Spatially Resolved Decoherence of Donor Spins in Silicon Strained by a Metallic Electrode
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2021-08-16 |
| Journal | Physical Review X |
| Authors | V. Ranjan, B Albanese, E. Albertinale, Billaud E, D Flanigan |
| Institutions | Centre National de la Recherche Scientifique, Lawrence Berkeley National Laboratory |
| Citations | 8 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This research presents a comprehensive study on mitigating decoherence in shallow-implanted Bismuth (Bi) donor electron spins in isotopically purified 28Si, focusing on the detrimental effects of device interfaces and metallic electrodes.
- Spatial Decoherence Mapping: The study successfully uses strain-induced frequency shifts (fΔ), caused by the differential thermal contraction of the aluminum (Al) electrode, to spatially map spin coherence (T2) as a function of depth and lateral position relative to the electrode.
- Record Coherence Time: By operating the spins at a magnetic-field-insensitive Clock Transition (CT) near 27 mT, the coherence time (T2) was extended up to 300 ms at a mean donor depth of only 100 nm.
- Noise Source Identification: The use of transition-dependent effective gyromagnetic ratios (γeff) allowed for the separation of noise sources:
- Magnetic Noise (dominant away from CT) originates from fluctuating paramagnetic defects (dangling bonds) at the Si/SiO2 interface.
- Charge Noise (dominant at CT) originates from 1/f charge fluctuations at the interface, causing quadratic Stark shifts.
- Interface Quantification: The surface paramagnetic defect density (σ) was quantified: 4 x 1012 cm-2 away from the Al wire, and 1012 cm-2 below the wire, suggesting a passivating effect by the aluminum.
- Strain Inhomogeneity: Spectral analysis confirms that strain broadening dominates the spectrum, and the strain field exhibits local fluctuations (~20% variation) on a scale of approximately 50 nm.
- Quantum Device Relevance: The combination of strain splitting and the Clock Transition extends T2 lifetimes by up to two orders of magnitude, confirming the viability of shallow donors for quantum technologies despite interface proximity.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Substrate Material | Isotopically purified 28Si | N/A | 0.05% residual 29Si concentration. |
| Donor Species | Bismuth (Bi) | N/A | Electron spin S=1/2, Nuclear spin I=9/2. |
| Implantation Depth | ~75 | nm | Mean depth below the surface. |
| Operating Temperature | ~15 | mK | Base temperature of dilution refrigerator. |
| Maximum Coherence Time (T2) | 300 | ms | Measured at the Clock Transition (CT). |
| Minimum Coherence Time (T2) | 3 | ms | Measured far from the wire (magnetic noise limited). |
| Clock Transition (CT) Field (B0) | 27 | mT | Magnetic field where γeff = 0. |
| Zero Field Splitting (ZFS) | 7.375 | GHz | Separation between F=4 and F=5 manifolds. |
| Hyperfine Coupling (A/2π) | 1.475 | GHz | Bi donor in Si. |
| Surface Defect Density (σ1) | 4 x 1012 | cm-2 | Away from the Al wire (Si/SiO2 interface). |
| Surface Defect Density (σ2) | 1012 | cm-2 | Below the Al wire (reduced density). |
| Strain Inhomogeneity (σB) | ~20 | % | Fluctuation around the modeled strain value. |
| Stark Effect Coefficient (η) | (-0.26 ± 0.05) x 10-3 | µm2/V2 | Quadratic dependence of ΔA(E)/A0 on electric field E. |
| Resonator Material | Aluminum (Al) | N/A | 50 nm thick superconducting film. |
| Resonator Linewidth (κ/2π) | ~150 | kHz | Typical resonator bandwidth. |
| Spin-Photon Coupling (g0/2π) | 102 - 103 | Hz | Enhanced due to small mode volume. |
Key Methodologies
Section titled “Key Methodologies”The experiment relies on advanced nanofabrication, cryogenic measurement, and sophisticated pulse sequences combined with finite element modeling (FEM).
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Device Fabrication:
- Substrate Preparation: Use of a silicon (100) chip with an epitaxial layer of isotopically purified 28Si.
- Implantation: Bismuth donors are shallow-implanted (~75 nm mean depth).
- Resonator Patterning: Three LC superconducting resonators (Res1, Res2, Res3) with varying inductor widths (5 µm, 2 µm, 1 µm) are patterned using electron-beam lithography (EBL) and aluminum evaporation (50 nm thick).
