Towards Piezo-Nuclear Microgenerators: Beta Radiation Conversion Experiments and a Proposed Protocol

Towards Hybrid Betavoltaic–Ferroelectric Microgenerators: Experimental Validation Protocol Paolo Giordana [email protected] September 20, 2025 Abstract This document proposes a revised experimental protocol aligned with the latest theoretical framework (Version 8 of the “Abstract for the Creation of a New Class of Nuclear Microreactors”). Earlier hypotheses assumed a purely piezoelectric conversion mechanism, in which βelectrons would directly induce strain and polarization in ceramic domains. Subsequent bounding calculations, however, showed that this pathway is fundamentally limited to efficiencies η≲10−6, making it unsuitable for practical power generation. The protocol is therefore redefined around a hybrid betavoltaic–ferroelectric (BV+FE) architecture. In this scheme, wide-bandgap betavoltaic junctions (SiC, GaN, diamond) perform the primary conversion by generating electron–hole pairs from βdeposition. An ultrathin ferroelectric assist layer (HfZrO2or advanced PZTX) enhances charge separation, reduces recombination, and provides a rectifying field. The experimental objectives are twofold: (i) to demonstrate a measurable relative efficiency boost (∆ηrel ≥20%) of BV+FE devices compared to BV-only controls, and (ii) to verify the unambiguous ferroelectric signature, namely inversion of the zero-bias current under poling reversal. Rigorous blind controls (non-ferroelectric dielectrics, unpoled and above-TCPZT) and anti-artifact strategies (isothermal conditions, beam modulation with lock-in detection, guard electrodes, insulating interlayers) are retained from previous versions. The revised protocol therefore represents a decisive Go/No-Go test for the hybrid BV+FE concept: if successful, it validates a new class of compact nuclear microgenerators; if negative, it establishes clear limits on the role of ferroelectrics in direct β-to-electric conversion. 1 Introduction The direct conversion of β−radioactive decay energy into electricity remains a key research field for autonomous, long-duration power generation in extreme environments where maintenance is impossible or economically unsustainable. Traditional solutions, such as betavoltaic cells or radioisotope thermoelectric generators (RTGs), suffer from intrinsic limitations: BV devices typically offer limited efficiencies, while RTGs require bulky thermal stages and moving parts. Earlier research proposed that ceramic piezoelectrics might enable direct conversion of βenergy into electrical signals without macroscopic motion. That hypothesis has 1 now been conclusively dismissed, as theoretical bounds confirm that pure piezoelectric transduction cannot exceed negligible efficiencies. The present focus is therefore redirected toward the more physically consistent BV+FE hybrid architecture, where ferroelectric thin films act as efficiency boosters for conventional betavoltaic junctions. The present protocol defines the first systematic experimental approach to testing this hybrid concept. It specifies materials, irradiation methods, measurement criteria, and success thresholds, with particular emphasis on measurable efficiency boost and polingdependent inversion — the unique signatures of ferroelectric assistance. The aim is to establish a clear experimental pathway for validating or rejecting the BV+FE architecture as a basis for nuclear microgenerators. 