Dielectric and Electrical Properties of Materials

Prof. Graham Williams: representation can be converted into resonance (ESR) spectroscopy, any other e. g. Y=1/Z, M = 1/ε etc. quasi-elastic light scattering Dielectric and As a result, different approaches (QELS), Fourier transform infra-red electrical to the electrical/dielectric properties spectroscopy (FTIR) and of materials have been made over fluorescence depolarization (FD). properties of the years and their inter- These methods are often materials relationships have been neglected. complementary to DRS for studying Dielectrics Relaxation (using ε), physical processes in materials. The dielectric and electrical Impedance Spectrosocopy (using Z) Fortunately, the situation has properties of insulating and semi- and Electrical Relaxation changed dramatically during the conducting dielectric materials as Spectroscopy (using M) are all past ten years. The arrival of fast measured over wide ranges of inter-related since the experiments accurate impedance analyzers, frequency and temperature have actually measure Z (=1/Y) in all frequency response analyzers and been the subject of considerable cases. This is being appreciated interest in recent years. increasingly so we should accept new technologies In terms of the measurements, a that apparently-different researches now available sample in the frequency range 10-6 are actually inter-related and that to 108 Hz is regarded as a lumped- pulsed-transient equipment for the the electrical quantities used are a circuit element having a frequency- range 10-6 to 109 Hz and fast matter of choice, based on prior dependent complex impedance Z(f) accurate network analyzers and knowledge of the electrical- while at higher frequencies, ranging time-domain reflectometry equip- /dielectric phenomena that may be from the UHF through the ment for the range 108 to 1010 Hz involved in each case. microwave range to the far infra-red together with the computer control Having noted the different re- region, i. e. 108 to 1012 Hz a of measurement, data acquisition presentations that are presently used sample is regarded as a distributed and data-processing and computer for the electrical/dielectric circuit element having a frequency- control of sample temperature has properties of materials, we observe dependent complex propagation enabled DRS, IS and ERS to take that up to about ten years ago most coefficient γ(f). their rightful place alongside NMR, experimental studies of materials Experimental data, in terms of ESR, QELS and FD in the range of were made over limited frequency Z(f) of γ(f), covering the entire modern methods used to study the bands by a manual point-by-point frequency range 10-6 to 1012 Hz physical properties of materials. procedure. may be re-expressed in different Commercial equipment is now Thus, typically, using a low ways. Traditionally, different areas available which provides fast frequency bridge, measurements at of research have used different accurate measurements of the 16 frequencies equally-spaced in derived quantities as is shown in dielectric/electrical properties of the log f scale would take up to 30 table 1. 10 liquid and solid materials over a minutes to complete. While the Thus dielectric properties, range of prescribed temperatures measurements were accurate, the expressed in terms of ε(f), are used and frequencies, where the inability to obtain data quickly when studying molecular motion in measurements are made severely hampered the use of solid polymers while electrical automatically and the data are dielectric relaxation spectroscopy properties expressed in terms of processed on-line into any (DRS) or its equivalents impedance Z(f), M(f) or γ(f) are used when convenient form. spectroscopy (IS) and electrical studying conduction processes in Such equipment is provided, for relaxation spectroscopy (ERS). At ionic solids or liquid electrolytes, example, by the range of the same time rapid advances were etc. etc. It is important to stress that NOVOCONTROL dielectric being made in other physical the electrical/dielectrical properties spectrometers each working over a methods such as nuclear magnetic of a material can be expressed in wide frequency band i. e. 10-5 to resonance (NMR) relaxation 7 6 9 9 10 these different ways and one should 10 Hz, 10 -10 Hz and 10 - 10 spectroscopy, electron-spin remember that a particular Hz.

