Impedance spectroscopy : theory, experiment, and applications
04 Apr 2005-
Abstract: Preface. Preface to the First Edition. Contributors. Contributors to the First Edition. Chapter 1. Fundamentals of Impedance Spectroscopy (J.Ross Macdonald and William B. Johnson). 1.1. Background, Basic Definitions, and History. 1.1.1 The Importance of Interfaces. 1.1.2 The Basic Impedance Spectroscopy Experiment. 1.1.3 Response to a Small-Signal Stimulus in the Frequency Domain. 1.1.4 Impedance-Related Functions. 1.1.5 Early History. 1.2. Advantages and Limitations. 1.2.1 Differences Between Solid State and Aqueous Electrochemistry. 1.3. Elementary Analysis of Impedance Spectra. 1.3.1 Physical Models for Equivalent Circuit Elements. 1.3.2 Simple RC Circuits. 1.3.3 Analysis of Single Impedance Arcs. 1.4. Selected Applications of IS. Chapter 2. Theory (Ian D. Raistrick, Donald R. Franceschetti, and J. Ross Macdonald). 2.1. The Electrical Analogs of Physical and Chemical Processes. 2.1.1 Introduction. 2.1.2 The Electrical Properties of Bulk Homogeneous Phases. 2.1.2.1 Introduction. 2.1.2.2 Dielectric Relaxation in Materials with a Single Time Constant. 2.1.2.3 Distributions of Relaxation Times. 2.1.2.4 Conductivity and Diffusion in Electrolytes. 2.1.2.5 Conductivity and Diffusion-a Statistical Description. 2.1.2.6 Migration in the Absence of Concentration Gradients. 2.1.2.7 Transport in Disordered Media. 2.1.3 Mass and Charge Transport in the Presence of Concentration Gradients. 2.1.3.1 Diffusion. 2.1.3.2 Mixed Electronic-Ionic Conductors. 2.1.3.3 Concentration Polarization. 2.1.4 Interfaces and Boundary Conditions. 2.1.4.1 Reversible and Irreversible Interfaces. 2.1.4.2 Polarizable Electrodes. 2.1.4.3 Adsorption at the Electrode-Electrolyte Interface. 2.1.4.4 Charge Transfer at the Electrode-Electrolyte Interface. 2.1.5 Grain Boundary Effects. 2.1.6 Current Distribution, Porous and Rough Electrodes- the Effect of Geometry. 2.1.6.1 Current Distribution Problems. 2.1.6.2 Rough and Porous Electrodes. 2.2. Physical and Electrochemical Models. 2.2.1 The Modeling of Electrochemical Systems. 2.2.2 Equivalent Circuits. 2.2.2.1 Unification of Immitance Responses. 2.2.2.2 Distributed Circuit Elements. 2.2.2.3 Ambiguous Circuits. 2.2.3 Modeling Results. 2.2.3.1 Introduction. 2.2.3.2 Supported Situations. 2.2.3.3 Unsupported Situations: Theoretical Models. 2.2.3.4 Unsupported Situations: Equivalent Network Models. 2.2.3.5 Unsupported Situations: Empirical and Semiempirical Models. Chapter 3. Measuring Techniques and Data Analysis. 3.1. Impedance Measurement Techniques (Michael C. H. McKubre and Digby D. Macdonald). 3.1.1 Introduction. 3.1.2 Frequency Domain Methods. 3.1.2.1 Audio Frequency Bridges. 3.1.2.2 Transformer Ratio Arm Bridges. 3.1.2.3 Berberian-Cole Bridge. 3.1.2.4 Considerations of Potentiostatic Control. 3.1.2.5 Oscilloscopic Methods for Direct Measurement. 3.1.2.6 Phase-Sensitive Detection for Direct Measurement. 3.1.2.7 Automated Frequency Response Analysis. 3.1.2.8 Automated Impedance Analyzers. 3.1.2.9 The Use of Kramers-Kronig Transforms. 3.1.2.10 Spectrum Analyzers. 3.1.3 Time Domain Methods. 