SPECIAL TOPIC—Dielectric materials and physics
DOI: 10.7498/aps.69.120101
电介质材料有许多独特的物理性质, 如介电、压电、热释电、铁电、电光、非线性光学及其耦合特性等, 在传感、换能、探测、医疗、通信、国防等众多领域具有广泛的应用价值. 相关的物理研究主要涉及介电材料内部束缚电荷在电、磁、光、力、热等外场作用下的极化过程和与极化相关的各种物理现象; 通过设计材料的成分与结构等, 揭示诸多性能的调控规律和微观机制, 在此基础上开发高性能电子器件.
今年恰逢发现铁电材料 100 周年. 铁电性作为电介质材料物理内涵的重大发现之一, 源于法国人 Joseph Valasek 在 1920 年 4 月 23 日美国物理学会春季会议上报道的罗息盐 (酒石酸钾钠,NaKC4H4O6·4H2O, 1672 年前后由法国药剂师 Pierre Seignette 发明) 晶体存在铁电性. 百年来, 包括铁电材料在内的多种电介质材料及其应用研究均取得了重要突破, 电介质材料与微电子材料和器件一样, 在现代电子元器件技术与产业中占据了不可替代的地位. 例如: BaTiO3 的发明推进了电容器的大容量和小型化; PZT 压电陶瓷的发明促使声纳、微机电等技术的飞跃发展; 低损耗微波介质材料研究的突破使得移动通信的实用化成为现实.
进入 21 世纪以来, 得益于第一性原理、相场模拟等理论计算方法的迅速发展, 以及微纳尺度的结构分析、物性表征和器件研制技术的快速提升, 人们以各种微纳结构、畴形态、周期结构、界面工程等设计为代表的创新研究思路, 极大地促进了电介质材料物理性能的优化和提高, 使其研究进入了新的发展范式. 我国科研人员也在这一领域做出了突出贡献. 同时, 我们也客观地看到, 同凝聚态物理、材料物理与化学等其他研究领域相比, 电介质研究领域包括铁电领域的发展速度相对缓慢.
为进一步促进国内同行的交流, 中国物理学会电介质专业委员会联合《物理学报》, 组织出版了“电介质材料和物理”专题, 邀请活跃在本领域的部分专家, 从电介质物理和材料的实验和理论诸方面, 以不同的视角介绍本领域的最新进展和未来趋势. 鉴于电介质材料和物理属于交叉学科, 具有多样性及复杂性的特点, 本专题只能重点介绍电介材料和物理领域的部分研究成果, 与读者和同行分享. 从研究内容上, 可大致分为两类: 一是探索电介质材料特别是铁电、压电材料的物理规律;二是探索这些材料的器件物理和应用研究. 内容主要涵盖以下六方面: 1) 电介质材料基础理论;2) 相变、结构和畴结构; 3) 无铅铁电压电材料和性能; 4) 铁电光电效应; 5) 介电储能、热释电和电卡效应; 6) 微波介电材料.
我们希望本专题能有助于扩大电介质研究在海内外华人学者中的影响, 吸引更多学者尤其是年轻学者的关注和加入, 为我国在本领域的蓬勃发展增添新生力量.
2020, 69 (12): 127702.
doi: 10.7498/aps.69.20200311
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Spin topologies, including flow-closure, vortex, meron, skyrmion and other spin configurations, are usually found in magnetic materials. The emergence of the topological structures will trigger a number of intriguing functionalities and physical properties. Recent studies have shown that the trival domain structures can be transformed into polar topological domain structures under certain boundary conditions, such as size-confining, interfacial coupling, and epitaxial strain. In this paper, we review the observations of polar topologies and their formation mechanism in ferroelectric nanoparticles, thin films, and superlattice films, and focus on the intriguing properties, including ferroelectric, piezoelectric, dielectric, and photoelectric performances, which arise from the formation of polar topologies. We also review the highlights of recent studies of the manipulations and evolutions of polar topologies under the external field loading in ferroelectric materials. Finally, the future research directions of polar topological structure and potential application directions are proposed.