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Cryogenic Measurement Setup:
- Temperature: Measurements performed in a dilution refrigerator at ~15 mK.
- EPR Detection: Quantum-limited Electron Paramagnetic Resonance (EPR) spectroscopy is performed using the superconducting LC resonators coupled to the spins.
- Amplification: Reflected signals are amplified using a Josephson Traveling Wave Parametric Amplifier (TWPA) for high sensitivity (103 spins/√Hz range).
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Coherence Measurement Techniques:
- Hahn Echo Sequence: Used to measure the coherence time (T2) via the sequence π/2-τ-π-τ-echo.
- Dynamical Decoupling (DD): Uhrig Dynamical Decoupling (UDD) and Carr-Purcell-Meiboom-Gill (CPMG) sequences were used to characterize the noise power spectrum S(ω), confirming an approximate 1/f noise scaling (N-1/2).
- Instantaneous Diffusion (ID) Study: T2 measured as a function of refocusing pulse angle (θ) and bandwidth (Ω) to quantify local inhomogeneous broadening and donor concentration (found to be 5 x 1014 cm-3).
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Modeling and Analysis:
- Strain Simulation: Finite Element Simulations (COMSOL) calculate the strain tensor (ε) resulting from differential thermal contraction between Al and Si during cooldown (from 300 K to 15 mK).
- Spectral Fitting: The strain tensor is used to predict the strain-induced frequency shift (fΔ) and fit the measured EPR spectra, confirming strain as the dominant broadening mechanism.
- Magnetic Noise Modeling: A minimal model discretizes surface paramagnetic defects into point dipoles (Bohr magneton magnitude) to calculate the rms magnetic noise (δB(x, y)) and spatially map the surface defect density (σ).
Commercial Applications
Section titled “Commercial Applications”The findings regarding high-coherence shallow donors and the detailed understanding of interface noise are critical for the development and scaling of solid-state quantum devices.
- Solid-State Quantum Computing: Bismuth donors in 28Si are leading candidates for spin qubits. Achieving T2 times up to 300 ms near the surface is essential for integration with metallic gates and readout circuitry (CMOS compatibility).
- Quantum Memories: The long coherence times (T2 and T1) make these donor ensembles suitable for long-lived microwave quantum memories, potentially interfacing with superconducting qubits.
- Quantum Sensing: The high sensitivity of the donor spins to local magnetic fields (away from CT) and electric fields (at CT) enables the development of highly localized quantum sensors for characterizing noise in semiconductor environments.
- Interface Engineering and Reliability: The quantification of paramagnetic defect densities (4 x 1012 cm-2) and the spatial mapping of noise provide crucial feedback for optimizing the Si/SiO2 interface fabrication processes, which is relevant for minimizing 1/f noise in advanced CMOS and superconducting circuits (flux noise mitigation).
- Advanced Semiconductor Metrology: The technique of using strain gradients to achieve spatial resolution of spin properties can be applied to characterize defects and noise in other critical materials systems, such as defects in diamond (NV centers) or silicon carbide (SiC).
View Original Abstract
Electron spins are amongst the most coherent solid-state systems known. However, to be used in devices for quantum sensing and information processing applications, they must typically be placed near interfaces. Understanding and mitigating the impacts of such interfaces on the coherence and spectral properties of electron spins is critical to realizing such applications, but it is also challenging: Inferring such data from single-spin studies requires many measurements to obtain meaningful results, while ensemble measurements typically give averaged results that hide critical information. Here, we report a comprehensive study of the coherence of near-surface bismuth donor spins in 28-silicon at millikelvin temperatures. In particular, we use strain-induced frequency shifts caused by a metallic electrode to infer spatial maps of spin coherence as a function of position relative to the electrode. By measuring magnetic-field-insensitive clock transitions, we separate magnetic noise caused by surface spins from charge noise. Our results include quantitative models of the strain-split spin resonance spectra and extraction of paramagnetic impurity concentrations at the silicon surface. The interplay of these decoherence mechanisms for such near-surface electron spins is critical for their application in quantum technologies, while the combination of the strain splitting and clock transition extends the coherence lifetimes by up to 2 orders of magnitude, reaching up to 300 ms at a mean depth of only 100 nm. The technique we introduce here to spatially map coherence in near-surface ensembles is directly applicable to other spin systems of active interest, such as defects in diamond, silicon carbide, and rare earth ions in optical crystals.