Immittance Spectroscopy – Applications to Material Systems

<p>Background of this Book xiii</p>
<p>Acknowledgments xxiii</p>
<p>1 Introduction to Immittance Spectroscopy 1</p>
<p>1.1 Basic Definition and Background 1</p>
<p>1.2 Scope and Limitation 5</p>
<p>1.3 Applications of the Immittance Studies to Various Material Systems 6</p>
<p>1.4 Concept of the Linear Circuit Elements: Resistance, Capacitance, and Inductance 9</p>
<p>1.5 Concept of Impedance, Admittance, Complex Capacitance, and Modulus 13</p>
<p>1.6 Immittance Functions 21</p>
<p>1.7 Series Resonant Circuit 22</p>
<p>1.8 Parallel Resonant Circuit 23</p>
<p>1.9 Capacitance and Inductance in Alternating Current 24</p>
<p>Problems 24</p>
<p>References 25</p>
<p>2 Basics of Solid State Devices and Materials 27</p>
<p>2.1 Overview of the Fundamentals of Physical Electronics 27</p>
<p>2.2 Basics of Semiconductors 33</p>
<p>2.3 Single–Crystal and Polycrystal Materials 35</p>
<p>2.4 SCSJ and MPCHPH Systems 37</p>
<p>2.5 Representation of the Competing Phenomena 42</p>
<p>2.6 Effect of Normalization of the Electrical Parameters 43</p>
<p>Problems 46</p>
<p>References 47</p>
<p>3 Dielectric Representation and Operative Mechanisms 49</p>
<p>3.1 Dielectric Constant of Materials: Single Crystals and Polycrystals 49</p>
<p>3.2 Dielectric Behavior of Materials: Single Crystals and Polycrystals 53</p>
<p>3.3 Origin of Frequency Dependence 58</p>
<p>3.4 Effect of Polarization 60</p>
<p>3.5 Equivalent Circuit Representation of the Mechanisms and Processes 67</p>
<p>3.6 Defects and Traps 69</p>
<p>3.7 Point Defects and Stoichiometric Defects 77</p>
<p>3.8 Leaky Systems 78</p>
<p>Problems 79</p>
<p>References 80</p>
<p>4 Ideal Equivalent Circuits and Models 85</p>
<p>4.1 Concept of Equivalent Circuit 85</p>
<p>4.2 Simple and Basic Circuits in Complex Planes: R, C, R–C Series, and R–C Parallel 86</p>
<p>4.3 Debye Circuits: Single Relaxation 89</p>
<p>4.4 Duality of the Equivalent Circuits: Multiple Circuits for a Single Plane 97</p>
<p>4.5 Duality of Equivalent Circuits between Z∗– and M∗–Planes for Relaxations without Intercept 98</p>
<p>4.6 Duality of Equivalent Circuits between Y∗– and C∗–Planes for Relaxations without Intercept 100</p>
<p>4.7 Duality of Equivalent Circuits for Simultaneous Z∗–, Y∗–, C∗–, and M∗–Planes Relaxations 102</p>
<p>4.8 Proposition of Equivalent Circuit: Polycrystalline Grains and Grain Boundaries 103</p>
<p>Problems 105</p>
<p>References 106</p>
<p>5 Debye and Non–Debye Relaxations 109</p>
<p>5.1 Ideal Systems 109</p>
<p>5.2 Non–Ideal Systems 116</p>
<p>5.3 Non–Ideal Systems Implying Distributed Time Constants 122</p>
<p>5.4 D–C Representation, Depression Parameter, and Equivalent Circuit: Conventional Domain 128</p>
<p>5.5 Depression Parameter Based on peak = 1: Complex Domain 134</p>
<p>5.6 Optimization of ZHF: Complex Domain 137</p>
<p>5.7 Depression Parameter Based on peak = 1 139</p>
<p>5.8 Feature of the Depression Parameter Based on 1 145</p>
<p>5.9 Analysis of the Havriliak–Negami Representation 146</p>
<p>5.10 Geometrical Interpretation of H–N Relaxation at the Limiting Case 151</p>
<p>5.11 Extraction of the Relaxation Time and the H–N Depression Parameters and 154</p>
