capable of withstanding high temperature and other hostile environments. Boron phosphide (BP) is such an attractive candidate with exceptional properties; however, it has mainly been studied theoretically because of the difficulty in sample preparation. In this work, we report successful synthesis of large millimeter-sized single-crystal BP. The final product has a zinc-blende structure with a unique electronic structure and is optically transparent with a moderate band gap of ∼2.1 eV. Our experiments, in conjunction with ab initio simulations, reveal that the compound exhibits extraordinary strain stiffening and unusually high load-invariant hardness of ∼38 (3) GPa, which is close to the 40-GPa threshold for superhard materials, making BP the hardest among all known semiconductors. Based on the first-principles calculations, the fracture mechanisms in BP under tensile and shear deformations can be attributed to the formation of a metastable hexagonal phase. Further spectroscopic measurements indicate that an unusual electronic transition occurs at high pressures of ∼13 GPa, resulting in an asymptotically enhanced covalent bonding state. The pressure dependence of multiphonon processes is also determined by Raman measurement. In addition, our studies suggest a phonon-assisted photoluminescence process and evidence for the photon-pumped étalon effect at 707 nm.

Figure 1

Structure and morphology of as-prepared samples. (a) Refined XRD pattern for sample powders synthesized at 1000 °C for 2 h. Black circles and red lines denote the observed and calculated profiles, respectively. The difference curve between the observed and calculated profiles is shown in cyan color. The blue tick marks correspond to the peak positions. Inset is the crystal structure of BP with the zinc-blende symmetry. (b) Optical images of typical BP single crystals grown at 1200 °C (upper panel, in orange) and 1150 °C (bottom panel, in golden yellow). The scale bar for both optical images is 200 μm.

Figure 2

Thermal stability analysis for BP. Thermogravimetry–differential thermal analysis, TG-DTG, performed in an Ar atmosphere. The decomposition of BP starts at $T_d=1135\left(5\right){}^{\circ }\mathrm{C}$ with a rate of ∼7.6 mg/min at around 1200 °C. At a relatively low temperature of ∼670 °C, a clear fluctuation in weight that would be attributed to the disassociation of surface adsorbed gases. Attempts to determine the thermal stability of BP in air is unsuccessful, because the Pt-Rh thermocouple of the instrument was damaged by an unknown process, likely an associated reaction between Pt-Rh and decomposed P.

Figure 3

XPS measurements and valence states of BP. (a) XPS spectra of $\mathrm{B}1s,\mathrm{P}2s$, and $\mathrm{P}2p$. (b) XPS spectra of $\mathrm{P}2p_{3/2,1/2}$. In (a,b), the solid dots and red solid lines in the top panels denote the observed and fitted XPS spectra, respectively. The solid red lines in the bottom panels are fitted XPS spectra for $\mathrm{P}2s,\mathrm{P}2p$, and $\mathrm{B}1s$. On the high-energy shoulder of the main peak in (a,b), a few weak peaks occur and may correspond to some unidentified oxides such as $\mathrm{P}{{\mathrm{O}}_4}^{3-}$ and ${\mathrm{B}}_2{\mathrm{O}}_3$, likely associated with possible surface contamination of the sample. (c) Binding energy of $\mathrm{B}1s$ of the known compounds as a function of valence states of boron. The linear relationship has a slope of ∼1.46 eV/valence state. (b,c) Binding energy of $\mathrm{P}2p$ and $\mathrm{P}2s$ of the known compounds as a function of valence states of phosphorus. Because the split of $\mathrm{P}2p$ is very small, the average value of $\mathrm{P}2p$ is used to evaluate the valence state of P.

Figure 4

Hardness and elastic properties of BP determined using nano- and microindentation methods. (a) Load-displacement data taken during different loading and unloading cycles at a series of target maximum displacements or loads. Red dashed line denotes a fit of the load versus displacement to a power low, $\alpha {\left(h-h_f\right)}^{\gamma }$, for the elastic unloading process under an 8-mN load. The blue dashed line defines the slope for the upper portion of the unloading curve (i.e., contact stiffness). The derived parameters are included in (a). (b) Hardness and reduced effective elastic modulus as a function of indenter displacement based on the data in (a). (c) Vickers hardness $\left(H_V\right)$ and fracture toughness $\left(K_{\mathrm{IC}}\right)$ versus the applied load for single-crystal BP. Inset is a typical SEM image to show the indentation pyramid with cracks at a load of 490 mN. (d) $H_V$ as a function of the product $k^{2}G\left(k=G/B\right)$ for a number of semiconductors. Inset is hardness versus band gap for typical refractory semiconductors.

