PUND Measurements in Ferroelectric Devices

• PUND measurements are an electrical pulse protocol employing four defined pulses (P, U, N, D) to separate switching currents from background leakage.
• They enable accurate extraction of remanent polarization and coercive fields by subtracting non-switching currents from total measured charge.
• The technique is adaptable across ferroelectric and antiferroelectric systems, aiding in diagnosing defect evolution, fatigue, and interface effects.

Positive-Up-Negative-Down (PUND) measurements are a class of electrical pulsed protocols developed to quantitatively disentangle switching (hysteretic, ferroelectric or antiferroelectric) currents from non-switching (linear/dielectric displacement, leakage, and parasitic) currents using selective voltage-pulse sequencing. The PUND methodology is universally adopted for robust extraction of intrinsic remanent polarization and coercive field in both conventional ferroelectric, antiferroelectric, and emerging high-leakage or low-P systems, as well as for tracking defect-related degradation processes and benchmarking device reliability under stress.

1. Concept and Pulse Protocols

The canonical PUND sequence consists of four main voltage pulses—Positive (P), Up (U), Negative (N), Down (D)—applied in succession to a ferroelectric or antiferroelectric capacitor. Each pulse has a defined polarity, amplitude, rise/fall time, and plateau:

• P (Positive switching pulse): Swaps polarization "down"→"up" and records both switchable and non-switchable currents.
• U (Up non-switching pulse): Same polarity immediately after P, designed not to switch domains; measures only non-switching background.
• N (Negative switching pulse): Reverses "up"→"down," capturing switching plus background.
• D (Down non-switching pulse): Follows N, same polarity, records only background in "down" state.

Each pulse is parameterized to saturate switching (field amplitude Eₚ > E_c, typical widths from microseconds to milliseconds), with carefully controlled relaxation intervals to allow dissipation of transient non-ferroelectric current components (Chowdhury et al., 2016, Tong et al., 11 Nov 2025, Yousefian et al., 2 May 2025).

For antiferroelectrics, as in the AFE-PUND protocol, the pulse architecture is doubled: two four-pulse blocks are applied at positive and negative relaxation biases to account for dual transitions (AFE ↔ FE) inherent to field-induced phase switching (Magagnin et al., 9 Jan 2025).

2. Mathematical Framework: Extraction of Switching and Non-Switching Components

PUND analysis centers on current transient integration and background subtraction:

• Switched charge (ΔQ): For each switching pulse (P, N), subtract the corresponding non-switching pulse (U, D):
  • ΔQ⁺ = Q_P – Q_U (positive branch)
  • ΔQ⁻ = Q_N – Q_D (negative branch)
• Total polarization (normalized by area, A):
  • P_sw⁺ = ΔQ⁺ / A
  • P_sw⁻ = ΔQ⁻ / A
  • Full-cycle (remanent) polarization: P_r = (P_sw⁺ + |P_sw⁻|) / 2

This subtraction removes both dielectric displacement and leakage (Ohmic and trap-assisted) currents as long as these are repeatable across pulses of identical amplitude and shape. Non-switching polarization P_ns can be quantified by averaging U and D responses, providing a sensitive metric for defect-related leakage evolution (Smith et al., 22 Jun 2025).

For antiferroelectric AFE-PUND, switched and non-switched charge are integrated over each sub-cycle (Q_SW,1/Q_NSW,1 and Q_SW,2/Q_NSW,2) and summed to yield total cycle values. Coercive field E_c is determined at the field corresponding to the maximum dP/dE or by identifying the voltage of peak switching current (Magagnin et al., 9 Jan 2025).

3. Experimental Realizations and Protocol Variants

PUND implementations are tailored to sample type, leakage magnitude, and time constants:

• Bulk and thick-film FE systems: Rectangular or triangular pulses of ms-range duration; little sensitivity to leakage (Chai et al., 2011).
• Improper, low-P, highly leaky, or nanoscopic ferroelectrics: PUND is essential for eliminating large background currents. For the lowest-P and most resistive samples (e.g., LuFeO₃ with P_r ~ nC/cm²), only extended multi-pulse trains (up to 14 pulses) yield fully time-relaxed, intrinsic polarization (Chowdhury et al., 2016).
• High-leakage/ultrathin systems: Standard four-pulse PUND remains effective only if background conduction is state-independent; otherwise, advanced corrections (such as Asymmetric Least Squares baseline subtraction) must be applied (Mohapatra et al., 2022).
• Antiferroelectric thin films (e.g., ZrO₂): AFE-PUND with dual blocks is mandatory, employing adaptive relaxation voltages and careful baseline correction, reflecting the complexity of AFE↔FE double transitions (Magagnin et al., 9 Jan 2025).
• CMOS-grade wurtzite nitrides (e.g., AlBScN, AlScN): Short rectangular pulses (ns–µs), probe stations with triaxial cabling, and synchronization for accurate current capture under high-field stress and over wide temperature ranges (Tong et al., 11 Nov 2025, Yousefian et al., 2 May 2025).