2020, 69 (12): 127704.
doi: 10.7498/aps.69.20200312
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Ferroelectric materials with domains being the basic microstructures, have been investigated for about 100 years. With the development of the material fabrication method and the characterization technique, the important influence of domain configuration on the physical properties of ferroelectrics becomes more and more prominent. Recent researches even reveal that the domains and domain walls can act as individual functional units of micro-nano electronic devices, possessing wide potentials in the areas of information storage, energy transformation, electro-mechanical drive, quantum computation, etc. In this paper, starting from group theory analysis of domain structures, we introduce first the formation and the structures of ferroelectric domains, and then the macroscopic mechanical spectra as well as the electrical properties of the ferroelectric materials. Finally, the recent research progress of polarization switching and domain characterization by piezoresponse force microscopy are also reviewed.
2020, 69 (12): 127706.
doi: 10.7498/aps.69.20200287
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There are two types of perovskites, i.e. ABO3-type oxides and ABX3-type (X = F, Cl, Br and I) halides. Both of them exhibit rich physical properties and excellent photoelectric properties, such as ferroelectric and photocatalytic properties. In this paper we introduce the methods of preparing the ferroelectric semiconductors (i.e. BiFeO3 and
2020, 69 (12): 127707.
doi: 10.7498/aps.69.20200288
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Due to excellent piezoelectric properties and electromechanical coupling properties, lead-based piezoelectric ceramics represented by lead zirconate titanate Pb(ZrxTi1–x)O3 (PZT) are widely used in science and technology, industry, military and daily life. However, the content of Pb in PZT-based ceramics exceeds 60% (mass ratio), which will cause serious damage to human ecological environment in the process of their production, use and waste treatment. Therefore, the development of lead-free piezoelectric ceramics has become one of the hot research spots. Potassium sodium niobate (K0.5Na0.5)NbO3 (KNN) lead-free piezoelectric ceramics are considered as one of the most promising material systems to substitute for lead-based piezoelectric ceramics because of their good piezoelectric properties and higher Curie temperature. Through many years of researches, the piezoelectric properties of modified KNN based lead-free piezoelectric ceramics have approached to or even exceeded those of some lead-based piezoelectric ceramics. Combining with our relevant work, we comprehensively review the research progress of high piezoelectric activity of KNN based lead-free piezoelectric ceramics, especially focus on the research progress of high-performance potassium sodium niobate lead-free piezoelectric ceramics, preparation technology and related theoretical mechanisms. The future research direction and prospect of KNN-based lead-free piezoelectric ceramics are also presented.
2020, 69 (12): 127708.
doi: 10.7498/aps.69.20200303
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Due to the excellent pyroelectric properties, ferroelectric ceramics containing lead element are widely used as sensitive materials in pyroelectric infrared detectors at present. The research and development of lead-free ferroelectric ceramics for this kind of detector has become a hot research spot in the areas of dielectric physics and materials in recent years. In this article, the recent research progress of the pyroelectric effect in series of important lead-free ferroelectric ceramic systems is reviewed, including barium titanate, sodium bismuth titanate, potassium sodium niobite, barium strontium niobite, etc. The methods of enhancing the pyroelectric effect are summarized, including doping modification, phase boundary design, process improvement, etc. Through comparative analysis of the relationship between pyroelectric properties and depolarization temperatures of different systems, it is concluded that bismuth sodium titanate based ceramics are the most potential lead-free materials in the future. The prospective research work of lead-free ferroelectric ceramics for infrared detection is also suggested.
2020, 69 (12): 127711.
doi: 10.7498/aps.69.20200301
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Ferroelectric/piezoelectric perovskites are an important class of functional material and have broad application prospects in commercial, industrial, military and other areas because of their high dielectric constants, high piezoelectric coefficients, and high electromechanical coupling coefficients. Their structures, applications, and physical mechanisms have been intensively studied in condensed matter physics and material science. The piezoelectric properties of ferroelectric materials mainly originate from the intrinsic field-induced lattice distortion and extrinsic domain inversion and domain wall motion. Therefore, the understanding of and the distinguishing between these mechanisms are important for ascertaining the origin of the high-piezoelectric properties and developing new functional materials. In this article, we review the research progress of technical means and methodology of analyzing the changes of crystal lattices and magnetic domains of materials under the action of an externally applied electric field through the high-energy synchrotron X-ray diffraction experiments. The techniques and analysis methods involved in the review cover the time-resolved X-ray diffraction, single/double-peak analysis, full-pattern refinement, center-of-mass calculation, and field-induced phase transformation analysis, which are used to study the intrinsic and extrinsic contributions to sample’s macroscopic properties. It is expected to provide the research methods, which fulfill the individual experimental requirements, and the technical support for the mechanism analysis of various piezoelectric materials through the introduction and review of various methods.
