Table of contents

Lead-zirconate-titanate (PZT) thin films were prepared on oxidized Si(100)-substrate with a thin film electrode by laser ablation. Ferroelectric perovskite phase was obtained in the PZT films on Ni-alloy/SiO₂/Si substrate with the substrate temperature above 500°C, but it was not obtained in the films on Pt/SiO₂/Si. The switching voltage of remanent polarization (P_r) decreased with decreasing PZT film thickness. The 0.15-µm-thick film showed P_r of 15 µC/cm² with a swing voltage of 5 V.

Ferroelectric PbTiO₃ thin films have been formed on based electrodes of Pt or oxide superconductor ((La, Sr)₂CuO₄) by an ArF excimer laser ablation technique. A second laser irradiation at the substrate surface is quite effective in the crystallization of the films at low substrate temperature below 400°C. The suitable energy density of the irradiation laser is in the range of 30-100 mJ/cm². X-ray diffraction patterns of PbTiO₃ thin films show c-axis orientation, with FWHM (full width at half maximum) of rocking curve of 0.5°-1.0°. These films exhibit a ferroelectric hysteresis loop. The dielectric constant and remanent polarization of the PbTiO₃ films are in the range of 120-150 and 20-25 µC/cm², respectively.

ZnO and PbZr_0.9Ti_0.1O₃ (PZT) thin films were prepared by laser ablation using a KrF excimer laser. The c-axis-oriented ZnO thin films were successfully grown at substrate temperatures of 180-400°C in Ar and Ar+O₂. The deposition rates of the films obtained ranged from 150 to 700 Å/min, and these values were larger than those of films grown by conventional magnetron sputtering. Perovskite-type PZT thin films with a rhombohedral structure were also successfully grown at 680°C. The deposition rates of the films obtained ranged from 40 to 240 Å/min, and these values were also larger than those of films grown by magnetron sputtering.

PbTiO₃ thin films were prepared by reactive ionized cluster beam (R-ICB) deposition on highly (100)-oriented Pt films formed on SiO₂/Si substrates. PbTiO₃ thin films consisting of c-axis- and a-axis-oriented crystallines with perovskite structure were obtained at a comparatively low substrate temperature of 430°C. We think tensile stress exists in PbTiO₃ thin films, and it may be the cause of a-axis orientation. It is considered that fabricating high-density PbTiO₃ thin films by applying an acceleration voltage decreases the tensile stress in the film and is advantageous for preparation of c-axis-oriented PbTiO₃ thin films.

To generate surface acoustic waves (SAW) and to fabricate substrates for superconducting Bi-compound film, piezoelectric PbTiO₃ films with preferred c-axis orientation were prepared on MgO (100) substrates by the rf-sputtering method. By using an interdigital electrode fabricated on PbTiO₃ film for generation and detection of SAW, it has been confirmed that SAW with the frequency of 192 MHz are propagated on PbTiO₃ film/MgO substrate, as-deposited Bi-compound film/PbTiO₃/MgO substrate and heat-treated superconducting Bi-compound film/PbTiO₃/MgO substrate. The temperature dependence of the SAW attenuation coefficient has been investigated below room temperature in detail, especially in the neighborhood of the superconducting transition temperature, and found to exhibit almost monotonic decreasing behavior with decreasing temperature.

Optimum conditions for preparing PbTiO₃ films on Si and SrTiO₃ substrates are investigated in the dual-beam vacuum evaporation method using PbO and TiO₂. It has been found that tetragonal PbTiO₃ films are formed on Si substrates at temperatures ranging from 550°C to 600°C, and that the stoichiometric composition of the films is easily obtained at 600°C by supplying excess PbO molecules to the substrate. It has also been found that PbTiO₃ films grow epitaxially on SrTiO₃ substrates at temperatures around 550°C.

Heteroepitaxial SrTiO₃ films of perovskite structure with thicknesses of 46 to 184 nm were prepared by rf magnetron sputtering, holding substrate temperature at 400°C, on Pt films which were also epitaxially grown on a MgO(100) substrate in advance. The relative dielectric constant was estimated to be more than 300, and the leakage current density was less than 10^-8 A/cm². The analysis of the leakage current suggests Schottky barrier formation at the interface between SrTiO₃ and Pt films, with a barrier height of about 1 V.

