Band Alignment in Monolayer Boron Phosphide with Janus $\mathrm{Mo}\mathrm{S}\mathrm{Se}$ Heterobilayers under Strain and Electric Field

Recent studies have revealed that Janus structures and heterobilayers made from them might have properties superior to those of two-dimensional (2D) materials. We construct 2D monolayer boron phosphide (MBP)/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP heterobilayers and describe comprehensively their optoelectronic properties in the presence of biaxial in-plane and uniaxial out-of-plane strain and the effects of electric fields using first-principles methods. The electronic bands of both MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP heterobilayers display a peculiarity in the direct gap, with different band-gap values in the pristine forms. Remarkably, it is shown that different varieties of band alignments are induced for different orders of the van der Waals (vdW) heterobilayers. Electric fields and in-plane and out-of-plane strain give rise to important changes in the electronic and optical properties. The band alignments can transform from type I to type II under the influence of an electric field and strain. The main absorption peaks of pristine forms of both heterobilayers have in the visible region (approximately 2.67 eV), while in the presence of biaxial strain are redshifted. Since the absorption peaks of the pristine forms of the heterobilayers are in the visible region, the heterobilayers recommended here can be used in photovoltaic applications, and the presence of effects of external electric fields and strain promises functional optoelectronic devices.

Figure 1

Stacking patterns considered for the MBP ($\mathrm{Mo}\mathrm{S}\mathrm{Se}$)/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ (MBP) heterostructures.

Figure 2

(a),(b) Top and side views of stable atomic configurations, (c),(d) electronic band structures, and (e),(f) phonon dispersion curves for the optimized MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP heterobilayers.

Figure 3

Variation of total energy of MBP ($\mathrm{Mo}\mathrm{S}\mathrm{Se}$)/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ (MBP) heterobilayers as a function of interlayer distance.

Figure 4

Electronic band structures of (a) pristine MBP and (b) Janus $\mathrm{Mo}\mathrm{S}\mathrm{Se}$ from PBE method (solid lines) and HSE06 method (dashed lines).

Figure 5

Layer-dependent projected electronic band structures for (a) MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and (b) $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP heterobilayers. (c) Schematic representation of band alignments of heterobilayers. $E_F$ and $E_{\mathrm{vac}}$ represent the Fermi and vacuum energies, respectively.

Figure 6

(a),(b) Band-decomposed charge-density differences and (c),(d) in-plane average electrostatic potential in MBP ($\mathrm{Mo}\mathrm{S}\mathrm{Se}$)/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ (MBP) heterobilayers. The blue and yellow colors represent charge-depletion and accumulation regions, respectively. The isosurface value is set to 0.0002 $e$ Å${}^{-3}$.

Figure 7

Variation of (a) dipole moment, (b) electronic band gap, and (c) interlayer charge transfer in the presence of an external electric field. Variation of (d) total energy, (e) electronic band gap, and (f) interlayer charge transfer as a function of biaxial strain in MBP ($\mathrm{Mo}\mathrm{S}\mathrm{Se}$)/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ (MBP) heterobilayers. Variation of (g) total energy, (h) electronic band gap, and (i) interlayer charge transfer as a function of out-of-plane strain in MBP ($\mathrm{Mo}\mathrm{S}\mathrm{Se}$)/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ (MBP) heterobilayers.

Figure 8

Energy-band spectra of (a)–(e) MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and (f)–(j) $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP heterobilayers under the influence of a perpendicular electric field.

Figure 9

Layer-dependent electronic band structures of (a)–(k) MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and (l)–(w) $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP in the presence of an external perpendicular electric field.

Figure 10

Variation of the band alignments of (a)–(k) MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and (l)–(w) $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP in the presence of an external electric field.

Figure 11

Electronic band spectra of (a)–(g) MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and (h)–(n) $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP under the influence of biaxial strain.

Figure 12

Orbital-projected electronic band structures of pristine (a) MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and (b) $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP heterobilayers.

Figure 13

Layer-dependent projected electronic band structures of MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP heterobilayers under the effect of biaxial strain.

Figure 14

Evolution of band alignments of MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP heterobilayers under the effect of biaxial strain.

Figure 15

Electronic band structure of (a)–(e) MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and (f)–(j) $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP in the presence of out-of-plane strain.

Figure 16

Evolution of dipole moments of MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP heterobilayers in the presence of out-of-plane strain.

Figure 17

Layer-dependent projected electronic band spectra under the effect of (a) $-0.2\mathrm{\%}$, (b) $-0.1\mathrm{\%}$, (c) 0.0%, (d) 0.1%, and (e) 0.2% out-of-plane strain for MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ heterobilayer and (f) $-0.2\mathrm{\%}$, (g) $-0.1\mathrm{\%}$, (h) 0.0%, (i) 0.1%, and (j) 0.2% out-of-plane strain for $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP heterobilayer.

Figure 18

Variation of band alignments of MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP heterobilayers under the effect of out-of-plane strain.

Figure 19

Frequency-dependent imaginary dielectric function [${\epsilon }_2(\omega )$] of MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ and $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP heterobilayers.

Figure 20

Schematic representation of a $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP heterobilayer solar cell.

Figure 21

Frequency-dependent imaginary dielectric functions of MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ for (a) $x$-$y$, (b) $z$ directions, and $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP (c) $x$-$y$,(d) $z$ directions under an external perpendicular electric field.

Figure 22

Frequency-dep-endent imaginary dielectric functions of MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ for (a) $x$-$y$, (b) $z$ directions, and $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP (c) $x$-$y$, (d) $z$ directions under the effect of biaxial strain.

Figure 23

Frequency-dependent imaginary dielectric functions of MBP/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ for (a) $x$-$y$ and (b) $z$ directions, and of $\mathrm{Mo}\mathrm{S}\mathrm{Se}$/MBP for (c) $x$-$y$ and (d) $z$ directions under the effect of out-of-plane strain.

Figure 24

Schematic representation of the synthesis of MBP ($\mathrm{Mo}\mathrm{S}\mathrm{Se}$)/$\mathrm{Mo}\mathrm{S}\mathrm{Se}$ (MBP) heterobilayers using the proposed liquid-transfer technique.