2 State of the Art: Known Experiments Over the past twenty years, numerous studies have investigated direct conversion of βdecay energy, primarily through betavoltaic devices or hybrid microelectromechanical (MEMS) systems. •Haim et al. (2018): demonstrated a Ni-63 device that produced 22.5 nW with 6.6% efficiency1. The mechanism was purely capacitive, with no piezoelectric or ferroelectric role. •Duggirala et al. (2008): integrated a ZnO cantilever with Ni-63, achieving pulsed power up to 750 µW2. This design relied on macroscopic mechanical motion, making it unsuitable for static solid-state architectures. •Bulyarskii et al. (2017): provided theoretical optimization of Si p-i-n betavoltaics3, but did not address ferroelectric enhancements. •Wang et al. (2023): reviewed piezoelectric harvesting under cyclic mechanical stress4, without exploring radiation-driven effects. Overall, no prior work has tested hybrid BV+FE devices or identified ferroelectric signatures under βirradiation. This absence defines the novelty of the present protocol, which explicitly targets efficiency boost and poling-dependent inversion as primary observables. 3 Limitations of Existing Approaches The literature analysis highlights critical gaps that the new protocol addresses: •No ferroelectric-assisted betavoltaics tested. Existing experiments omit the role of ferroelectric thin films as efficiency boosters. 1Y. Haim, Y. Marciano, G. deBotton, “Tunable direct beta-radiation harvester at the nanowatt scale”, Sensors and Actuators A, 2018. https://doi.org/10.1016/j.sna.2018.03.007 2R. Duggirala, H. Li, A. Lal, “High efficiency beta radioisotope energy conversion”, Applied Physics Letters, 2008. https://doi.org/10.1063/1.2898204 3S. V. Bulyarskii et al., “Direct conversion of β-decay energy into electrical energy”, Russian Microelectronics, 2017. https://link.springer.com/article/10.1134/S1063739717010024 4S. Wang et al., “Piezoelectric-Based Energy Conversion and Storage Materials”, Batteries, 2023. https://doi.org/10.3390/batteries9040192 2 •Lack of comparative BV-only vs BV+FE measurements. No studies report relative boost metrics (∆ηrel) or systematic J–V comparisons. •No detection of ferroelectric signatures. The inversion of zero-bias current under poling reversal — the hallmark of ferroelectric coupling — has never been experimentally verified in this context. •Neglect of stability under dose. Long-term polarization retention, leakage current evolution, and dielectric degradation under continuous βflux remain unexplored. These limitations justify the present experimental protocol, which establishes rigorous and replicable methods to confirm or reject the BV+FE concept as a foundation for nuclear microgenerators. 4 The Proposed Experiment The revised protocol systematically tests the hybrid betavoltaic–ferroelectric (BV+FE) concept. The design (i) compares BV-only devices against BV+FE devices under controlled βirradiation, (ii) identifies the unique ferroelectric signature (poling-dependent inversion at V=0), and (iii) enforces rigorous controls to exclude artifacts and ensure replicability. Devices Under Test and Controls •BV-only (controls): wide-bandgap betavoltaic junctions (SiC, GaN, or diamond), e.g., p–i–n or Schottky; active region thickness ∼5–50 µm. These provide the baseline J–Vand Pmax under βexposure. •BV+FE (test): same BV junctions with an ultrathin ferroelectric (FE) assist layer (10–30 nm) on the emitter/contact side. Candidates: HfZrO2(CMOS-compatible) or thin PZT/PZT-X; use guard-ring electrodes to suppress surface leakage and define the active area. •Reference controls: inert dielectrics (glass, sapphire, amorphous Si); unpoled PZT and PZT measured above TC(domains suppressed). Where practical, mount two BV+FE samples with opposite poling and acquire differential readout to cancel common-mode artifacts (RIC/EMI). Irradiation, Modulation, and Mapping •Sources: Sr-90/Y-90 (collimated, shielded) or linac at 0.5 MeV to 2 MeV (tunable current, duty cycle, modulation frequency fmod). Document energy, fluence, spot size, and position. •Modulation & reference: use an optical shutter/chopper as lock-in reference (decoupled from accelerator electronics). For Sr-90, implement a motorized shutter. •Spatial mapping: scan the beam (or translate the sample) on a grid; the signal amplitude must track the active area and invert sign with poling. Provide co-registered 2D amplitude/phase maps and dosimetry. 