Direct band gap carbon superlattices with efficient optical transition

We report pure carbon-based superlattices that exhibit direct band gaps and excellent optical absorption and emission properties at the threshold energy. The structures are nearly identical to that of cubic diamond except that defective layers characterized by five- and seven-membered rings are intercalated in the diamond lattice. The direct band gaps lie in the range of 5.6–5.9 eV, corresponding to wavelengths of 210–221 nm. The dipole matrix elements of direct optical transition are comparable to that of GaN, suggesting that the superlattices are promising materials as an efficient deep ultraviolet light emitter. Molecular dynamics simulations show that the superlattices are thermally stable even at a high temperature of 2000 K. We provide a possible route to the synthesis of superlattices through wafer bonding of diamond (100) surfaces.

Figure 1

The atomic structures of the C(100)${}_n$/C(5–7) superlattices for (a) $n=1$, (b) $n=2$ (type I), (c) $n=2$ (type II), and (d) $n=3$. Colored cyan and brown circles denote the C atoms which belong to the C(100) and C(5–7) layers, respectively. The black parallelepiped represents the unit cell spanned by the lattice vectors ${\vec{a}}_1, {\vec{a}}_2$, and ${\vec{a}}_3$.

Figure 2

The PBE band structure of the C(100)${}_{n=5}$/C(5–7) superlattice with the valence band maximum set to zero. The thickness of red colored bands represents the degree of confinement in the defective region.

Figure 3

The squares of the dipole matrix elements $|M_{\mathrm{C}\left(100\right){}_n/\mathrm{C}(5–7)}{|}^2$ for the optical transition at the threshold energy in the C(100)${}_n$/C(5–7) superlattices are compared with that of GaN, $|M_{\mathrm{GaN}}{|}^2$.

Figure 4

For the C(100)${}_{n=5}$/C(5–7) superlattice, (a) isosurfaces (0.07 electrons/Å${}^3$) of the charge densities of VBM (yellow) and CBM (red) and (b) their planar-averaged charge densities (in units of ${10}^{-2}$ electrons/Å${}^3$) are plotted along the superlattice direction ($z$ axis). Black vertical lines denote the positions of the C atoms in the C(5–7) layers.

Figure 5

The total energy versus volume and enthalpy versus pressure curves for various carbon allotropes [15, 16, 19] and the C(100)${}_n$/C(5–7) superlattices are calculated by using the PBE functional.

Figure 6

The full phonon spectra of the C(100)${}_n$/C(5–7) superlattices with $n=1–4$. The dynamical matrices are calculated by using the $4\times 3\times 3, 4\times 3\times 3, 4\times 3\times 2$, and $4\times 3\times 2$ supercells for $n=1$, 2, 3, and 4, respectively.

Figure 7

The variations of potential energies during finite-temperature ab initio molecular dynamics simulations at 2000 K are shown for the C(100)${}_n$/C(5–7) superlattices with $n=1–4$. The $4\times 2\times 3, 4\times 2\times 3, 4\times 2\times 1$, and $4\times 2\times 1$ supercells are chosen for $n=1$, 2, 3, and 4, respectively.

Figure 8

The variation of total energy is plotted as a function of the distance between two clean C(100) surfaces.

Figure 9

The calculated band structures of the C(100)${}_n$/C(5–7) superlattices with $n=1–4$ by using the PBE functional. The energy of the valence band maximum is set to zero.

Figure 10

The calculated band structures of the C(100)${}_n$/C(5–7) superlattices with $n=6–10$ by using the PBE functional. The energy of the valence band maximum is set to zero.

Figure 11

The orbital characteristics of the VBM, CBM, and second CBM states at the $\mathrm{\Gamma }$ point of the C(100)${}_{n=5}$/C(5–7) superlattice. Black solid lines indicate the first BZ of the fcc lattice of cubic diamond. The size of red circles is proportional to the degree of contributions from the bulk states in the fcc BZ of cubic diamond. Note that the wave function of VBM is mostly distributed in the C(100) layers, and its character is mainly derived from the bulk states around the $\mathrm{\Gamma }$ point. While the wave function of CBM is mostly confined in the defective layers, a small portion of its wave function is also distributed in the C(100) layers, and its orbital character is similar to those for the bulk states around the $\mathrm{\Gamma }$ point. On the other hand, the second CBM state is contributed from the bulk states around the $X$ valley and thus attributed to the zone folding effect.