Breakdown-to-Coercive Field Ratio (EBD/Ec)

Updated 18 November 2025

Breakdown-to-Coercive Field Ratio (EBD/Ec) is a dimensionless metric comparing the dielectric breakdown field with the coercive field to define the safe operating window for ferroelectric switching.
It aids in benchmarking device robustness and scaling by linking measurement techniques like PUND, C–V, and Weibull analysis to material reliability and endurance.
Optimizing EBD/Ec is crucial for CMOS integration and advancing nonvolatile memory and logic applications, as it directly impacts switching performance and energy efficiency.

The breakdown-to-coercive-field ratio (EBD/Ec) is a quantitative metric central to the design, scaling, and reliability analysis of ferroelectric thin-film devices. It compares the dielectric breakdown field (EBD)—the threshold for irreversible failure—with the coercive field (Ec)—the minimum field required to reversibly switch polarization. This dimensionless ratio defines the safe operational voltage window in which polarization switching can be reliably achieved without incurring catastrophic dielectric failure. Across current literature, EBD/Ec is recognized as a critical figure of merit for evaluating new ferroelectric materials, benchmarking device robustness, and assessing integration maturity for advanced logic, memory, and photonic platforms.

1. Formal Definitions and Measurement Protocols

The coercive field, Ec, is the electric field at which 50% of the remanent polarization reverses sign in a ferroelectric capacitor. In practice, Ec is extracted using one or more of the following techniques:

PUND (Positive-Up-Negative-Down) sequence: The "hump" in the dynamic current response is used to identify the voltage, VC, at which switching occurs; Ec is then calculated as Ec = VC / t, where t is the ferroelectric film thickness (Wang et al., 14 Apr 2025, Tong et al., 11 Nov 2025, Casamento et al., 2021).
Capacitance–voltage (C–V) butterfly measurements: Inflection points in the quasi-static C–V curve determine VC and hence Ec (Wang et al., 14 Apr 2025, Tong et al., 11 Nov 2025).

The breakdown field, EBD, denotes the field where the dielectric becomes suddenly and irreversibly conductive (hard breakdown). EBD is determined via:

I–V (current–voltage) sweeps: The abrupt vertical jump in the current marks breakdown; EBD = VBD / t (Wang et al., 14 Apr 2025).
For statistical reliability, EBD values are often subjected to Weibull analysis to extract scale (E₀) and shape (β) parameters, establishing the breakdown field at a defined failure probability (commonly F = 63.2%) (Tong et al., 11 Nov 2025).

2. Experimental Observations in Representative Material Systems

Measured values of Ec and EBD—and therefore the EBD/Ec ratio—are highly material- and process-dependent. A summary of explicit results across wurtzite ferroelectrics and related systems is provided below.

Material	Thickness (nm)	Ec (MV/cm)	EBD (MV/cm)	EBD/Ec	Reference
Al₀.₈Sc₀.₂N	163	4.0 (300 K), 7.0 (4 K)	8.5 (300 K), 12.6 (4 K)	2.1 (300 K), 1.8 (4 K)	(Wang et al., 14 Apr 2025)
AlBScN	10	4.6 (PUND)	10.0 (Weibull, 10 μm)	2.2	(Tong et al., 11 Nov 2025)
Sc₀.₁₈Al₀.₈₂N (MBE on GaN)	100	0.65–0.7 (300 K)	3.5 (GaN, literature)	~5.0–5.4	(Casamento et al., 2021)
	200	1.2	3.5	~2.9	(Casamento et al., 2021)

In Al₀.₈Sc₀.₂N, Ec increases monotonically upon cooling, reaching 7.0 MV/cm at 4 K. EBD also rises but saturates below 200 K, with a measured value of 12.6 MV/cm at 4 K; the EBD/Ec ratio narrows to 1.8 at deep cryogenic temperatures (Wang et al., 14 Apr 2025).

For 10 nm AlBScN, Ec from PUND pulses is 4.6 MV/cm, while Weibull-statistics yield EBD ≈ 10.0 MV/cm for 10 μm diameter capacitors, resulting in EBD/Ec = 2.2 (Tong et al., 11 Nov 2025).

Epitaxial Sc₀.₁₈Al₀.₈₂N/GaN heterostructures display substantially lower Ec (0.65–1.2 MV/cm at 100–200 nm thickness), with EBD set by the GaN substrate at approximately 3.5 MV/cm, yielding breakdown-to-coercive-field ratios from 2.5 to >5, contingent on parameter selection (Casamento et al., 2021).

3. Temperature, Thickness, and Operational Dependencies

Both Ec and EBD are sensitive to temperature, thickness, switching frequency, and material microstructure.

