Light emission from direct band gap germanium containing split-interstitial defects

The lack of useful and cost-efficient group-IV direct band gap light emitters still presents the main bottleneck for complementary metal-oxide semiconductor-compatible short-distance data transmission, single-photon emission, and sensing based on silicon photonics. Germanium, a group-IV element like Si, is already widely used in silicon fabs. While the energy band gap of Ge is intrinsically indirect, we predict that the insertion of Ge-Ge split-[110] interstitials into crystalline Ge can open up a direct band gap transmission path. Here, we calculate from first principles the band structure and optical emission properties of Ge, Sb, and Sn split-[110] interstitials in bulk and low-dimensional Ge at different doping concentrations. Two types of electronic states provide the light-emission enhancement below the direct band gap of Ge: a hybridized L-$\mathrm{\Gamma }$ state at the Brillouin zone center and a conduction band of $\mathrm{\Delta }$ band character that couples to a raised valence band along the $\mathrm{\Gamma }$-X direction. Majority carrier introduced to the system through doping can enhance light emission by saturation of nonradiative paths. Ge-Sn split interstitials in Ge shift the top of the valence band towards the $\mathrm{\Gamma }$-X direction and increase the $\mathrm{\Gamma }$ character of the L-$\mathrm{\Gamma }$ state, which results in a shift to longer emission wavelengths. Key spectral regions for datacom and sensing applications can be covered by applying quantum confinement in defect-enhanced Ge quantum dots for an emission wavelength shift from the midinfrared to the telecom regime.

Figure 1

Calculated atomic structure of a Ge crystal containing (a) a Ge-Ge split-[110] self-interstitial and (b) a Ge-Sb split-[110] interstitial defect. Ge atoms are indicated as violet spheres while the Sb atom is depicted in gold.

Figure 2

Electronic band structure of a Ge interstitial in bulk Ge with the TB-mBJ $(c=1.158)$ potential. The concentration is 1 interstitial per 128 Ge atoms. The points labeled L and X on the reduced Brillouin zone correspond to the ½ L and ¼ X points in the unfolded zone shown below in Fig. 3. The empty circles' size is proportional to the partial charge of the state on the interstitial atoms. The color indicates the band index.

Figure 3

Left panel: (blue) Calculated band structure of undisturbed crystalline Ge, using the self-consistent value of the TB-mBJ potential. Gray: Unfolded electronic band structure of a Ge-Ge split-[110] self-interstitial. The concentration of additional Ge atoms is 1 interstitial per 128 Ge atoms. The darkness of the gray points indicates the proportion of overlap with a plane wave with the corresponding wave vector. Right panel: Calculated DOS in units of states per eV per atom for Ge bulk (blue), for the atoms contributing to the Ge split interstitial (black), and for the next-nearest Ge atoms to the split interstitial (red dashed line).

Figure 4

Left panels: Unfolded electronic band structure (using the self-consistent value of the TB-mBJ potential) of (a) a Sb-Ge split-[110] interstitial, (b) a Ge-Sn split-[110] interstitial, both with a concentration of 1 split-interstitial per 128 Ge atoms. Notice in (b) for the Sn-Ge interstitial that the top of the VB is ¼ along the $\mathrm{\Gamma }$-X line, rather than at the $\mathrm{\Gamma }$ point. The darkness of the gray points denotes the proportion of overlap with a plane wave with the corresponding wave vector. Right panel in (a) and (b): Calculated density of states in units of states per eV per atom for Ge bulk (blue), for the Ge, Sb, and Sn atoms contributing to the split interstitial (black) and for the next-nearest Ge atoms to the split interstitial (red dashed lines).

Figure 5

Calculated PL spectrum of a Ge with 1/128 Ge-Ge split-[110] self-interstitials for a different number of excitons, $N_{\mathrm{eh}}$. The three distinctive peaks at 1800, 1550, and 1400 nm are due to the $\mathrm{\Gamma }$-L state to the top of the valence band, the ${\mathrm{\Gamma }}_{\mathrm{cb}}$ state in pure Ge to the first and second topmost of the valence band, and the ${\mathrm{\Gamma }}_{\mathrm{cb}}$ state to the third topmost valence band. Contributions from the valence-band maxima to the conduction-band pinned state at ¼ X ($\mathrm{\Delta }$ direction) introduce additional intensity.

