On-Chip ESR Spectroscopy

• On-chip ESR spectroscopy is an integrated approach that embeds resonant structures on semiconductor chips to achieve highly sensitive electron spin detection at femtoliter-scale volumes.
• It utilizes diverse architectures—including planar LC resonators, microstrips, and hybrid quantum circuits—to enhance spectral resolution and enable single-spin detection.
• The technique powers applications in quantum information, semiconductor metrology, and nanoscale magnetism, driving advances in device miniaturization and detection limits.

On-chip electron spin resonance (ESR) spectroscopy refers to the implementation of ESR detection, control, and analysis methodologies within integrated, microfabricated chip architectures. These systems combine advanced planar resonator or microcoil designs, superconducting elements, optical/microwave control, and potentially quantum-limited amplifiers or detectors, enabling ESR with exceptional sensitivity, spectral resolution, and sample miniaturization across diverse material platforms. On-chip ESR spectrometers provide access to ultra-small detection volumes—including femtoliter (fL) and even single-spin regimes—and have become critical tools in fields such as quantum information processing, semiconductor device metrology, materials science, and nanoscale magnetism.

1. Device Architectures and Resonator Implementations

On-chip ESR spectrometers are primarily characterized by their integration of lumped-element or distributed microwave resonators directly onto semiconductor or dielectric chips. Key architectural variants include:

• Planar $LC$ resonators: These feature interdigitated capacitors and nanowire or spiral inductors patterned from thin superconducting films (e.g., Al, Nb) on high-purity substrates (such as isotopically enriched $^{28}$Si) (2002.03669, Wang et al., 2023). For example, a 50 nm Al film with a 100 nm $\times$ 10 $\mu$m nanowire confining microwave magnetic field $B_1$ to a few-fL mode volume achieves resonance at $\omega_0 \approx 2\pi\times7.25$ GHz and $Q_L\approx2.2\times10^4$.
• Microstrip and coplanar waveguide ($\lambda/2$) resonators: Atomically flat, epitaxial Cu strips on c-plane sapphire realize high-$Q$ microstrip resonators (e.g., $Q_\mathrm{exp}\approx 210$ at RT, $300$ at 10 K; mode volume set by $W\times \ell \sim$ mm$^2$) for ultra-high vacuum ESR of surface spin ensembles (Cho et al., 2023).
• Planar spiral microcoils: Two-turn coils ($\sim$270 $\mu$m diameter, $\sim$2.3 $\mu$m Al thickness) embedded in a CMOS process act both as ESR excitation and detection transducers (nominal $Q\sim10-17$), concentric with NMR coils for dynamic nuclear polarization (DNP) applications (Solmaz et al., 2020).
• Hybrid quantum circuit architectures: Designs coupling electron spins to superconducting flux qubits, transmon qubits, or single-microwave-photon detectors, often incorporating tunable resonators and dispersive bifurcation amplifiers for quantum-limited ESR spectroscopy (Budoyo et al., 2020, Kubo et al., 2012, Wang et al., 2023).
• Electrically-detected ESR with internal cavity excitation: Silicon quantum wells sandwiched between superconducting $\delta$-barriers exploit Josephson emission in planar microcavities, where ESR is detected via magnetoresistance rather than direct microwave pickup (Bagraev et al., 2013).

Optical access is incorporated for NV-center-based magnetometry platforms; confocal or waveguide networks provide local fluorescence collection (650–800 nm) for ensemble or single-defect ESR protocols (Abeywardana et al., 2015, Bucher et al., 2019, Hall et al., 2015).

2. Detection Modalities and Spin–Photon Coupling

The essential feature enabling high sensitivity in these platforms is tight confinement of the microwave magnetic field $B_1$ to small mode volumes ($V_\mathrm{mode}\sim6$ fL for $LC$ devices (2002.03669), $\sim10$ $\mu$m$^3$ for planar superconducting resonators (Wang et al., 2023)), maximizing the vacuum Rabi coupling $g_0$ between a single electronic spin and the resonator:

$$g_0(\mathbf{r}) = \frac{g_e\mu_B}{\hbar} \left\langle 0|S_x|1\right\rangle \delta B_1(\mathbf{r}),$$

where $g_e\simeq2$, $\mu_B$ is the Bohr magneton. Measured single-spin couplings reach $g_0/2\pi\simeq 3$ kHz in Bi-doped Si and erbium-doped crystals (2002.03669, Wang et al., 2023), relevant for Purcell-enhanced radiative decay and single-spin detection.

