Distribution Of Time Constants Research Articles

Dielectric bi-layer model for electrochemical impedance spectroscopy characterisation of oxide film

In this study, the impedance response of a passive material is investigated, attributing it to a normal time constant distribution caused by resistivity variations within the passive film. Two models, namely the Power Law Model (PLM) and the recently developed Dielectric Bi-Layer Model (DBLM), are employed to express the impedance data. The PLM considers an oxide film as a single layer with a power-law distribution of resistivity, while the DBLM incorporates two distinct layers: an inner layer with constant resistivity (ρ0) and an outer layer with resistivity following Young's theory. Application of both models to 316L stainless steel immersed in a borate buffer solution exhibit that PLM and DBLM fitting results are in good agreement with experimental data. While the models differ mainly in resistivity profiles at the vicinity of the outer interface, the results suggest that deviations in regressed parameters indicate similar ranges for resistivity profiles calculated by both models. DBLM, in particular, is highlighted as promising for interpreting impedance data of passive materials due to its reliance on physical concepts.

Nanoscale visualization of fast carrier dynamics in organic thin-film transistors by time-resolved electrostatic force microscopy

Fast carrier dynamics in organic thin-film transistors (OTFTs) was investigated by time-resolved electrostatic force microscopy (tr-EFM). We found that the carrier diffusion in the OTFTs proceeded in two stages: fast diffusion and slow diffusion. By applying the instantaneous frequency method to EFM, the temporal evolution of the spatial distribution of fast carriers in the channel region of the OTFTs, which took place on the timescale of several hundreds of nanoseconds, was evaluated. The inhomogeneous distribution of the local decay time constant showed that the carrier diffusion of the OTFTs was limited by the grain boundaries between each crystalline region. The quantitative capability of the method was verified by comparing the values of the carrier mobility estimated by the tr-EFM measurement and a numerical simulation. The mobility estimated from the experiment and the simulation showed good agreement, showing the possibility of the tr-EFM to evaluate the time evolution of dynamic phenomena in semiconductor devices.

Relaxation kinetics of interface states and bulk traps in atomic layer deposited ZrO2/β-Ga2O3 metal-oxide-semiconductor capacitors

The study of interface states and bulk traps and their connection to device instability is highly demanded to achieve reliable β-Ga2O3 metal-oxide-semiconductor (MOS) devices. However, a comprehensive analysis of the capture/emission behavior of interface states and bulk traps can be challenging due to widespread time constant distribution. In this study, using capacitance transient measurement tools, trap states of the ZrO2/β-Ga2O3 MOS gate stack were explicitly investigated, particularly its bias- and temperature-dependent relaxation kinetics. As forward bias is enlarged, it is observed that the interface state density (Dit) increases by 12.6%. Two bulk traps with discrete levels identified as 0.43 eV (E1) and 0.74 eV (E2) below the conduction band minimum were extracted by deep-level transient spectroscopy. It is further revealed that the emission processes of E1 and E2 are thermally enhanced, while the capture processes remain insensitive to temperature. The electric-field dependence of E1 indicates that the dominant mechanism follows the rule of Poole–Frenkel emission. The capacitance–voltage (C–V) hysteresis deteriorated at a higher forward bias due to the higher trap density and increased population of trapped charges. These findings provide an important framework for future device optimization to improve the reliability and performance of β-Ga2O3 MOS devices.

Enhancing interfacial Li+ transport and dielectric properties in poly(ethylene oxide)-based all-solid electrolytes via inactive g-C3N4 nanosheets filler incorporation

The advancement of all-solid-state Li metal batteries (ASSLMBs) faces a major challenge in the growth of lithium dendrites on the anode-electrolyte interface. In this study, we propose a dual-filler approach using poly(ethylene oxide) (PEO)-based solid polymer electrolytes (SPEs) that combine Li1.4Al0.4Ti1.6(PO4)3 (LATP) ion-conductive particles with graphitic carbon nitride (g-C3N4) nanosheets. Analysis through second harmonic resonance enhanced electrostatic force microscopy and critical current density (CCD) tests reveal that the g-C3N4 additives form nano-capacitors at the SPE-lithium interface, effectively reducing sudden changes in current densities. The distribution of relaxation time constant (DRT) measurements confirms that the g-C3N4 filler suppresses uncontrolled Li dendrite growth, effectively mitigating battery aging caused by anode interfacial degradation. Furthermore, X-ray photoelectron spectroscopy (XPS) analysis indicates that the nitrogen-containing organic groups in g-C3N4 are reduced to form a stable interfacial layer with lithium metal. As a result of these enhancements, the electrolyte demonstrates remarkable interfacial stability in Li/Li symmetrical cells at 0.65 mA/cm2 and delivers promising performance in assembled Li-LiFePO4 batteries, achieving a reversible capacity of 121.6 mAh/g at 1 C after 200 cycles. These findings highlight the potential of dual-filler PEO-based SPEs for promoting interfacial lithium-ion transport in all-solid-state Li metal batteries.

