This book emphasizes the use of four complex plane formalisms (impedance, admittance, complex capacitance, and modulus) in a simultaneous fashion. The purpose of employing these complex planes for handling semicircular relaxation using a single set of measured impedance data (ac small-signal electrical data) is highly underscored. The current literature demonstrates the importance of template version of impedance plot whereas this book reflects the advantage of using concurrent four complex plane plots for the same data. This approach allows extraction of a meaningful equivalent circuit model attributing to possible interpretations via potential polarizations and operative mechanisms for the investigated material system. Thus, this book supersedes the limitations of the impedance plot, and intends to serve a broader community of scientific and technical professionals better for their solid and liquid systems. This book addresses the following highlighted contents for the measured data but not limited to the:- (1) Lumped Parameter/Complex Plane Analysis (LP/CPA) in conjunction with the Bode plots; (2) Equivalent circuit model (ECM) derived from the LP/CPA; (3) Underlying Operative Mechanisms along with the possible interpretations; (4) Ideal (Debye) and non-ideal (non-Debye) relaxations; and(5) Data-Handling Criteria (DHC) using Complex Nonlinear Least Squares (CNLS) fitting procedures.
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Scrivener Publishing100 Cummings Center, Suite 541JBeverly, MA 01915-6106
Mohammad A. Alim
Department of Electrical Engineering and Computer Science Alabama A & M University Huntsville, Alabama, U.S.A.
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Library of Congress Cataloging-in-Publication Data
In the name of Allah, the Beneficent, the Merciful
Mohammad Alim Biswas
, M.Sc., Ph.D., D.I.C., (1927 – 2009) son of
Mohammad Bhadu (Bahadur) Biswas (1885 – 1961) and
Saleha Khatun (1894 – 1970), who provided inspiration to comprehend general science beside navigating mathematics, chemistry, physics, history, geography, philosophy, and exposing world religions including exercising english and other global languages;
(1934 –), daughter of
Mohammad Boytullah Mondol (1894 – 1976) and
Rowshan Ara Khatun (1904 – 1990), who guided to comprehend Bangla language making literature easy and walking through mathematics;
, M.Sc., M.S., M.S.M.E., (1957 –), daughter of Muhammad Aminuddin (1919 – 2001) and
Anosha Khatun (1930 – 1989), who helped in achieivng academic and professional goals; and
: Nasiha Muna, Sabiha Runa, Maliha Lubna, and Mohammad E. Alim who helped in many ways to materialize this work.
While the complicated multi-component polycrystalline system was hunting the answer for the underlying operative mechanisms (UOMs), a few questions emerged a few decades ago despite speculated theories bouncing all over reputed journals. At that time impedance spectroscopy began walking. What is the meaning of the term ‘spectroscopy’ for the measured impedance or the admittance or the phasor data? Is it just data acquisition as a function of applied frequency or something else? Is it only the impedance plot that causes the term impedance spectroscopy? Why is there no presence of an admittance plot when the same data are acquired and used though the name admittance spectroscopy is used? In order to answer these questions the materialization of this book emerged to help the understanding of the investigators and the new learners for the generations to come. As of today, the three existing books on the subject demonstrated successfully and efficiently single complex plane (SCP) analysis for the measured data along with elegant theories, relevant or non-relevant, but therein it remained difficult to comprehend the meaning of spectroscopy when it involves impedance or admittance or phasor form of the measured data.
In the most recent decades, a separate assertive parasitic name emerged as the electrochemical impedance spectroscopy (EIS) among the users of the immittance data. What is EIS? In general, impedance spectroscopy is in use for a variety of solid material systems that include electronic or ionic type single crystals and polycrystals, hybrid semiconductors, electrolytes, composites, etc., beside the liquid and biological systems emphasizing reactions in many electrochemical materials. Each material system is not limited to the use of impedance spectroscopy. A widespread frequency range strengthens the horizon of the investigation. Therefore, using an emphasized “word” in front of this term does not increase the horizon or density or intensity or importance of the in-depth investigation.
The generalized form of impedance spectroscopy is already adequate or self-contained for every material system as the fathom depends only on the acquisition of the ac small-signal electrical data. Does one need hybrid impedance spectroscopy as a hybrid system investigator, or quality impedance spectroscopy as a quality control professional? The entire theory and basis of impedance spectroscopy (IS) are the same regardless of the material system. The acronym “IS” is ready to alternate between impedance spectroscopy and immittance spectroscopy though it is used in the first book for impedance spectroscopy in 1987.
The terms impedance spectroscopy and admittance spectroscopy (AS) are explained vividly using relevant situations and cases. The real-world situation is more complicated with respect to the nature of the material systems. For the polycrystalline systems, obtaining two consecutive semicircles in the impedance plane does not mean that grains and grain boundaries are explored. What about the role of the defects and traps having discontinuities in grain-to-grain contacts though ohmic contacts for the electrodes are ignored? Are these defects relaxed or non-relaxed? Are these traps distributed over a range of energy levels? What is the distribution of time constant?
