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NASA NTRS1993

Delay analysis of combinations of pass transistors and classical logic gates

Combinations of pass transistors and logic gates driving nonlinear capacitive loads are analyzed for the presence of characteristics that will permit easier and more accurate digital logic simulation. Accurate time delay models are developed by studying the nature of the response of simplified circuit models to variations of input waveform rise and fall times and output loading. The nonlinear effects of the CMOS logic devices are minimized to permit easier interpretation of the influence of nonlinear capacitive loads. The performance of a CMOS inverter with a complex nonlinear load consisting of a pass transistor that separates a range of capacitances is compared to the same inverter circuit with a linear capacitive load to develop an understanding of the unique requirements of modeling a nonlinear system. Several methods of modeling the delay of CMOS circuits are reviewed, and a multi-parameter linear model is described. General guidelines for designing CMOS circuits with complex load circuits are developed, emphasizing that the circuit output rise delays and fall delays must be separately analyzed.

Gibson, Jonathan S.↗

NASA NTRS1995

High input impedance amplifier

High input impedance amplifiers are provided which reduce the input impedance solely to a capacitive reactance, or, in a somewhat more complex design, provide an extremely high essentially infinite, capacitive reactance. In one embodiment, where the input impedance is reduced in essence, to solely a capacitive reactance, an operational amplifier in a follower configuration is driven at its non-inverting input and a resistor with a predetermined magnitude is connected between the inverting and non-inverting inputs. A second embodiment eliminates the capacitance from the input by adding a second stage to the first embodiment. The second stage is a second operational amplifier in a non-inverting gain-stage configuration where the output of the first follower stage drives the non-inverting input of the second stage and the output of the second stage is fed back to the non-inverting input of the first stage through a capacitor of a predetermined magnitude. These amplifiers, while generally useful, are very useful as sensor buffer amplifiers that may eliminate significant sources of error.

Kleinberg, Leonard L.↗

NASA NTRS2005

Variable electronic shutter in CMOS imager with improved anti smearing techniques

A leakage compensated snapshot imager provides a number of different aspects to prevent smear and other problems in a snapshot imager. The area where the imager is formed may be biased in a way that prevents photo carriers including electrons and holes from reaching a storage area. In addition, a number of different aspects may improve the efficiency. The capacitance per unit area of the storage area may be one, two or more orders of magnitude greater than the capacitance per-unit area of the photodiode. In addition, a ratio between photodiode capacitance and storage area capacitance is maintained larger than 0.7.

Pain, Bedabrata↗

NASA NTRS1977

Ferroelectric liquid crystal display

A ferroelectric liquid crystal display device employs capacitance spoiling layers to minimize unneeded capacitances created by crossovers of X and Y address lines and to accurately define desired capacitances. The spoiler layers comprise low dielectric constant layers which space electrodes from the ferroelectric at crossover points where capacitance is not needed for device operation.

York, Paul K.↗

NASA NTRS2007

Increasing Linear Dynamic Range of a CMOS Image Sensor

A generic design and a corresponding operating sequence have been developed for increasing the linear-response dynamic range of a complementary metal oxide/semiconductor (CMOS) image sensor. The design provides for linear calibrated dual-gain pixels that operate at high gain at a low signal level and at low gain at a signal level above a preset threshold. Unlike most prior designs for increasing dynamic range of an image sensor, this design does not entail any increase in noise (including fixed-pattern noise), decrease in responsivity or linearity, or degradation of photometric calibration. The figure is a simplified schematic diagram showing the circuit of one pixel and pertinent parts of its column readout circuitry. The conventional part of the pixel circuit includes a photodiode having a small capacitance, CD. The unconventional part includes an additional larger capacitance, CL, that can be connected to the photodiode via a transfer gate controlled in part by a latch. In the high-gain mode, the signal labeled TSR in the figure is held low through the latch, which also helps to adapt the gain on a pixel-by-pixel basis. Light must be coupled to the pixel through a microlens or by back illumination in order to obtain a high effective fill factor; this is necessary to ensure high quantum efficiency, a loss of which would minimize the efficacy of the dynamic- range-enhancement scheme. Once the level of illumination of the pixel exceeds the threshold, TSR is turned on, causing the transfer gate to conduct, thereby adding CL to the pixel capacitance. The added capacitance reduces the conversion gain, and increases the pixel electron-handling capacity, thereby providing an extension of the dynamic range. By use of an array of comparators also at the bottom of the column, photocharge voltages on sampling capacitors in each column are compared with a reference voltage to determine whether it is necessary to switch from the high-gain to the low-gain mode. Depending upon the built-in offset in each pixel and in each comparator, the point at which the gain change occurs will be different, adding gain-dependent fixed pattern noise in each pixel. The offset, and hence the fixed pattern noise, is eliminated by sampling the pixel readout charge four times by use of four capacitors (instead of two such capacitors as in conventional design) connected to the bottom of the column via electronic switches SHS1, SHR1, SHS2, and SHR2, respectively, corresponding to high and low values of the signals TSR and RST. The samples are combined in an appropriate fashion to cancel offset-induced errors, and provide spurious-free imaging with extended dynamic range.