Investigation of the degradation of proton exchange membrane water electrolysis cells using electrochemical impedance spectroscopy with distribution of relaxation times analysis

Reduction of catalyst loading on Proton Exchange Membrane (PEM) Electrolysis Cells (EC) is needed because of scarcity and high price of the catalyst. Monitoring the degradation of these cells is important to be able to allocate the different processes taking place. Electrochemical Impedance Spectroscopy (EIS) might be suitable for this purpose, but in its usual implementation, the system and the contribution of its components to the total resistance must be already known to build a suitable equivalent circuit model (ECM). Furthermore, the overlap of different processes in the Nyquist and Bode plots hinders the identification of single components of the system. The Distribution of Relaxation Times (DRT) analysis converts the EIS data into a distribution of time constants of individual processes. The contribution of each component to the full cell resistance can be identified by varying different operation parameters. In this work, a PEMEC with low iridium loading was analyzed by DRT and the faradaic processes were identified. A long-term test was carried out and the degradation of the cell was investigated by DRT analysis, to determine the components and processes which limit the cell performance.

Analysis of random telegraph noise in resistive memories: The case of unstable filaments

Through Random Telegraph Noise (RTN) analysis, valuable information can be provided about the role of defect traps in fine tuning and reading of the state of a nanoelectronic device. However, time domain analysis techniques exhibit their limitations in case where unstable RTN signals occur. These instabilities are a common issue in Multi-Level Cells (MLC) of resistive memories (ReRAM), when the tunning protocol fails to find a perfectly stable resistance state, which in turn brings fluctuations to the RTN signal especially in long time measurements and cause severe errors in the estimation of the distribution of time constants of the observed telegraphic events, i.e., capture/emission of carriers from traps. In this work, we analyze the case of the unstable filaments in silicon nitride-based ReRAM devices and propose an adaptive filter implementing a moving-average detrending method in order to flatten unstable RTN signals and increase sufficiently the accuracy of the conducted measurements. The τe and τc emission/capture time constants of the traps, respectively, are then calculated and a cross-validation through frequency domain analysis (Lorentzian fitting) was performed proving that the proposed method is accurate.

Impedance spectroscopy of amorphous/crystalline silicon heterojunction solar cells under dark and illumination

In this article, the electronic properties of a-Si:H/c-Si heterojunction (SHJ) solar cells are analyzed by performing impedance spectroscopy (IS) characterization in the dark and under controlled illuminations. Various dynamic electrical processes occurring at different time scales, ranging from microseconds to milliseconds, are observed mainly in the operating regime of the device. Several distinct characteristics are observed: a) time constant distribution characteristic of the disordered junction, b) typical bias voltage and illumination intensity dependence of the recombination time constant, and c) an additional time constant indicative of a fast process, which appears only under illumination. The impedance spectra of the SHJ cell are best modelled by including a dispersion element, the constant phase element (CPE), in place of a pure capacitor, in its small signal electrical equivalent circuit (EEC), aside from the pure resistive and capacitive elements arranged in a simple configuration. The CPE behavior is assigned to the complex small signal response originating from the distribution of trap levels in the disordered p+-a-Si:H/n-Si heterojunction. Under illumination, a distinct dynamic process is observed compared to the dark condition in the impedance spectra of the device. The variation of the dispersion parameter, resistances, capacitance, and time constants with external stimuli is discussed. In particular, the variation of the recombination time constant with bias is remarkable under different illumination intensities due to the change in the quasi-fermi levels splitting.

Study on field-based superconducting cable for magnetic energy storage devices

During the design of superconducting magnets, the Ic(B) curve is widely used to evaluate the critical current density distribution in the magnet, safety factor is determined by the lowest value of critical current density and operating current. However, other parts of the magnets will work in over-safe state, which leads to a huge waste of superconducting properties as well as budget problem. This article presents a Field-based cable to improve the utilizing rate of superconducting magnets in SMES system. The quantity of HTS tapes are determined by the magnetic field distribution. By this approach, the cost of HTS materials can be potentially reduced. Firstly, the main motivation as well as the entire design method are introduced. Then, a typical no-insulation coil is designed and fabricated based on Field-based stacked cable to validate the feasibility of this method. Both charging/discharging test and the magnetic field test are carried out to explore the working mechanism of this coil. The unique working performance on time constant and field distribution are analyzed in detail.

