Optical properties of the neutral silicon split-vacancy center in diamond

The zero-phonon line (ZPL) at 1.68 eV has been attributed to the negatively charged silicon split-vacancy center in diamond, (Si-V)${}^{-}$, and has been extensively characterized in the literature. Computational studies have predicted the existence of the neutral charge state of the center, (Si-V)${}^0$, and it has been experimentally observed using electron paramagnetic resonance (EPR). However, the optical spectrum associated with (Si-V)${}^0$ has not yet been conclusively identified. In this paper the 1.31 eV band visible in luminescence and absorption is attributed to (Si-V)${}^0$ using an approach which combines optical absorption and EPR measurements. The intensities of both 1.68 eV and 1.31 eV bands are found to increase in deliberately Si-doped chemical vapor deposition (CVD) grown diamond, and also after electron irradiation and annealing, suggesting the involvement of both Si and a vacancy in the centers. The 1.31 eV ZPL is unambiguously associated to Si by its shift to a lower energy when the dominant Si isotope is changed from ${}^{28}$Si to ${}^{29}$Si. Charge transfer between (Si-V)${}^{-}$ and (Si-V)${}^0$ induced via ultraviolet photoexcitation or heating in the dark allows calibration factors relating the integrated absorption coefficient of their respective ZPLs to the defect concentration to be determined. Preferential orientation of (Si-V)${}^0$ centers in CVD diamond grown on $\left\{110\right\}$-oriented diamond substrates is observed by EPR. The (Si-V)${}^0$ centers are shown to grow predominantly into CVD diamond as complete units, rather than by the migration of mobile vacancies to substitutional Si (${\mathrm{Si}}_{\mathrm{S}}$) atoms. Corrections for the preferential alignment of trigonal centers for quantitative analysis of optical spectra are proposed and the effect is used to reveal that the 1.31 eV ZPL arises from a transition between the ${}^3{A}_{2g}$ ground state and ${}^3{A}_{1u}$ excited state of (Si-V)${}^0$. A simple rate equation model explains the production of (Si-V)${}^0$ upon irradiation and annealing of Si-doped CVD diamond. In as-grown Si-doped diamond the (Si-V) defects only account for a fraction of the total silicon present; the majority being incorporated as ${\mathrm{Si}}_{\mathrm{S}}$. The data show that both ${\mathrm{Si}}_{\mathrm{S}}$ and (Si-V) are effective traps for mobile vacancies.

Figure 1

(a) Schematic of the silicon split-vacancy defect in diamond, (Si-V), with the $\left\{110\right\}$ mirror plane highlighted. The silicon atom is illustrated as a large yellow sphere lying halfway between two vacant lattice sites; all other atoms are carbon, with the dangling orbitals shown in blue. The silicon atom is equidistant from six nearest-neighbor carbon atoms. (b) Simple molecular-orbital model for (Si-V): The central silicon atom and ligand orbitals interact, resulting in the molecular orbitals illustrated. The arrows indicate the 10 unpaired electrons available to fill the energy levels for (Si-V)${}^0$.

Figure 2

(a) NIR absorption and (b) PL spectra of sample A (after annealing at 2000 ${}^{\circ }\mathrm{C}$), taken at 77 K. In the absorption spectrum the peaks at 1.447 $\pm$ 0.001 eV and 1.493 $\pm$ 0.002 eV related to the photoconductivity threshold at 1.5 eV are visible.[35] The photoconductivity produces a rise in absorption which partially obscures the vibronic band of the 1.310 $\pm$ 0.001 eV feature. Vibronic structure can be resolved in the PL spectrum, though it is noteworthy that the data have not been corrected for the detector response, which decreases with decreasing energy and so may reduce the apparent size of the band.

Figure 3

Raman-normalized PL spectra measured at 5 K of sample A when it was (a) as-grown and (b) annealed at 2000 ${}^{\circ }\mathrm{C}$. The 1.31 eV feature was visible in both absorption and PL; all other labeled features were not detected in absorption.

Figure 4

(a) Integrated absorption coefficient of the 1.31 eV ZPL as a function of the sample temperature. The solid curve is the best fit to the data using Eq. (1). (b) Temperature variation of the 1.31 eV ZPL Raman-normalized PL integrated intensity, measured using 785-nm excitation. The broken curve shows the variation in the absorption and is for comparison only. The solid line is the best fit of the data to Eq. (2). Uncertainties on the integrated absorption and the Raman-normalized PL integrated intensity measurements are estimated to be $\pm 10\%$. These experiments were made using sample A after it had been annealed at 2000 ${}^{\circ }\mathrm{C}$.

Figure 5

Visible/NIR absorption spectra obtained at 4 K for samples B (thin, blue line) and C (thick, red line), which have ${}^{29}$Si isotopic abundances of $90\%$ and $4.7\%$, respectively. The spectral intensities have been normalized to the maximum height of the each band to facilitate comparison. The (a) 1.31 eV and (b) 1.68 eV bands shift to a lower energy by 0.4 $\pm$ 0.1 meV when the ${}^{29}$Si abundance was increased.