3.1.3.1 Introduction. 3.1.3.2 Analog-to-Digital (A/D) Conversion. 3.1.3.3 Computer Interfacing. 3.1.3.4 Digital Signal Processing. 3.1.4 Conclusions. 3.2. Commercially Available Impedance Measurement Systems (Brian Sayers). 3.2.1 Electrochemical Impedance Measurement Systems. 3.2.1.1 System Configuration. 3.2.1.2 Why Use a Potentiostat? 3.2.1.3 Measurements Using 2, 3 or 4-Terminal Techniques. 3.2.1.4 Measurement Resolution and Accuracy. 3.2.1.5 Single Sine and FFT Measurement Techniques. 3.2.1.6 Multielectrode Techniques. 3.2.1.7 Effects of Connections and Input Impedance. 3.2.1.8 Verification of Measurement Performance. 3.2.1.9 Floating Measurement Techniques. 3.2.1.10 Multichannel Techniques. 3.2.2 Materials Impedance Measurement Systems. 3.2.2.1 System Configuration. 3.2.2.2 Measurement of Low Impedance Materials. 3.2.2.3 Measurement of High Impedance Materials. 3.2.2.4 Reference Techniques. 3.2.2.5 Normalization Techniques. 3.2.2.6 High Voltage Measurement Techniques. 3.2.2.7 Temperature Control. 3.2.2.8 Sample Holder Considerations. 3.3. Data Analysis (J. Ross Macdonald). 3.3.1 Data Presentation and Adjustment. 3.3.1.1 Previous Approaches. 3.3.1.2 Three-Dimensional Perspective Plotting. 3.3.1.3 Treatment of Anomalies. 3.3.2 Data Analysis Methods. 3.3.2.1 Simple Methods. 3.3.2.2 Complex Nonlinear Least Squares. 3.3.2.3 Weighting. 3.3.2.4 Which Impedance-Related Function to Fit? 3.3.2.5 The Question of "What to Fit" Revisited. 3.3.2.6 Deconvolution Approaches. 3.3.2.7 Examples of CNLS Fitting. 3.3.2.8 Summary and Simple Characterization Example. Chapter 4. Applications of Impedance Spectroscopy. 4.1. Characterization of Materials (N. Bonanos, B. C. H. Steele, and E. P. Butler). 4.1.1 Microstructural Models for Impedance Spectra of Materials. 4.1.1.1 Introduction. 4.1.1.2 Layer Models. 4.1.1.3 Effective Medium Models. 4.1.1.4 Modeling of Composite Electrodes. 4.1.2 Experimental Techniques. 4.1.2.1 Introduction. 4.1.2.2 Measurement Systems. 4.1.2.3 Sample Preparation-Electrodes. 4.1.2.4 Problems Associated With the Measurement of Electrode Properties. 4.1.3 Interpretation of the Impedance Spectra of Ionic Conductors and Interfaces. 4.1.3.1 Introduction. 4.1.3.2 Characterization of Grain Boundaries by IS. 4.1.3.3 Characterization of Two-Phase Dispersions by IS. 4.1.3.4 Impedance Spectra of Unusual Two-phase Systems. 4.1.3.5 Impedance Spectra of Composite Electrodes. 4.1.3.6 Closing Remarks. 4.2. Characterization of the Electrical Response of High Resistivity Ionic and Dielectric Solid Materials by Immittance Spectroscopy (J. Ross Macdonald). 4.2.1 Introduction. 4.2.2 Types of Dispersive Response Models: Strengths and Weaknesses. 4.2.2.1 Overview. 4.2.2.2 Variable-slope Models. 4.2.2.3 Composite Models. 4.2.3 Illustration of Typical Data Fitting Results for an Ionic Conductor. 4.3. Solid State Devices (William B. Johnson and Wayne L. Worrell). 4.3.1 Electrolyte-Insulator-Semiconductor (EIS) Sensors. 4.3.2 Solid Electrolyte Chemical Sensors. 4.3.3 Photoelectrochemical Solar Cells. 4.3.4 Impedance Response of Electrochromic Materials and Devices (Gunnar A. Niklasson, Anna Karin Johsson, and Maria Stromme). 