AC RTN: Testing, Modeling, and Prediction

Random telegraph noise (RTN) adversely induces time dependent device-to-device variations and requires modeling to optimize circuit design. Many early works were focused under dc test conditions, although digital circuits typically operate under ac conditions and it has been reported that ac RTN is substantially different from dc RTN. Tests on ac RTN were carried out mainly on individual traps, and a reliable statistical distribution of trap time constants for ac RTN is still missing. This prevents verifying the statistical accuracy of Monte Carlo ac RTN simulation based on compact models, especially in terms of their ability to predict ac RTN as time window increases. Recently, an integral methodology has been proposed for dc RTN, which can not only model it at short time but also predict it at long time. By introducing the concept of effective charged traps, the need for statistical distribution of trap time constants is removed, making RTN prediction similar to aging prediction. The objectives of this work are to report statistical experimental ac RTN data and to test the applicability of integral methodology to them. For the first time, it will be shown that a model extracted from a time window of 7.8 s can be used to predict the statistical distribution of long-term ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\times 10^{{4}}$ </tex-math></inline-formula> s) ac RTN. The dependence of ac RTN on frequency and time window is analyzed, and the contributions of carrier tunneling from gate and substrate are assessed.

Determination of the Time Constant Distribution of a Defect-Centric Time-Dependent Variability Model for Sub-100-nm FETs

The origin of some time-dependent variability phenomena in FET technologies has been attributed to the charge carrier trapping/detrapping activity of individual defects present in devices. Although some models have been presented to describe these phenomena from the so-called defect-centric perspective, limited attention has been paid to the complex process that goes from the experimental data of the phenomena up to the final construction of the model and all its components, specifically the one that pertains to the time constant distribution. This article presents a detailed strategy aimed at determining the defect time constant distribution, specifically tailored for small area devices, using data obtained from conventional characterization procedures.

Analytical distribution function of relaxation times for porous electrodes and analysis of the distributions of time constants

Based on the work by Boukamp (Boukamp, 2017), the method of Fuoss and Kirkwood (Fuoss and Kirkwood, 1941) is applied to derive an analytical distribution function of relaxation times for physics based porous electrode impedance cases. These impedance models are typically described by transcendental transfer functions. The porous electrode impedance treated here reflects a balance of the effective ionic and electronic impedances inside a porous electrode consisting of particles. Therefore, first the DFRT of the single particle interface impedance is derived. This includes treatment of charge transfer, double layer charging, solid state diffusion inside the particles, open-circuit voltage variations due to solid-state concentration, and insulating layers surrounding the particles. The resulting single particle DFRT relations are then incorporated into a mathematical description of the porous electrode DFRT. The results show that the DFRT of the porous electrode can be clearly separated into distributions of time constants corresponding to charge transfer, solid state diffusion and in case of intercalating particles, like in lithium-ion batteries, a third distribution of time constants is identified. A novelty of this work is the explicit treatment of the low-frequency capacitance and the resulting distribution of time constants in porous electrode systems. Analytical relations for the individual time constants are derived and reported. Since the ideal distribution of time constants can be represented by a series of R||C circuit elements, validation is performed by reconstruction of the impedance spectra, based on the analytical results.

On the Graphical Analysis of the Impedance Response of Passive Electrodes

The analysis of the capacitive behavior of a passive electrode is often a difficult subject because the response obtained by electrochemical impedance spectroscopy (EIS) is characterized by a non-ideal behavior that we try to model by using a constant phase element (CPE) or a Young impedance [1, 2]. In doing so, both the contribution of the double layer and the effects of the current and potential distributions due to the geometry of the electrode are usually neglected.In the case of the contribution of the double layer, such an approximation can be verified a posteriori when data analysis is performed assuming that each of the contributions is a capacitance and that the double layer capacitance, the value of which is usually in the range 10 to 50 µF cm-2, is at least one order of magnitude larger than the value of the impedance of the passive film. However, this simplified approach is often invalid since both the impedance of passive film and the double layer relaxation usually exhibit a non-ideal behavior, thus resulting in the use of CPEs to account for the distribution of dielectric properties of the interface as well as experimental factors (position of the reference electrode, adsorption of impurities...).We present in this work, a new method that uses the graphical analysis of the experimental data in the different frequency ranges (Figure 1), including the low-frequency domain, in order to determine the values of the capacitances without resorting to fitting procedures involving complex functions. This analysis, which is based on the electrical description of the interface, allows the determination of the thickness of a thin layer at the interface, independently of the use of a CPE to describe the distribution of time constants [3]. This will be first demonstrated on synthetic data and then used for the determination of thickness of the oxide film formed on Al electrode.In a second part, we will show that this analysis can be extended to more complicated cases, including when frequency dispersion is observed in the high frequency domain [4]. In that case, the ohmic impedance needs to be properly estimated and then corrected on the experimental results before any data analysis.

