V2 Silicon Vacancy in 4H-SiC

• V2 silicon vacancy defect is a negatively charged site in 4H-SiC with a quartet (S=3/2) spin state and distinct optical emission near 916–917 nm.
• It exhibits precise atomic structure and spin Hamiltonian parameters, including axial zero-field splitting and hyperfine interactions, critical for solid-state quantum devices.
• Optimized via nitrogen doping and annealing, V2 centers enable high-fidelity spin readout and scalable integration for quantum sensing and network applications.

The V2 silicon vacancy defect refers to a negatively charged silicon vacancy (V$_\text{Si}^-$) at the cubic (k) site in the 4H polytype of silicon carbide (SiC), exhibiting a quartet spin ground state ($S=3/2$) and intense zero-phonon optical emission near 916–917 nm. It is foundational for solid-state quantum devices, combining long spin coherence, robust charge-state stability, spin-dependent optical transitions, and favorable photo-electrical properties.

1. Atomic Structure, Electronic Configuration, and Symmetry

The V2 center is formed by the absence of a silicon atom at a quasi-cubic site in the 4H-SiC lattice. The local symmetry is C$_{3v}$, with a tetrahedron of four inward-relaxed carbon neighbors (three basal at 1.90 Å, one axial at 2.02 Å) (Csóré et al., 2021). The defect hosts a negatively charged state ($q=-1$), stabilized between the calculated (0/-) and (-/2-) charge transition levels at 1.26 eV and 2.47 eV above the valence band edge (Csóré et al., 2021). Electron irradiation and subsequent annealing are required for appreciable V2 production (Abraham et al., 2020, Carter et al., 20 Jun 2025).

In the electronic structure, the ground manifold is $^4A_2$ (quartet, $S=3/2$), arising from half-filled $a_1$ and $e$ defect orbitals in the gap (Dong et al., 2018). The first excited manifold is $^4E$. DFT calculations provide formation energies for V$_\mathrm{Si}^{(-)}$ around 7.47 eV–$E_F$ under stoichiometric conditions (Csóré et al., 2021).

2. Spin Hamiltonian, Zero-Field Splitting, and Hyperfine Interactions

The effective spin Hamiltonian for both ground and excited states in the defect’s symmetry frame is: $$H = D\,S_z^2 + E\,(S_x^2 - S_y^2) + \mu_B \bigl[ g_\parallel B_z S_z + g_\perp (B_x S_x + B_y S_y) \bigr]$$ with $S=3/2$, $E\approx0$ by symmetry, and $g_\parallel \approx g_\perp \approx 2.0028$ (Steidl et al., 11 Oct 2024, Csóré et al., 2021, Abraham et al., 2020). The axial zero-field splitting has ground-state $D_g/h$ values in the range 35–70 MHz, and excited-state $D_e/h\approx$1.0–1.03 GHz (Csóré et al., 2021, Banks et al., 2018). Hyperfine coupling to $^{13}$C neighbors is typically $\sim$10–15 MHz (Csóré et al., 2021).

The ground manifold comprises four substates ($m_s = \pm3/2, \pm1/2$), with the $|\pm3/2\rangle$ levels always lying lower in energy due to $D>0$. Spin transitions can be coherently manipulated via RF or microwave fields at the ZFS frequency.

3. Optical Properties: Zero-Phonon Line, Phonon Sideband, Lifetimes, and Linewidths

V2 is characterized by a sharp zero-phonon line (ZPL) at $E_\text{ZPL} \approx 1.352$–1.353 eV ($\lambda_\text{ZPL} \approx 916$–917 nm) (Steidl et al., 11 Oct 2024, Banks et al., 2018, Csóré et al., 2021, Okajima et al., 27 Nov 2025). Spin-selective optical transitions separate the $m_s=\pm3/2$ and $m_s=\pm1/2$ states by ~1.03 GHz (Banks et al., 2018). The associated phonon sideband spans 920–1300 nm (Carter et al., 20 Jun 2025), with a Debye–Waller factor (ZPL emission fraction) in the range 0.1–0.3 (Banks et al., 2018, Baranov et al., 2013).

Radiative lifetimes from time-resolved photoluminescence and master equation fits range from 6–11 ns; Fourier-limited linewidths are 14–24 MHz (Banks et al., 2018, Steidl et al., 11 Oct 2024). Experimentally, resonance fluorescence FWHM reaches 40–80 MHz under optimal bias, with further narrowing to the radiative limit in depleted devices (Steidl et al., 11 Oct 2024).

Thermal broadening follows $\Gamma(T) = \Gamma_0 + \alpha T^3$; ZPL energy shifts by $-80$ GHz/K are predicted for low temperatures (Steidl et al., 11 Oct 2024). Under reverse bias in Schottky geometries, linewidths narrow and charge-state switching is suppressed (Steidl et al., 11 Oct 2024).

4. Charge-State Dynamics, Photoionization, and Electrical Readout

The V2 center features robust charge-state stability under resonant optical excitation due to its ZPL’s position being farther from the ionization onset than V1. Ionization of V2 occurs with cross-section $\sigma_i(\lambda)$ rising at shorter wavelengths. Key measurements (Okajima et al., 27 Nov 2025):

Wavelength (nm)	Energy (eV)	$\sigma_i(\lambda)$ ($10^{-18}$ cm$^2$)
789	1.573	2.4 ± 0.3
852	1.455	1.8 ± 0.2
905	1.370	1.1 ± 0.1
940	1.319	0.7 ± 0.1

Carbon vacancies produce a steeply increasing background photocurrent. Single-defect photocurrent fraction (PCF) peaks in the 852–920 nm window, limited by background ionization; ensemble PCF favors longer wavelengths up to 940 nm for V2 selectivity (Okajima et al., 27 Nov 2025).