<p>5.12 Checking Generalized Depression Parameter when is Real 159</p>
<p>5.13 Checking Generalized Depression Parameter when is Real 160</p>
<p>5.14 Effect of and on the H–N Distribution Function 162</p>
<p>5.15 Meaning of the Depression Parameters and 166</p>
<p>5.16 Relaxation function with Respect to the Depression</p>
<p>Parameters and 168</p>
<p>Problems 170</p>
<p>References 170</p>
<p>6 Modeling and Interpretation of the Data 175</p>
<p>6.1 Equivalent Circuit Model for the Single Complex Plane (SCP) Representation 175</p>
<p>6.2 Models and Circuits 177</p>
<p>6.3 Nonconventional Circuits 184</p>
<p>6.4 Multiple Equivalent Circuits for Multiple Relaxations in a Single Complex Plane 186</p>
<p>6.5 Single Equivalent Circuit for Multiple Complex Planes 187</p>
<p>6.6 Equivalent Circuit for Resonance 189</p>
<p>6.7 Single Equivalent Circuit from Z∗– and M∗–Planes 189</p>
<p>6.8 Temperature and Bias Dependence of the Equivalent Circuit Modeling 190</p>
<p>6.9 Equivalent Circuit: Zinc Oxide (ZnO) Based Varistors 191</p>
<p>6.10 Equivalent Circuit: Lithium Niobate LiNbO3 Single Crystal 196</p>
<p>6.11 Equivalent Circuit: Polycrystalline Yttria (Y2O3) 200</p>
<p>6.12 Equivalent Circuit: Polycrystalline Calcium Zirconate (CaZrO3) 201</p>
<p>6.13 Equivalent Circuit: Polycrystalline Calcium Stannate (CaSnO3) 202</p>
<p>6.14 Equivalent Circuit: Polycrystalline Titanium Dioxide (TiO2) 203</p>
<p>6.15 Equivalent Circuit: Multi–Layered Thermoelectric Device (Alternate SiO2/SiO2+Ge Thin–Film) 204</p>
<p>6.16 Equivalent Circuit: Polycrystalline Tungsten Oxide (WO3) 206</p>
<p>6.17 Equivalent Circuit: Biological Material E. Coli Bacteria 207</p>
<p>Problems 208</p>
<p>References 209</p>
<p>7 Data–Handling and Analyzing Criteria 213</p>
<p>7.1 Acquisition of the Immittance Data 213</p>
<p>7.2 Lumped Parameter/Complex Plane Analysis (LP/CPA) 214</p>
<p>7.3 Spectroscopic Analysis (SA) 222</p>
<p>7.4 Bode Plane Analysis (BPA) 225</p>
<p>7.5 Misrepresentation of the Measured Data 227</p>
<p>7.6 Misinterpretation of the Bode Plot: Equivalent Circuit 230</p>
<p>Problems 232</p>
<p>References 233</p>
<p>8 Liquid Systems 241</p>
<p>8.1 Non–Crystalline Systems: Liquids 241</p>
<p>8.2 Warburg and Faradaic Impedances 245</p>
<p>8.3 Constant Phase Element (CPE) 249</p>
<p>8.4 Biological Liquid: E. Coli Bacteria 251</p>
<p>Problems 255</p>
<p>References 256</p>
<p>9 Case Study 259</p>
<p>9.1 Analysis of the Measured Data: Aspects of Data–Handling/Analyzing Criteria 259</p>
<p>9.2 Case 1: Proper Physical Geometrical Factors 260</p>
<p>9.3 Case 2: Improper Normalization 262</p>
<p>9.4 Case 3: Effect of Electrode and Lead Wire 264</p>
<p>9.5 Case 4: Identification of Contributions to the Terminal Immittance 265</p>
<p>9.6 Case 5: Use of Proper Unit 267</p>
<p>9.7 Case 6: Demonstration of the Invalid Plot 270</p>
<p>9.8 Case 7: Obscuring Frequency Dependence 271</p>
<p>9.9 Case 8: Misnomer Nomenclature for the Complex Plane Plot 273</p>
<p>9.10 Case 9: Extraction of Equivalent Circuit from the Straight Line or the Non–Relaxation Curve 274</p>
<p>Problems 277</p>
<p>References 278</p>
<p>10 Analysis of the Complicated Mott–Schottky Behavior 283</p>
<p>10.1 Capacitance Voltage (C–V) Measurement 283</p>