An Integral Methodology for Predicting Long-Term RTN

Random telegraph noise (RTN) adversely impacts circuit performance and this impact increases for smaller devices and lower operation voltage. To optimize the circuit design, many efforts have been made to model RTN. RTN is highly stochastic, with significant device-to-device variations (DDVs). Early works often characterize individual traps first and then group them together to extract their statistical distributions. This bottom-up approach suffers from limitations in the number of traps it is possible to measure, especially for the capture and emission time constants, calling the reliability of extracted distributions into question. Several compact models have been proposed, but their ability to predict long-term RTN is not verified. Many early works measured RTN only for tens of seconds, although a longer time window increases RTN by capturing slower traps. The aim of this work is to propose an integral methodology for modeling RTN and, for the first time, to verify its capability of predicting the long-term RTN. Instead of characterizing properties of individual traps/devices, the RTN of multiple devices was integrated to form one dataset for extracting their statistical properties. This allows using the concept of effective charged traps (ECTs) and transforms the need for time constant distribution to obtain the kinetics of ECT, making long-term RTN prediction similar to predicting aging. The proposed methodology opens the way for assessing RTN impact within a window of ten years by efficiently evaluating the probability of a device parameter at a given level.

High frequency impedance measurements of sodium solid electrolytes

Solid-state sodium batteries are currently gaining enormous interest as a lower-cost and more environmentally friendly alternative to lithium batteries. They contain significantly less critical rare elements in both the electrolyte and the active material. However, to date, there is no efficient material combination of metallic anode, cathode, and solid electrolyte for room temperature applications that does not require an additional liquid electrolyte while maintaining high energy density. NaPSiO-based glass-ceramics show high ionic conductivity at room temperature, good corrosion resistance against ambient humidity and CO2, and stability against metallic sodium. However, the conductivity mechanisms of this promising class of materials are currently poorly understood. Herein, high frequency impedance measurements up to 108 Hz shed light on the contributions of grains and grain boundaries to the total impedance, including the distribution of relaxation time constants of the fully crystallized material. In addition, analysis of the temperature dependence allows separation of electrode contributions and determination of activation energies for grain and grain boundary conductivities. Our study provides the basis for fine-tuning the stoichiometry of NaPSiO-based glass-ceramics in terms of maximizing the conductive phase fraction to optimize the performance of future solid-state sodium batteries.

Exploring the electrical behavior of iodine substituted CaCu3Ti4O12-xIx by impedance and modulus spectroscopy

This study explores the effect of iodine (an anion) substitution on the dielectric and resistive properties of CaCu3Ti4O12-xIx (x = 0, 0.005, 0.05, and 0.20) sintered at 1100 °C for 12 h with the help of impedance and modulus spectroscopy. The electrical measurements were done with varying temperatures (300–450 K) and frequency (20 Hz-1 MHz). The ionic distribution of different ions and iodine and their oxidation states were revealed by EDX and XPS analysis, supporting the synthesis of CCTO ceramics with iodine substitution. The complex plane plots (Z″ vs. Z′ and M″ vs. M′) and spectroscopic plots (Z″ vs. log f and M″ vs. log f) of various compositions at different temperatures suggest that the grains, grain boundaries, and sample-electrode interface contribute to their electrical response and can be represented by a combination of three R–C or R-CPE equivalent circuits. The depressed arcs in the Z″ vs. Z′ plot revealed multiple relaxations with a narrow distribution of time constants. The scaled master plots confirm that the resistive and polarization mechanisms are independent of temperature and are Maxwell-Wagner relaxations type. Broad relaxation peaks and mismatch in peak frequencies of Z″ and M″ vs. log f plots suggest that the relaxation mechanism is dominated by the short-range (localized) movement of charge carriers. The activation energies for grain and grain boundary relaxation processes are ∼0.15 eV and ∼0.2 eV, respectively. Increasing iodine doping from x = 0.005 to x = 0.05 leads to a large increase in the resistance of the specimen, which has been explained based on change of charge compensation for IO• defects from electronic defect e/ to ionic defects VCu// and/or VTi////. The dielectric constant is maximum for the composition, x = 0.2, whereas loss, tan δ is minimum for x = 0.05.