1 Dielectrics Newsletter march 1994

Measured Quantity Symbol Application

Impedance Z = R +iX Conduction in ionic liquids and R = Resistance solids, polymer electrolytes, X = Reactance semiconductors

Admittance Y = G + iX' As for impedance G = Conductance X' = inverse reactance

Permittivity ε = ε' - iε'' Dielectric relaxation in dipolar ε' = real permittivity liquids, liquid crystals and solids, ε''= loss factor polymers and glass forming liquids

Dielectric Modules M = M' + iM'' Electrical relaxation in ionic liquids and solids, electrolytes, molten salts, semiconductors

Electrical Conductivity σ = σ' + iσ'' Conduction in ionic liquids and σ' = real conductivity solids, semiconductors

Complex Propagation γ = α + iβ Dielectric and far infra-red Coefficient at wavelength λo, α = attenuation factor absorption in dipolar liquids and β π λ solids = 2 n'/ o Complex refractive index n n = n'+ in''

Table 1

The availability of such modern continual sweeping and recording liquids, molten salts and glassy equipment makes possible high the time of each measurement, ionic solids. quality research into the yielding ε'(f,t) and ε''(f,t) throughout 2. Liquid-crystalline Materials dielectrical/electrical properties of a the time-dependent process. Post- Low molar mass and polymeric wide range of organic and inorganic processing of data allows (ε',ε'') thermotropic liquid crystals materials - as an extension of earlier values to be determined as a including nematic, smectic, work - and of new functional function of frequency at given times chiral-nematic and ferroelectric materials that are of importance in t. Such studies open up an entirely materials, lytropic liquid crystals relation to their electrical, dielectric, new domain of application of including rod-like polymers or electro-optical and conduction modern dielectric-relaxation surfactants with solvents, hybrid properties. spectroscopy, especially for liquid-crystalline polymer net- In addition, measurements are polymerizing organic systems. works, polymer-dispersed liquid now possible, through the speed Similar time-dependent crystals. and practical convenience of the dielectric/electrical phenomena may modern techniques, with systems be envisaged for inorganic materials 3. Crystalline Material that were not feasible using the (e. g. the dynamics of phase- Ionic crystals as insulators, traditional manual point-by-point transformations in inorganic solids). semiconductors and electrolytes, methods. Table 2 shows examples of molecular crystals including materials and t-dependent system rotator-phase crystals and real-time dielectric that are being studied using modern crystalline polymers, ferro- spectroscopy techniques: electric crystals, crystalline semi- In particular, the techniques of real- conductors and photo- time dielectric spectroscopy is 1. Amorphous Organic And conductors. Inorganic Materials emerging as a means of studying the 4. Time-dependent Systems Molecular liquids including dielectric/electrical behaviour of Systems undergoing bulk poly- glass-forming liquids, materials whose physical or merization e. g. thermosets, bulk amorphous polymers, chemical properties are changing addition polymerization by ther- semiconductors and photo- with time. In this case the dielectric mal or photochemical initiation, conductors, liquid, solid and permittivity ε(f) is determined systems undergoing crystal- polymer electrolytes, ionic across a frequency range by lization e. g. crystallizing