Barium lead zirconate titanate (or (Ba, Pb)(Zr, Ti)O₃, BPZT) thin films have been successfully fabricated from a stoichiometric target by rf-magnetron sputtering. The dielectric properties of these films were investigated. They were found to have good properties for LSI capacitor applications, e.g., high dielectric constant (ε≈400), low temperature coefficient, low leakage current, and low crystallization temperature (550°C).

Recently, metal β-diketonato complexes have been used as a gas source for preparing ferroelectric thin films by metalorganic chemical vapor deposition (MOCVD). Since we have synthesized highly purified metal dipivaloylmethanato (DPM) complexes such as Pb(DPM)₂, Sr(DPM)₂ and Ba(DPM)₂ for ferroelectric thin films, we have investigated several properties of these chelate compounds related to depositing thin films. Their volatility and toxicity have also been investigated. As a result, it has been found that these chelate compounds have low vapor pressure, but present the advantages of easy handling because of the low toxicity and the possibility of forming thin films at lower temperature.

Pb-bis-dipivaloylmethane [Pb(DPM)₂], Zr(DPM)₄ and Ti(DPM)₂(i-OC₃H₇)₂ are developed as the new chemical vapor deposition (CVD) sources for lead zirconate titanate (PZT) thin film. The growth rate of each of the single metal oxides PbO, ZrO₂ and TiO₂, was studied as a function of oxygen partial pressure. The growth rates of ZrO₂ and TiO₂ were independent of the input oxygen partial pressure, while the growth rate of PbO increased with increasing input oxygen partial pressure. PZT films were grown on (100) MgO substrates at 2.0 Torr by metalorganic chemical vapor deposition (MOCVD). The film grown at 500°C was amorphous. The film grown at 550°C was a mixed phase of a-axis- and c-axis-oriented perovskite. The film grown at 600°C was a single-phase c-axis-oriented perovskite.

Dipivaloylmethane (DPM) metalorganic precursors, Pb(DPM)₂, Zr(DPM)₄ and Ti(OPrⁱ)₂(DPM)₂, are used as starting materials in the metalorganic chemical vapor deposition (MOCVD) method for the preparation of Pb(Zr_xTi_1-x)O₃ (PZT) thin films. The films are deposited at the rate of 150 to 700 Å/min under atmospheric pressure and reduced pressure of 10∼30 Torr. The deposition rate is about ten times as high as that of the conventional sputtering method. The dielectric constant of the film (X=0.2) on a Pt/Si substrate is about 300 at room temperature. This value agrees with that of ceramic or sputtered films.

Growth of PbTiO₃ thin films was carried out by the photo-chemical vapor deposition (photo-CVD) method and by varying the growth parameters of substrate temperature, reaction pressure and UV light irradiation. In order to clarify the effects of these parameters on the thin film growth, a three-way-lay-out factorial experiment was done. In the higher temperature and pressure region the vapor phase reaction is dominant. At lower temperatures and pressures, the reaction on the substrate becomes significant. These tendencies were observed under conditions with and without UV light irradiation. The synthesis of PbTiO₃ on Pt/sapphire was assisted by UV light irradiation.

Pb(Zr, Ti)O₃ thin films were grown by photoenhanced chemical vapor deposition (CVD) using Pb(C₂H₅)₄, Zr(O-t-C₄H₉)₄, Ti(O-i-C₃H₇)₄ and O₂. Two types of perovskite Pb(Zr, Ti)O₃ films (tetragonal films and rhombohedral films) were successfully obtained at 600-635°C by controlling the carrier flow ratio of the Zr source to Ti source. The Zr/Ti flow ratio also affected the growth rate, composition and electrical properties of films. In this study, it was proven that significant increases in both growth rate and Zr/Ti compositional ratio were caused by photoirradiation. Dielectric and ferroelectric properties, switching characteristics and I-V characteristics of the obtained Pb(Zr, Ti)O₃ films were also described in detail.

Substrate temperature dependence of ZnO film properties such as c-axis orientation and optical transmittance was investigated. When the film bombardment became small at higher gas pressure such as 0.1 Torr, the degree of c-axis orientation of the film was improved at above 350°C, but the grain size of film was not dependent on the substrate temperature. When the film-was bombarded by energetic O^- ions and O atoms at lower gas pressures, the film was degraded severely. The recovery of the film properties due to the elevated temperature was small. More defects were likely to be induced in the film at a high substrate temperature such as 350°C under film bombardment by the energetic particles.

