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Transition metal impurities in silicon - computational search for a semiconductor qubit

MetadataDetails
Publication Date2022-08-19
Journalnpj Computational Materials
AuthorsCheng‐Wei Lee, Meenakshi Singh, Adele C. Tamboli, Vladan Stevanović
InstitutionsNational Renewable Energy Laboratory, Colorado School of Mines
Citations8
AnalysisFull AI Review Included
  • Core Challenge Addressed: The search targets optically active, deep point defects in crystalline silicon (Si) to overcome the limited scalability and extremely low operating temperatures (<10 K) of current Si-based qubits (e.g., 31P donors).
  • Goal: Identify defects analogous to the high-temperature, optically addressable Nitrogen-Vacancy (NV) centers in diamond, but hosted in scalable Si.
  • Methodology: A comprehensive computational screening of 3d, 4d, and 5d Transition Metal (TM) impurities (substitutional and interstitial) using the HSE06(+U) Density Functional Theory (DFT) method.
  • Key Achievement: Seven TM impurities were identified as promising candidates, satisfying the criteria for stable spin-triplet ground states (S=1) and having optically allowed triplet-triplet transitions within the Si band gap.
  • Optical Properties: The predicted optical transitions occur in the mid-infrared (mid-IR) range (0.4-0.6 eV, or 2066-3100 nm).
  • Most Promising Candidates: Interstitial defects (Sci+1, Vi+1, Zri0, Zri+2) are favored due to lower formation energies. Zri defects are particularly attractive due to their predicted low diffusion coefficients, suggesting high immobility post-creation.
  • Impact: This work provides the first step toward developing Si-based qubits with potential for higher operating temperatures for quantum sensing and establishes a pathway for mid-IR spin-photon interfaces.
ParameterValueUnitContext
Host MaterialCrystalline Silicon (Si)N/AMature semiconductor platform.
Computational MethodHSE06(+U) DFTN/AUsed to correct band gap and d-orbital overlocalization.
Calculated Si Band Gap1.16eVIn excellent agreement with experimental value (1.17 eV).
Calculated Si Lattice Constant5.43AIn agreement with experimental value.
Required Spin StateTriplet (S=1)N/AGround and excited states required for NV-center-like operation.
Triplet Transition Energy0.4-0.6eVIn-gap optical transition range.
Triplet Transition Wavelength2066-3100nmMid-infrared (Mid-IR) range.
Absorption Coefficient (alpha)103-104cm-1Predicted high transition probability for first peaks.
Thermal Excitation Gap (TM in Si)0.1-0.2eVSmallest energy difference in single-particle defect-level diagram (DLD).
NV Center Thermal Excitation Gap0.3-0.9eVComparison value for diamond NV centers.
31P in Si Operating Temperature<10KCurrent limitation for Si donor qubits.
Candidate Substitutional TMsCoSi-1, CuSi-1, ZnSi0N/AIdentified stable charge states.
Candidate Interstitial TMsSci+1, Vi+1, Zri0, Zri+2N/AIdentified stable charge states.
  1. Defect Structure Generation: Calculations were performed on 216-atom supercells for two primary defect types: substitutional (TM replacing Si) and tetrahedral interstitial (TMi). Si-vacancy/TM-substitutional complexes were also investigated but yielded no viable candidates.
  2. Total Energy Calculation: Spin-polarized Generalized Hybrid DFT (HSE06) was used, employing the standard mixing parameter (alpha = 0.25) to accurately predict the Si band gap and lattice constant.
  3. Koopmans’ Condition Correction (HSE06+U): To address the overlocalization of TM d-orbitals by HSE06, an occupation-dependent potential (equivalent to a DFT+U correction) was applied to the TM d-orbitals if the non-Koopmans’ energy (ENK) deviation was greater than 0.2 eV.
  4. Thermodynamic Screening (CTL): Defect formation energies and thermodynamic Charge Transition Levels (CTLs) were calculated. A minimum of two CTLs within the Si band gap was required to potentially host both a triplet ground state and a triplet excited state.
  5. Spin State and Localization Screening: Single-particle defect-level diagrams (DLDs) were analyzed to ensure a stable spin-triplet ground state (S=1) and to confirm that the mid-gap defect states were sufficiently localized (using charge density visualization) and far from the band edges (Delta E > 0.05 eV).
  6. Optical Transition Verification: One-particle optical absorption coefficients (alpha) were calculated using the linear response approach to verify that the predicted triplet-triplet transitions were symmetry-allowed and possessed high transition probability (alpha > 103 cm-1).
  • Quantum Sensing (Higher Temperature): The identified TM defects offer a pathway to develop Si-based quantum sensors that can operate at temperatures significantly higher than current Si donor qubits, potentially approaching room temperature sensing capabilities seen in diamond NV centers.
  • Spin-Photon Interfaces: These defects provide a natural optical interface for coupling and reading out spin donor qubits in silicon, a critical missing component for Si-based quantum computing architectures.
  • Mid-Infrared (Mid-IR) Free-Space Communication: The 2-3 ”m transition wavelengths fall within atmospheric windows, making these TM impurities potential mid-IR emitters for long-distance, free-space optical communication, bypassing the high attenuation of silica fiber in this range.
  • Integrated Quantum Photonics: Leveraging the mature Si manufacturing platform to integrate quantum emitters directly into silicon photonic circuits, essential for scalable quantum device fabrication.
  • Quantum Memory: Specific candidates like Zri0 and Zri+2, which exhibit low predicted diffusion coefficients (immobility), are highly suitable for serving as stable hosts for long-lived nuclear spin quantum memories.
View Original Abstract

Abstract Semiconductors offer a promising platform for physical implementation of qubits, but their broad adoption is presently hindered by limited scalability and/or very low operating temperatures. Learning from the nitrogen-vacancy centers in diamond, our goal is to find equivalent optically active point defect centers in crystalline silicon, which could be advantageous for their scalability and integration with classical devices. Transition metal (TM) impurities in silicon are common paramagnetic deep defects, but a comprehensive theoretical study of the whole 3 d series that considers generalized Koopmans’ condition is missing. We apply the HSE06(+U) method to examine their potential as optically active spin qubits and identify seven TM impurities that have optically allowed triplet-triplet transitions within the silicon band gap. These results provide the first step toward silicon-based qubits with higher operating temperatures for quantum sensing. Additionally, these point defects could lead to spin-photon interfaces in silicon-based qubits and devices for mid-infrared free-space communications.