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polymers, systems undergoing using the traditional point-by-point Prof. Friedrich Kremer: phase separation e.g. polymer method of measurement. His former mixtures at elevated tem- supervisor, Professor Mansel Dielectric peratures. Davies, remarked in the early 1960's spectroscopy: that any expansion of dielectrics Old spectroscopic research would only occur when Particular interest in the future is commercial dielectric measuring technique gains likely to be given to the dielectric assemblies became available. and electro-optical properties of new actuality It has taken over 30 years for that liquid crystals, novel hybrid organic to be achieved and we can now say Dielectric spectroscopy is an old liquid-crystal-polymer-networks with complete confidence that the spectroscopic technique, which has and polymer-dispersed liquid modern broadband dielectric roots going back to the last century. crystalline display materials spectrometers will enable research Claurius, Mosotti, Lorenz, Maxwell what comes next ? into the dielectric and conduction - just to mention some of the properties of materials of all kinds pioneers - made important where the dielectric properties will to be conducted quickly, accurately contributions to the understanding vary with an applied AC or DC and conveniently at the highest of electrical and dielectric biasing field. Such behaviour has professional level to yield infor- phenomena. been studied extensively by Kremer mation that is crucial to our under- In the second decade of this (Mainz / Leipzig) for ferroelectric standing of polarization and charge century Debye formulated the crystals and has given important transport processes in both theory of dielectric dispersion information on the mechanisms for conventional materials and the new which is outlined in his famous the electro-optical response in such classes of novel electroactive and book on "Polar Molecules". This materials. photoactive materials now being formed the basis of a microscopic The nature of charge motion, and provided for modern technology. understanding of dielectric its associated relaxation, in relaxation processes, which was inorganic and organic semi- refined later by Kirkwood, Fröhlich, Prof. Graham Williams conductors and photoconductors Onsager and Cole. Department of Chemistry may be investigated using University College of Swansea broadband DRS, or its equivalents Singleton Park, new actuality IS and ERS, and this is an area to Swansea SA2 8PP, U.K. Nowadays, dielectric spec- which the modern equipment will troscopy is gaining new actuality. In be applied increasingly. its modern form it covers easily It is clear that the availability of more than 12 decades in frequency. modern equipment capable of For that, different measurement making fast accurate measurements systems based on different physical of dielectric / electrical properties of measurement principles have to be the range of materials shown in combined (see below). This table 2 will stimulate an expansion outstanding dynamic range makes in dielectrics research for time- dielectric methodology especially dependent and time-independent valuable as a spectroscopic tool. systems. The expansion in research Studies on the scaling of relaxation -3 activity in the frequency range 10 processes, on the dynamic of liquid 7 to 10 Hz is already apparent in the crystals or the frequency literature but the use of the higher dependence of charge transport in 8 10 frequency range 10 to 10 Hz is in (polymeric) semiconductors are its infancy and we await new based on the huge frequency studies in this little-explored region window which is readily accessible for the materials and systems with modern equipment. described in table 2. The writer has been active in modern impedance dielectrics research for nearly forty analyzers save time years and for much of that time has A more practical advantage of laboured, with his students, to dielectric spectroscopy results from obtain comprehensive dielectric the measurement speed of modern data for amorphous and crystalline impedance analyzers, e.g. a polymers and glass-forming liquids frequency sweep from 106 Hz to

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109 Hz with 10 points per decade their dielectric function if exposed requires not more than 30 seconds. Dr. Gerhard Schaumburg to gases or liquids are used in This opens complete new fields sensor applications. of research, for instance the fast Overview: Modern Broadband dielectric spectro- monitoring of chemical reactions, measurement scopy links up with optical and IR- the control of cure in thermosets, techniques in spectroscopy for the low frequency the monitoring of charge transport, region between 1011 and 10-5 Hz. etc. In modern production control Broadband The material under test generally is dielectric methods play a significant Dielectric placed between two electrodes role. Spectroscopy forming a kind of capacitor as A further advantage of dielectric sketched in fig. 1. spectroscopy results from the fact This article is the first of a series that the capacitance of a sample about modern measurement capacitor is inversely proportional techniques in broadband dielectric Electrodes to its thickness. Hence, as long as a spectroscopy. Its intention is to give Sample material sample material can be prepared as an overview about the most an (ultra)-thin capacitor, the common techniques currently Fig.1: Sample material placed into a sensitivity of the measurement is available and to show which is measurement capacitor increasing with decreasing convenient for particular thickness, i.e. decreasing amount of measurement problems. Each of the sample material. This aspect is of techniques will be discussed in The sample capacitors impedance special importance in modern detail in the following newsletters. ZS is connected to the dielectric materials sciences, where newly Broadband dielectric spectro- function by synthesised materials are often scopy measures the complex −i ε = ε' −iε' ' = (1) obtained in mg quantities only. dielectric function ε = ε' - iε'' of π 2 f ZS C 0 Last not least: Compared to other materials in dependence on ε spectroscopic techniques like frequency. reflects the molecular where f denotes frequency and C0 is Nuclear Magnetic Resonance, relaxation and transport processes the vacuum capacity of the sample dynamic light scattering or dynamic of the material, which depend on capacitor. In most cases, ε is mechanical spectroscopy, dielectric nearly any other physical quantity measured as a function of two or methods are much less expensive. like e.g. temperature, time, even three parameters (e.g. Prof. Dr. Friedrich Kremer superimposed electromagnetic frequency, temperature, DC-bias). Universität Leipzig fields, pressure, etc.. Therefore As these multi dimensional Fakultät für Physik und applications in science and measurements produce large Geowissenschaften technology seem to be almost amounts of data and also long Linnéstraße 5 04103 Leipzig, Germany unlimited. Some examples for measurements times are involved, scientific applications are studies of automatical measurement systems the: are required. • studies on the molecular Therefore, a dielectric spectro- dynamics of liquids, liquid meter generally consists of the crystals and polymers, following components : • charge transport in • a sample cell with the sample semiconductors, organic crystals, capacitor, ceramics, etc., • a system being able to measure • monitoring of chemical reactions the complex impedance of the or polymerization processes, sample capacitor over a wide • structural material properties like frequency and impedance range phase compositions, phase with high precision, transitions and crystallization • a system allowing to expose the processes, sample capacitor to other • non-linear electrical and optical physical quantities like effects. temperature, DC-bias, etc., • Industrial applications are in a computer which controls the quality control, characterization of measurement flow, the isolating materials and compatibility of the devices and semiconductors. Materials changing the evaluation of the measured

