Spatially Resolved Decoherence of Donor Spins in Silicon Strained by a Metallic Electrode

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	UNSW Sydney, CEA Grenoble
Citations	8
Analysis	Full AI Review Included

Technical Documentation & Analysis: Spatially-Resolved Decoherence in Silicon Donor Spins

This document analyzes the research paper “Spatially-resolved decoherence of donor spins in silicon strained by a metallic electrode” to provide technical specifications and highlight how 6CCVD’s advanced CVD diamond materials and fabrication capabilities can accelerate and scale similar quantum research, particularly in diamond-based spin systems.

Executive Summary

This study successfully maps the spatial dependence of decoherence in shallow Bismuth (Bi) donor spins in isotopically purified ²⁸Si, providing critical insights into interface noise mechanisms relevant for solid-state quantum devices.

Core Achievement: Achieved long coherence times (T₂ up to 300 ms) in near-surface Bi donor spins (mean depth 100 nm) by utilizing magnetic-field-insensitive Clock Transitions (CT).
Decoherence Mechanism: Decoherence is spatially dependent and primarily limited by magnetic noise originating from paramagnetic impurities (dangling bonds/P_b defects) at the Si/SiO₂ interface.
Strain Dominance: Mechanical strain, caused by the differential thermal contraction between the Aluminum (Al) electrode and the Si substrate, is confirmed as the dominant spectral broadening mechanism.
Spatial Mapping: Strain-induced frequency shifts enabled the spatial mapping of spin coherence, revealing a surface spin defect density of $4 \times 10^{12}$ cm^-2 away from the wire.
CT Limitation: At the Clock Transition, the residual decoherence is limited by non-magnetic charge noise, suggesting the need for improved interface engineering.
6CCVD Relevance: The methodology is explicitly applicable to other spin systems, including defects in diamond (e.g., NV centers), where 6CCVD’s ultra-high purity Single Crystal Diamond (SCD) substrates offer a path to mitigate the observed surface noise limitations.

Technical Specifications

The following hard data points were extracted from the experimental results and device parameters:

Parameter	Value	Unit	Context
Maximum Coherence Time (T₂)	300	ms	Measured at the Clock Transition (CT) in Res1.
Mean Donor Depth	100	nm	Estimated mean depth of Bi donors below the surface.
Operating Temperature	~15	mK	Base temperature of the dilution refrigerator.
Substrate Isotopic Purity	0.05	%	Residual ²⁹Si concentration in epitaxial layer.
Aluminum Electrode Thickness	50	nm	Thickness of the superconducting LC resonator inductor.
Resonator Inductor Widths (w)	5, 2, 1	µm	Res1, Res2, and Res3 geometries, respectively.
Magnetic Noise Magnitude ($\delta$B)	5	nT	Estimated average fluctuation for spins below the inductor.
Surface Spin Density ($\sigma_1$)	$4 \times 10^{12}$	cm^-2	Estimated density away from the Al wire (Si/SiO₂ interface).
Non-Magnetic Decoherence Rate ($\Gamma_{non}$)	3	s^-1	Measured at CT, attributed to charge noise.
Strain Inhomogeneity	~20	%	Local fluctuation of the strain tensor around the modeled value.

Key Methodologies

The experiment combined advanced material processing with quantum-limited microwave spectroscopy to achieve spatial resolution of spin decoherence.