2020, 69 (12): 127712.
doi: 10.7498/aps.69.20200738
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Rare earth doping is an important method to improve the properties of optoelectronic functional materials. Combining rare earth doping ferroelectric materials and rare earth photoluminescence can create new functional properties of ferroelectric materials. For example, choosing and using an appropriate rare earth element to be doped into a bismuth titanate ferroelectric material, the bismuth titanate will exhibit good photoluminescent properties as well as ferroelectric properties. Recently, photoluminescence properties originating from rare earth ions in oxide ferroelectric materials have attracted much attention for possible integrated photoluminescent ferroelectric device applications. In this paper, we briefly review the research status and progress of photoluminescence in rare earth photoluminescent ferroelectric materials, and we place the emphasis on our own research work in photoluminescent ferroelectric thin films such as (Bi,Eu)4Ti3O12, (Bi,Er)4Ti3O12, and codoped bismuth titanate thin films, and nanocomposite (Bi,Eu)4Ti3O12 ferroelectric thin films. Our results show that the rare earth doped bismuth titanate ferroelectric thin films exhibit good photoluminescent and ferroelectric properties due to unique compositions and layered perovskite structure, that the Eu3+ fluorescent structure probe can provide a new path for further studying the relationship between structure and property of Eu-doped ferroelectric thin films, that the rare earth photoluminescence can be used to examine the existence of morphotropic phase boundary in certain ferroelectric thin films such as Pr-doped x(K1/2Bi1/2)TiO3-(1－x)(Na1/2Bi1/2)TiO3 thin films, and nanocomposite materials of ZnO nanomaterials, and that Au nanoparticles, Ag nanoparticles with Eu-doped bismuth titanate exhibit obviously enhanced photoluminescent properties.
2020, 69 (12): 127301.
doi: 10.7498/aps.69.20200280
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The photovoltaic effect of ferroelectric BiFeO3 (BFO)-based heterojunction has been one of hot subjects of theoretical and experimental studies due to its important application prospects, and the coexistence of varieties of photovoltaic effect mechanisms (bulk photovoltaic effect, domain wall effect, interfacial barrier effect, etc.) can bright rich and complicated physics nature. In order to investigate the important role that the interface plays in the photovoltaic effect, we prepare the Pt/BFO(60 nm)/Nb:SrTiO3 (NSTO) heterojunction with an asymmetric metal/ferroelectric/semiconductor structure, and systematically investigate the photovoltaic effect under laser irradiation with different wavelengths (365 nm and 445 nm). The heterojunction exhibits much stronger open-circuit voltage (Voc, ～0.55 V at 74 mW/cm2) and short-circuit current density (Jsc, ～ 208 μA/cm2 at 74 mW/cm2) for the laser irradiation with 365 nm wavelength than those for the laser irradiation with 445 nm wavelength, and the Voc and Jsc are both strengthened with the increase of light intensity. This is because the 365 nm light with the photon energy ～3.4 eV can stimulate photon-induced carriers in both BFO (band gap ～2.7 eV) and NSTO (band gap ～3.2 eV) at both the Pt/BFO interface and the BFO/NSTO interface, while the 445 nm light with the photon energy ～2.8 eV can only generate carriers in BFO. Thus the photovoltaic voltage is much bigger for the 365 nm light. Furthermore, the laser absorption process is much more efficient for the 365 nm light (79% absorbed in BFO and 21% absorbed in NSTO) than for the 445 nm light (21% absorbed in BFO). In addition, the temperature dependent Voc and Jsc are also investigated. It is found that for the 365 nm and 445 nm laser irradiation, the Voc increases with temperature decreasing, which is possibly due to the variations of the built-in potential, concentration of thermal charge carriers, and/or electron-phonon scatterings. The sharper variation of Voc above ～ 200 K may suggest the more significant role of thermal charge carriers at high temperatures. Interestingly, the temperature dependent Jsc behaves differently for the 365 nm and 445 nm light. Under the 365 nm laser irradiation, the Jsc remains almost unchanged below 170 K and increases sharply with temperature increasing above 170 K, which may be related to the dominant role of thermal excitation for the 365 nm light. While for the 445 nm light, the Jsc decreases with temperature increasing, which follows the variation trend of its Voc. What is more, the conduction mechanism of Pt/BFO/NSTO heterojunction under laser irradiation is also studied. It is found that the conduction for the 445 nm light can be nicely described by the space-charge-limited bulk conduction (SCLC) model and the photon-generated carriers may fill the traps and thus leading the transition voltage to decrease. While for the 365 nm light, the conduction is more complicated and cannot be described by the SCLC model. Our findings may be helpful in understanding the photovoltaic effect in transition-metal oxide based heterojunctions and designing photovoltaic devices.