Figure 6

EPR spectra of (Si-V)${}^0$ at $X$-band frequencies for the as-grown sample A with the magnetic field aligned parallel to the (a) $\left[\overline{1}1\overline{1}\right]$ or (b) [111] directions, where the growth plane is assumed to be (110). The former direction lies in the growth plane while the other lies out of the growth plane. The difference in the relative resonance line intensities of the spectra is attributed to the preferential alignment of the centers in this sample. If the centers were statistically aligned along each crystallographically equivalent direction the resulting spectra would look like the simulated spectrum (c).

Figure 7

Correlation between the integrated absorption coefficient of the 1.31 eV ZPL (recorded at 77 K) and the concentration of (Si-V)${}^0$ as determined by EPR. The black circles represent data for samples where the (Si-V)${}^0$ centers are statistically aligned. The remaining data points were recorded for samples where the (Si-V)${}^0$ centers exhibited a degree of preferential alignment, which could be quantified using EPR. The effect of preferential alignment on the absorption measurements has been corrected assuming that the 1.31 eV band is produced by either an $A$ $\to$ $A$ transition (green squares) or an $A$ $\to$ $E$ transition (blue triangles).

Figure 8

Raman-normalized PL intensity of the (a) 1.31 eV and (b) 1.68 eV zero-phonon lines as a function of silicon concentration in a sample D consisting of layers with different Si-doping levels. The sample has been electron irradiated and annealed twice in order to produce vacancy complexes. Please refer to the text for treatment details. The data for the 1.31 eV band (open symbols) were acquired at 100 K while the 1.68 eV data (solid symbols) were measured at 77 K. The uncertainties for the Raman-normalized PL intensity and silicon concentration measurements are both $\pm 10\%$. The dashed lines are included to guide the eye of the reader.

Figure 9

Schematic representation of the energy levels of (Si-V)${}^0$ (not to scale) used to explain 1.31 eV emission and absorption. There is an allowed optical ZPL transition from the ${}^3{A}_{2g}$ ground state to the 1.31 eV excited state and an intermediate state $\Delta E_t$ below the 1.31 eV excited state to which optical transitions from the ground state are forbidden. The 1.31 eV ZPL emission could be excited using a 785-nm (1.58 eV) laser in two ways. (a) An electron is excited directly from the ${}^3{A}_{2g}$ ground state into the vibronic band of the 1.31 eV excited state. Relaxation to the bottom of the 1.31 eV excited state followed by emission is possible, but a nonradiative transition to the intermediate state could also occur. (b) Excitation of an electron from the valence band to the 1.31 eV excited or intermediate states and trapping of the resultant hole by the ${}^3{A}_{2g}$ ground state. Again, once the electron reaches the bottom of the excited state 1.31 eV ZPL emission is possible. In both cases, if the excited electron ends up in the intermediate state emission will not occur unless it is thermally excited into the 1.31 eV state, as illustrated by a zig-zag arrow.

Figure 10

Cartoon of a view along a (110) growth plane, displaying the atomic scale roughness of the surface. Bonds that lie in the growth plane ($\left[\overline{1}1\overline{1}\right]$ and $\left[1\overline{1}\overline{1}\right]$) are shown in red and those that are out of the growth plane ([111] and $\left[\overline{1}\overline{1}1\right]$) are indicated by blue bonds.

Figure 11

Theoretical polarization dependence of the optical excitation for trigonal defects with their symmetry axes aligned parallel to $\langle 111\rangle$ directions lying in [dashed (black) and thin solid (red) curves] and out of [thick solid (blue) curve] the growth plane for CVD diamond grown on a $\left\{110\right\}$-oriented substrate for (a) an $A\to A$ transition and (b) an $A\to E$ transition.

Figure 12

Schematic of the main phenomena occurring during the charge transfer process involving (Si-V)${}^0$, (Si-V)${}^{-}$, ${\mathrm{N}}_{\mathrm{S}}^0$, ${\mathrm{N}}_{\mathrm{S}}^{+}$, and the neutral and negative charge states of an unknown trap T. (a) When samples are heated for 20 min at 577 ${}^{\circ }\mathrm{C}$ (Si-V)${}^0$ centers are converted to (Si-V)${}^{-}$ centers by two processes: Electrons are thermally released from the valence band to the (Si-V)${}^0$ acceptor levels, converting them into (Si-V)${}^{-}$ centers. Electrons are also thermally excited from the ${\mathrm{N}}_{\mathrm{S}}^0$ levels into the conduction band, from which they can de-excite into the (Si-V)${}^0$ level. Simultaneously, recombination between T${}^{-}$ and the holes in the valence band occurs. (b) Illuminating with light of energy equal to or greater than the band gap excites electrons from the valence band into the conduction band. The electrons can then migrate and de-excite into the ${\mathrm{N}}_{\mathrm{S}}^{+}$ and T${}^0$ levels. Some of the holes which were consequently produced in the valence band trap electrons from the (Si-V)${}^{-}$ centers, increasing the (Si-V)${}^0$ concentration.

Figure 13

(Si-V)${}^0$ concentration in the different layers of sample D after electron irradiation and annealing treatments 1 and 2 (Table ). The lines indicate the simulated behavior when the system is modeled to include the loss of vacancies to dislocations and the formation (and destruction) of (Si-V) and (Si-V${}_2$) centers via the reactions $\text{Si}+\text{V}\to \text{(Si-V)}$ and $\text{(Si-V)}+\text{V}\to \text{(Si-V}{}_2\text{)}$.