4.3.4.1 Introduction. 4.3.4.2 Materials. 4.3.4.3 Experimental Techniques. 4.3.4.4 Experimental Results on Single Materials. 4.3.4.5 Experimental Results on Electrochromic Devices. 4.3.4.6 Conclusions and Outlook. 4.3.5 Time-Resolved Photocurrent Generation (Albert Goossens). 4.3.5.1 Introduction-Semiconductors. 4.3.5.2 Steady-State Photocurrents. 4.3.5.3 Time-of-Flight. 4.3.5.4 Intensity-Modulated Photocurrent Spectroscopy. 4.3.5.5 Final Remarks. 4.4. Corrosion of Materials (Digby D. Macdonald and Michael C. H. McKubre). 4.4.1 Introduction. 4.4.2 Fundamentals. 4.4.3 Measurement of Corrosion Rate. 4.4.4 Harmonic Analysis. 4.4.5 Kramer-Kronig Transforms. 4.4.6 Corrosion Mechanisms. 4.4.6.1 Active Dissolution. 4.4.6.2 Active-Passive Transition. 4.4.6.3 The Passive State. 4.4.7 Point Defect Model of the Passive State (Digby D. Macdonald). 4.4.7.1 Introduction. 4.4.7.2 Point Defect Model. 4.4.7.3 Electrochemical Impedance Spectroscopy. 4.4.7.4 Bilayer Passive Films. 4.4.8 Equivalent Circuit Analysis (Digby D. Macdonald and Michael C. H. McKubre). 4.4.8.1 Coatings. 4.4.9 Other Impedance Techniques. 4.4.9.1 Electrochemical Hydrodynamic Impedance (EHI). 4.4.9.2 Fracture Transfer Function (FTF). 4.4.9.3 Electrochemical Mechanical Impedance. 4.5. Electrochemical Power Sources. 4.5.1 Special Aspects of Impedance Modeling of Power Sources (Evgenij Barsoukov). 4.5.1.1 Intrinsic Relation Between Impedance Properties and Power Sources Performance. 4.5.1.2 Linear Time-Domain Modeling Based on Impedance Models, Laplace Transform. 4.5.1.3 Expressing Model Parameters in Electrical Terms, Limiting Resistances and Capacitances of Distributed Elements. 4.5.1.4 Discretization of Distributed Elements, Augmenting Equivalent Circuits. 4.5.1.5 Nonlinear Time-Domain Modeling of Power Sources Based on Impedance Models. 4.5.1.6 Special Kinds of Impedance Measurement Possible with Power Sources-Passive Load Excitation and Load Interrupt. 4.5.2 Batteries (Evgenij Barsoukov). 4.5.2.1 Generic Approach to Battery Impedance Modeling. 4.5.2.2 Lead Acid Batteries. 4.5.2.3 Nickel Cadmium Batteries. 4.5.2.4 Nickel Metal-hydride Batteries. 4.5.2.5 Li-ion Batteries. 4.5.3 Impedance Behavior of Electrochemical Supercapacitors and Porous Electrodes (Brian E. Conway). 4.5.3.1 Introduction. 4.5.3.2 The Time Factor in Capacitance Charge or Discharge. 4.5.3.3 Nyquist (or Argand) Complex-Plane Plots for Representation of Impedance Behavior. 4.5.3.4 Bode Plots of Impedance Parameters for Capacitors. 4.5.3.5 Hierarchy of Equivalent Circuits and Representation of Electrochemical Capacitor Behavior. 4.5.3.6 Impedance and Voltammetry Behavior of Brush Electrode Models of Porous Electrodes. 4.5.3.7 Impedance Behavior of Supercapacitors Based on Pseudocapacitance. 4.5.3.8 Deviations of Double-layer Capacitance from Ideal Behavior: Representation by a Constant-phase Element (CPE). 4.5.4 Fuel Cells (Norbert Wagner). 4.5.4.1 Introduction. 4.5.4.2 Alkaline Fuel Cells (AFC). 4.5.4.3 Polymer Electrolyte Fuel Cells (PEFC). 4.5.4.4 Solid Oxide Fuel Cells (SOFC). Appendix. Abbreviations and Definitions of Models. References. Index.