Temperature effects: In Al₀.₈Sc₀.₂N, Ec increases linearly as temperature decreases from 400 K to 4 K (cryogenic coefficient −5.06 kV·cm⁻¹·K⁻¹), whereas EBD increases and then plateaus at low temperatures due to a transition from Poole–Frenkel hopping to Fowler–Nordheim tunneling in conduction processes. EBD/Ec decreases but remains above unity over the full temperature range (Wang et al., 14 Apr 2025).
Thickness scaling: In MBE-grown ScAlN/GaN, Ec increases as film thickness increases (0.65→1.2 MV/cm from 100→200 nm), reducing the EBD/Ec margin. Thinner films maximize breakdown margin but may show lower remanent polarization (Casamento et al., 2021).
Frequency: Ec exhibits frequency dependence, increasing with higher measurement frequencies, thus decreasing the breakdown margin at RF switching speeds (Casamento et al., 2021).
Statistical spread: Weibull shape parameter β increases as capacitor area decreases, indicating reduced scatter in breakdown field and predictable endurance for scaled devices (Tong et al., 11 Nov 2025).

4. Significance for Device Design, Reliability, and CMOS Integration

EBD/Ec quantifies the operational safety margin for ferroelectric switching. Ratios substantially greater than unity ensure that write fields can be applied robustly without risking catastrophic dielectric failure.

Memory endurance: Margins of EBD/Ec > 2 enable switching cycles > 2 × 10⁶ in Al₀.₈Sc₀.₂N, supporting high-endurance nonvolatile memory applications even at deep cryogenic temperatures (Wang et al., 14 Apr 2025).
Voltage scaling: Low Ec enables scaling towards low-voltage operation in 10 nm AlBScN, while maintaining a margin of ~2.2 for reliable device operation and lower energy consumption (switching energy ∝ C·V²) (Tong et al., 11 Nov 2025).
CMOS-compatibility: Boron incorporation in AlBScN reduces leakage by two orders of magnitude without sacrificing margin, establishing CMOS back-end-of-line compatibility (Tong et al., 11 Nov 2025).
Integration with GaN logic: MBE-grown ScAlN layers with low Ec allow switching within the GaN breakdown limit, a prerequisite for monolithic integration of nonvolatile ferroelectrics with GaN electronic and photonic circuits (Casamento et al., 2021).

5. Comparative Perspective with Other Ferroelectric Systems

Relative EBD/Ec values in leading ferroelectric systems:

HfO₂-based ferroelectrics: Ultrathin (a few nm) generally display EBD/Ec ≈ 2–3, comparable to AlBScN and superior to thick conventional AlScN (Tong et al., 11 Nov 2025).
Perovskite ferroelectrics (e.g., PZT): Ratios can exceed 4–5, but aggressive thickness scaling below 20 nm presents substantial challenges (Tong et al., 11 Nov 2025).
AlScN thin films: Comparable thicknesses yield Ec up to 9.8 MV/cm and EBD/Ec ratios as low as 1.0, often restricting voltage margin for reliable switching (Tong et al., 11 Nov 2025).

AlBScN successfully combines low Ec, robust EBD/Ec ratio (~2.2), and ultrathin scaling, positioning it favorably for next-generation embedded and standalone memory applications.

6. Implications, Uncertainties, and Design Considerations

Margin requirements: Practical device operation requires EBD/Ec > 1.0 under all operational conditions to preclude destructive breakdown (Casamento et al., 2021).
Uncertainty quantification: Measurement error in PUND-derived Ec is typically ±0.1 MV/cm; Weibull-derived EBD uncertainty is ±0.2–0.5 MV/cm. The propagated uncertainty in EBD/Ec is generally ±0.1 (Tong et al., 11 Nov 2025).
Device scaling: Smaller capacitor areas exhibit higher Weibull β values, suggesting breakdown becomes increasingly defect-limited and less stochastic, which is beneficial for array-level uniformity (Tong et al., 11 Nov 2025).
Materials trade-offs: Lowering Ec through epitaxial control, dopant incorporation, or compositional optimization remains essential for maximizing the breakdown-to-coercive-field margin, but must be balanced against potential reductions in remanent polarization and endurance (Casamento et al., 2021, Tong et al., 11 Nov 2025).

7. Broader Context and Outlook

EBD/Ec is an indispensable metric for benchmarking the voltage window available for ferroelectric switching. Advances in process integration, compositional engineering (e.g., boron doping in AlScN), and epitaxial quality (as in MBE ScAlN/GaN) continue to drive improvements in this ratio, thus enabling:

Wide-temperature nonvolatile memories operational from cryogenic quantum computing environments up to standard microelectronics (Wang et al., 14 Apr 2025).
Reliable ferroelectric switching at deeply scaled voltages and dimensions, ultimately facilitating 3D integration and heterogeneous logic/memory in advanced CMOS and GaN-based circuits (Tong et al., 11 Nov 2025, Casamento et al., 2021).

Ongoing research focuses on further narrowing measurement uncertainties, controlling extrinsic breakdown pathways, and extending EBD/Ec margins through advanced materials design. The robust assessment and optimization of EBD/Ec remain central to the realization of high-reliability, energy-efficient, and densely integrated ferroelectric technologies.