2020, 69 (12): 127701.
doi: 10.7498/aps.69.20200296
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As the electric field can affect the polarization and dielectric constant, the phenomenological coefficient a0 is an implicit function of electric field. The phenomenological coefficient a0 is determined by the polarization and the reciprocal of permittivity, and a nonlinear function of electric field in the ferroelectric phase regime. In the paraelectric phase regime, however, a0 is merely subjected to the reciprocal of permittivity, and also a nonlinear function of electric field. In this paper, we investigate the electric field dependence of phenomenological coefficient in ferroelectric copolymers, terpolymers and Ba0.85Ca0.05Sr0.1TiO3 ceramics. It is indicated that the phenomenological coefficient increases with the increasing electric field, the maximum value is obtained to be about 2 times the original value. Moreover, the electrocaloric strength is used to measure the magnitude of electrocaloric effect of electrocaloric materials in an external electric field. It can be used to find out novel and efficient electrocaloric materials through studying the electrocaloric strength. Based on the thermodynamic theory, the analytical expression of electrocaloric strength is deduced. It is found that the phenomenological coefficient, phase transition, specific heat capacity, and permittivity versus temperature peak value at the phase transition temperature have a clear influence on the electrocaloric strength. The expression can be applied to 1st order, 2nd order phase transition materials and relaxor ferroelectrics.
2020, 69 (12): 127703.
doi: 10.7498/aps.69.20200213
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Lead-free dielectric ceramics with high energy-storage density and efficiency are ideal energy materials for sustainable development of the enery resource. In this paper, (1–x)K0.5Na0.5NbO3–xBi(Mg0.5Ti0.5)O3 ((1–x)KNN-xBMT, x = 0.05, 0.10, 0.15, 0.20) lead-free relaxor ferroelectric ceramics are prepared by the traditional solid-state method. The effects of BMT on the phase structure, microstructure, dielectric properties and energy storage behavior of KNN based ceramics are studied. With the increase of BMT content, the crystal structures of (1–x)KNN-xBMT ceramics gradually change from orthorhombic to pseudo-cubic phase, and transform into cubic phase finally. The addition of BMT can suppress grain growth of the ceramics, resulting in the average grain size decreasing from 850 to 195 nm when x increases from 0.05 to 0.20. Dielectric properties exhibit that the Curie temperature decreases with BMT content increasing, and dielectric peak at Curie temperature is broadened due to the addition of BMT. In addition, ferroelectric properties demonstrate that the addition of BMT reduces the remnant polarization (Pr) and coercive field (Ec) of the ceramics. The results indicate that (1–x)KNN-xBMT ceramics transform from ferroelectric to relaxor ferroelectric phase. Based on the calculation of hysteresis loop, the best energy storage performance is obtained at x = 0.15, of which the recoverable energy storage density (Wrec) and the energy storage efficiency (η) are 2.25 J·cm–3 and 84% at its dielectric breakdown strength of 275 kV·cm–1. Meanwhile, the ceramic with x = 0.15 exhibits good stability in a frequency range of 1–50 Hz, with an energy density variation of less than 5%, and temperature stability in a range of 25–125 ℃ with change of less than 8%. Moreover, based on direct measurement, the energy storage density (Wdis) of the ceramic with x = 0.15 is 1.54 J·cm–3, and the discharge time is only 88 ns. The research shows that (1–x)KNN-xBMT ceramics have a wide application prospect in the field of environmentally friendly capacitors with high energy storage density.