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TL;DR: In this article, the authors describe a photovoltaic cell, created from low-to medium-purity materials through low-cost processes, which exhibits a commercially realistic energy-conversion efficiency.
Abstract: THE large-scale use of photovoltaic devices for electricity generation is prohibitively expensive at present: generation from existing commercial devices costs about ten times more than conventional methods1. Here we describe a photovoltaic cell, created from low-to medium-purity materials through low-cost processes, which exhibits a commercially realistic energy-conversion efficiency. The device is based on a 10-µm-thick, optically transparent film of titanium dioxide particles a few nanometres in size, coated with a monolayer of a charge-transfer dye to sensitize the film for light harvesting. Because of the high surface area of the semiconductor film and the ideal spectral characteristics of the dye, the device harvests a high proportion of the incident solar energy flux (46%) and shows exceptionally high efficiencies for the conversion of incident photons to electrical current (more than 80%). The overall light-to-electric energy conversion yield is 7.1-7.9% in simulated solar light and 12% in diffuse daylight. The large current densities (greater than 12 mA cm-2) and exceptional stability (sustaining at least five million turnovers without decomposition), as well as the low cost, make practical applications feasible.
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Abstract: This book is based on the author's experience with calculations involving polynomial splines. It presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines. After two chapters summarizing polynomial approximation, a rigorous discussion of elementary spline theory is given involving linear, cubic and parabolic splines. The computational handling of piecewise polynomial functions (of one variable) of arbitrary order is the subject of chapters VII and VIII, while chapters IX, X, and XI are devoted to B-splines. The distances from splines with fixed and with variable knots is discussed in chapter XII. The remaining five chapters concern specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting. The present text version differs from the original in several respects. The book is now typeset (in plain TeX), the Fortran programs now make use of Fortran 77 features. The figures have been redrawn with the aid of Matlab, various errors have been corrected, and many more formal statements have been provided with proofs. Further, all formal statements and equations have been numbered by the same numbering system, to make it easier to find any particular item. A major change has occured in Chapters IX-XI where the B-spline theory is now developed directly from the recurrence relations without recourse to divided differences. This has brought in knot insertion as a powerful tool for providing simple proofs concerning the shape-preserving properties of the B-spline series.
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"Impedance spectroscopy : theory, ex..." refers background in this paper
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04 Jul 1990
TL;DR: In this article, the authors present a characterization of the resistivity of a two-point-versus-four-point probe in terms of the number of contacts and the amount of contacts in the probe.