It is amazing that the conceptual term for impedance or admittance of a circuit came to the scientists and engineers shortly after Michael Faraday offered modern electricity to mankind. Nearly a hundred years after Michael Faraday, immittance emerged as a hybrid word originating from impedance and admittance. Though the common sense wisdom serves better, it is known that the impedance plot did not float before the classic Cole-Cole plot in 1941. This breakthrough indicated that the material systems, liquids or solids, require a broader window for investigation to understand the science or engineering aspects of learning. How does the impedance plot become the sole single complex plane (SCP) analytical tool for the entire material systems? How does admittance spectroscopy never use an admittance plot but instead uses some other plot?
Despite the existence of the three separate books on impedance spectroscopy covering both solid and liquid systems, this book is prepared to serve a broad range professionals handling concurrent relaxations in multiple complex planes for the same set of measured ac small-signal electrical data. Through this book the use of multiple complex plane analysis in a simultaneous fashion for the same set of measured electrical data is strongly encouraged, and exercised with demonstrations to surmount every stack of problems. The pedagogical or tutorial contents available today on this subject do not address adequately the use of concurrent multiple complex planes (CMCP) apart from the advantages or disadvantages of apprehending complicated underlying operative mechanisms (UOMs) within the device under test (DUT). The extraction of the meaningful and logical equivalent circuit model possessing interpretation follows from the concurrent multiple complex plane analysis (CMCPA) of the data.
This book is certainly designed to serve the advanced knowledge seekers dealing with benefits of multiple complex plane representations of the data to unravel the UOMs for the DUT. This book encourages to wide-open the window of investigation. It is also designed to serve as a broad range reference on the immittance spectroscopy where complexity of the material system is severe. Thus, this book is directed toward the advanced researchers as well as the learners comprising of graduate and undergraduate students in several disciplines at any global corner. The undergraduate students of all disciplines of engineering, physics, chemistry, and applied sciences can use this book as a reference for the fundamentals of electrical circuits, basics of semiconductor physical electronics, electrical properties of material systems, and characterization of engineering materials besides undertaking senior design and analysis projects in this area of technology.
This book is organized in such a way that there is no duplication or repetition or redundancy as the concept of Concurrent Multiple Complex Plane Formalisms (CMCPFs) is established serving applications and purpose of the DUT. A few problems are incorporated at the end of each chapter to serve practice sessions. It is expected that the learners and the investigators are used to with the computers and spreadsheets beside the access to the available software for data acquisition and necessary analyses. Overall the content provides a worthy source of information for the investigators working in multidisciplinary areas. Background principles, basics of measurements, knowledge on instrumentation, and detailed analysis or analytical procedures are not included in this book because similar content already exists.
The immittance spectroscopy is such a subject that one has to get absorbed or immersed in it with heart and mind possessing strong inspection capability, and subsequent assessment for any set of frequency window possessing number of data points. There is no scope of guessing or speculation for extrapolation of the observed behavior of the DUT. It is a fact that with the level of experience it is possible to visualize the duality of the circuits or duality of the complex planes just seeing or inspecting the feature of one complex plane. Bode plots often mask such tangential behavior. This achievement requires heavy practice and understanding the walking nature of the data points on the semicircle for any DUT. This book has attempted to provide that kind of concept to the interested readers, learners, and investigators.
The CMCPFs apply to all four complex planes in a simultaneous fashion for the same set of measured data. Representation of the measured data in one selected choice of a complex plane via impedance or admittance or capacitance or modulus plot is referred to as the SCP plot besides using a number of favorable and non-favorable Bode plots. This approach somehow paves the initial road for understanding lumped contribution for the DUT. When all four complex planes are used concurrently the road becomes wider. Thus, the effect of using lumped parameter/complex plane analysis (LP/CPA) and Bode plane analysis (BPA) is emphasized together with spectroscopic analysis (SA).
The meaning of the duality of the equivalent circuit models (ECMs) obtained from one or more complex planes in a simultaneous fashion is explained. The complexities of these equivalent circuits originated from a single set of measured data are not averted but dealt with by way of published examples. Converting one form of circuit to another form clearly demonstrates how LP/CPA can influence each complex plane. Nevertheless, two simultaneous circuits obtained from two complex planes allow a more visionary window than a single circuit obtained from a single complex plane via better exposure of the underlying operative phenomena. Among the highlighted topics, concurrent multi-plane analysis and their usefulness of developing equivalent circuit is an important issue, particularly, when no usual semicircular relaxation appears in the template impedance plot or classic Cole-Cole plot.
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