4 Dielectrics Newsletter march 1994

data. In addition, special techniques and equipment to prepare the sample capacitor may be required.

The impedance ZS of the sample capacitor may be determined either from a measurement in the time domain or in the frequency domain. In the time domain, the sample is excited with a short voltage pulse time domain measurement Fig. 2 : Measurement of ZS using frequency response analysis. or step and the decreasing sample current I(t) is measured as a function of time. The impedance

ZS(f) in the frequency range is calculated by means of a discrete Fourier transformation. The advantage of this technique, is that it is as fast as in principle possible. On the other hand, it is sensitive to electrical disturbance like noise and leakage currents, and requires high speed electronics at frequencies above 10 kHz. For these reasons Fig. 3 : Measurement principle of an AC impedance bridge. measurements in the time domain are generally less accurate than in the frequency domain. The time arrangement is shown in fig. 2. current to voltage converter is domain will be discussed in detail The generator drives the sample mounted in an active head directly in a later Dielectrics Newsletter. with the voltage US, being directly above the sample cell. As a result of This paper will focus on the that, errors caused by the frequency domain, where the frequency response measurement cables at high sample is excited with a harmonic analysis frequencies are minimized. In signal U (f) at the measurement S measured with Ch I of a vector addition to this, each sample frequency. Z is determined by S voltage analyzer (VVA). I is measurement is compared to a sensing the amplitude of the sample S measured with VVA's Ch II after it reference capacitor which is current with respect to U (f). S has been transformed by a current automatically adjusted close to the Depending on the frequency range, to voltage converter. The VVA is sample impedance. This allows the frequency response analysis, AC- using the same principle as lock-in elimination of all linear errors in the bridge methods or coaxial line amplifiers. Two internal harmonic whole system. reflectometry is providing the best reference signals being shifted by The system operates fully results. -5 90° in phase are multiplied with the automatic at frequencies from 10 - Frequency response analysis 107 Hz with a resolution in tan(δ) < measured signal. After averaging covers the range from 10-5 - 107 Hz -5 over many periods, both signals 10 and covers an impedance range with high precision. from 10-1 Ω - 1014 Ω. It is correspond directly to the input The sample current I (f), the S signal's real and imaginary parts. An particularly suited for sophisticated sample voltage U (f) and the phase S additional advantage of this applications in scientific or shift between them are measured technique is that all harmonic industrial research where high directly. The sample impedance is components that differ from the precision and a large frequency calculated from measurement frequency are range is required. U AC-bridge methods cover the = + = S (2) suppressed. Therefore frequency Z Z' iZ ' ' frequency range from 10 Hz - 10 IS response analysis is not sensitive to noise or non linear distortions. MHz with medium precision. They where U and I are written in S S In modern systems like the can be seen as an economical complex notation. The principle NOVOCONTROL BDS 40, the alternative to the frequency

