Strong excitonic effects in the optical properties of graphitic carbon nitride $g$-C${}_{3}$N${}_{4}$ from first principles

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Strong excitonic effects in the optical properties of graphitic carbon nitride $g$ -C $_{3}$ N $_{4}$ from first principles

Wei Wei and Timo Jacob

Phys. Rev. B 87, 085202 – Published 8 February 2013

Abstract

Graphitic carbon nitride ( $g$ -C $_{3}$ N $_{4}$ ) has recently triggered extensive investigations due to its potential applications, such as in direct photochemical water splitting, CO $_{2}$ activation, and transition-metal-free spintronics. However, electronic, and particularly the optical properties of $g$ -C $_{3}$ N $_{4}$ still have not been well established. Based on one of the state-of-the-art approaches—many-body Green's function theory (i.e., $G W$ $+$ BSE)—absorption of ultraviolet light by $g$ -C $_{3}$ N $_{4}$ is found to be determined by strong excitonic effects with a significantly large binding energy assigned to the bound excitons. Dark states have also been found in $g$ -C $_{3}$ N $_{4}$ , which can affect the photoluminescence yield of $g$ -C $_{3}$ N $_{4}$ . We find that the band gap of $g$ -C $_{3}$ N $_{4}$ probably can be tuned by adjusting the condensation (dimensionality) to initiate excitonic absorption in the visible light region, which might help improve the solar energy conversion efficiency.

Received 6 November 2012

DOI:https://doi.org/10.1103/PhysRevB.87.085202

Authors & Affiliations

Wei Wei and Timo Jacob^*

Institute of Electrochemistry, Ulm University, Albert-Einstein-Allee 47, D-89081 Ulm, Germany

^*timo.jacob@uni-ulm.de

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Issue

Vol. 87, Iss. 8 — 15 February 2013

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Images

Figure 1
Unit cell of $g$ -CN1 (triazine) (a) and $g$ -CN2 (tri- $s$ -triazine) (b). Gray and blue spheres respectively represent C and N atoms, while dashed lines indicate the lattice.Reuse & Permissions
Figure 2
Band structure of $g$ -CN1 (a) and $g$ -CN2 (b) in the two-dimensional hexagonal Brillouin zone; the arrows indicate the vertical interband transitions contributing to the bound excitons $I^{1}$ and $I^{2}$ , and the Fermi level was set at zero. Imaginary part of the macroscopic dielectric function $ɛ_{M}$ for light polarization parallel ( $E_{para}$ , black lines) and perpendicular ( $E_{perp}$ , red lines) to the surface plane of $g$ -CN1 (c) and $g$ -CN2 (d) calculated with (solid lines) and without (dotted lines) consideratoin of LFE.Reuse & Permissions
Figure 3
Imaginary part of the macroscopic dielectric function $ɛ_{M}$ for light polarization parallel to the $g$ -CN1 surface plane calculated with (black line) and without (red dot line) consideration of the e–h interactions, i.e., $G W$ $+$ BSE and $G W$ $+$ RPA, respectively. Five occupied and ten empty bands are included when calculating the optical absorption spectrum at the $G W$ $+$ BSE level. A Lorentzian broadening of 0.1 eV was adopted.Reuse & Permissions
Figure 4
Imaginary part of the macroscopic dielectric function $ɛ_{M}$ for light polarization parallel to the $g$ -CN2 surface plane calculated with (black line) and without (red dot line) consideration of the e-h interactions, i.e., $G W$ $+$ BSE and $G W$ $+$ RPA, respectively. Five occupied and ten empty bands are included when calculating the optical absorption spectrum at the $G W$ $+$ BSE level. A Lorentzian broadening of 0.1 eV was adopted.Reuse & Permissions
Figure 5
Three-dimensional electron probability distributions $| ψ (r_{e}; r_{h}) |^{2}$ in real space as a function of electron position with the hole position (black dot) fixed slightly above a N atom for the excitonic states $I^{1}$ and $I^{2}$ of $g$ -CN1 [(a) and (b)], and of $g$ -CN2 [(c) and (d)].Reuse & Permissions
Figure 6
$g$ -C $_{3}$ N $_{4}$ structure in bulk phase (a); gray and blue spheres represent C and N atoms, respectively. Imaginary part of the macroscopic dielectric function $ɛ_{M}$ for light polarization parallel to the $g$ -C $_{3}$ N $_{4}$ layer calculated with (black line) and without (red dot line) consideration of the $e$ - $h$ interactions, i.e., $G W$ $+$ BSE and $G W$ $+$ RPA, respectively (b); five occupied and ten empty bands are included when calculating the optical absorption spectra at the $G W$ $+$ BSE level; a Lorentzian broadening of 0.1 eV was adopted. Three-dimensional electron probability distributions $| ψ (r_{e}; r_{h}) |^{2}$ in real space for the excitonic states $I^{1}$ (c) and $I^{2}$ (d) of $g$ -C $_{3}$ N $_{4}$ in the bulk phase. The hole position (black dot) had been fixed slightly above a N atom.Reuse & Permissions

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