First-principles investigation on the structural, vibrational, mechanical, electronic, and optical properties of $M{\mathrm{Si}}_2{Z}_4$ ($M$: Pd and Pt, $Z$: N and P) monolayers

The recent synthesis of two-dimensional (2D) layered crystals of ${\mathrm{MoSi}}_2{\mathrm{N}}_4$ and ${\mathrm{WSi}}_2{\mathrm{N}}_4$ has received significant attention due to their novel properties and potential applications. The inclusion of silicon during chemical vapor deposition growth enhances the ambient stability of transition metal nitrides and enables large-scale growth in monolayer limit. The transition metal and nitrogen elements can potentially be replaced with other metal and pnictogen atoms, which can constitute a new and large 2D family. In this respect, based on first-principles calculations, we design $M{\mathrm{Si}}_2{Z}_4$ ($M$: Pd and Pt, $Z$: N and P) monolayers and investigate their structural, vibrational, mechanical, electronic, and optical properties. The dynamical, thermal, and mechanical stabilities of the proposed systems are confirmed through phonon band dispersion calculations, ab initio molecular dynamics simulations, and elastic tensor analyses, respectively. The computed Raman and infrared spectra of the nanosheets reveal that the frequency and the intensity of the most prominent peaks are specified by the type of pnictogen atom in the structures. The mechanical response of the considered systems in the elastic regime is investigated in terms of in-plane stiffness ($Y_{\text{2D}}$) and the Poisson's ratio ($\nu$). The obtained values of $Y_{\text{2D}}$ indicate that $M{\mathrm{Si}}_2{\mathrm{N}}_4$ monolayers are stiffer than $M{\mathrm{Si}}_2{\mathrm{P}}_4$ nanosheets and the $\nu$ values are found to be within the same range and close to the ductile-brittle transition limit. The electronic structure investigation shows that while $M{\mathrm{Si}}_2{\mathrm{N}}_4$ monolayers are quasidirect wide-band-gap semiconductors, the $M{\mathrm{Si}}_2{\mathrm{P}}_4$ monolayers are semiconductors with an indirect narrow band gap. Additionally, these monolayers have isotropic optical spectra and, depending on the type of pnictogen atom, significant optical absorption peaks within the infrared, visible, and ultraviolet regions can be attained. Additionally, it is found that $M{\mathrm{Si}}_2{\mathrm{N}}_4$ monolayers possess multiple bound excitons with strong exciton binding when electron-hole interactions are taken into account. Our results not only expand the class of 2D $M{\mathrm{Si}}_2{Z}_4$ crystals but also offer valuable insights on the physical properties of the designed systems and suggest them as promising materials in diverse optoelectronic applications.

Figure 1

(a) Side and (b) top views for the $M{\mathrm{Si}}_2{Z}_4$ monolayers in the $T$ phase and the corresponding electron localization functions (ELFs) for (c) $M{\mathrm{Si}}_2{\mathrm{N}}_4$ and (d) $M{\mathrm{Si}}_2{\mathrm{P}}_4$ monolayers, respectively. A color scheme with linear scaling from blue (low) to red (high) indicates the probability of electron localization around the atoms. The relevant structural parameters are displayed.

Figure 2

Phonon dispersion diagrams for the $M{\mathrm{Si}}_2{Z}_4$ structures and the corresponding phonon density of states (PhDOS).

Figure 3

The total energy fluctuations of the $M{\mathrm{Si}}_2{Z}_4$ monolayers with respect to the simulation time at 300 K. The insets represent the final snapshot of the atomic configurations at the end of simulation.

Figure 4

Calculated (a) Raman and (b) infrared (IR) spectra of the $M{\mathrm{Si}}_2{Z}_4$ monolayers and (c) the corresponding atomic displacements of the optical phonon modes in the structures.

Figure 5

The electronic band structures [calculated within the level of GGA-PBE (red solid lines) and HSE06 (dashed blue lines)] of the $M{\mathrm{Si}}_2{Z}_4$ monolayers. The Fermi level is set to zero.

Figure 6

The variation of the absorbance $\left[A\right(\omega \left)\right]$ with respect to the photon energy for the $M{\mathrm{Si}}_2{Z}_4$ monolayers (in-plane light polarization). The blue and red lines represent the calculated optical response at the level of ${\mathrm{G}}_0{\mathrm{W}}_0$-RPA and ${\mathrm{G}}_0{\mathrm{W}}_0$-BSE, respectively.