Dielectric-dependent hybrid functional calculations on the electronic band gap of $3d$ transition metal doped ${\mathrm{SnS}}_2$ and their optical properties

This paper is a computational investigation of the electronic band gap and optical properties of ${\mathrm{SnS}}_2$ and $3d$-series transition metal doped ${\mathrm{SnS}}_2$ systems. The ${\mathrm{SnS}}_2$ crystal is a nonmagnetic indirect band gap semiconductor both in bulk and in the monolayer limit. The transition metal substitution at Sn site induces magnetism inside the crystal. Therefore studying its doping by $3d$-series transition metals is essential from an application perspective. We use the dielectric-dependent hybrid functionals of ab initio calculations for computing the electronic band gap. The dielectric-dependent hybrid computations rely on the electronic static dielectric constant. In these calculations, we iteratively update the dielectric constant and exchange parameter from one another until the convergence. As a result, we present a range of possible band gap values. Specifically, we determine the lower and upper bounds of possible experimental band gap values for all these doped systems. Further, we explore the optical properties of each doped system in the monolayer and bulk forms. We discuss the absorption spectra, optical constants, and exciton binding energy of all the doped systems. We conclude that the transition metal doped ${\mathrm{SnS}}_2$ is a good candidate for optoelectronic device applications.

Figure 1

Top view of ${\mathrm{SnS}}_2$ crystal doped with transition metal atom. Blue, yellow, and red balls represent Sn, S, and transition metal atom, respectively.

Figure 2

Formation energy of transition metal doped bulk and ML-${\mathrm{SnS}}_2$.

Figure 3

Orbital projected band structure of bulk ${\mathrm{SnS}}_2$ calculated using HSE06 functional with 25% exchange.

Figure 4

Orbital projected band structure of monolayer ${\mathrm{SnS}}_2$ calculated using HSE06 functional with 25% exchange.

Figure 5

Dielectric-dependent HSE06 and PBE0 band gap values of 1T-${\mathrm{TiS}}_2$.

Figure 6

Orbital projected band structure of (a) Ti, (b) V, (c) Cr, (d) Mn, (e) Fe, (f) Co, (g) Ni, (h) Cu, and (i) Zn-doped bulk ${\mathrm{SnS}}_2$ calculated using HSE06 functionals with an exchange of $25\%$. Fermi energy is set to zero.

Figure 7

Orbital projected band structure of (a) Ti, (b) V, (c) Cr, (d) Mn, (e) Fe, (f) Co, (g) Ni, (h) Cu, and (i) Zn-doped monolayer ${\mathrm{SnS}}_2$ calculated using HSE06 functionals with an exchange of 25%. Fermi energy is set to zero.

Figure 8

Optical absorption spectra of pristine ${\mathrm{SnS}}_2$ and TM-doped bulk and monolayer ${\mathrm{SnS}}_2$ systems for semiconductors.

Figure 9

Reflectivity and refractivity spectra of pristine ${\mathrm{SnS}}_2$ and TM-doped bulk and monolayer ${\mathrm{SnS}}_2$ systems for semiconductors.

Figure 10

Exciton binding energy in TM-doped monolayer and bulk ${\mathrm{SnS}}_2$ systems.