Layer-dependent properties ofSnS2andSnSe2two-dimensional materials

The layer-dependent structural, electronic, and vibrational properties of ${\mathrm{SnS}}_{2}$ and ${\mathrm{SnSe}}_{2}$ are investigated using first-principles density functional theory (DFT). The in-plane lattice constants, interlayer distances and binding energies are found to be layer-independent. Bulk ${\mathrm{SnS}}_{2}$ and ${\mathrm{SnSe}}_{2}$ are both indirect band gap semiconductors with ${E}_{g}=2.18$ and $1.07\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, respectively. Few-layer and monolayer 2D systems also possess an indirect band gap, which is increased to 2.41 and $1.69\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ for single layers of ${\mathrm{SnS}}_{2}$ and ${\mathrm{SnSe}}_{2}.$ The effective mass theory of 2D excitons, which takes into account the combined effect of the anisotropy, nonlocal 2D screening and layer-dependent 3D screening, predicts strong excitonic effects. The binding energy of indirect excitons in monolayer samples, ${E}_{x}\ensuremath{\sim}0.9\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, is substantially reduced to ${E}_{x}=0.14\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ in bulk ${\mathrm{SnS}}_{2}$ and ${E}_{x}=0.09\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ in bulk ${\mathrm{SnSe}}_{2}$. The layer-dependent Raman spectra display a strong decrease of intensities of the Raman active ${A}_{1g}$ mode upon decreasing the number of layers down to a monolayer, by a factor of 7 in the case of ${\mathrm{SnS}}_{2}$ and a factor of 20 in the case of ${\mathrm{SnSe}}_{2}$, which can be used to identify the number of layers in a 2D sample.