Detection strategies include:

• Reflection-based homodyne detection: Microwave echoes (e.g., Hahn-echo) routed via circulators to quantum-limited parametric amplifiers (JPA, JBA), providing sensitivity at the $\sim12$ spins$/\sqrt{\mathrm{Hz}}$ level (2002.03669).
• Photon counting with superconducting qubit detectors: Release of Purcell-enhanced fluorescence photons into a single-microwave-photon detector (SMPD), enabling single-spin SNR $\approx$2 in 1 s and anti-bunching signatures for unambiguous single-spin identification (Wang et al., 2023).
• Frequency-shift detection with flux qubit bifurcation amplifiers: ESR-induced dispersive shift of qubit transition frequency inferred from change in switching probability of a Josephson bifurcation amplifier (JBA); achieves minimum spin detection $N_\mathrm{min}=20$ spins in a 6 fL volume (Budoyo et al., 2020).
• Electrically-detected ESR: Spin resonance modulates edge channel magnetoresistance in Si quantum wells with integrated microcavities, producing normal-mode coupling signatures as doublet splittings in conductance without external microwave hardware (Bagraev et al., 2013).
• NV-based detection: NV centers in diamond serve as local field sensors, either via coherent control (Ramsey/echo/DEER) or via $T_1$ relaxation enhancement in the presence of ESR noise, sensitive down to single or few (<50) bath spins within $\sim 180$ nm$^3$ (Abeywardana et al., 2015, Hall et al., 2015, Bucher et al., 2019).

3. ESR Protocols, Pulse Sequences, and Readout Strategies

On-chip spectrometers employ a broad range of pulsed ESR protocols adapted to both device constraints and target spin systems:

• Hahn echo and dynamical decoupling: Standard $(\pi/2)_x-\tau-\pi_y-\tau$ and CPMG protocols, with pulse durations from 20 ns to 1 μs, enable measurement of transverse ($T_2$) and longitudinal ($T_1$) relaxation times and maintain sensitivity to coherence in dilute spin ensembles (2002.03669, Cho et al., 2023).
• ENDOR (electron-nuclear double resonance) and Rabi nutation: RF coils and modulation schemes integrated into on-chip setups allow hyperfine spectroscopy and advanced coherence manipulation on nanoscale samples (Cho et al., 2023).
• Phase cycling and optimal control: Introduced to mitigate drift and $B_1$ inhomogeneity; phase cycling reduces technical noise, while optimal control pulses can recover multi-echo gains otherwise suppressed by field inhomogeneity (2002.03669).
• NV-$T_1$ ESR/relaxometry: All-optical protocols using laser-pumped and fluorescence-readout NV centers, with variable static field sweeping the NV transition across the bath spectrum, exploiting the convolution of bath spectral density with the NV longitudinal relaxation filter function (Hall et al., 2015, Bucher et al., 2019).
• Single-photon and qubit-detected ESR: Microwave photon counting after pulsed inversion of individual rare-earth ions or spin ensembles, with time-resolved statistics to probe decay rates and second-order correlations (Wang et al., 2023, Kubo et al., 2012).

Typical repetition rates approach 100 Hz (dictated by recovery lifetimes and cooling loads), with single-shot and averaging strategies leveraged according to experimental and sensitivity requirements.

4. Sensitivity, Detection Volume, and Quantitative Benchmarks

On-chip ESR platforms have achieved unprecedented sensitivity and miniaturization, as summarized below:

Device type	Sensitivity	Detection Volume	Key References
Superconducting $LC$ + JPA	$12 \pm 3$ spins$/\sqrt{\mathrm{Hz}}$	$V_\mathrm{mode}\approx6$ fL	(2002.03669)
Planar resonator + SMPD	SNR $\approx$ 2, single spin in 1 s	$\sim$10 $\mu$m$^3$	(Wang et al., 2023)
Flux qubit + JBA	$N_\mathrm{min}=20$ spins in 1 s	6 fL	(Budoyo et al., 2020)
NV center (confocal, DEER)	$\leq$50 spins	$\sim$180 nm$^3$	(Abeywardana et al., 2015)
CMOS planar coil $LC$	$10^{14}$–$10^{15}$ spins/cm$^3$/kHz	$\sim$ 0.02 nL	(Solmaz et al., 2020)
Microstrip X-band (UHV)	$2.6 \times 10^{11}$ spins/(G·Hz$^{1/2}$)	mm$^3$-scale, thin films	(Cho et al., 2023)
Electrically-detected Si-QW	$10^3$–$10^4$ spins	$\sim 10^{-9}$ cm$^3$	(Bagraev et al., 2013)

These sensitivities are enabled by quantum-limited amplification (JPAs), minimized resonator mode volumes, optimized sample placement/filling factors, and, where applicable, statistical enhancement (e.g., $\sqrt{N}$ scaling for NV ensembles).