2020, 69 (12): 127705.
doi: 10.7498/aps.69.20200277
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Potassium sodium niobate ((K0.5Na0.5)NbO3)-based lead-free piezoelectric ceramics are excellent ferroelectric materials and have been demonstrated to have many practical applications. Recent studies have revealed that chemical doping plays a crucial role in optimizing the electromechanical coupling properties of (K0.5Na0.5)NbO3-based piezoelectric ceramics. In this paper, MnO2 is doped into potassium niobate (KNbO3) and (K0.5Na0.5)NbO3 piezoelectric ceramics prepared by the conventional solid-state reaction method. The influences of doped Mn cation on KNbO3 and (K0.5Na0.5)NbO3 piezoelectric ceramics including microstructure and macroscopic electrical properties are systematically investigated. The doping effects of Mn cation on the KNbO3 and (K0.5Na0.5)NbO3 piezoelectric ceramics are significantly different from each other. For the Mn-doped KNbO3 piezoelectric ceramics, the sizes of ferroelectric domains are reduced. Meanwhile, the diffused orthorhombic-tetragonal phase transition is observed, which is accompanied by reducing dielectric loss and Curie temperature, and broadening vibration peaks in Raman spectrum. It is known that the oxygen vacancy can be formed to compensate for the charges created by the acceptor doping of Mn into the B site of perovskite, and thus forming a defect dipole with the acceptor center. From the ferroelectric measurement, a double hysteresis loop (P-E curve) and a recoverable electric-field-induced strain due to the formation of defect dipole are observed. On the contrary, for the Mn-doped (K0.5Na0.5)NbO3 piezoelectric ceramics, the sizes of ferroelectric domains are not reduced. Meanwhile, the Curie temperature and vibration peaks in Raman spectrum are not changed. A rectangular hysteresis loop (P-E curve) and an unrecoverable electric-field-induced strain are observed in the ferroelectric measurement. The difference between these systems might originate from the greater ionic disorder and lattice distortion in (K0.5Na0.5)NbO3 piezoelectric ceramics. The difference in ionic radius between Na+ and K+ can affect the migration and distribution of oxygen vacancies, which makes it difficult to form stable defect dipoles in the Mn-doped (K0.5Na0.5)NbO3 piezoelectric ceramics. The results will serve as an important reference for preparing high-performance (K0.5Na0.5)NbO3-based piezoelectric ceramics via chemical doping.
2020, 69 (12): 127709.
doi: 10.7498/aps.69.20200309
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Ferroelectric films, are an important class of photoelectric functional material, which possess the following characteristics: the breaking of their symmetry can lead to self-polarization and this polarization state can be regulated by external stimuli. The photovoltaic properties of ferroelectric films have been extensively investigated due to their potential applications in the field of photodetection, energy conversion harvesting and nonvolatile storage. In view of the small photocurrent density and the degradation of photovoltaic property caused by the depolarization effect in ferroelectric films, it is necessary to explore an approach to improving the self-polarization phenomenon and regulating the conduction mechanism to further optimize their photovoltaic properties. Here in this work, BiFeO3 (BFO) films dispersed with Au nanoparticles are deposited on FTO glass substrates by the sol-gel method to obtain the Au-BFO nanocomposite films. Moreover, the relationships between Au content (0 mol%, 0.25 mol%, 0.5 mol%, 1 mol% and 3 mol%) and microstructure, electrical and photovoltaic properties of Au-BFO nanocomposite films are investigated to determine the optimal Au content. Piezoresponse force microscopy studies show that the Au-BFO nanocomposite film with 0.5 mol% Au has the strong self-polarization phenomenon. With the increase of Au content, the conduction mechanism of the Au-BFO nanocomposite films is described by the space-charge limited current theory but not the Schottky emission model any more. The photovoltaic properties of the Au-BFO nanocomposite films first increase and then decrease. When Au content is 0.5 mol%, the Au-BFO nanocomposite film has the best photovoltaic property. The open-circuit voltage and short-circuit photocurrent density of the Au-BFO nanocomposite film with 0.5 mol% Au increase nearly 3 and 5 times counterparts of the BFO film, respectively. The photovoltaic effects of Au-BFO nanocomposite films are improved mainly by regulating the self-polarization phenomenon and conduction mechanism. This study demonstrates the merits of BFO films dispersed with Au nanoparticles, specifically, the photovoltaic properties of Au-BFO nanocomposite films are further optimized. In this work, we propose a simple and effective method to regulate the electrical and photovoltaic properties of ferroelectric films, which provides a new perspective for further understanding the photovoltaic effects of ferroelectric films.