Pain, Bedabrata↗

NASA NTRS2014

Dielectric Performance of a High Purity HTCC Alumina at High Temperatures - a Comparison Study with Other Polycrystalline Alumina

A very high purity (99.99+%) high temperature co-fired ceramic (HTCC) alumina has recently become commercially available. The raw material of this HTCC alumina is very different from conventional HTCC alumina, and more importantly there is no glass additive in this alumina material for co-firing processing. Previously, selected HTCC and LTCC (low temperature co-fired ceramic) alumina materials were evaluated at high temperatures as dielectric and compared to a regularly sintered 96% polycrystalline alumina (96% Al2O3), where 96% alumina was used as the benchmark. A prototype packaging system based on regular 96% alumina with Au thickfilm metallization successfully facilitated long term testing of high temperature silicon carbide (SiC) electronic devices for over 10,000 hours at 500 C. In order to evaluate this new high purity HTCC alumina for possible high temperature packaging applications, the dielectric properties of this HTCC alumina substrate were measured and compared with those of 96% alumina and a previously tested LTCC alumina from room temperature to 550 C at frequencies of 120 Hz, 1 KHz, 10 KHz, 100 KHz, and 1 MHz. A parallel-plate capacitive device with dielectric of the HTCC alumina and precious metal electrodes were used for measurements of the dielectric constant and dielectric loss of the co-fired alumina material in the temperature and frequency ranges. The capacitance and AC parallel conductance of the capacitive device were directly measured by an AC impedance meter, and the dielectric constant and parallel AC conductivity of the dielectric were calculated from the capacitance and conductance measurement results. The temperature and frequency dependent dielectric constant, AC conductivity, and dissipation factor of the HTCC alumina substrate are presented and compared to those of 96% alumina and a selected LTCC alumina. Other technical advantages of this new co-fired material for possible high packaging applications are also discussed.

Electronic packaging↗

NASA NTRS2012

Dielectric Performance of High Purity HTCC Alumina at High Temperatures - A Comparison Study with Other Polycrystalline Alumina

A very high purity (99.99+) high temperature co-fired ceramic (HTCC) alumina has recently become commercially available. The raw material of this HTCC alumina is very different from conventional HTCC alumina, and more importantly there is no glass additive in this co-fired material. Previously, selected HTCC and LTCC (low temperature co-fired ceramic) alumina materials were evaluated at high temperatures as dielectric and compared to a regularly sintered 96 polycrystalline alumina (96 Al2O3), where 96 alumina was used as the benchmark. A prototype packaging system based on regular 96 alumina with Au thick-film metallization successfully facilitated long term testing of high temperature silicon carbide (SiC) electronic devices for over 10,000 hours at 500C. In order to evaluate this new HTCC alumina for possible high temperature packaging applications, the dielectric properties of this HTCC alumina substrate were measured and compared with those of 96 alumina and a LTCC alumina from room temperature to 550C at frequencies of 120 Hz, 1 KHz, 10 KHz, 100 KHz, and 1 MHz. A parallel-plate capacitive device with dielectric of the HTCC alumina and precious metal electrodes were used for measurements of the dielectric constant and dielectric loss of the co-fired alumina material in the temperature and frequency ranges. The capacitance and AC parallel conductance of the capacitive device were directly measured by an AC impedance meter, and the dielectric constant and parallel AC conductivity of the dielectric were calculated from the capacitance and conductance measurement results. The temperature and frequency dependent dielectric constant, AC conductivity, and dissipation factor of the HTCC alumina substrate are presented and compared to those of 96 alumina. Other technical advantages of this new co-fired material for possible high packaging applications are also discussed.