Piezoelectric properties of ZnO films were investigated for the first time by means of an electron cyclotron resonance (ECR) sputtering system. It is confirmed that this system is capable of depositing a ZnO film with a large specific resistance, a good piezoelectric property and good c-axis orientation on an interdigital transducer (IDT)/glass substrate at a low temperature (less than 200°C) and under low gas pressure (∼10^-4 Torr). These ZnO films exhibited excellent surface acoustic wave (SAW) characteristics (insertion losses) and effective electromechanical coupling factors (k_eff) compared with ZnO films deposited by a conventional RF magnetron sputtering system. Furthermore this ECR sputtering system was capable of depositing a ZnO film capable of driving a Rayleigh SAW of 700 MHz, without heating the substrate (room temperature), while it was impossible to drive such a wave conventionally, using other sputtering systems.

Orientation control of aluminum nitride (AlN) films deposited on a-SiN/(110)Si was investigated by controlling the assisted nitrogen ion beam. Films were deposited using an electron cyclotron resonance (ECR) dual ion beam sputtering system having an ECR ion gun for irradiation and Kaufman-type ion gun for sputtering. It was found that AlN films with perpendicular and parallel orientation to the substrate could be obtained. These films consisted of micrograins. However, it was confirmed from reflection high energy electron diffraction (RHEED) and selected area electron diffraction (SAED) patterns that the former was c-axis oriented film and the latter was nearly single crystal.

Ferroelectric lead zirconate-titanate (PZT) thin films have been prepared on Pt-coated oxidized Si substrates (Pt/Ti/SiO₂/Si) utilizing a multitarget magnetron sputtering system with three Pb(Zr_0.5, Ti_0.5)O₃ targets and one PbO target. Crystal structure and dielectric properties of the films have been studied as functions of substrate temperature (T_s) and Pb content. The Pb content in the film has been precisely controlled by optimizing the rf input power for the PbO target (P_PbO). As a result, single-phase perovskite films have been prepared fairly easily with appropriate combinations of T_s and P_PbO. A film with atomic ratios of Pb/(Zr+Ti)=1.3 and Zr/(Zr+Ti)=0.5 prepared at T_s=600°C exhibited a dielectric constant of 780 and remanent polarization of 19 µC/cm².

Dielectric SrTiO₃ thin films have been prepared on Pt/SiO₂/Si-wafer by means of a conventional rf-magnetron sputtering technique. Electric and dielectric properties of the films have been studied. It is demonstrated that the leakage current of the films is strongly dependent on the atmosphere during deposition. The SrTiO₃ film 75 nm in thickness fabricated in pure O₂ of 26.6 Pa at 600°C obtained the lowest leakage current density of 4.0×10^-9 A/cm² at 2 V. Analysis of the leakage current vs applied voltage characteristic indicated that the conduction in the higher electric field was due to the Pool-Frenkel emission.

The preparation of PbTiO₃ thin films by multiple cathode rf-magnetron sputtering was investigated. The effects of incident Pb/Ti ratio, the kind of substrates, substrate temperatures and film thickness on the crystalline structure of the PbTiO₃ thin films prepared were studied. The thin films with perovskite PbTiO₃ structure on Si wafers were obtained by deposition at an incident Pb/Ti ratio of 1.2 at a substrate temperature of 460∼500°C. The X-ray photoemission spectroscopy (XPS) depth profile revealed that less reaction of the thin films with the Si substrate was observed at the interface at lower substrate temperatures.

This paper describes the effect of microstructure on dielectric and piezoelectric properties in the (Pb_1-xCa_x)[(Co_1/2W_1/2)_0.04Ti_0.96]O₃ system. It is demonstrated that they are influenced by the microstructure, especially the grain size of the sintered bodies. The data of piezoelectric constants are compared with those of the values calculated using the theoretical model.

