  Bilayer borophene has recently attracted much interest due to its outstanding
mechanical and electronic properties. The interlayer interactions of these
bilayers are reported differently in theoretical and experimental studies.
Herein, we design and investigate bilayer beta12-borophene, by first-principles
calculations. Our results show that the interlayer distance of the relaxed
AA-stacked bilayer is about 2.5 A, suggesting a van der Waals (vdW) interlayer
interaction. However, this is not supported by previous experiments, therefore
by constraining the interlayer distance, we propose a preferred model which is
close to experimental records. This preferred model has one covalent interlayer
bond in every unit cell (single-pillar). Further, we argue that the preferred
model is nothing but the relaxed model under a 2% compression. Additionally, we
designed three substrate-supported bilayers on the Ag, Al, and Au substrates,
which lead to double-pillar structures. Afterward, we investigate the AB
stacking, which forms covalent bonds in the relaxed form, without the need for
compression or substrate. Moreover, phonon dispersion shows that, unlike the AA
stacking, the AB stacking is stable in freestanding form. Subsequently, we
calculate the mechanical properties of the AA and AB stackings. The ultimate
strengths of the AA and the AB stackings are 29.72 N/m at 12% strain and 23.18
N/m at 8% strain, respectively. Moreover, the calculated Young's moduli are 419
N/m and 356 N/m for the AA and the AB stackings, respectively. These results
show the superiority of bilayer borophene over bilayer MoS2 in terms of
stiffness and compliance. Our results can pave the way for future studies on
bilayer borophene structures.