High temperature↗

NASA NTRS2016

Carbon Nanotube Tape Vibrating Gyroscope

A vibrating gyroscope includes a piezoelectric strip having length and width dimensions. The piezoelectric strip includes a piezoelectric material and carbon nanotubes (CNTs) substantially aligned and polled along the strip's length dimension. A spindle having an axis of rotation is coupled to the piezoelectric strip. The axis of rotation is parallel to the strip's width dimension. A first capacitance sensor is mechanically coupled to the spindle for rotation therewith. The first capacitance sensor is positioned at one of the strip's opposing ends and is spaced apart from one of the strip's opposing faces. A second capacitance sensor is mechanically coupled to the spindle for rotation therewith. The second capacitance sensor is positioned at another of the strip's opposing ends and is spaced apart from another of the strip's opposing faces. A voltage source applies an AC voltage to the piezoelectric strip.

Tucker, Dennis Stephen↗

DOE OSTI2020

Keratin-derived functional carbon with superior charge storage and transport for high-performance supercapacitors

In this work, we report a scalable method to synthesize hierarchically porous, hetero-atom doped activated carbon nanosheet from waste biomass-human hair, and demonstrates the use of this carbon as an ultra-high performance electrode material for supercapacitor applications. Microscopic analyses reveal that sheet size ranges from 50 to 200 nm having a thickness of 15–27 nm. As-synthesized, carbon nanosheets possess a hierarchical porous structure having a specific surface area of 1548 m 2 g -1 . Heteroatom concentration (nitrogen, oxygen, and sulfur) of around 25% is confirmed from XPS analysis. Therefore, the novel interconnected hierarchical porous nanosheets structure enables fast adsorption and transportation of ions during electrochemical processes. Also, the abundant chemically available electroactive heteroatom species in the material enhance the wettability of ions and contribute to pseudocapacitance. The electrochemical analyses through cyclic voltammetry and galvanostatic charge-discharge measurements in 6 M KOH reveal the quasi-EDLC behavior of the activated carbons due to the presence of heteroatoms. A reprensentative KOH activated carbon shows an excellent specific capacitance value of 999 F g -1 at a current density of 1 A g -1 . Furthermore, the symmetrically assembled two-electrode device also delivers a maximum energy density of 32 W h Kg -1 at a power density of 325 W Kg -1 . In addition, excellent cyclic stability of 98% capacitance retention is observed after 10,000 continuous GCD cycles even at a high current density of 5 A g -1 . Symmetric flexible supercapacitor device using KOH-PVA-K3FeCN6 as redox gel polymer electrolyte shows a synergistic specific capacitance of 145 mF cm -1 at a current density of 0.8 mA cm -1 exhibiting very less deviation in bending mode. Therefore, this waste biomass derived heteroatom doped hierarchical porous carbon nanosheets can be a promising material for cost-effective high- performance supercapacitor.

42 ENGINEERING↗

DOE OSTI2022

Robust hierarchical three dimensional nickel cobalt tungstate-MXene nanocomposite for high performance symmetric coin cell supercapacitors

Design of rational electrode materials with hierarchically structured pseudocapacitive materials has been identified as a successful strategy for revamping the electrochemical characteristics of supercapacitors. However, the simultaneous assurance of strong electrical conductivity and higher specific capacitance via a simple and cost-effective synthesis protocol is of concern today. In this work, Ni-CoWO 4 incorporated MXene nanocomposite has been successfully prepared by a facile hydrothermal process. The structure, morphology, stoichiometry, and chemical characterization of the prepared Ni-CoWO 4 , Ti 3 C 2 T x , and Ni-CoWO4@MXene nanocomposite were explored extensively. MXene demonstrated a layered 2D nanoscale structure whereas pure Ni-CoWO 4 was composed of spherical nanoparticles. The composite Ni-CoWO 4 @MXene revealed the morphology of spherical Ni-CoWO 4 nanoparticles decorated on MXene sheets. Furthermore, a series of electrochemical characterizations illustrated the contribution of the delightful morphology of Ni-CoWO 4 @MXene composite to excellent electrochemistry. The resultant Ni-CoWO 4 @MXene electrode exhibited high specific capacitance of 582 Fg -1 at 1 A g -1 and 93.5 % capacitance retention over the 10,000 cycles., which is higher than that of the individual counterparts Ni-CoWO 4 and MXene. The excellent electrochemical performance of Ni-CoWO 4 @MXene is attributed to the synergistic interaction between Ni-CoWO4 nanoparticles and nanolayered MXene that may create new active sites that enhanced the charge transfer, charge/discharge kinetics and the electrical conductivity. Significantly, the unique Ni-CoWO 4 @MXene supercapacitor prototype delivered a higher energy density of 85.7 Wh kg -1 and power density of 0.85 kW kg -1 establishing its superiority over other Cosingle bondW based supercapacitors. A theoretical study was also performed to correlate the improved charge storage capacity of the prepared Ni-CoWO 4 @MXene composite.