Sintering of Pb(Zr_0.53Ti_0.47)O₃ with a CO₂ laser is discussed to indicate the possibility of a new method of synthesizing piezoelectric ceramics. The starting materials are (1) PbO, ZrO₂ and TiO₂, and (2) Pb₃O₄, ZrO₂ and TiO₂. The green oxide pellets are irradiated with a CO₂ laser at various powers of 143, 286 and 1857 W/cm² in a flow rate of 350 cm³/min of O₂/Ar(10⁵ Pa). In both cases, the formations of Pb(Zr, Ti)O₃ were recognized by XRD (X-ray diffraction) analysis although some starting materials remained at the lower power. The microstructures are also discussed.

A low-hysteresis lead zirconate titanate (PZT) actuator with fine-grained ceramics is realized by an alkoxide method followed by a hot isostatic press (HIP) or a hot-press method. The HIP or the hot-press method is effective for increasing the density of the fine-grained actuator without further grain growth. It is concluded from the transmission electron microscopy (TEM) observations that the fine-grained ceramics are composed of grains with a size of around 1 µm, which include still smaller particles ranging from 20 nm to 50 nm in size. The smaller particles seem to be traces of the boundaries of the alkoxide-prepared starting powders. The improved hysteresis characteristics may be related to the traces left in the component grains.

The effects of sintering temperature and manganese concentration on microstructure and electromechanical property were studied in [Pb_0.9La_0.1][Zr_0.5Ti_0.5]O₃ piezoelectric ceramics with the substitution of the B-site by manganese by means of scanning electron microscope (SEM) and electron spin resonance (ESR). Grain growth is enhanced by increasing temperature but suppressed by manganese substitution. There was no relationship between Qm (inverse of mechanical vibration loss) and the grain size. Some part of manganese is considered to be reduced to Mn²⁺ ions during sintering. Qm is considered to be affected by the reduction of manganese ions because it was proportional to Mn²⁺ concentration, not to total manganese content.

The piezoelectric and dielectric constants of a PbZrO₃-based ceramic substrate and the propagation characteristics of Lamb waves are described. The Lamb wave phase velocities are analyzed numerically under various electrical and mechanical boundary conditions. The numerical results confirmed experimentally are given in the form of a function of the product of the wave number and the substrate thickness, which suggest that a Lamb wave device can be constructed to operate in a single mode as well as in multimodes. The S₀ mode Lamb wave device shows satisfactory performance as a single-mode operation.

Change of piezoelectric properties with the number of loading cycles was measured under various driving conditions, i.e., temperature, preset pressure and driving voltage. Although ε₃₃^T/ε₀ changed very little, K_p decreased markedly. K_p decrease is affected by driving condition factors, i.e., minus voltage, preset pressure and temperature, in that order. By optimal arrangement of these factors, K_p decrease could be reduced considerably. K_p decrease is mainly due to 90° switching of the domain. Improvement of mechanical strength for the piezoelectric material is effective both for the suppression of microcrack occurrence and for prevention of K_p decrease. We found that microcrack occurrence caused domain switching. We suggest a deterioration mechanism for piezoelectric ceramics.

Vibration-level characteristics of lead-zirconate-titanate ceramics were studied using the constant current driving method. It was found that resonant frequency and mechanical Q markedly decreased with increasing vibration level, accompanying heat generation. The heat generation was assumed to be caused by vibration loss. The vibration loss was reduced by doping Fe atoms to the ceramics. On the contrary, the vibration loss was increased by doping Nb atoms.

The effects of MnO₂ addition on k₃₁ and Q_m were investigated for Pb(Zr_0.5Ti_0.5)O₃(PZT). The MnO₂ addition increased Q_m and k₃₁ in a low poling field. This result indicated that Mn-doped PZT possessed properties of `soft' and `hard' piezoelectrics simultaneously. Electron spin resonance measurement indicated that Mn²⁺, Mn³⁺ and Mn⁴⁺ coexisted in PZT. The tetragonality of the PZT lattice and the Curie temperature decreased with MnO₂ content. From these results, it was found that the increase in k₃₁ of Mn-doped PZT was due to the change of the crystal structure toward a cubic system, and the increase in Q_m to Mn²⁺ and Mn³⁺ ions working as acceptor dopants. The characteristic feature of Mn is that its addition to PZT decreases tetragonality, and various valence states coexist in proper ratio in Mn-doped PZT sintered in atmosphere.