3 Deposited Power and Normalization Define deposited power in the semiconductor active region and, when relevant, in the FE layer: Pdep ≡ZVBV∪VFE dE dtdV, with region tagging in Geant4 (exclude electrodes/holders). Report Pdep and uncertainty; cross-check with PSTAR/ESTAR stopping-power data and, if feasible, ultra-sensitive calorimetry at fmod. Primary Measurements and Metrics •Electrical characterization: full J–Vunder irradiation for BV-only and BV+FE; extract Voc,Isc, fill factor (FF), Pmax. •Efficiency boost (primary metric): ∆ηrel =PBV+FE max −PBV max PBV max (target: ∆ηrel ≥20%; strong: ≥50%). •Ferroelectric signature (must-have):inversion of zero-bias current (sign change at V=0) with poling reversal, accompanied by lock-in phase rotation ∼180◦. •Stability under dose/temperature: drift limits ∆Pmax ≤10% and ∆Ps≤10% after TID equivalent to ≥1–2 years and thermal cycling (−20 to +100 ◦C). Lock-in/FFT and Load Selection •Lock-in: record amplitude and phase at fmod; avoid mains bands (fallback windows 17–23 Hz or 41–47 Hz). Prefer 100–300 Hz when beamline allows (reduces 1/f and device Ropt); acquire second harmonic to help separate thermoelastic components. •Loads: sweep a dense set to capture Pmax. Window A: 100 kΩ, 200 kΩ, 330 kΩ, 560 kΩ, 1 MΩ, 2.2 MΩ, 4.7 MΩ. Window B: 10 MΩ–10 GΩ (log-spaced). Report Ropt at each fmod. Anti-Artifact Strategy (Preemptive) 1. Radiation-induced conductivity (RIC): signals persisting at V=0 without sign inversion or scaling linearly with dose-rate ⇒classify as RIC. Use V=0 checks and differential opposite-poling samples. 2. Pyroelectric/thermal: run isothermal; inject controlled thermal micro-steps to calibrate pyro; verify frequency roll-off inconsistent with FE-assisted BV response. 3. SEE / impact charges: add 30–100 nm Al2O3/SiO2on electrodes (A/B tests); prefer low-Ztop contact; perform ±Vbias sweeps to identify asymmetries not reversing with poling. 4. EMI (linac): grounded dummy inside the Faraday cage; optical reference; fiber links for triggers; single-point ground; RF filters. 4 Environment and Surface Integrity Operate in light vacuum (10−3–10−2mbar) or dry N2. Bake-out/dry-box (50–60◦C, >1 h) before mounting. Continuously log T/RH/pressure. Measure surface resistivity pre-/postrun; reject runs with anomalous drift. Minimum Instrument Specs •Electrometer/TIA: input noise ≤10 fA/√Hz @ 1 Hz; input bias <10 mV; absolute calibration with injected charge. •DAQ:≥16-bit, synchronized, differential inputs; triax <1 m, driven guard; Faraday cage; isolated supplies. Phased Plan 1. Phase 0 (commissioning): dummy + glass; lock-in SNR ≈0 baseline. 2. Phase 1 (killer demo): same BV device with/without FE. Endpoints: ∆ηrel ≥ 20% and inversion at V=0 with poling. Go/No-Go #1. 3. Phase 2 (dose/thermal robustness): TID and thermal cycling; drift limits as above. Go/No-Go #2. 