25 ENERGY STORAGE↗

DOE OSTI2026

Predicting critical heat flux using localized sensing at invisible vapor-liquid interfaces

Predicting critical heat flux (CHF) in two-phase electronics cooling systems remains a significant challenge due to the sudden onset of boiling crisis and the difficulty in directly visualizing vapor-liquid interfaces. Existing sensing methods rely on lagging temperature measurements, optically accessible systems, or spatially averaged signals that cannot pinpoint CHF initiation at localized high-heat-flux regions. Here, we report a planar capacitive sensing approach that enables real-time, localized detection of vapor-liquid interface dynamics for CHF prediction in boiling heat transfer. The capacitive sensor exploits the dielectric constant difference between liquid and vapor phases to capture bubble nucleation, growth, and departure dynamics with a temporal resolution down to 2 ms. The capacitive sensing reveals distinct signals across boiling regimes: from high-frequency fluctuations during strong nucleate boiling to low-frequency fluctuations with increased amplitudes when approaching CHF. The multi-sensor array experiments demonstrate real-time localized sensing, where each sensor responds exclusively to boiling in its immediate vicinity without crosstalk from neighboring regions. This non-intrusive sensing approach provides predictive rather than lagging sensing signals of CHF occurrence, offering predictive diagnosis of two-phase liquid cooling for the thermal management of high-power-density electronics.

CHF↗

DOE OSTI2022

Additively manufactured strain sensors for in-pile applications

Accurate, real-time monitoring of strain in fuel, cladding, and structural components of nuclear reactors is critical to better understand radiation induced phenomena during reactor tests and operations. The data provided is crucial to verify physics-based, multiscale modeling and simulation efforts, which aim to shorten the timeline for the development of new nuclear materials. Resistive strain gauges have limited performance during in-pile experiments due to the harsh operating conditions and limited physical space between fuel and cladding components. In this work, aerosol jet printing using silver nanoparticle inks was used to fabricate interdigitated electrode capacitive strain gauges on aluminum alloy 6061 tensile specimens. Here to simulate the temperatures of a traditional light water reactor, the capacitive strain gauges were tested with a mechanical test frame up to 300 °C and compared to commercially available bondable resistive strain gauges. The printed capacitive strain gauges exhibited a gauge factor of 1.0 and showed higher reproducibility and predictability of strain sensing performance than the resistive strain gauge. The results demonstrate the potential of aerosol jet printing to fabricate strain sensors with predictable performance and reduced invasiveness for high-temperature applications with confined spacing.

36 MATERIALS SCIENCE↗

DOE OSTI2023

High-Mass Loading of Flower-like Ni-MoS 2 microspheres Toward Efficient Intercalation pseudocapacitive Electrode

This work reports the exploration of intercalation pseudocapacitance in a thicker electrode of flowerlike Ni-doped MoS 2 microspheres that features a mass loading of ~10 mg/cm 2 without sacrificing the gravimetric capacitance (~425 F/g at 5 mV/s). Integration of Ni atoms into MoS 2 microspheres not only stabilized the structural integrity but also ameliorated the rapid intercalation and deintercalation of electrolyte ions even at a commercial-level mass loading. The energy instability by Ni doping significantly changed the local bonding behavior and the overall electronic structure of MoS 2 , facilitating the breaking of the MoS 2 layer and generation of more active edge sites, which are responsible for faster reaction kinetics. The experiments attribute the overall capacitance enhancement in (Mo-Ni)S 2 to the increased rate of electrolyte ion insertion and extraction, which is confirmed by b-values close to 0.5, at different potentials, indicating that the current response predominantly depends on the diffusive mechanism for both MoS 2 and Ni-MoS 2 thicker electrodes. The symmetric device constructed with Ni-MoS 2 microspheres exhibited a capacitance value of 101 F/g in 1 mV/s, for which the energy density is 9 Wh/kg, as well as attained an outstanding cycling stability of 10000 cycles with 60% retention at 2 A/g. In addition to providing insights into the development of 2D TMDs, this work explores the design of robust and highly efficient intercalation electrode material for electrochemical energy storage devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Vertically Aligned Carbon Nanotubes Grown on Copper Foil as Electrodes for Electrochemical Double Layer Capacitors