This paper presents a piezoelectric-ceramic vibratory gyroscope with a new structure. The vibrator of this vibratory gyroscope consists of a piezoelectric-ceramic circular cylinder and no adhesion process is necessary. On its outer cylindrical surface, six elongated electrodes are formed in parallel with each other along the central axis. These electrodes are used both for poling treatment and AC excitation as well as detection. Adjustment of resonant frequencies between each of the three terminals by trimming helps eliminate any compensations of circuit constants, so that simple circuitry can be obtained. Because of its small size and simple structure, this vibratory gyroscope is expected to be used in the shake sensor for cameras and hand-held video cameras.

A deposition process of epitaxial Al film on a quartz substrate was studied to obtain Al electrodes of surface acoustic wave (SAW) devices having high resistance to stress migration. A vapor deposition system was used under relatively moderate deposition conditions: (1) pressure range of 10^-5 Pa; (2) deposition temperature of 150°C; (3) deposition rate in the range of 120∼240 nm/min. The growth mode of epitaxial Al film differed from that of polycrystalline Al film on quartz.

The displacement characteristics of the applied voltage on porous-Pb(Zr, Ti)O₃ (P-PZT) are measured by the laser interferometry system. The static displacement characteristics are measured by applying DC voltage to avoid the interference from the various vibration modes. Also, the dynamic displacement characteristics are measured by applying AC voltage of the resonance frequency at 200 kHz. These displacement characteristics showed a dependence on the porosity of P-PZT, and the displacements increased as the porosity of P-PZT increased. P-PZT is applied to the echo sounder to evaluate the transmitting properties in water, and the improved transmitting sensitivity of 3.5 dB in reference to the conventional (nonporous) PZT, is obtained when the porosity of P-PZT is increased to 27%.

A surface acoustic wave (SAW) sensor utilizing the acoustoelectric effect has been designed for measurement of humidity in sensing ambient atmosphere. Most of the studies reported on sensors utilize the effect of mass loading. In this paper, we propose a somewhat different SAW humidity sensor that uses the changes in the film conductivity rather than the mass. A 30 MHz dual SAW delay line fabricated on 128° YX LiNbO₃ was coated with the sodium salt of poly(styrene) sulfonate. This hygroscopic polymer coating caused the SAW velocity change of 10 m/s per 10% relative humidity. The response was quite linear in the range from 20 to 70%RH.

This paper deals with thin rotary and linear ultrasonic motors using a double-mode piezoelectric ceramic vibrator; a rectangular plate vibrator of the first longitudinal and second bending modes is utilized. A specific merit of the motors is that their thickness can meet the restriction of 10 mm, which is one of the practical requirements of a light load gearless motor. The rotary motor is intended for application in card forwarding, and the linear motor, in magnetic-head traveling and so on. Construction and characteristics of the motors are described herein.

The present paper deals with some ultrasonic motors using longitudinal and bending multimode vibrators with their mode couplings caused by externally additional asymmetry or internal nonlinearity. A rectangular plate vibrator with two corners on one diagonal line cut to make its resonance modes couple with each other was used, along with a rectangular plate vibrator under the condition that two resonance frequencies are obtained, for example, as f_L/f_B=2.0, because internal nonlinear coupling of parametric vibration between two resonance modes is generated under this condition. Using these vibrators with mode couplings, it was found that some ultrasonic motors of simple form can be constructed. The ultrasonic motor using the phenomenon of mode-coupling vibrations dealt with here is not completely new, and a few trial constructions have already been reported [Jpn. J. Appl. Phys. 24 (1985) Suppl. 24-2, p. 739]. However, their motions were not reversible in ordinary driving with an electrical signal of a constant frequency. In contrast, the motors that the authors proposed in this paper can be expected to have a reversible motion.

Displacement characteristics for a bimorph-type actuator, made with lead zinc niobate-based (PBZM) ceramics were investigated at temperatures from -20°C to 60°C by driving the actuator with the bias driving method. Displacement was found to depend on both the temperature and the bias electric field; in particular, the temperature dependence of displacement can be improved by increasing the bias field strength. It was found that this displacement dependence is closely related to the relative dielectric constants of the ceramics.