4. Phase 3 (mini-stack): extended operation (500–1000 h) of a small-area BV+FE stack; verify output stability and power electronics matching. Statistics and Decision Rules ABAB (on/off) blocks with N≥20 cycles; randomized durations (15–25 s); Allan deviation over 10–100 s to assess drift. Success requires all: (i) lock-in SNR ≥5 and coherence ≥0.8; (ii) on–off mean difference >3σ; (iii) phase rotation ∼180◦with poling inversion; (iv) Pmax vs Pdep proportionality (slope ≈1 in log–log) over ≥1 decade (Phase 1); (v) stability limits met (Phase 2). Failure at Phase 1 ⇒stop or FE/interface redesign. Radiological Safety and Layout Adopt graded-Zshielding (polyethylene/Al/thin Ta/Al) and separate the beamline, sample, cables, and instruments. For Sr-90: report activity, distance, collimator, lateral shielding. For linac: energy, current/fluence, fmod, dosimetry. Operate under applicable authorizations. Data, Preregistration, and Sharing Preregister primary metrics, thresholds, and stopping rules. Release raw J–Vdata (CSV), Pmax, lock-in amplitude/phase, FFT/PSD, environmental logs, dosimetry, and MC inputs (geometry, physics lists) to enable independent recomputation of Pdep. 5 Success Criteria (Summary) 1. ∆ηrel ≥20% (BV+FE vs BV-only). 2. Inversion of the zero-bias current with poling (lock-in phase ∼180◦). 3. Pmax ∝Pdep over ≥1 decade (Phase 1). 4. Drift limits: ∆Pmax ≤10%, ∆Ps≤10% after target TID/thermal cycling (Phase 2). 5 Scientific Added Value The revised protocol contributes along three axes: •First systematic BV-only vs BV+FE comparison under βirradiation. It isolates the FE contribution via quantitative boost metrics and poling-dependent inversion, enabling unambiguous discrimination from RIC/pyro/SEE artifacts. •Materials-to-device linkage. It couples ferroelectric material metrics (switchability, leakage, Psstability) to device-level performance (Voc,Isc, FF, Pmax) and long-term dose tolerance. •Actionable Go/No-Go. Clear thresholds (boost, inversion, stability) de-risk subsequent investment in kW-class modular microgenerators by validating the only physically consistent path to higher efficiency. 6 Conclusion The original piezoelectric-only hypothesis has been rejected by fundamental efficiency bounds. The present protocol targets the hybrid BV+FE pathway, defining decisive experimental signatures (relative efficiency boost and poling-dependent inversion) and stability criteria under dose and temperature cycling. A positive outcome validates ferroelectricassisted betavoltaics as a credible foundation for compact nuclear microgenerators; a negative outcome still establishes valuable limits on ferroelectric roles in direct β-to-electric conversion, closing the piezo-only avenue and guiding future efforts toward alternative architectures. 6 Appendix – Methodological Protocol and Operational Checklist This appendix provides a comprehensive and reproducible protocol for validating the ferroelectric-assisted betavoltaic (BV+FE) concept. It integrates detailed definitions, explicit thresholds, calibration methods, and statistical decision rules. The goal is to reduce ambiguity, ensure comparability across laboratories, and prevent false positives. 1. Devices and Controls The experiment requires a structured set of test devices and reference controls: BV-only controls. •Wide-bandgap betavoltaic junctions (e.g., SiC, GaN, diamond), fabricated as p–i–n or Schottky devices with active region thickness 5–50 µm. •These serve as the baseline for J–Vand Pmax under βirradiation. BV+FE test devices. •Same BV structures with an ultrathin ferroelectric (FE) layer (10–30 nm) deposited at the emitter/contact side. •Candidate FE materials: Hf0.5Zr0.5O2(CMOS-compatible) or thin PZT/PZT-X (Nb/Mn co-doped, partial Pb substitution). •Guard-ring electrodes are required to suppress leakage; report deposition method, anneal conditions, poling field (≥1 MV/cm for thin films), and Ps,Ec, leakage before irradiation. Reference controls. •Inert dielectrics (fused silica, sapphire, amorphous Si) to exclude generic dielectric signals. •Unpoled FE films and FE above TCto test domain suppression. •Opposite-poling BV+FE samples measured in differential mode to reject commonmode artifacts. 