Photoionization rates are given by $I(\lambda)=q \sigma_i(\lambda) \Phi$, with $q$ the elementary charge and $\Phi$ the photon flux. In diode-integrated devices, two-color ionization shows a sharp threshold at 1.31 eV (948 nm) for V$^{-}$ to V$^{2-}$ transition, matching HSE-DFT predictions (Steidl et al., 11 Oct 2024).

5. Spin-Photon Dynamics, Optical Polarization, and Readout Protocols

In the V2 defect, spin initialization and selective population of the $|\pm1/2\rangle$ or $|\pm3/2\rangle$ sublevels proceeds via resonant optical excitation and intersystem crossing (ISC) through metastable shelving states. ISC rates exhibit strong spin selectivity—the $|\pm3/2\rangle$ ES sublevels relax three times faster to the doublet state than $|\pm1/2\rangle$ (Banks et al., 2018). Optical spin-readout contrasts reach up to 18% by monitoring photon emission from spin-selective lines (Banks et al., 2018). Theoretical models predict initialization fidelities approaching unity in sub-µs timescales (Dong et al., 2018).

Two distinct optical pumping channels exist:

• Channel I (ZPL-driven): polarization into $|\pm1/2\rangle$,
• Channel II (higher-energy excitation): adjustment of polarization into $|\pm3/2\rangle$ or $|\pm1/2\rangle$, determined by ISC decay rates (Dong et al., 2018).

Readout and control protocols have been implemented for repetitive single-shot spin state measurement, charge resonance check (CRC), and nuclear/electron spin quantum memory (Steidl et al., 11 Oct 2024).

6. Effects of Doping, Defect Engineering, and Materials Processing

Nitrogen-doping and controlled annealing play critical roles in modulating the charge state, photoluminescence (PL), and ODMR (optically detected magnetic resonance) contrast in V2 centers. Nitrogen donors (N$_\text{C}$) efficiently transfer electrons to V$_\text{Si}$, stabilizing the bright $q=-1$ charge state; excess nitrogen leads to overcharging (dark $q=-2$ state) or defect complexes (Carter et al., 20 Jun 2025).

Key outcomes from (Carter et al., 20 Jun 2025):

• PL versus irradiation dose is linear at low doping; at high doping, nonmonotonic dependence reflects multi-donor charge state stabilization.
• ODMR contrast increases 3× with $10^{17}$–$10^{18}$ cm$^{-3}$ N-doping plus annealing at 500–600 °C, at marginal loss in PL intensity.
• Shot-noise-limited magnetometry sensitivity improves by 1.6×, retaining $\sim100$ ns $T_2^*$ coherence times.
• Annealing reduces spin–lattice and strain-induced broadening.

Room-temperature quantum sensing and compatible on-chip integration are enabled by leveraging wafer-scale SiC and standard thermal processing (Carter et al., 20 Jun 2025, Abraham et al., 2020).

7. Quantum Sensing, Spin Coherence, and Device Implications

The V2 center is a premier candidate for quantum sensing (magnetometry, thermometry) due to:

• High-fidelity spin readout governed by defect-origin photocurrent fraction (Okajima et al., 27 Nov 2025).
• Room-temperature spin–lattice relaxation times $T_1\sim$1–10 ms, spin–spin coherence $T_2\sim$100–500 µs (dynamical decoupling) (Csóré et al., 2021, Abraham et al., 2020).
• Telecom-wavelength emission for low-loss fiber-coupling and remote quantum network applications (Abraham et al., 2020).
• Kramers-protected ZFS with negligible temperature drift ($\Delta D < 1$ kHz/K), robust operation over 10–300 K (Abraham et al., 2020).
• Implementation in Schottky diodes offers electrical Stark tuning, enhanced spectral homogeneity, and charge-state stabilization for networked photonic interfaces (Steidl et al., 11 Oct 2024).

V2 centers enable vector magnetometry and qudit protocols exploiting the $S=3/2$ manifold (Abraham et al., 2020), and their spin–photon interfaces are compatible with scalable device integration and future quantum technologies (Okajima et al., 27 Nov 2025, Carter et al., 20 Jun 2025, Steidl et al., 11 Oct 2024).

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References:

• “Photoionization current spectroscopy of individual silicon vacancies in silicon carbide” (Okajima et al., 27 Nov 2025)
• “nanoTesla magnetometry with the silicon vacancy in silicon carbide” (Abraham et al., 2020)
• “The influence of nitrogen doping and annealing on the silicon vacancy in 4H-SiC” (Carter et al., 20 Jun 2025)
• “Single V2 defect in 4H Silicon Carbide Schottky diode at low temperature” (Steidl et al., 11 Oct 2024)
• “Resonant optical spin initialization and readout of single silicon vacancies in 4H-SiC” (Banks et al., 2018)
• “Spin polarization through Intersystem Crossing in the silicon vacancy of silicon carbide” (Dong et al., 2018)
• “Point defects in SiC as a promising basis for single-defect, single-photon spectroscopy with room temperature controllable quantum states” (Baranov et al., 2013)
• “Identification of silicon vacancy-related electron paramagnetic resonance centers in 4H SiC” (Csóré et al., 2021)