Cubic BeB$_2$: A metastable $p$-type conductive material from first principles

TL;DR

This work predicts that cubic BeB$_2$ (c-BeB$_2$) is a metastable phase with a diamond-like boron network stabilized by Be donation, offering a near-ideal platform for $p$-type transport and potential superconductivity. Using a full first-principles pipeline (DFT, $GW$, BSE, DFPT, EPW, and Eliashberg theory) and defect thermodynamics, the authors show an indirect gap of $E_g \approx 1.5$ eV, very light hole effective masses, and high intrinsic hole mobility, with Be vacancies acting as shallow acceptors that promote degenerate $p$-type behavior. They further demonstrate that heavy hole doping can induce superconductivity with $T_c$ up to about $3.6$ K, depending on the treatment of dopants and phonon softening. The results propose c-BeB$_2$ as a multifunctional material with potential electronic, optoelectronic, and superconducting applications, while noting the practical challenges of bulk synthesis and suggesting epitaxial thin-film routes on lattice-matched substrates.

Abstract

Boron forms a wide variety of compounds with alkaline earth elements due to its unique bonding characteristics. Among these, binary compounds of Be and B display particularly rich structural diversity, attributed to the small atomic size of Be. Cubic BeB$_2$ is a particularly interesting phase, where Be donates electrons to stabilize a diamond-like boron network under high pressure. In this work, we employ \textit{ab initio} methods to conduct a detailed investigation of cubic BeB$_2$ and its functional properties. We show that this metastable phase is dynamically stable under ambient conditions, and its lattice match to existing substrate materials suggests possible epitaxial stabilization via thin-film growth routes. Through a comprehensive characterization of its electronic, transport, and superconductivity properties, we demonstrate that cubic BeB$_2$ exhibits high hole concentrations and high hole mobility, making it a potential candidate for efficient $p$-type transport. In addition, cubic BeB$_2$ is found to exhibit low-temperature superconductivity at degenerate doping levels, similar to several other doped covalent semiconductors such as diamond, Si, and SiC.

Figures (8)

• Figure 1: Atomic structure of $c$-BeB$_2$ (cF12, space group F4$\bar{3}$m, No.216), with Be donating two electrons to B, allowing B to form a network. The two B atoms are crystallographically inequivalent, with differing distances to the Be atom, giving the structure a zinc blende-like character rather than a homogeneous diamond-like network. The two boron atoms are marked by B$_1$ (closer to Be) and B$_2$ (farther from Be), respectively.
• Figure 2: (a) Electronic band structure of $c$-BeB$_2$ evaluated within the HSE06 exchange-correlation functional. With HSE06, the material is found to be an indirect gap semiconductor with a fundamental gap of 1.52 eV. (b) Phonon dispersion indicating dynamical stability of $c$-BeB$_2$.
• Figure 3: Zero-point and finite-temperature band-gap renormalization due to electron-phonon interactions in $c$-BeB$_2$. The electron-phonon interactions induce a zero-point renormalization of 189 meV and a further temperature-induced reduction of the band gap of 43 meV at 300 K.
• Figure 4: Optical spectra of $c$-BeB$_2$ evaluated with quasiparticle effects only (black dotted line) and with additional inclusion of excitonic effects (black solid line) in the intrinsic material. Carrier concentration-dependent optical spectra including excitonic effects are shown for two doping levels with red dot-dashed and blue dashed lines. A weak excitonic effect can be seen at the optical absorption onset. Inter-valance band transitions can be clearly seen from the strong optical absorption below a photon energy of 2 eV in the heavily doped material.
• Figure 5: Formation energy of intrinsic (V$_{\text{Be}}$, Be$_{\text{B}}$) and extrinsic (Li$_{\text{Be}}$, H$_\text{Be}$) acceptor-type point defects in $c$-BeB$_2$ as a function of Fermi level (referenced to the valence band maximum $E_V$) under (a) B-rich and (b) Be-rich conditions. As the material is metastable with a low formation enthalpy (-0.054 eV/f.u.), the allowed chemical potential range is narrow, thus defect formation energies are similar under both B-rich and Be-rich conditions. The ionization enegies of the acceptors considered are all less than 100 meV. The Be vacancy, in particular, acts as a shallow acceptor and has a negative formation energy, suggesting potential degenerate $p$-type behavior.