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Theory of Epitaxial Growth of Borophene on Layered Electride: Thermodynamic Stability and Kinetic Pathway

Based on first-principles calculations, we propose that a layered electride Mg2O can serve as an effective substrate, in place of metal substrate, to grow honeycomb borophene (h-borophene). We first confirm the thermodynamic stability of h-B@Mg2O heterostructure by energetics analysis and dynamic stability by absence of imaginary frequency in phonon spectra. Then, kinetically, we identify the atomistic pathways for a preferred 2D growth mode over 3D growth, and reveal a growth transition from 2D compact islands to h-borophene at ~13-atom cluster size, indicating the feasibility of epitaxial growth of h-borophene on Mg2O. The h-borophene is found to be stabilized by nearly one electron transfer from Mg2O to h-borophene based on the Bader charge analysis. Moreover, the intrinsic band structure of the free-standing h-borophene is only weakly perturbed by the Mg2O substrate, a significant advantage over metal substrate. We envision that layered electrides provide an attractive family of substrates for epitaxial growth of a range of 2D materials that can otherwise only be grown on undesirable metal substrates.

Two-dimensional (2D) materials have drawn intensive attention for both fundamental interests and potential applications [1][2][3][4]. While high quality small-size 2D materials, such as graphene [5,6] and transition metal dichalcogenides [7,8], may be prepared by mechanical exfoliation, it is highly desirable to grow 2D materials for large size and mass quantity to further our study and realize their potential applications. However, many 2D materials can only be grown on metal substrates, which is unwanted because the ample metallic states will inevitably destroy the intrinsic, especially non-metallic properties of 2D materials. In this Letter, using honeycomb borophene (h-borophene, a monolayer boron sheet) as a prototypical example, we demonstrate that layered electrides provide a new class of substrates, in place of metal, to effectively grow 2D materials with significant advantages.
Boron is one of the most versatile elements, forming various 3D bulk polymorphs [9][10][11][12][13]. Similarly, different 2D borophene have been theoretically proposed [14][15][16][17][18] and experimentally realized [19][20][21]. Most excitingly, one recent experiment succeeded in growing h-borophene on Al(111) surface [21]. Analogous to graphene, a free-standing h-borophene will host massless Dirac fermions and exhibit fascinating electronic properties. Furthermore, in the well-known high-Tc superconductor, MgB2, boron also possesses a planar h-borophene structure, which is primarily responsible for the superconductivity [22,23]. A recent study also showed MgB2 to be a topological semimetal [24]. Thus, synthesis of h-borophene may not only provide new opportunities for 2D high-Tc superconductivity but also topological superconductivity. However, the growth of h-borophene on metal substrate has some drawbacks. It is unlikely to exfoliate hborophene away from the metal substrate. The high conductivity of metal will mask the intrinsic transport properties of h-borophene due to high electron density of states of metal near the Fermi level [25]. Therefore, searching for an insulating or weak metal substrate to grow h-borophene is of great interest.
Since boron has three valence electrons, the electron deficiency makes its honeycomb lattice energetically unstable. Thus, neither semiconductors nor insulators can serve as good substrates to grow h-borophene. Instead, we have identified layered electride, a "weak metal", to be an effective substrate to grow h-borophene.
Electrides are crystals with cavity-trapped electrons acting as anions. They were first synthesized by Dye in 1983 [26], in the form of 0D and 1D confined electrons [27][28][29]. Interestingly, a layered electride, di-calcium nitride (Ca2N), was experimentally reported in 2013 to possess delocalized "2D electron gas (2DEG)" sandwiched between the cationic layers [30]. Ca2N was then studied as an efficient electron donor for hydrogenation in alkynes and alkenes [31]. And several carbides [32][33][34][35][36], nitrides [32,[34][35][36][37][38], and oxides [32,33,36] have since been predicted as layered electrides. We hypothesize that the presence of 2DEG on the layered electride surface provides an effective means to compensate the electron deficiency of hborophene. In addition, the layered structure of electride can facilitate the exfoliation or growth of h-borophene on monolayer or thin films of electrides to minimize the substrate influence. Finally, as a weak metal, the significantly reduced density of states from the electride at the Fermi level helps to retain the most, if not all, intrinsic electronic and transport properties of h-borophene.