Figure 5

Calculations of the dual tensile and shear strengths for BP. (a) Crystal structure at equilibrium. Arrow lines denote the high-symmetry directions, along which the tensile and shear deformations are calculated. (b) Stress responses under tensile strains along various high-symmetry directions. (c) Stress responses under pure shear strains in the selected high-index planes (110), (100), and (111) along a few typical shear directions. (d) Snapshots of crystal and electronic structures under four typical shear strains as denoted with S1, S2, S3, and S4 in (c).

Figure 6

Calculated tensile deformation along high-symmetry [100], [110], and [111] directions. (a) Crystal structure of BP at equilibrium with three marked high-symmetry tensile directions. (b) Polyhedral view of the $\left[\mathrm{P}{\mathrm{B}}_4\right]$ tetrahedral coordination formed by P atoms and its four neighboring B atoms. At equilibrium, the bond length and bond angle are 1.945 Å and 109.47°, respectively. (c) Stress responses under tensile strain along the selected high-symmetry directions. (d) Tensile deformation along the [100] direction. All four bonds are equivalent and have an identical bond length. (e) Tensile deformation along the [110] direction with two stretched bonds and two compressed bonds. (f) Tensile deformation along the [111] direction with one stretched bond and three compressed bonds.

Figure 7

Calculated stress-strain relationships for both zinc-blende BP (a) and cubic BN (b). Curves with open symbols represent tensile deformation, and curves with solid symbols denote shear deformation. Inset is an enlargement of the $\left(111\right)\left[11\overline{2}\right]$ shearing slip system for cubic BP and c-BN; for simplicity, the yield point of the shear mode is defined using the proportional limit of the elastic region, as denoted by the black arrow.

Figure 8

High-$P$ Raman spectra for BP. (a) First-order Raman lines ${\mathrm{\Gamma }}_{\mathrm{TO}}$ and ${\mathrm{\Gamma }}_{\mathrm{LO}}$ taken at selected pressures. The letter “D” denotes the data taken on decompression. (b) Phonon frequencies of TO and LO modes as a function of pressure. Black lines represent the best fits to the pressure dependence of phonon frequencies for three different pressure regions of 0–13 GPa, 13–36 GPa, and 36–56 GPa (see Fig. S9 in the Supplemental Material [37]; also see [15, 24, 39]). A few phonon modes appear on the edges of the ${\mathrm{\Gamma }}_{\mathrm{TO}}$ and ${\mathrm{\Gamma }}_{\mathrm{LO}}$ lines at high pressure. The inset shows the pressure dependence of the peak intensity ratio between ${\mathrm{\Gamma }}_{\mathrm{TO}}$ and ${\mathrm{\Gamma }}_{\mathrm{LO}},I_{\mathrm{TO}}/I_{\mathrm{LO}}$. The black line denotes the best fit of experimental data to a square-power law. (c) The Born transverse effective charge, $e_T^{*}$, and ${\omega }_{\mathrm{LO}}^2-{\omega }_{\mathrm{TO}}^2$ as a function of pressure. Inset is the calculated valence charge using the Bader method.

Figure 9

High-$P$ second-order Raman spectra for BP. (a) Raman patterns taken upon compression with intensity plotted in a logarithmic scale to show the weak multiphonon processes. Each second-order phonon mode in the frequency range of $500-1800\mathrm{c}{\mathrm{m}}^{-1}$ is identified as a combination of the first-order phonon modes of acoustic and optical branches (Ref. [15]). The inset is the calculated phonon dispersion for BP at ambient pressure (Ref. [14]). The longitudinal (L) and transverse (T) modes of optical (O) and acoustic (A) bands are denoted with LO, TO, LA, and TA, respectively. (b) Phonon frequencies of the second-order Raman modes versus pressure. Phonon modes of ${\mathrm{\Gamma }}_{\mathrm{TO}}$ and ${\mathrm{\Gamma }}_{\mathrm{LO}}$ are also plotted for comparison.

Figure 10

High-$P$ PL measurement for BP. (a) Selected high-$P$ spectra taken on compression and decompression (marked with the “D” letter) at room temperature. Vertical sticks denote four components A–D of the spectrum. Gray-black squares and dots denote the PL and second-order Raman peaks of the diamond anvil, respectively. The indirect band gap $E_g$ is estimated using the high-energy edge of the PL spectrum. (b) Energies of the four PL components and the band gap as a function of pressure. Red dots and blue solid squares represent the $E_g$ value measured from the ultraviolet spectrum and calculated from ab initio theory, respectively. (c) Excitation-power dependence of the 706.8-nm emission spectrum band composed of several sharp fringes, based on the photon-driven emission using a 4.5-μm thin-plate single crystal [see Fig. 1]. The wavelength of the excitation laser is 532 nm and the spectra are taken at ambient conditions. (d) Fringe mode spacing, Δλ, as a function of wavelength of the fringe center, λ.