Figure 6

Influence of the Ge-Ge split-[110] self-interstitial (s.i.) concentration on the PL for different exciton concentrations, $N_{\mathrm{eh}}=5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$ (black) and at $N_{\mathrm{eh}}=2.5\times {10}^{19}\mathrm{c}{\mathrm{m}}^{–3}$ (red). The concentration of interstitials considered increases from 1/128 (solid line) to 1/64 (dashed line).

Figure 7

Calculated photoluminescence spectra obtained for a Ge crystal containing Ge-Ge split-[110] self-interstitials and a exciton concentration of $N_{\mathrm{eh}}=5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$. Additional concentrations of electrons $N_{\mathrm{n}}$ (a) and holes, $N_{\mathrm{p}}$ (b) in the range from $5\times {10}^{18}$ to $2.5\times {10}^{19}\mathrm{c}{\mathrm{m}}^{–3}$ are introduced.

Figure 8

Comparison of the effects of a Sn (dashed line) and Ge (solid line) split-[110] interstitial (in figure labeled as s.i.) on the calculated photoluminescence at two exciton concentrations, $N_{\mathrm{eh}}=5\times {10}^{18}$ and $2.5\times {10}^{19}\mathrm{c}{\mathrm{m}}^{–3}$. The PL emission due to the Sn-Ge interstitial has been multiplied by a factor of 60 and 6 times, respectively, to compare to the Ge self-interstitial.

Figure 9

(a) Calculated PL emission from Sn-Ge split-[110] interstitial at an exciton density of $2.5\times {10}^{19}\mathrm{c}{\mathrm{m}}^{–3}$ without (blue) and with additional $p$-type doping density of $2.5\times {10}^{19}\mathrm{c}{\mathrm{m}}^{–3}$ (red). The PL response from a Ge-Ge split-[110] self-interstitial without doping is depicted in black. The green line shows the contribution from the $\mathrm{\Gamma }$-L mixed state at $N_{\mathrm{p}}=2.5\times {10}^{19}\mathrm{c}{\mathrm{m}}^{–3}$. The contribution from the top of the valence band at ¼ $X_{\mathrm{orig}}$ to the first CB at ¼ $X_{\mathrm{orig}}$ to the overall PL is negligible at low $N_{\mathrm{eh}}$. (b) Same case as (a) except for a lower exciton concentration $N_{\mathrm{eh}}$ of $5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{–3}$.

Figure 10

(a) Calculated PL emission from Sn-Ge split-[110] interstitial at an exciton density of $2.5\times {10}^{19}\mathrm{c}{\mathrm{m}}^{–3}$ without (blue) and with additional $n$-type doping density of $2.5\times {10}^{19}\mathrm{c}{\mathrm{m}}^{–3}$ (red). The PL response from a Ge-Ge split-[110] self-interstitial without doping is depicted in black. The green curve shows the contribution from the top of the valence band at ¼ $X_{\mathrm{orig}}$ to the first conduction band, also at ¼ $X_{\mathrm{orig}}$, to the overall PL with doping. The contribution from the ¼ $X_{\mathrm{orig}}$ bands without doping is close to zero. (b) Same case as (a) with exciton concentration $N_{\mathrm{eh}}=5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{–3}$.

Figure 11

Calculated photoluminescence of Ge with a Ge-Ge split-[110] self-interstitial at a different number of excitons that are quantum confined in a $3\times 20\times 20\mathrm{n}{\mathrm{m}}^3$ box. The peak at longer wavelength is due to the L-$\mathrm{\Gamma }$ mixed band. The ${\mathrm{\Gamma }}_{\mathrm{cb}}$ band in pure Ge to the top valence bands forms the peak at shorter wavelengths.