5 Dielectrics Newsletter march 1994

response analysis for applications in particularly suited for time impedance is measured with a which low frequency measurements dependent monitoring of poly- microwave reflectometer. are not important. The principle of merization processes and chemical For this purpose, the incoming measurement is shown in fig. 3. reactions. Also applications largely and reflected waves are separated The impedance bridge consists of the sample capacity and the adjustable compensation impedance Cryostat ZC. On the left side of the bridge, Cell the generator drives the Sample Sample Capacitor AC-bridge methods r(0) PC7 Connector sample with the fixed and known Coaxial AC voltage US which causes the Precision Line current IS to flow into P1. On the ≈ r(l) right hand side of the bridge, the Generator variable amplitude - phase generator (VAPG) feeds the current U*In U*Ref IC through the compensation Coaxial Line Reflectometer impedance ZC into P1. The bridge will be balanced, if IC = -IS which corresponds to I = 0. Any 0 Fig. 4 : Dielectric measurement using coaxial line reflectometry deviation is detected by the zero between 1 MHz - 10 GHz. voltage detector which changes the amplitude and phase of the VAPG depending on temperature like with two directional couplers and ≠ characterizations of phase compo- are phase sensitively measured. r is as long as I0 0. In balanced state, the sample impedance is calculated sitions, phase transitions and defined as the ratio of the voltages by crystallization processes can be (or electrical fields) of the reflected solved by AC-bridge methodes wave to the incoming wave on the U U = S = − S ZS ZC (3) successfully. line. It depends on the location of I U S C the measurement on the line. coaxial line Automatic bridges which are also U ( x) reflectometry = Ref used in NOVOCONTROL r ( x) (4) U In ( x) dielectric measurement systems are Coaxial line geometry can be used HP 4284 (20 Hz - 1 MHz, at frequencies from 1 MHz - 10 For an ideal line, r(l) which is resolution tan(δ) < 5.10-4, 1 mΩ - GHz. In contrast to the low measured by the reflectometer can 100MΩ) and HP 4192 (10 Hz - 10 frequency techniques already be transformed to the reflection MHz, resolution tan(δ) < 10-3). For described, above 10 MHz the factor r(0) at the sample end of the dielectric measurements a standard measurement cables always line by sample cell is required which is 2 l ( α+iβ) contribute to the sample impedance. r ( 0 ) = r ( l ) e (5) connected by BNC cables to the Above approximate 30 MHz bridge. In practice the lines shift the standing waves arise at the line and where α is the damping constant high frequency measurement limit a direct measurement of the sample and β = 2πl/λ (λ : wavelength) the to approximately 0.5 MHz. Also the impedance completely fails. This propagation constant of the line. low frequency limit may not be can be avoided by application of From (5), the sample impedance is reached except for dielectric microwave techniques taking the calculated by samples with high losses (tan(δ) > measurement line as the main part + = 1 r ( 0 ) ZS Z0 (6) 1) as the sample impedance exceeds of the measured impedance into 1 − r ( 0 ) the high impedance measurement account /e.g. 1, 2/. Therefore, limit of the bridge. precision lines with defined where Z0 is the wave resistance of Nevertheless AC-impedance propagation constants are required. the line. As can be seen from (6), bridges offer a suitable and The principle of measurement is the measurement range is limited to inexpensive solution for shown in fig. 4. sample impedance ZS being in the applications which do not need a The sample capacitor is used as range of Z0. If this is not the case, large frequency range. As the the termination of a precision the reflection r(0) becomes nearly 1 measurement time is lower coaxial line. The complex reflection or -1 and the measured r(l) changes compared with the frequency factor r(l) at the analyzer end of the only marginally. response analysis, AC-bridges are line depending on the sample In practice, the lines are not ideal