Abstract: Preface to Third Edition. 1 Resistivity. 1.1 Introduction. 1.2 Two-Point Versus Four-Point Probe. 1.3 Wafer Mapping. 1.4 Resistivity Profiling. 1.5 Contactless Methods. 1.6 Conductivity Type. 1.7 Strengths and Weaknesses. Appendix 1.1 Resistivity as a Function of Doping Density. Appendix 1.2 Intrinsic Carrier Density. References. Problems. Review Questions. 2 Carrier and Doping Density. 2.1 Introduction. 2.2 Capacitance-Voltage (C-V). 2.3 Current-Voltage (I-V). 2.4 Measurement Errors and Precautions. 2.5 Hall Effect. 2.6 Optical Techniques. 2.7 Secondary Ion Mass Spectrometry (SIMS). 2.8 Rutherford Backscattering (RBS). 2.9 Lateral Profiling. 2.10 Strengths and Weaknesses. Appendix 2.1 Parallel or Series Connection? Appendix 2.2 Circuit Conversion. References. Problems. Review Questions. 3 Contact Resistance and Schottky Barriers. 3.1 Introduction. 3.2 Metal-Semiconductor Contacts. 3.3 Contact Resistance. 3.4 Measurement Techniques. 3.5 Schottky Barrier Height. 3.6 Comparison of Methods. 3.7 Strengths and Weaknesses. Appendix 3.1 Effect of Parasitic Resistance. Appendix 3.2 Alloys for Contacts to Semiconductors. References. Problems. Review Questions. 4 Series Resistance, Channel Length and Width, and Threshold Voltage. 4.1 Introduction. 4.2 PN Junction Diodes. 4.3 Schottky Barrier Diodes. 4.4 Solar Cells. 4.5 Bipolar Junction Transistors. 4.6 MOSFETS. 4.7 MESFETS and MODFETS. 4.8 Threshold Voltage. 4.9 Pseudo MOSFET. 4.10 Strengths and Weaknesses. Appendix 4.1 Schottky Diode Current-Voltage Equation. References. Problems. Review Questions. 5 Defects. 5.1 Introduction. 5.2 Generation-Recombination Statistics. 5.3 Capacitance Measurements. 5.4 Current Measurements. 5.5 Charge Measurements. 5.6 Deep-Level Transient Spectroscopy (DLTS). 5.7 Thermally Stimulated Capacitance and Current. 5.8 Positron Annihilation Spectroscopy (PAS). 5.9 Strengths and Weaknesses. Appendix 5.1 Activation Energy and Capture Cross-Section. Appendix 5.2 Time Constant Extraction. Appendix 5.3 Si and GaAs Data. References. Problems. Review Questions. 6 Oxide and Interface Trapped Charges, Oxide Thickness. 6.1 Introduction. 6.2 Fixed, Oxide Trapped, and Mobile Oxide Charge. 6.3 Interface Trapped Charge. 6.4 Oxide Thickness. 6.5 Strengths and Weaknesses. Appendix 6.1 Capacitance Measurement Techniques. Appendix 6.2 Effect of Chuck Capacitance and Leakage Current. References. Problems. Review Questions. 7 Carrier Lifetimes. 7.1 Introduction. 7.2 Recombination Lifetime/Surface Recombination Velocity. 7.3 Generation Lifetime/Surface Generation Velocity. 7.4 Recombination Lifetime-Optical Measurements. 7.5 Recombination Lifetime-Electrical Measurements. 7.6 Generation Lifetime-Electrical Measurements. 7.7 Strengths and Weaknesses. Appendix 7.1 Optical Excitation. Appendix 7.2 Electrical Excitation. References. Problems. Review Questions. 8 Mobility. 8.1 Introduction. 8.2 Conductivity Mobility. 8.3 Hall Effect and Mobility. 8.4 Magnetoresistance Mobility. 8.5 Time-of-Flight Drift Mobility. 8.6 MOSFET Mobility. 8.7 Contactless Mobility. 8.8 Strengths and Weaknesses. Appendix 8.1 Semiconductor Bulk Mobilities. Appendix 8.2 Semiconductor Surface Mobilities. Appendix 8.3 Effect of Channel Frequency Response. Appendix 8.4 Effect of Interface Trapped Charge. References. Problems. Review Questions. 9 Charge-based and Probe Characterization. 9.1 Introduction. 9.2 Background. 9.3 Surface Charging. 9.4 The Kelvin Probe. 9.5 Applications. 9.6 Scanning Probe Microscopy (SPM). 9.7 Strengths and Weaknesses. References. Problems. Review Questions. 10 Optical Characterization. 10.1 Introduction. 10.2 Optical Microscopy. 10.3 Ellipsometry. 10.4 Transmission. 10.5 Reflection. 10.6 Light Scattering. 10.7 Modulation Spectroscopy. 10.8 Line Width. 10.9 Photoluminescence (PL). 10.10 Raman Spectroscopy. 10.11 Strengths and Weaknesses. Appendix 10.1 Transmission Equations. Appendix 10.2 Absorption Coefficients and Refractive Indices for Selected Semiconductors. References. Problems. Review Questions. 11 Chemical and Physical Characterization. 11.1 Introduction. 11.2 Electron Beam Techniques. 11.3 Ion Beam Techniques. 11.4 X-Ray and Gamma-Ray Techniques. 11.5 Strengths and Weaknesses. Appendix 11.1 Selected Features of Some Analytical Techniques. References. Problems. Review Questions. 12 Reliability and Failure Analysis. 12.1 Introduction. 12.2 Failure Times and Acceleration Factors. 12.3 Distribution Functions. 12.4 Reliability Concerns. 12.5 Failure Analysis Characterization Techniques. 12.6 Strengths and Weaknesses. Appendix 12.1 Gate Currents. References. Problems. Review Questions. Appendix 1 List of Symbols. Appendix 2 Abbreviations and Acronyms. Index.