This study reports a binder-free, catalyst-free method for fabricating vertically aligned carbon nanotubes (VACNTs) directly on copper (Cu) foil using plasma-enhanced chemical vapor deposition (PECVD) for electrochemical double-layer capacitor (EDLC) applications. This approach eliminates the need for catalyst layers, polymeric binders, or substrate pre-treatments, simplifying electrode design and enhancing electrical integration. The resulting VACNTs form a dense, uniform, and porous array with strong adhesion to the Cu substrate, minimizing contact resistance and improving conductivity. Electrochemical analysis shows gravimetric specific capacitance (C grav ) and areal specific capacitance (C areal ) of 8 F g −1 and 3.5 mF cm −2 at a scan rate of 5 mV/s, with low equivalent series resistance (3.70 Ω) and charge transfer resistance (0.48 Ω), enabling efficient electron transport and rapid ion diffusion. The electrode demonstrates excellent rate capability and retains 92% of its initial specific capacitance after 3000 charge–discharge cycles, indicating strong cycling stability. These results demonstrate the potential of directly grown VACNT-based electrodes for high-performance EDLCs, particularly in applications requiring rapid charge–discharge cycles and sustained energy delivery.

25 ENERGY STORAGE↗

NASA NTRS2011

Development of Sample Verification System for Sample Return Missions

This paper describes the development of a proof of-concept sample verification system (SVS) for in-situ mass measurement of planetary rock and soil sample in future robotic sample return missions. Our proof-of-concept SVS device contains a 10 cm diameter pressure sensitive elastic membrane placed at the bottom of a sample canister. The membrane deforms under the weight of accumulating planetary sample. The membrane is positioned in proximity to an opposing substrate with a narrow gap. The deformation of the membrane makes the gap to be narrower, resulting in increased capacitance between the two nearly parallel plates. Capacitance readout circuitry on a nearby printed circuit board (PCB) transmits data via a low-voltage differential signaling (LVDS) interface. The fabricated SVS proof-of-concept device has successfully demonstrated approximately 1pF/gram capacitance change

Electrodes↗

DOE OSTI2022

Hexagonal Distributed Embedded Energy Converters (HexDEECs)

Distributed Embedded Energy Converter Technologies (DEEC-Tec) is a new domain for marine renewable energy research that utilizes a conglomeration of small distributed embedded energy converters (DEECs) that, in aggregate, form larger metamaterial frameworks. These resulting DEEC-Tec metamaterials can then, in turn, be used to construct flexible ocean wave energy converters called flexWECs. DEEC-Tec enables flexWECs: (i) to be inherently broad-banded ocean wave frequency energy converters and (ii) to have an inherent lack of highly loaded rigid bodies. The DEEC-Tec domain also benefits the marine renewable energy domain by inherently availing ways that marine energy can be harvested and converted that heretofore has not yet been considered possible: real-time execution of transforming topologies (e.g., actively changing a flexWEC's shape and form) and morphologies (e.g., actively changing a flexWEC's stiffness and damping throughout its entire structure). Presented, is one specific type of DEEC, a HexDEEC, that shows promise in aiding the adoption and further development of the DEEC-Tec domain - it is a small energy transducer being developed by the United States National Renewable Energy Laboratory. The HexDEEC is a small (characteristic length approximating a centimeter) energy transducer that converts the dynamic deformations of an elastomer into electricity through a charging-discharging cycle of a capacitor whose capacitance is varied by those elastic deformations. The HexDEEC is composed of a hyperelastic hexagonal housing (nominally silicon rubber) with six electrodes on its inner faces. The upper three electrodes share the same charge while the lower three electrodes oppose the upper electrode charges. Externally, the HexDEEC has two arms extending away from the middle vertices of the hexagon. Via principles governing the relationship between electrical capacitance and electrical potential (voltage and charge), electricity is generated when the HexDEEC's arms are dynamically pulled or released under tensile loading as doing so causes the distance between the upper and lower sets of electrodes to change - varying the energy converter's overall capacitance. Analytical and numerical modeling have already been used to estimate the electrical energy produced by a HexDEEC. The cursory models approximate the HexDEEC as a parallel plate variable capacitor - simplifying from six to two opposing plates with a constant dielectric volume between those two plates. To account for the elastic HexDEEC material properties, software such as SolidWorks and STAR-CCM+ have been used to generate hyperelastic models; notably, Mooney-Rivlin based models. Individual HexDEECs have been fabricated by drawing uncured liquid silicon rubber into molds via vacuum pressure. To simplify manufacturing, HexDEEC sub-components - e.g., electrodes, wires - can be placed within those molds such that they are directly embedded into the hexagonal housing during the curing process. Furthermore, DEEC-Tec metamaterials can be created by interweaving or sequentially layering multiple HexDEEC strands together. The HexDEEC based metamaterial could then generate electricity through its gross deformations. Ultimately, HexDEECs represent a specific type of energy transducer that can be leveraged, by the DEEC-Tec domain, to create metamaterials used to construct novel flexWECs.