2. Geometry and Irradiation Geometry. •Standard stack: top electrode / FE (optional) / BV semiconductor / back electrode. •Guard-ring electrodes (width ≥0.5–1 mm, defined separation) mandatory. •Low-Ztop electrodes (Al) recommended to mitigate bremsstrahlung and SEE; optional Al2O3/SiO2insulating capping (30–100 nm) for A/B tests. 7 Irradiation sources. •Sr-90/Y-90 source: shielded, collimated; report activity, distance, and shielding. Estimate flux and energy spectrum at sample. •Electron beam (linac, 0.5–2 MeV): tunable current, duty cycle, fmod. Document spot size, fluence, and position. Prefer an optical shutter or beam chopper as lock-in reference (decoupled from accelerator electronics). Deposited power and power density. •Determine penetration depth and Pdep via Monte Carlo (Geant4) with region tagging of BV and FE volumes. •Define power density pdep =Pdep/Vact [W/cm3], where Vact includes the semiconductor and FE layer. •Cross-check with NIST PSTAR/ESTAR; include uncertainties from density, porosity, and beam parameters. 3. Environment and Surface Integrity •Measurements in light vacuum (10−3–10−2mbar) or dry N2to suppress ionization/leakage. •Bake-out or dry-box conditioning (50–60◦C, >1 h) before mounting. Continuously log Tand RH. •Measure surface resistivity (e.g., ring probe) before/after runs. Reject datasets with anomalous drift. 4. Geometric–Functional Transfer Parameter κ For BV+FE devices, the effective stress/polarization coupling is linked to deposited power density: T0=κppdep, κp[Pa/(W ·cm−3)]. Here T0represents the effective stress or field acting along the poling axis, combining thermoelastic and ferroelectric switching pathways. Calibration provides bounds for κp: Calibration procedures. •Thermal calibration (lower bound): sinusoidal heating with thin-film resistor (0.1–10 mW) at fmod; thermoelastic response sets a baseline κth p. •Electrical/ferroelectric calibration (upper bound): apply a known sinusoidal poling field or mechanical load to induce FE switching; derive T0from Psand area, yielding κFE p. Report κpas an interval [κth p, κFE p] with uncertainties and calibration traces. 8 5. Measurement Chain and Wiring Specifications. •Electrometer/TIA: fA–pA sensitivity; input noise ≤10 fA/√Hz at 1 Hz; input bias <10 mV; absolute calibration via known injected charge. •Lock-in amplifier: optical or mechanical reference (shutter/chopper). 1. Low-frequency fallback: 17–23 Hz or 41–47 Hz (avoiding exact mains harmonics). 2. Preferred regime: 100–300 Hz, to suppress 1/f noise and reduce effective device impedance. Wiring. •Short triaxial cables (<1 m), driven guard, Kelvin connection to electrodes. •Single-point ground; RF feedthrough filters; Faraday cage around the sample stage. •Isolated power supplies; fiber-optic links for reference/trigger in linac experiments. 6. Observables, Loads, and Derived Metrics J–V and load sweeps. Measure Voc,Isc, fill factor (FF), and extract the maximum power point Pmax by sweeping two load windows: •Window A (optimized for 100–300 Hz): 100 kΩ, 200 kΩ, 330 kΩ, 560 kΩ, 1 MΩ, 2.2 MΩ, 4.7 MΩ. •Window B (high-impedance characterization): 10 MΩ–10 GΩ (log-spaced). Efficiency metrics. ∆ηrel =PBV+FE max −PBV max PBV max , ηelec =Pmax Pdep . Analytical relations (hybrid diode model). The irradiated junction follows: J(V) = J0e qV nkT −1−Jgen, with Jgen ∝Pdep. The ferroelectric layer modifies the internal field and carrier separation, producing measurable shifts in Voc, FF, and Pmax. Phase metric (ferroelectric signature). Lock-in detection must show ∼180◦phase rotation upon reversal of FE poling, together with inversion of the zero-bias current. 7. Spatial Mapping (linac only) Translate the beam spot (or the device) over a 2D grid, logging lock-in amplitude and phase. The signal must follow the irradiated area and invert with FE poling. Provide co-registered maps with dosimetry. 9