To test the above hypotheses, we investigate both thermodynamic stability of h-B@Mg2O and kinetic pathways of boron growth on Mg2O surface using first-principles calculations. The dynamic stabilities of Mg2O and heterostructure of h-B@Mg2O are confirmed by the absence of imaginary frequency in phonon spectra. The calculated electron localization function (ELF) indicates the existence of interlayer 2DFEG in Mg2O. Nearly one electron transfers from Mg2O substrate to each boron atom to stabilize h-borophene based on the Bader charge analysis. We identify the atomistic kinetic pathways for boron growth on Mg2O surface with a preferred 2D growth mode over 3D mode. A critical growth transition from compact-triangular structure to hexagonal-ring structure is revealed with increasing boron cluster size. All these findings point to the feasibility of epitaxial growth of h-borophene on layered electride.
The layered electride Mg2O is chosen to have an appropriate lattice constant as the prototypical substrate to grow h-borophene.  It is crucial to characterize Mg2O as an electride in a chemical formula [Mg2O] m+ · me -, where m is the number of electrons, and confirm the existence of 2DEG. The ground-state band structure of monolayer Mg2O is shown in Fig. 2(a) without spin polarization. The two parabolic bands arising from Mg-s and O-p orbitals indicate the existence of 2DEG. This is also confirmed by the plots of partial charge density in Fig. S1(a) to (c) in Supplemental Materials [41]. The degree of electron delocalization can be quantitatively described by ELF. On both surfaces of monolayer Mg2O, a delocalized ELF feature is clearly shown in Fig. 2(b). Also, for Mg2O monolayer with one and two valence electrons removed, the delocalized ELF features on both surfaces gradually disappear [ Fig. 2(c) and (d)]. This indicates that electron transfer away from Mg2O will first vacate the 2DFEG states, suggesting that the 2DEG can be used as an effective electron donor to compensate the electron deficiency in h-borophene upon growth. The ELF analysis also indicates that Mg2O is a layered electride with a formula of [Mg2O] 2+ · 2e -. In bulk, the anionic electrons locate within the interlayer space between the [Mg2O] 2+ layers [see, e.g., Fig. S1(d) and (e)] [41]. Since there are two boron atoms in one unit cell of h-B@Mg2O, one electron is expected to transfer from Mg2O substrate to each boron atom to stabilize h-borophene. Previous theoretical studies have already indicated that free-standing h-borophene is unstable [42]. The substrate used to grow h-borophene must play a crucial role in stabilizing the honeycomb lattice. To better understand the stabilization mechanism, we calculate the formation energy of h-borophene on different substrates and perform the Bader charge analysis [43]. The formation energy is defined as: where Etot is the total energy of h-borophene on the substate, Esub is the energy of the substrate, EB is the energy of the isolated boron atom, and N is the number of boron atoms [44]. Different from previously calculations [21,45], we take the energy of isolated boron atom as EB instead of the cohesive energy of bulk α-B12 because atomic boron source prepared by e-beam evaporator under ultrahigh vacuum condition is used during growth [19][20][21]. The calculated formation energy for h-B@Mg2O and h-B@Al(111) are -6.28 and -6.35 eV/atom, respectively. According to the Bader charge analysis, about 0.6 electrons on average are transferred from Mg2O to each boron atom, which is about the same as that (0.7 electrons) in h-B@Al(111) [21]. Apparently, there is no significant difference in formation energy and electron transfer between h-B@Mg2O and h-B@Al(111) [21], which indicates that the layered electride Mg2O could potentially replace metal Al to grow h-borophene. Next, we establish the preferred growth mode and identify the atomic pathways for boron growth on Mg2O substrate, by investigating initial stage of growth up to 13 atoms. Although growth of borophene on metal substrates [45][46][47] have been studied previously, fundamental mechanisms of borophene growth on layered electride are unknown. We adopted a 5×5 monolayer Mg2O as the substrate [ Fig. 3(a)], which is confirmed to be sufficiently large to avoid inter-cluster interaction for up to 13-atom clusters.