Large amplitude driving of ferroelectric actuators has been investigated. Displacement ξ, electric charge Q and current I were measured with varying alternating voltage V_AC at various frequencies f (120, 500 and 1000 Hz) under voltage bias V_bias (0 to 75 V). Effective piezoelectric and dielectric constants were evaluated from initial slopes of ξ and Q vs V_AC, respectively. It is concluded that 90° domain reorientation makes some contribution to linear electromechanical interaction even when the strain level is low. It seems difficult to distinguish electrostriction from piezoelectricity.

Thin films of lead zirconate titanate (PZT) were fabricated by the hydrothermal method which consisted of two steps in the hydrothermal process: "nucleation" and "crystal growth" processes. The PZ nuclei were formed by the reaction at 140°C in a solution containing 4N potassium hydroxide. The growth rate of PZT crystals decreased at temperatures below and above 120°C. Bimorph-type bending actuators were made using as-deposited PZT films. The actuators showed large and visible electric-field-induced displacement even at driving voltage less than 10 V. From the displacement-voltage curve of an unimorph actuator and that of a heat-treated specimen, it may be concluded that the polar axes of PZT crystals had an orientation toward the substrate, giving rise to the piezoelectric effect without poling procedure.

Liquid viscosity measurement using shear horizontal (SH) wave propagation characteristics on a piezoelectric ceramic thin plate is described. The mode conversion loss associated with the compressional component U₃ is zero, because the SH wave on the piezoelectric ceramic substrate poled along the horizontal axis has only the horizontal component U₂, The IDT has a much larger electromechanical coupling factor for the S₀ mode SH wave than that of the SH surface acoustic wave (SAW). The metal-coated condition of the liquid-loaded surface is essential for detecting the liquid viscosity. There exists a linear relationship between the fractional phase velocity change of the S₀ mode and the square root of the liquid viscosity. The measured results on liquid viscosity using the S₀ mode SH wave devices, for some concentrations of glycerol-water solutions, are in good agreement with the theoretical prediction.

Electron emission into vacuum has been observed by applying pulse voltage to a thin plate of PZT ferroelectric ceramic. This electron emission has been obtained even in low vacuum of less than 10^-1 Torr. The lowest pulse voltage for this emission is 75 V, and the largest emission current in a sample having a 7×0.3 mm² electrode is 30 mA. The electrons are considered to be emitted from the surface of the ferroelectric plate near the electrode by very high field induced by polarization reversal. This electron emission can be applied as the electron emitter in vacuum electronic devices such as micro-triodes and flat panel displays.

Transient changes of temperature and current were numerically analyzed in BaTiO₃ semiconductors with a multilayer structure to which a constant electric field was applied. The numerical analysis required the radiation coefficient of the multilayer sample and the temperature dependence of resistivity of the material as input data. Temperature distribution of the sample was modeled to be uniform since the material possesses positive temperature coefficients of resistivity in the temperature range above the Curie point. The results of the numerical analysis agreed qualitatively with experimental results in the transient response, although the numerical analysis yielded some disagreements with experimental results when the applied electric field was low. The disagreements between analytical and experimental results are discussed with a focus on temperature distribution in samples.

A Bi₂O₃-TiO₂ phase diagram was determined using differential thermal analysis (DTA) apparatus. Bi₄Ti₃O₁₂ (BIT) micalike single crystals grown by a flux method were clear and slightly grayish in color. Ferroelectric and dielectric properties of BIT crystals were observed from measurements of electric displacement vs electric field hysteresis loops and the dielectric constant. Also, the polarization switching characteristics of BIT crystals were investigated. The switching time and switching current density were read from the transient waveforms.

The anomalous dielectric absorption current of BaTiO₃ ceramics when an electric field is applied at above the Curie point was measured. The results cannot be explained by the famous Maxwell-Wagner double layer theory. The total charge of the charging and discharging absorption current was more than 1000 µC/cm². The giant space charge produces "internal bias field" in the opposite direction to the first applied field. Another space charge is generated during the aging process after poling at below the Curie point. In this report, two types of space charge effects are described and discussed respect to "space charge stabilized effects" for electromechanical strength and the difficulties of polarization reversal applications due to "space charge asymmetric effects".

