Application of Measurement Models to Impedance Spectroscopy: II . Determination of the Stochastic Contribution to the Error Structure

Agarwal, Pankaj; Crisalle, O.D.; Orazem, Mark E.; García‐Rubio, Luis H.

doi:10.1149/1.2048478

Cited by 141 publications

(103 citation statements)

References 6 publications

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“…The expression used for σ corresponds to an assumption that the standard deviation for the impedance measurement was equal to one percent of the modulus. An improved regression could be obtained by experimental determination of the error structure using, for example, the measurement model concept promoted by Agarwal et al 25 This would not have a significant influence on the results reported here because, to a first approximation, the errors obtained under potentiostatic modulation are proportional to the modulus of the impedance. As the weight applied was the same for all regressions, changes in the value of χ 2 provide a good indication of the comparative quality of the fit.…”

Section: Methodsmentioning

confidence: 88%

Interpretation of Electrochemical Impedance for Corrosion of a Coated Silver Film in Terms of a Pore-in-Pore Model

Amor

Sutter

Takenouti

et al. 2014

J. Electrochem. Soc.

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Electrochemical impedance spectroscopy was used to study the degradation behavior of thin multilayer stacks; Si 3 N 4 /Ag/Si 3 N 4 . Measurements were carried out in 0.5 M Na 2 SO 4 adjusted at pH 10. The impedance data collected at the open circuit potential were analyzed with a physical model where all elements are clearly defined. The results suggest a constant phase element behavior at the electrolyte dielectric interface assigned to an in-depth distribution of local resistivity through the dielectric layer induced by the electrolyte penetration. To explain the electrochemical behavior of the thin silver layer, a localized corrosion in a delaminated zone between the upper dielectric and the silver layers was adopted. The localized corrosion was found to be related to the granular structure of the silver layer in which pores are formed between the grains of silver. This model is equivalent to a recently developed double porosity or pore-in-pore model.Thin film deposition of metallic, dielectric, and semiconducting materials is widely used in many applications, including microelectronic devices, optical coatings, solar cells, and thin-film batteries. [1][2][3][4] Silver is the most used metal for industrial optical applications. This metal possesses the highest reflectivity, from 400 nm through the IR, and the lowest polarization splitting among all metals. 5 Silver also has the lowest emissivity of all metals in the visible and IR regions. However, in aggressive environments, a silver layer is susceptible to deterioration. This deterioration depends on many factors, such as pH, humidity, temperature, type and concentrations of pollutants, and exposure time. [6][7][8][9][10][11][12][13][14][15] To study the degradation behavior of silver thin films in such environments, different analytical methods are commonly employed. The most commonly used techniques are transmission electron microscopy, atomic force microscopy, and recently time-of-flight secondary ion mass spectrometry. 16,17 These various techniques provide only very local information and often require complex sample preparation. Recently, electrochemical methods, and, more specifically, electrochemical impedance spectroscopy (EIS), have emerged as an alternate way to study material and interface properties of thin film stacks. [18][19][20] The interpretation of EIS results is usually done through the construction of equivalent electric circuits that simulate the system under investigation. This allows the extraction of physical parameters related to the film microstructure that are not easily accessible by other techniques. 21 For instance, Zeng et al. 18 show that EIS can be applied to measure the nano-porosity of diamond-like carbon films deposited on silicon substrates. They used an equivalent circuit that took into account both open and closed pores. Tse Chu et al. 22 showed that dielectric protected silver reflectors can be reasonably described by an equivalent circuit consisting of two constant phase element (CPE) components. They considered only ...

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Section: Methodsmentioning

confidence: 88%

Interpretation of Electrochemical Impedance for Corrosion of a Coated Silver Film in Terms of a Pore-in-Pore Model

Amor

Sutter

Takenouti

et al. 2014

J. Electrochem. Soc.

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“…Following the procedure described by Agarwal et al, 10,11 sequential Voigt elements were added to the model until the addition of an element did not improve the fit and one or more model parameters included zero within their 95.4 percent (2σ) confidence interval.…”

Section: The Approachesmentioning

confidence: 99%

Dielectric Properties of Materials Showing Constant-Phase-Element (CPE) Impedance Response

Orazem

Frateur

Tribollet

et al. 2013

J. Electrochem. Soc.

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425

165

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Constant-Phase Elements (CPE) are often used to fit impedance data arising from a broad range of experimental systems. Four approaches were used to interpret CPE parameters associated with the impedance response of human skin and two metal oxides in terms of characteristic frequencies and film thickness. The values obtained with each approach were compared against independent measurements. The power-law model developed recently by Hirschorn et al. 1,2 provided the most reliable interpretation for systems with a normal distribution of properties. Readers are cautioned that the CPE parameter Q does not provide an accurate value for capacitance, even when the CPE exponent α is greater than 0.9.Electrical circuits invoking constant-phase elements (CPE) are often used to fit impedance data arising from a broad range of experimental systems. The impedance for a film-covered electrode showing CPE behavior may be expressed in terms of ohmic resistance R e , a parallel resistance R || , and CPE parameters α and Q aswhere f is the frequency in units of Hz. When α = 1, the system is described by a single time-constant, and the parameter Q has units of capacitance; otherwise, Q has units of s α / cm 2 or F/s (1−α) cm 2 . 3 Under conditions that (2πf ) α R || Q 1,

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“…From an experimental point of view, all the requirements for performing a global impedance measurement (i.e. linearity, stability, and causality) remain the same for LEIS, and the validity of the measurements can be checked using the Kramers-Kronig relationship directly or through use of the measurement model [52][53][54].…”

Section: Potential Difference Measurement and Spatial Resolutionmentioning

confidence: 99%

Local electrochemical impedance spectroscopy: A review and some recent developments

Huang

Orazem

et al. 2011

Electrochimica Acta

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100

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a b s t r a c tLocal electrochemical impedance spectroscopy (LEIS), which provides a powerful tool for exploration of electrode heterogeneity, has its roots in the development of electrochemical techniques employing scanning of microelectrodes. The historical development of local impedance spectroscopy measurements is reviewed, and guidelines are presented for implementation of LEIS. The factors which control the limiting spatial resolution of the technique are identified. The mathematical foundation for the technique is reviewed, including definitions of interfacial and local Ohmic impedances on both local and global scales. Experimental results for the reduction of ferricyanide show the correspondence between local and global impedances. Simulations for a single Faradaic reaction on a disk electrode embedded in an insulator are used to show that the Ohmic contribution, traditionally considered to be a real value, can have complex character in certain frequency ranges.

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Application of Measurement Models to Impedance Spectroscopy: II . Determination of the Stochastic Contribution to the Error Structure

Cited by 141 publications

References 6 publications

Interpretation of Electrochemical Impedance for Corrosion of a Coated Silver Film in Terms of a Pore-in-Pore Model

Interpretation of Electrochemical Impedance for Corrosion of a Coated Silver Film in Terms of a Pore-in-Pore Model

Dielectric Properties of Materials Showing Constant-Phase-Element (CPE) Impedance Response

Local electrochemical impedance spectroscopy: A review and some recent developments

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