We first determine the preferred adsorption site for boron adatom. Fig. 3(b) shows seven different absorption sites on Mg2O surface, as labeled 1 to 7, and Fig. 3(c) shows the corresponding adsorption energy. The most stable one is Site 1 [top of middle-O atom, see Fig. 4(a)], followed by Site 2 (center of bridge1-3) and 3 (top of bottom-Mg atom). A boron adatom is unstable on other four positions, especially Site 5 (above top-Mg atom). Thus, the boron adatom is kinetically hindered from climbing onto Site 5. Also, the distance between Site 1 and 2 is shorter than the B-B bond length, so that these two sites cannot be occupied simultaneously owing to Coulomb repulsion. Hence, we tend to use Site 1 and 3 to construct the geometries for boron clusters at the initial growth stage.
After structural relaxation, the preferred stable configurations of small boron clusters (N = 1 to 5) are depicted in Fig. 4(a) to (e), respectively. As illustrated in Fig. 4(b), the most stable positions for a boron dimer are Site 1 and 3, which is also expected from the adatom absorption energy. For a larger cluster, such as a trimer, a chain-type structure occupying Site 1 and 3 is most stable, as shown in Fig. 4(c). Adding another adatom to the chain-trimer, it prefers to diffuse to the periphery to form a 2D rhomboid-shaped tetramer [ Fig. 4(d)], with two atoms locating in Site 1 and one locating in Site 3. By continuously adding adatom, the pentamer [ Fig. 4(e)], hexamer [ Fig. S4(a)], heptamer [ Fig. S4(b)] and octamer [ Fig. S4(c)] [41] will form in sequence, and they all have the 2D structures as the most stable configurations. In particular, all the preferred 2D configurations have the adatoms occupying exclusively Site 1 and 3 to form a compact-triangular structure. As a comparison, we also constructed the initial cluster configurations with a hexagonal ring, which is the desired building block for h-borophene, as shown for N = 13 in Fig. 4(g). For N < 13, such ring structures [e.g., N = 6, 7, 8, and 10 in Fig. S4(i) to (l)] are unstable, and will spontaneously transform into a nearly equilateral-triangle shape [ Fig. S4(e) to (h)], which are metastable compared to the compact islands [ Fig. S4(a) to (d)] [41]. Importantly, however, for N = 13, the atom in the middle of the equilateral-triangle structure has three nearest neighbors, which assume already the geometry of h-borophene, as indicated by the yellow-dashed circle in Fig. 4(h). By evaluating the relative stability between the ring and compact configurations, we found that their energy differences are 0.056, 0.169, 0.174, 0.019, and -0.001 eV/atom, respectively, as depicted in Fig. 4(i). The significant energy difference for N = 7 and 8 is due to the unsaturated atoms on the periphery [see Fig. S4(f) and (g)] [41]. Most importantly, however, the ring cluster in Fig. 4(h) is more stable than the compact one [ Fig. 4(f)]. This indicates that with the increasing cluster size, a growth transition from the equilateral-triangle shape to h-borophene will occur at N = 13. We further confirmed this at the infinite 2D limit of a periodic structure. We constructed the initial configuration of borophene with 6-atom equilateral-triangle cluster to begin with, and it spontaneously transforms into the h-borophene, as illustrated in Fig. S5 [41]. The above results imply that the electride Mg2O substrate facilitates not only the 2D growth mode of planar island but also a transition to the ultimate h-borophene sheet with the increasing coverage of boron atoms during growth.
Finally, beyond establishing the growth of h-borophene on Mg2O substrate, we further compare the monolayer Mg2O versus four-layer Al(111) for growing h-borophene. Most notably, the electronic states of h-borophene grown on Mg2O are much less perturbed than those grown on Al(111), as evidenced by much less metallic states coming from the former than the latter, as shown in Fig. S6 [41]. This signifies a distinctive advantage of layered electride substrate over conventional metal substrate for growing h-borophene.
In conclusion, we propose for the first time that a layered electride Mg2O can serve as an effective substrate to grow h-borophene. Both thermodynamic stability of h-B@Mg2O and kinetic pathways of boron growth have been investigated using first-principles calculations. The 2DEG in Mg2O surface will compensate the electron deficiency in h-borophene to stabilize the honeycomb structure and facilitate the 2D growth mode. Our findings open a new avenue for epitaxial growth of h-borophene using layered electride substrates with notable advantages over metal substrates, which will stimulate immediate theoretical and experimental interests. Broadly, the layered electrides may be used as effective substrates for epitaxial growth of various 2D materials that can otherwise only be grown on undesirable metal substrates.