A BaTiO₃ single crystal, whose dimensions were 3.9×3.9×3.6 mm³, was mechanically and electrically poled to remove its 90° and 180° ferroelectric domain walls, respectively. After mechanical poling, four-step electrical poling was applied to the crystal, which did not include 90° domain walls, with the aim of removing the 180° domains gradually. In each of these steps, the dielectric constant of the crystal was measured using an impedance analyzer. Prior to the electrical poling, the dielectric constant in the [001] direction was 137 at 100 kHz (unclamped) and 133 at 10 MHz (clamped). By applying four-step poling, these values varied gradually with the progress of poling, and became 130 and 58, respectively, after the final step, i.e., in a single-domain state.

Frequency-dependent complex impedances were measured in Nb-doped (Ba_0.6Sr_0.4)TiO₃ PTC (positive temperature coefficient) ceramics. The complex impedance data were analyzed in Cole-Cole-type equivalent circuits by the computer fitting method in order to determine individual resistance and capacitance values of the bulk grain and grain boundary. The PTC effect was found to have originated from the temperature-sensitive behavior of the grain boundary resistance. The temperature dependences of dielectric constants of both the bulk grain and grain boundary calculated on the basis of the two-layer model agreed closely to those predicted by Heywang's model. The width and potential height of the grain boundary layer were estimated to be 0.26 µm and 0.1 eV, respectively, in the temperature range below -20°C. The estimated donor density of 6×10¹⁸ cm^-3 was much lower than calculated from the amount of Nb₂O₅ added.4

Excess WO₃ and higher sintering temperature were used for decreasing the temperature dependence of the dielectric constant in Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃-Pb(Mg_1/2W_1/2)O₃ ternary systems. Under some conditions, materials with both JIS YB specifications (dielectric constant change less than 10% over the temperature range from -25 to 85°C) and high dielectric constant, 5000-7400, were obtained. In the materials, core-shell-like distributions of B-site components were observed. These core-shell structures consist of W-rich regions and Ti, Nb-rich regions. In the compositions containing 2% WO₃, sintered at 1150°C, core-shell-like domain structures are observed. The fringe pattern corresponded to the Ti, Nb-rich region, and superlattice electron diffraction spots indicating B-site ordering were observed in the W-rich region. In addition, the amounts of WO₃ varied the appearance of the core-shell structure.

Lead based-complex perovskite solid solutions Pb(In_(1-x)/2Yb_x/2Nb_1/2)O₃ were prepared through wolframite phase oxides (InNbO4 and YbNbO4), and their dielectric properties were investigated. For Yb concentrations x<0.20, the diffuse phase transition, which was characterized by the broad maximum for the temperature dependence of the permittivity and the dielectric dispersion in the transition region was observed. With increasing x, the maximum permittivity increases. For x>0.20, in addition to the dielectric dispersion, a new frequency-independent dielectric anomaly appears at temperature T_t. With increasing x, T_t increases rapidly and the dielectric dispersion decreases. There is a structural change which is characterized by the splitting of the structure-sensitive maximum of the (200) reflection of X-ray diffraction (XRD) patterns around x=0.20. Thus, the morphotropic phase boundary exists at around x=0.20.

Dielectric resonator materials with the formula (Ba_1-xSr_x)(Mg_1/3Ta_2/3)O₃ have been studied in order to clarify the factors controlling the resonant frequency as a function of temperature. Dielectric constant and thermal expansion are calculated from the resonant frequency measured by the dielectric resonator method and the capacitance obtained at 10 kHz. The results show that the temperature dependence of the resonant frequency originates mainly from the change in the dielectric constant with temperature. The dielectric constant exhibits a maximum at some critical temperature, which varies with increasing strontium content in the oxides.

Dielectric crystals having composition in the vicinity of Ba_3.75R_9.5Ti₁₈O₅₄ and/or BaR₂Ti₄O₁₂ (R=La, Nd and Sm) were obtained from the melts with BaR₂Ti₅O₁₄ composition. A superlattice with two times the fundamental lattice spacing along the c-axis has been found in the three kinds of crystals. Crystal data of the superlattice are as follows: orthorhombic, Pbn2₁ (No. 33) or Pbnm (No. 62); a=12.267(5), b=22.410(9), c=7.732(6) Å for Ba_3.75La_9.5Ti₁₈O₅₄; a=12.189(3), b=22.319(6), c=7.677(4) Å for Ba_3.75Nd_9.5Ti₁₈O₅₄; a=12.142(4), b=22.300(6), c=7.653(4) Å for Ba_3.75Sm_9.5Ti₁₈O₅₄. Space group of the fundamental lattice is Pba2 (No. 32) or Pbam (No. 55). The dielectric constants, ε_r, of Ba_3.75R_9.5Ti₁₈O₅₄ (R=Nd and Sm) are in the high range from 78 to 86, and unloaded Q values are in the range of 2400 to 3000. The excellent values of single phase are better than those of BaR₂Ti₅O₁₄ composition including secondary phases.