<p>10.2 The Mott–Schottky Plot 287</p>
<p>10.3 Arbitrary Measurement Frequency and Construction of the Deceiving Mott–Schottky Plot 296</p>
<p>10.4 Frequency–Independent Representation 297</p>
<p>10.5 Extraction of the Device–Related Parameters 299</p>
<p>Problems 302</p>
<p>References 303</p>
<p>11 Analysis of the Measured Data 307</p>
<p>11.1 Introduction and Background of the Immittance Data Analysis 307</p>
<p>11.2 Measurement of the Immittance Data and Complex Plane Analysis 312</p>
<p>11.3 Nonlinear Least Squares Estimation 314</p>
<p>11.3.1 Gauss–Newton Method (Algorithm) of Least Squares Estimation 317</p>
<p>11.3.2 Levenberg–Marquardt Method (Algorithm) of Least Squares Estimation 320</p>
<p>11.3.3 Numerical Procedure to Calculate Jacobian Matrix 321</p>
<p>11.3.4 Error Analysis: Analysis of Errors in Regression 321</p>
<p>11.3.5 Selection of the Weights 322</p>
<p>11.4 Complex Nonlinear Least Squares (CNLS) Fitting of the Data 323</p>
<p>11.4.1 Procedure 1: Geometrical Fitting in the Complex Plane 323</p>
<p>11.4.2 Procedure 2: Simultaneous Fitting of Real and Imaginary Parts 328</p>
<p>11.5 Graphical User&nbsp; Interface Implementation of the Nonlinear Least Square Procedures: Implementation of CNLS using MATLAB 330</p>
<p>11.5.1 Input Data Generation 330</p>
<p>11.5.2 Input Data Processing 331</p>
<p>11.5.2.1 Visualization of the Measured (Raw) Data 332</p>
<p>11.5.2.2 Selection of Data Points for Fitting 333</p>
<p>11.5.2.3 Fitting of the Semicircle: Geometric Fitting 334</p>
<p>11.5.2.4 Calculation of the Parameters from the Semicircle Fitting 335</p>
<p>11.5.2.5 Calculation of the Parameters from the Simultaneous Fitting of Real and Imaginary Parts 336</p>
<p>11.5.3 Output Generation: Output File 337</p>
<p>11.5.3.1 Parameters from the Semicircle Fitting 337</p>
<p>11.5.3.2 Nonlinear Regression: Semicircle Fitting Output 337</p>
<p>11.5.3.3 Linear Regression: Line Fitting Output 338</p>
<p>11.5.3.4 Parameters from Simultaneous Fitting of Real and Imaginary Data 338</p>
<p>11.5.3.5 Nonlinear Regression: Simultaneous Fitting of Real and Imaginary Data Output 338</p>
<p>11.5.3.6 Measured Data used in Analysis 339</p>
<p>11.6 Effect of Fitting Procedure, Measurement Noise, and Solution Algorithm on the Estimated Parameters 340</p>
<p>11.7 Case Studies: CNLS Fitting of the Measured Data in the Complex Planes 342</p>
<p>11.7.1 M∗–Plane Fitting: R–C Parallel Circuit 343</p>
<p>11.7.2 C∗– and M∗–Plane Representations of the Lithium Niobate (LN) Crystal 344</p>
<p>11.7.3 Z∗– and Y∗–Plane Representations of Multi–Layered Junction Device 349</p>
<p>11.7.4 Y∗–plane Representation of the E. Coli Bacteria in Brain Heart Infusion Medium 351</p>
<p>11.8 Summary 353</p>
<p>Problems 355</p>
<p>References 357</p>
<p>12 Items for Appendix 363</p>
<p>12.1 Appendix A: Sample Input Data for the R–C Parallel Circuit 363</p>
<p>12.2 Appendix B: R–C Parallel Circuit Data Analysis Output in Z∗–Plane 364</p>
<p>12.3 Appendix C: R–C Parallel Circuit Data Analysis Output in M∗–Plane 368</p>
<p>12.4 Appendix D: Lithium Niobate Crystal Data Analysis Output in C∗–Plane 370</p>
<p>12.5 Appendix E: Multilayer Junction Thermoelectric Device Data Analysis Output in Y∗–Plane 372</p>
<p>&nbsp;Index</p>