Electronic and optical properties of fluorinated graphene: A many-body perturbation theory study

The electronic and optical properties of fully fluorinated graphene i.e. fluorographene (CF), and partially fluorinated graphene (C${}_4$F) are studied by means of the first-principles many-body Green's function method, i.e. $GW$–Bethe–Salpeter equation. In conformity with experimental observations, fluorination of graphene causes relatively wide quasiparticle band gaps, 7.01 eV for CF and 5.52 eV for C${}_4$F. The optical absorption properties of CF and C${}_4$F are of excitonic nature, leading to the formation of bound excitons with significantly high binding energies of 1.96 and 1.31 eV assigned to the first bright exciton of CF and C${}_4$F, respectively. The disagreement between the ab initio calculated electronic band gap and the experimentally optical gap seems to be mainly due to the binding energy of excitons rather than the presence of defects. Contrary to previous theoretical predictions, this paper demonstrates that CF seems to be less likely to realize the excitonic Bose–Einstein condensation because the exciton wave functions are relatively delocalized and not well separated. In the case of C${}_4$F, however, it indicates a charge-transfer excitation.

Figure 1

Perspective views of optimized conformations of fluorinated graphene: (a) CF and (b) C${}_4$F. Carbon and fluorine atoms are represented by gray and blue spheres, respectively. The red and green arrows show the directions of light polarization parallel to the surface plane.

Figure 2

(a) Band structure of CF and (b) C${}_4$F. The red open circles represent the QP corrections to the LDA energires; the top of the valence band is set as zero.

Figure 3

Absorption spectra of CF for light polarization parallel to the surface plane (along $x$ direction, see Fig. 1) calculated with and without the consideration of $e$-$h$ Coulomb interactions, i.e. $GW$ + BSE and $GW$ + RPA, respectively. In the case of $GW$ + BSE, 10 occupied and 10 empty bands are adopted within the calculation, and a Lorentzian broadening of 0.1 eV is used. Inset (1) is the amplified absorption spectrum of CF in the energy range of 2.0–5.0 eV, while inset (2) is the optical absorption spectrum of CF for light polarization perpendicular to the surface plane.

Figure 4

Absorption spectra of C${}_4$F for light polarization parallel to the surface plane (along $x$ direction, see Fig. 1) calculated with and without the consideration of $e$-$h$ Coulomb interactions, i.e. $GW$ + BSE and $GW$ + RPA, respectively. In the case of $GW$ + BSE, 10 occupied and 10 empty bands are adopted within the calculation, and a Lorentzian broadening of 0.1 eV is used. The inset is the absorption spectrum of C${}_4$F for light polarization perpendicular to the surface plane.

Figure 5

Three-dimensional electron probability distribution $|\psi ({\mathit{r}}_e;{\mathit{r}}_h){|}^2$ in real space for the bound excitons (a) $I^1$ and (b) $I^2$ of CF (as shown in Fig. 3), the dark exciton (c) $D^1$ and the bound exciton (d) $I^1$ of C${}_4$F (as shown in Fig. 4). The electron probability distribution is obtained as a function of the electron position ${\mathit{r}}_e$, while the hole position ${\mathit{r}}_h$ (the black dot) has been fixed. Left and right panels show top and side views, respectively.