Over the entire range of composition in ternary system Pb(Mg_1/2W_1/2)O₃-Pb(Ni_1/3Nb_2/3)O₃-PbTiO₃ (PMW-PNN-PT), crystal structures and dielectric properties were investigated. On the compositional line of 30 mol% PNN content, dielectric relaxation, D-E hysteresis loop and long-range order parameter were measured in order to understand the effect of PMW content. From the results, a morphotropic phase boundary (MPB) was found on the compositional line with 45 to 50 mol% PT content. It was found that the PMW component was incorporated into ordered clusters in solid solutions in a PMW-rich compositional region. The degree of ordering was evaluated by the long-range order parameter S. The relationship between the long-range order parameter S and dielectric properties, especially compositional dependence of Curie temperature, in this system was discussed.

We have investigated the dielectric properties up to microwave frequencies of ceramics represented as (Pb_1-xCa_x)-(Me_mNb_1-m)O₃ where Me is selected from Li, Na, Mg, Zn, Ni, Co, Fe, Y, Yb, Al and Cr. High Q values and small temperature coefficients of resonant frequency were obtained in (PbCa)(Mg_1/3Nb_2/3)O₃, (PbCa)(Ni_1/3Nb_2/3)O₃ and (PbCa)-(Fe_1/2Nb_1/2)O₃ with perovskite structure. These dielectric constants and the Q values for a near-zero temperature coefficient are ε_r=73 with Q=1330, ε_r=59 with Q=1700 and ε_r=91 with Q=1650, respectively. The other ceramics with smaller amounts of perovskite phase had degraded characteristics, i.e., low Q values or large temperature coefficients. In lead- and calcium-based perovskite, it seems that the high dielectric constant occurs due to Pb content in A-sites and smaller average ion radius in B-sites.

Powder of the dielectric ceramic Sr(Zr, Ti)O₃ was prepared by a new chemical method using TiO₂ powder. The obtained fine and well-dispersed powder had good sinterability. The microscopic compositional uniformity in the sintered body was estimated by WDX, and the dielectric properties were measured at 6 GHz and 1 MHz. The samples prepared by the chamical method had excellent uniformity and a Q value (1/tan δ) 2.5 times that of the samples prepared by the conventional method.

We have investigated dielectric properties of several bismuth-based ceramics at microwave frequencies. BiNbO₄ ceramics containing CuO and V₂O₅, had a high Q value of Q=4260 (at 4.3 GHz), ε=43, and τ_f=+38 ppm/°C. In the Bi₂O₃-CaO-Nb₂O₅ system, Bi₁₈Ca₈Nb₁₂O₆₅ composition had a high dielectric constant of ε=59, Q=610 (at 3.7 GHz), and τ_f=+24 ppm/°C. The crystal structure of this composition is considered to be an ordered structure based on the body center tetragonal cell (a=0.377, c=0.542 nm). Furthermore, by substituting Zn for Ca, ε increased and τ_f changed to negative values. In the composition of 45.75BiO_3/2-21.75(Ca_0.725Zn_0.275)O-32.5NbO_5/2, excellent properties of ε=79, Q=360 (at 3.3 GHz), and τ_f=+1 ppm/°C were obtained. As all the above ceramics can be sintered below 950°C, they are applicable to multilayer microwave devices with Ag inner conductors.

Dielectric properties of two-phase mixture systems including rutile (TiO₂) have been investigated. One of its binary compounds-MnTiO₃, ZnTiO₃, PbTiO₃ and Al₂TiO₅-was chosen as the second component. Dielectric constants ε_r and their temperature coefficients τ_e were first examined at 1 MHz. