A CN complex as an alternative to the T center in Si

Abstract

We present a first-principles study of a carbon-nitrogen (CN) impurity complex in silicon as an isoelectronic alternative to the T center [(CCH)$_\mathrm{Si}$]. The latter has been pursued for applications in quantum information science, yet its sensitivity to the presence of hydrogen is still problematic. Our proposed complex has no hydrogen, thereby eliminating this issue. First, we show that the CN complex is stable against decomposition into substitutional and interstitial defects. Next, we show that due to being isoelectronic to the T center, the CN complex has a similar electronic structure, and therefore could be used in similar applications. We assess several low-energy configurations of the CN complex, finding (CN)$_\mathrm{Si}$ to be stable and have the largest Debye-Waller factor. We predict a zero-phonon line (ZPL) of 828 meV (in the telecom S-band) and a radiative lifetime of 4.2 $μ$s, comparable to the T center. Due to the presence of a bound exciton, choice of the exchange-correlation functional and also supercell-size scaling of the ZPL and transition dipole moment require special scrutiny; we rigorously justify our extrapolation schemes that allow computing values in the dilute limit.

Figures (5)

• Figure 1: Structure of (a) T center, (CCH)$_\mathrm{Si}$, (b) (CN)$_\mathrm{Si}$, and (c) C$_\mathrm{Si}$(NSi)$_\mathrm{Si}$.
• Figure 2: Defect formation energies as a function of Fermi level for the T center (orange), (CN)$_\mathrm{Si}$ (green), and C$_\mathrm{Si}$(NSi)$_\mathrm{Si}$ (blue). Blue and green shades indicate valence and conduction bands. The valence-band maximum (VBM) is set to 0, and the conduction-band minimum (CBM) is at 1.15 eV, our calculated Si band gap.
• Figure 3: Ground- (top row) and excited-state (bottom row) Kohn-Sham states for the neutral charge state. "e-h" ("h-e") labels the localized-electron (hole) case. Blue and green shades indicate valence and conduction bands. Red levels are the states associated with the defect, and blue levels are valence- and conduction-band states.
• Figure 4: Isosurfaces (yellow) of real-space Kohn-Sham probability densities for the neutral charge state of the ground-state in-gap empty spin-down state [(a)--(c)] and filled spin-up state [(d)], and of the excited-state in-gap filled spin-down state [(e)--(g) for localized-electron case] and empty spin-up state [(h) for localized-hole case]. Blue circles are Si; brown, C; light blue, N; and pink, H.
• Figure 5: Zero-phonon line energies for the T and CN centers, calculated using either single-shot PBE0 or HSE and plotted as a function of inverse supercell size ($N$ is the number of atoms in the defect-free supercell). The lines are linear fits. The horizontal orange line represents the measured ZPL of the T center, 935 meV from Ref. ref:bergeron.