2020, 69 (12): 127710.
doi: 10.7498/aps.69.20200209
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In real applications, antiferroelectric (AFE) ceramics are usually subjected to a pulse electric field with fast rising or falling speed. In the measurement of hysteresis loop at low frequency, the applied electric field has a low changing rate. Thus, the obtained results cannot reveal the polarization nor phase transition of AFE ceramics in real applications. In the present work, a platform to measure the pulse hysteresis loop is developed and the polarization and phase transition of Pb0.94La0.04[(Zr0.52Sn0.48)0.84Ti0.16]O3 (PLZST) AFE ceramics under pulse electric field on a μs scale are investigated. The obtained results indicate that the phase transition can be induced by pulse electric field. However, the maximum polarization decreases, the forward transition field increases and the backward one decreases, resulting in the variation of energy storage performance. Thus, the hysteresis loop at low frequency cannot reveal the performance of AFE ceramics under the action of a pulse electric field. The pulse hysteresis loop is of great significance in real applications.
2020, 69 (12): 127801.
doi: 10.7498/aps.69.20200310
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Ferroelectric domain structures and ferroelectric properties in the hetero-epitaxially constrained ferroelectric thin films can be manipulated by substrate misfit strain. In this work, three kinds of phase structures of PbZr(1–x)TixO3 thin films, including tetragonal, tetragonal- rhombohedral-mixed and rhombohedral phases, are investigated. Firstly, the ferroelectric domain structures at different substrate misfit biaxial strains are obtained by the phase-field simulation. Then we calculate the polarization-electric field hysteresis loops at different misfit strains, and obtain the coercive field, saturation polarization, and remnant polarization. In the tetragonal PbZr(1–x)TixO3 (x = 0.8) thin film, compressive strain contributes to the formation of out-of-plane c1/c2 domain, and tensile strain favors in-plane a1/a2 domain formation. With the increase of compressive strain, the tetragonal phase and the rhombohedral phase coexist in PbZr(1–x)TixO3 (x = 0.48) film near the morphotropic phase boundary, while the tensile strain reduces the rhombohedral domain size. In the rhombohedral PbZr(1–x)TixO3 (x = 0.2) film, the rhombohedral domains are steady states under compressive strain and tensile strain. As the misfit strain changes from –1.0% to 1.0%, the value of the coercive field, saturation polarization and remnant polarization decrease. Among them, for tetragonal-rhombohedral mixed phase, the reductions of saturation field and remnant polarization are larger than for tetragonal phase and rhombohedral phase. The coercive field of mixed phase decreases rapidly under the compressive strain, but deceases slowly under the tensile strain. It is worth noting that the remnant polarization decreases faster than the saturation polarization in three components of ferroelectric thin film. Due to the electromechanical coupling, when x = 0.48 at the morphotropic phase boundary it is shown that the remnant polarization reduction is faster than those of the other two types of ferroelectric thin films, and the small coercive field is obtained in the case of large tensile strain. Therefore, tensile strain can effectively improve the energy storage efficiency in ferroelectric thin films, and the efficiency of x = 0.48 thin film increases significantly compared with that of x = 0.8 or 0.2 thin film. Both the ratio of rhombohedral/tetragonal phase and the domain size will play a significant role in ferroelectric performance. Therefore, our results contribute to the understanding of the electromechanical coupling mechanism of PbZr(1–x)TixO3, and provide guidance for the experimental design of ferroelectric functional thin film materials.
2020, 69 (12): 128401.
doi: 10.7498/aps.69.20200275
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The metal resonant cavity method working with TE01δ mode is a universal method for evaluating the microwave dielectric properties of low-loss materials. All the microwave dielectric resonators are multi-mode resonators, so the correct identification of TE01δ mode is the basis for the microwave dielectric measurements. The TE01δ mode can be identified by predicting the resonant frequency and its variation with resonator size, expelling the spurious modes according to the exciting conditions, etc., while these methods are relatively complex and sometimes unreliable. In the present work, a simple method for accurately identifying the TE01δ mode is developed. A low-loss reference sample with known dielectric properties is introduced and placed in the cavity for the first step, and the to-be-measured sample is placed on the reference sample for the second step. The rough permittivity of the to-be-measured sample can be calculated from the TE01δ-mode resonant frequencies in the two steps through the finite element analysis, and is used to predict the resonant frequency for TE01δ mode when only the to-be-measured sample is placed in the cavity. The difference between the predicted and measured TE01δ-mode resonant frequencies for the to-be-measured sample is less than 1%, so that the TE01δ mode can be easily distinguished from the spurious modes and accurately identified.