Typical quantitative parameter settings are tabulated below for representative device classes:

Device	Pulse Width (μs–ms)	Field Amplitude (MV/cm)	Leakage Mitigation
AlBScN 10 nm	2	3–5.6	P–U, N–D baseline, triaxial
LuFeO₃ bulk	1–5	≈1	PUND/extended pulse train
ZrO₂ AFE	2	3.5	Two PUND blocks, U-subtr.
Al₀.₉₃B₀.₀₇N 190 nm	0.5	6	U–D correction, PL tracking

4. Protocol Limitations and Error Sources

While PUND is widely used, its accuracy is contingent on key physical and device parameters:

• Ferro-resistive anomalies: If leakage/conduction depends on the polarization state (e.g., in tunnel junctions or via trap occupancy modulation), the standard P–U subtraction is invalid; background subtraction approaches such as Asymmetric Least Squares (AsLS) yield improved and nearly offset-free polarization loops (Mohapatra et al., 2022).
• Metal–Ferroelectric–Dielectric–Metal (MFDM) stacks: Internal depolarization field, charge trapping, and injection at the dielectric interface lead to errors in the switched charge extraction. Numerical simulations show that errors can reach >90% for slow/sparse traps or thick dielectrics; fast and dense traps minimize error but mask true polarization switching (Segatto et al., 2022).
• Fatigue, imprint, and wake-up: Growing leakage or partially stabilized defect populations can artificially inflate or suppress the extracted P_r or shift coercive voltages over cycling. Comparison of the switched and non-switched PUND components is essential for diagnosing degradation (Smith et al., 22 Jun 2025, Magagnin et al., 9 Jan 2025).
• Pulse time constants: Non-relaxed charge and insufficient dwell lead to partial switching or overestimated non-switching baselines; empirically, pulse width ≥10×(RC) and delay ≥5×(RC) are mandatory in leaky/slow-relaxing systems (Chowdhury et al., 2016).

5. Microstructural, Defect, and Endurance Insights from PUND

PUND is applied not only for quantifying Pr and Ec, but also as a diagnostic tool for:

• Tracking fatigue and wake-up: The evolution of non-switched PUND polarization (P_ns) correlates directly with the buildup of defect populations (e.g., nitrogen vacancies in AlBScN) as confirmed by photoluminescence spectroscopy, with P_ns yielding a sensitive quantitative marker for fatigue precursors (Smith et al., 22 Jun 2025).
• Thickness and scaling behavior: In antiferroelectrics (e.g., ZrO₂), AFE-PUND cycles reveal empirical P_r∝t^0.3–0.4 and E_c∝t^–0.1–0.2 scaling, reflecting increasing domain stability and screening in thicker films (Magagnin et al., 9 Jan 2025).
• Microstructural correlations: PUND-extracted parameters, combined with XRD and TEM, inform on grain size, dead layer development, interface quality, and phase composition, closing the feedback loop between device physics and performance (Magagnin et al., 9 Jan 2025).

6. Application: High-Temperature and Low-Voltage Ferroelectric Devices

PUND measurements under extreme thermal and voltage environments directly benchmark new materials:

• In AlBScN vs. AlScN thin films, PUND-extracted P_r remains stable (<10% variation) up to 600°C (E_c(T) = 6.2 → 4.2 MV/cm), with two orders-of-magnitude lower leakage for boron-doped films (Yousefian et al., 2 May 2025). This underpins application in back-end-of-line (BEOL) CMOS memory and high-T logic.
• Ultrafast PUND on 10 nm AlBScN yields E_c = 4.6 MV/cm and E_BD/E_c ≈ 2.2 with 100-fold diminished leakage, supporting aggressive thickness scaling (Tong et al., 11 Nov 2025).
• In improper ferroelectrics with broad relaxation spectra, extended 14-pulse PUND trains enable fully relaxed, artifact-free P_r even at picocoulomb/cm² scales, extending quantitative measurement to previously inaccessible regimes (Chowdhury et al., 2016).

7. Current Best Practices and Recommendations

• Use PUND over simple triangular sweeps in any lossy, leaky, or low-P system.
• For systems where conduction is polarization state-dependent, supplement PUND subtraction with fitting-based background removal (AsLS or analogous).
• Match pulse duration and inter-pulse delay to the slowest relaxation and leakage decay constants in the device stack.
• In ferroelectric–dielectric heterostructures, complement PUND with low-frequency capacitance and charge-based probing to unmask depolarization and trapping artifacts (Segatto et al., 2022).
• Periodically monitor non-switced PUND polarization for early signs of device fatigue, correlation with spectroscopic defect signatures, or the onset of interfacial dead-layer effects (Smith et al., 22 Jun 2025, Magagnin et al., 9 Jan 2025).

In sum, Positive-Up-Negative-Down (PUND) measurement protocols are the field standard for the quantitative, artifact-minimized extraction of intrinsic switching properties in ferroelectric, antiferroelectric, and related dielectrics, provided that protocol parameters, background subtraction, and device-specific limitations are rigorously managed (Chowdhury et al., 2016, Magagnin et al., 9 Jan 2025, Chai et al., 2011, Smith et al., 22 Jun 2025, Segatto et al., 2022, Mohapatra et al., 2022, Yousefian et al., 2 May 2025, Tong et al., 11 Nov 2025).