DEEC-Tec↗

DOE OSTI2020

Covalent Graphene-MOF Hybrids for High-Performance Asymmetric Supercapacitors

In this work, the covalent attachment of an amine functionalized metal-organic framework (UiO-66-NH 2 = Zr 6 O 4 (OH) 4 (bdc-NH 2 ) 6 ; bdc-NH 2 = 2-amino-1,4-benzenedicarboxylate) (UiO-Universitetet i Oslo) to the basal-plane of carboxylate functionalized graphene (graphene acid = GA) via amide bonds is reported. The resultant GA@UiO-66-NH 2 hybrid displayed a large specific surface area, hierarchical pores and an interconnected conductive network. The electrochemical characterizations demonstrated that the hybrid GA@UiO-66-NH 2 acts as an effective charge storing material with a capacitance of up to 651 F g –1 , significantly higher than traditional graphene-based materials. The results suggest that the amide linkage plays a key role in the formation of a π-conjugated structure, which facilitates charge transfer and consequently offers good capacitance and cycling stability. Furthermore, to realize the practical feasibility, an asymmetric supercapacitor using a GA@UiO-66-NH 2 positive electrode with Ti 3 C 2 T X MXene as the opposing electrode has been constructed. The cell is able to deliver a power density of up to 16 kW kg –1 and an energy density of up to 73 Wh kg –1 , which are comparable to several commercial devices such as Pb-acid and Ni/MH batteries. Under an intermediate level of loading, the device retained 88% of its initial capacitance after 10 000 cycles.

2D materials↗

DOE OSTI2026

Electrochemical Modeling of PID Leakage Current of PV Modules: Steady-State Current, Transient Current, and RC-Equivalent Circuit

Potential-induced degradation (PID) remains a significant reliability concern for photovoltaic (PV) modules, arising when a voltage difference between the module frame and the solar cells drives unintended leakage current through the glass-encapsulant stack. Although PID ultimately manifests as PID-s, PID-p, or PID-c, the underlying behavior of the leakage current-its magnitude and time dependence-requires clearer electrochemical interpretation. Traditional explanations attribute the initial transient current to bulk capacitive elements of the glass, encapsulant, and antireflection coatings, and the steady-state current according to their effective ohmic resistance. More recent studies, however, indicate that electrochemical charge-transfer processes at the encapsulant-metallization interface can play a dominant role in defining the leakage-current path. This paper develops a unified electrochemical framework for modeling PID leakage current. First, an RC-equivalent circuit is formulated by combining conventional RC elements with a Randles-type interface to capture transient leakage current through double-layer capacitance and faradaic processes at ionic-electronic boundaries. Second, the steady-state current-voltage behavior is explained using a linearized Butler-Volmer relationship, showing that the measured ohmic response corresponds to the low-overpotential limit of charge-transfer kinetics. Analytical results demonstrate that, for typical module materials-3.2-mm soda-lime glass and 0.45-mm encapsulant-the dominant modulators to PID leakage current are the glass surface resistance (under dry-surface conditions), the glass bulk capacitance, and the encapsulant resistance (under wet-surface conditions), with soda lime glass surface and EVA/POE encapsulant resistances primarily governing steady-state current. The proposed electrochemical model is validated against measured leakage-current data, showing good agreement in both the magnitude and the time-dependent evolution of PID leakage current.

14 SOLAR ENERGY↗