6 Dielectrics Newsletter march 1994

and sophisticated calibration become extremely cumbersome procedures have to be applied. above 10 GHz which seems to be Nevertheless, low loss precision the practical limit for dielectric lines matching to the output measurements with temperature resistance of the reflectometer are control. Direct measurements to 60 Recommended: required. The line parameters α, β GHz on substrates using coplanar must be homogenous over the probe tips are reported in /3/. Literature whole line and also independent of Blythe, A.R., Electrical Properties temperature, as the calibration of Polymers, Cambridge University generally can only be carried out at Press, Cambridge 1979 room temperature. Böttcher, C.J.F., Theory of Electric Polarisation, Elsevier, Amsterdam 1973 Daniel, V.V., Dielectric Relaxation, Academic Press London 1967 Dattagupta, S.; Ralaxation Phenomena in Condensed Matter Physics, Academic Press, Orlando 1987 Dissado, L.A. and Forthergill, Fig. 5 : Reflection factors and J.C. Electrical degradation and impedance on a line terminated by breakdown in polymers, P. the sample impedance. Peregrinus Ltd., London 1992 Fröhlich, H., Therory of Dielectrics, Oxford University The same criteria mentioned for Press, London 1958 the line apply to the sample cell. Grant, E.H.; Sheppard, R.J. and Therefore an additional calibration Fig .6 : RF sample cell South, G.P., Dielectric Behaviour of which eliminates the influence of Biological Molecules in Solution, internal impedances in the sample Oxford University Press 1978 cell is required. References Hedvig, P., Dielectric Spectroscopy An example for a commercial of Polymers, Hilger, Bristol 1977 system based on the analyzer HP /1/ J. C. Slater, Microwave Jonscher, A.K., Dielectric Re- 4191A including the coaxial wave Electronics, D. van Nostrand laxation in Solids, Chelsea guide, sample cell (shown in fig. 6) Company, New York 1950 Dielectric Press Ltd., London 1983 and temperature control is the /2/ P. I. Somlo, J. D. Hunter, Matsuoka, S., Relaxation NOVOCONTROL BDS 5000. Microwave Impedance Phenomena in Polymers, Hanser, In order to keep the wave guide Measurements, London : Peter Munich 1992 as short as possible, the cryostat Peregrinus 1985 McCrum, N.G., Read, B.E., with the sample is directly mounted /3/ J. V. Bellantoni, R. C. Williams, G., Anelastic and Dielectric Effects in Polymeric at the front of the analyzer. The Compton, Millimeter-wave Solids, Wiley, New York 1967. system is automatically operated by applications of a vector Riande, E. and Saiz, E., Dipole a computer and all calibrations are network analyzer in coplanar Moments and Birefringence of done by software. probe tips. Microwave J., Mar. Polymers, Prentice-Hall, Engle- The frequency range is 1 MHz to (1991) 113 - 123 wood Cliffs, New Jersey 1992 δ 1 GHz with a resolution in tan( ) < Scaife, B.K.P., Principles of -3 10 and overlaps with the G. Schaumburg; Dielectrics, Clarendon Press, frequency response analysis Novocontrol GmbH Oxford 1989 methods. This is important, as the Obererbacher Str. 9 56414 Hundsangen, Germany Takashima S., Electrical Properties accuracy at the borders of the of Biopolymers and Membranes, measurement range rapidly Adam Hilger, Bristol 1989 decreases. At frequencies above 1 GHz, network analyzers can be used. Although these devices are specified to work in the millimeter range up to 300 GHz or even higher, calibration procedures

7 Dielectrics Newsletter march 1994

Dielectrics Newsletter is published by: Novocontrol GmbH Obererbacher Str. 9 56414 Hundsangen Germany ( ++49 - 6435 - 96230 fax: ++49 - 6435 - 962333

Editors: Dr. Gerhard Schaumburg Robert den Dulk

Abstracts and suggestions are always welcome. Send these directly to the publisher.

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