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TL;DR: In this paper, the double-layer and surface functionalities at Carbon were investigated and the double layer at Capacitor Electrode Interfaces: its structure and Capacitance.
Abstract: 1 Introduction and Historical Perspective 2 Similarities and Differences between Supercapacitors and Batteries for Electrical Energy Storage 3 Energetics and Elements of Kinetics of Electrode Processes 4 Elements of Electrostatics Involved in Treatment of Double-Layers and Ions at Capacitors Electrode Interfaces 5 Behavior of Dielectrics in Capacitors and Theories of Dielectric Polarization 6 The Double-Layer at Capacitor Electrode Interfaces: Its Structure and Capacitance 7 Theoretical Treatment and Modeling of the Double-Layer at Electrode Interfaces 8 Behavior of the Double-Layer in Non-Aqueous Electrolytes and Non-Aqueous Electrolyte Capacitors 9 The Double-Layer and Surface Functionalities at Carbon 10 Electrochemical Capacitors Based on Pseudocapacitance 11 The Electrochemical Behavior of Ruthenium Oxide (RuO2) as a Material for Electrochemical Capacitors 12 Capacitance Behavior of Films Conducting, Electrochemically Reactive Polymers 13 The Electrolyte Factor in Supercapacitor Design and Performance: Conductivity, Ion-Pairing and Solvation 14 Electrochemical Behavior at Porous Electrodes Applications to Capacitors 15 Energy-Density and Power-Density of Electrical Energy Storage Devices 16 AC Impedance Behavior of Electrochemical Capacitors and Other Electrochemical Systems 17 Treatments of Impedance Behavior of Various Circuits and Modeling of Double-Layer Capacitor Frequency Response 18 Self-Discharge of Electrochemical Capacitors in Relation to that of at Batteries 19 Technology Development 20 Patent Survey
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TL;DR: In this article, the empirical dielectric decay function γ(t)= exp −(t/τ 0)β was transformed analytically to give the frequency dependent complex dielectrics constant if β is chosen to be 0.50 in the range log(ωτ0) > −0.5.
Abstract: The empirical dielectric decay function γ(t)= exp –(t/τ0)β may be transformed analytically to give the frequency dependent complex dielectric constant if β is chosen to be 0.50. The resulting dielectric constant and dielectric loss curves are non-symmetrical about the logarithm of the frequency of maximum loss, and are intermediate between the Cole-Cole and Davidson-Cole empirical relations. Using a short extrapolation procedure, good agreement is obtained between the empirical representation and the experimental curves for the α relaxation in polyethyl acrylate. It is suggested that the present representation would have a general application to the α relaxations in other polymers. The Hamon approximation, with a small applied correction, is valid for the present function with β= 0.50 in the range log(ωτ0) > –0.5, but cannot be used at lower frequencies.
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