1/f noise under drift and thermal agitation in semiconductor materials

Voss and Clarke observed 1/f noise in the square of Johnson noise across samples in thermal equilibrium without applying a current. We refer to this phenomenon as “thermal 1/f noise”. Voss and Clarke suggested spatially correlated temperature fluctuations as an origin of thermal 1/f noise; they also showed that thermal 1/f noise closely matches the 1/f spectrum obtained by passing a current through the sample. An intermittent generation–recombination (g–r) process has recently been introduced to interpret 1/f noise in semiconductors. The square of this intermittent g–r process generates a 1/f noise component which correlates with Voss and Clarke’s empirical findings. Traps which intermittently rather than continuously generate g–r pulses are suggested as the origin of 1/f noise under drift and thermal agitation. We see no need to introduce correlated temperature fluctuations or oxide traps with a large distribution of time constants to explain 1/f noise.

Determination of Au and Pt Current Collector Activity to Avoid Interference in the Screening of Metal Oxide Catalyst Activity in SOECs

Since solid oxides electrolysis cells (SOECs) represent a promising technology for efficient CO2 conversion to useful chemical products, there is a demand for durable, highly active, and inexpensive electrode materials for use in these systems. Many metal oxide catalysts suitable for CO2 reduction have been studied, including La0.3Me0.7Fe0.7Cr0.3O3-δ (Me = Ca, Sr; LMFCr), developed by our research group. These catalysts have comparable activity and are much more stable than conventional metal-ionic conductor cermets, known for coke formation and sulfur poisoning. However, while observed catalyst stability can be easily compared for different materials, their activity is harder to differentiate. This is because the overwhelming majority of materials tested are porous in nature, thus making their true active area unknown. To avoid this issue, we are working on determining LMFCr activity and the CO2 reduction mechanism using thin, smooth catalyst layers, obtained by pulsed laser deposition on a YSZ-(001) electrolyte, then using noble metals as the current collector.Preliminary studies of current collector-LMFCr thin film-CO2/CO combinations suggest that the current collector/LMFCr interfaces may have an electrochemical activity that would contribute measurably to that of the LMFCr-gas dual phase boundary interface. Assuming that the metal/LMFCr interface activity would be similar to that at the metal/ionic conductor triple phase boundary, the goal of the present work is to determine the catalytic activity of both Pt and Au, which are the most common current collector materials used in fuel environments, towards the CO2 reduction reaction, with the activity of these metal/YSZ interfaces toward oxygen reduction used as a reference.Two different full cell configurations were used in this work. In one direction, porous Au or Pt layers were produced by metal paste deposition onto both sides of the YSZ electrolyte and then sintered at 600°C. A polymeric YSZ precursor was then infiltrated into the porous metal backbone and sintered at 750°C to form the YSZ phase. To ensure that the counter was as non-polarizable as possible, Pt in air was chosen due to its high activity in oxygen-containing environments, while also depositing it over 5X the area and ensuring 2X the thickness of the catalyst layer at the working electrode. In the porous electrode configuration, the working electrode was exposed to the testing gas, while the counter electrode was exposed in air to achieve as high an activity as possible. In the second configuration, 0.3 mm thick Pt or Au wires were attached to a 250 µm thick YSZ electrolyte to form a point-contact working electrode. A porous LSM-YSZ composite with a geometric surface area of 0.5 cm2 was painted on the opposite side of the electrolyte to serve as the counter electrode, exposing it to the same gas as the working electrode. Electrochemical performance testing for both cell types was conducted in air and CO2 environments at 750°C with a flow rate of 50 SCCM. Morphological and compositional investigation as well as microelectrode triple phase length determination was done using SEM and EDS elemental mapping.Analysis of the EIS and CV data for the porous electrodes showed that the Pt/YSZ and Au/YSZ electrodes are both active towards the oxygen and CO2 reduction reactions. Au is less so, showing up to 40 times lower activity towards oxygen reduction and 3 times lower activity than for CO2 reduction. This would imply that Au is the preferred current collector material for future electrochemical evaluation of metal oxide catalysts. However, SEM studies indicated that Pt and Au cells had different metal particle sizes, so the triple phase boundary length may be not comparable. In addition, the double layer capacitance, often used to estimate the triple phase boundary length, could not be used here due to the high surface inhomogeneity and distribution of time constants across these catalyst layers.To eliminate these issues, microelectrode studies are currently being conducted. Preliminary results show that Au/YSZ is at least 8 times less active in air and 60 times less active in the CO2 environment than Pt/YSZ, with the activity of both of these electrodes controlled by precisely controlled triple phase boundary length determination via SEM. The cyclic voltammetry data also indicate that CO2 reduction does not occur at Au/YSZ through the full potential range (0-1.6 V vs. the counter electrode), which also implies a very low catalytic activity of Au/YSZ. Further studies, including comparison with the porous composite electrode data, are underway. In addition, determination of the reaction steps is being carried out from EIS data equivalent circuit fitting as well as verification through the use of distribution relaxation times technique.