Substrate Preparation: Utilized an isotopically purified epitaxial layer of ²⁸Si (100) with a native silicon oxide layer.
Donor Implantation: Bismuth (Bi) atoms were shallow-implanted approximately 75 nm below the surface to create the spin ensemble.
Surface Cleaning: The chip underwent Piranha solution cleaning (3:1 mix of H₂SO₄ and H₂O₂ at 120°C) prior to resonator fabrication.
Superconducting Circuit Fabrication: Three LC superconducting resonators (Res1, Res2, Res3) were patterned using standard electron-beam lithography and 50 nm Aluminum (Al) evaporation.
EPR Spectroscopy: Measurements were performed using quantum-limited Electron Paramagnetic Resonance (EPR) spectroscopy at millikelvin temperatures (~15 mK), magnetically coupling the Bi spins to the Al resonator.
Coherence Measurement: The Hahn-echo sequence ($\pi/2 - \tau - \pi - \tau - \text{echo}$) was used to measure the coherence time (T₂) across various spin transitions.
Noise Differentiation: The transition-dependent effective gyromagnetic ratio ($\gamma_{eff}$) and the use of magnetic-noise-insensitive Clock Transitions (CT) were leveraged to separate magnetic noise (surface spins) from non-magnetic charge noise (interface fluctuations).
Strain Modeling: Finite element simulations (COMSOL) were employed to calculate the strain tensor ($\epsilon$) resulting from the differential thermal contraction between the Al wire and the Si substrate during cooldown.

6CCVD Solutions & Capabilities

The findings underscore the critical role of material purity, interface quality, and strain management in achieving long coherence times for near-surface solid-state qubits. 6CCVD’s expertise in MPCVD diamond directly addresses the limitations identified in this silicon-based study, offering superior platforms for next-generation quantum devices.

Applicable Materials

The research explicitly notes that this technique is applicable to defects in diamond. To replicate or extend this research using diamond spin qubits (e.g., NV, SiV centers), 6CCVD recommends:

Optical Grade Single Crystal Diamond (SCD): Essential for hosting highly coherent spin defects. 6CCVD provides SCD with ultra-low nitrogen and defect concentrations, minimizing the bulk spin bath noise that limits T₂.
High-Purity Polycrystalline Diamond (PCD): For applications requiring large-area coverage or thick substrates (up to 10 mm), 6CCVD PCD offers excellent thermal properties and mechanical stability, crucial for managing strain in hybrid devices.

Customization Potential

The experimental setup relied on precise material dimensions and electrode integration. 6CCVD offers tailored solutions to meet these demanding specifications:

Research Requirement	6CCVD Capability	Benefit to Quantum Research
Interface Quality	SCD Polishing: Ra < 1 nm	Minimizes surface dangling bonds and P_b defects, directly mitigating the dominant magnetic noise source identified in the paper ($\sigma \sim 10^{12}$ cm^-2).
Substrate Size	Plates/wafers up to 125 mm (PCD)	Enables scalable fabrication of large-scale quantum integrated circuits, moving beyond small lab-scale chips.
Electrode Integration	Custom Metalization (Au, Pt, Pd, Ti, W, Cu)	Allows precise deposition of superconducting or normal metal electrodes (like the 50 nm Al used here) with optimized adhesion and thermal properties to manage strain.
Thickness Control	SCD/PCD Thickness: 0.1 µm - 500 µm	Provides precise control over the depth of the spin ensemble (analogous to the 75 nm Bi implantation depth) or the thickness of the diamond substrate itself.
Strain Management	Custom Substrate Thickness (up to 10 mm)	Thicker, high-stiffness diamond substrates offer superior mechanical stability, reducing the impact of differential thermal contraction strain observed in the Al/Si system.

Engineering Support

6CCVD’s in-house PhD material science team specializes in optimizing CVD diamond for quantum applications. We offer consultation services to assist researchers in:

Material Selection: Choosing the optimal SCD grade and crystal orientation to minimize strain and maximize the coherence time of near-surface spin defects (e.g., NV centers).
Surface Termination: Advising on surface treatments necessary to maintain the ultra-low defect density required for high-coherence near-surface qubits, addressing the charge noise limitation observed at the Clock Transition.
Custom Fabrication: Designing metalization stacks and dimensions for integration with superconducting resonators or gate electrodes, ensuring compatibility with millikelvin operation.

Call to Action: For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

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.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevx.11.031036