5. Spectral Resolution, Spectroscopy of Hyperfine and Inhomogeneous Effects

Spectral discrimination in on-chip ESR spans hyperfine-resolved, kHz-scale linewidths to broadband, MHz–GHz detection:

• Hyperfine splitting and qubit-scale metrology: In Si:P donor dots, ESR multiplet patterns and spacings directly encode the number and arrangement of phosphorus nuclei and electrons. By correlating measured multiplet structures to tight-binding simulations, atomic-scale metrology (few-nm resolution) is achieved (Wang et al., 2016).
• Linewidth broadening: Substrate-induced strain (e.g., differential thermal contraction of Al/Si) introduces hydrostatic strains $\epsilon\sim3\times10^{-4}$ and broadens hyperfine transitions via $dA/d\epsilon$, overlapping ESR lines over $\sim100$ MHz and reducing spectral resolution near nanowires (2002.03669). Away from such strain centers, narrow hyperfine features re-emerge, enabling site-selective spectroscopy.
• Inhomogeneity and field gradients: Spatial variation in $B_1$ (from geometric or materials inhomogeneity) leads to Rabi-angle dispersion, suppressing echo train gains and complicating signal calibration. Compensation strategies include targeted pulse shaping and device optimization (2002.03669, Cho et al., 2023).
• Broadband detection: NV-based $T_1$ relaxometry, while optimal for rapid, broadband sensing, sacrifices MHz-level spectroscopy for GHz-wide, few-ms temporal resolution, suited for transition-metal or radical detection at surfaces (Bucher et al., 2019).

6. Application Domains and Impact

The integration of ESR spectroscopy onto chip platforms enables a broad range of scientific and technological applications:

• Quantum information sciences: Atomic-scale characterization and non-invasive verification of donor dots, interface quality, and coherence lifetimes essential for scalable silicon qubit arrays (Wang et al., 2016, Jock et al., 2011).
• Materials defect metrology: Quantitative mapping of shallow traps at Si/SiO$_2$ interfaces, resolving order-of-magnitude differences in band-tail DOS unobservable in mobility data, with direct implications for semiconductor device reliability (Jock et al., 2011). On-chip ESR also applies to electrically-active defects in nanostructured oxides and quantum wells (Bagraev et al., 2013).
• Surface and thin-film magnetism: Ultra-high-vacuum, microstrip-based ESR reveals spin behavior in nm-thick films, molecular monolayers, and ordered surfaces down to cryogenic T, enabling spectroscopies of molecular electronics, low-dimensional magnets, and correlated electron systems (Cho et al., 2023).
• Biological and chemical analysis: “Quantum diamond” NV sensors deliver non-invasive, nanoscale detection of transition metals, radicals, and biomolecules on surfaces at ambient conditions (Bucher et al., 2019). Sub-nL dynamic nuclear polarization (DNP) with integrated ESR/NMR platforms enhances sensitivity for cell-scale metabolomics (Solmaz et al., 2020).
• Single-spin science: Demonstrations of unambiguous single-spin ESR via microwave photon counting and anti-bunching, coupled with ms-scale coherence readout (T$_2$) defined by the Purcell regime (Wang et al., 2023), define route to ultrasensitive spin memory and quantum transduction interfaces.

7. Limitations, Sources of Spectral Degradation, and Prospects for Improvement

Despite dramatic advances, limitations persist:

• Field and coupling inhomogeneities: Strong spatial variations in $B_1$ and $g_0$ across device mode volumes suppress protocol gains and introduce inhomogeneous broadening. Advanced control pulses, device geometry optimization, or new materials (e.g., higher-$H_c$ superconductors) are suggested remedies (2002.03669, Cho et al., 2023).
• Substrate strain and line broadening: Electroelastic coupling to underlayers, particularly at cryogenic T, can wash out hyperfine spectra, motivating the adoption of flip-chip integration on low-expansion substrates or engineered stress-relief layers (2002.03669).
• Quantum noise and technical drifts: Near-quantum-limited detection is sensitive to correlated amplitude fluctuations, $1/f$ flux noise (for qubit-based sensors), and technical drifts, which saturate SNR scaling and necessitate drift cancellation or bath engineering (e.g., squeezed vacuum) (Budoyo et al., 2020).
• Device integration and scale-up: While on-chip ESR devices have been arrayed for parallel detection, mutual couplings (especially between concentric ESR/NMR resonators), electromagnetic compatibility, and process complexity pose nontrivial scaling challenges for THz regime or large array deployment (Solmaz et al., 2020).

Authors consistently propose avenues for performance improvement: reduction of $V_\mathrm{mode}$ with narrower or multilayer conductors, replacement of Al by high-${H_c}$ superconductors (e.g., NbTiN), increasing $Q_\mathrm{int}$ by dielectric optimization, and suppression of technical noise through active feedback, optimal control pulses, or advanced quantum readout chains (2002.03669, Wang et al., 2023, Cho et al., 2023).

Taken together, on-chip ESR spectroscopy now occupies a central role in quantum, materials, and device science—enabling measurements at scales, sensitivities, and experimental configurations unattainable by conventional ESR. Continued innovations in device integration, quantum-limited detection, and noise engineering are expected to push these frontiers to single-spin, sub-fL, and atomically-targeted sensing regimes across the next generation of solid-state quantum platforms.