Spectrally-tunable femtosecond single-molecule pump-probe spectroscopy.

Single-molecule spectroscopy has been extensively used to investigate heterogeneity in static and dynamic behaviors on millisecond and second timescales. More recently, single-molecule pump-probe spectroscopy emerged as a method to access heterogeneity on the femtosecond and picosecond timescales. Here, we develop a single-molecule pump-probe apparatus that is easily tunable across the visible region and demonstrate its utility on the widely-used fluorescent dye, Atto647N. A spectrally-independent, bimodal distribution of energetic relaxation time constants is found, where one peak corresponds to electronic dephasing (∼ 100 fs) and the other to intravibrational relaxation (∼ 300 fs). The bimodal nature indicates that relaxation within each individual molecule is dominated by only one of these processes. Both peaks of the distribution are narrow, suggesting little heterogeneity is present for either process. As illustrated here, spectrally-tunable single-molecule pump-probe spectroscopy will enable investigation of the heterogeneity in a wide range of biological and material systems.

Model-free capacitance analysis of electrodes with a 2D+1D dispersion of time constants

A constant phase element (CPE) is often used in electrochemical impedance spectroscopy to describe the non-ideal impedance of solid/electrolyte interfaces. The generalization of its mathematical description leads to the concept of a variable or generalized phase element αgpe, which, in association with Brug's expression, can be used to determine the interfacial capacitance of metallic electrodes, whose time-constant distribution is restricted to a bidimensional plane (C2D). In this work, a heuristic approach is used to extend the generalization principle even further, in order to arrive at an expression of capacitance, Cgpe, that is valid for electrodes with time-constant dispersions that also spread into the electrode bulk, causing a 2D+1D time-constant distribution. As a proof of concept, the proposed method is applied in the analysis of the electrochemical impedance of n-doped hydrogen-terminated Si(100) electrode in 100 mM Na2SO4, in a potential range that extends from accumulation to depletion. The single crystalline structure and polished surface of the electrode grants a quasi-ideal capacitive behavior to the system that allows comparison of the proposed analysis with the traditional representation of effective capacitance Ceff. Both methods yield similar results in the depletion region, where the impedance response is predominantly defined by the ideal behavior of the silicon space charge region. In accumulation, however, when impedance is influenced by the somewhat larger distribution of relaxation times of the electric double layer, Ceff shows frequency dispersion, whereas Cgpe does not. A dimensional analysis of the functional elements in Cgpe reveals the underlying reason for this intriguing behavior and also shows that C2D is, in fact, just an approximate expression of the more general Cgpe. It is also shown that the generalized capacitance representation allows for a clear detection of the onset of size border effects, and these appear at a higher frequency than what is observed in the Ceff representation.

Surface and electrochemical corrosion analysis of niobium oxide film formed in various wet media

Niobium metal has a wide range of applications in medical devices, nuclear applications, and solar cells. Therefore, niobium corrosion behavior and oxide film formation mechanisms are of great interest. Steady-state polarization and a.c transient techniques were employed to determine the effective capacitance, oxide film thickness, and the corrosion behavior of niobium through the time-constant distribution. In this report, we describe a cost-effective wet chemical method of surface treatment of niobium metal for the study of the metastable oxide film (Nb2O5) formed in different media such as NaCl, NaOH, HCl, and H2SO4 solutions. The investigations confirmed a time-dependent formation and dissolution of a protective oxide layer in all the tested media at different potentials, however, recommends short immersion time (<1 h) for H2SO4 and HCl, and > 1 h for NaCl and NaOH. The work developed a new understanding of the niobium corrosion behavior through effective capacitance and film morphology.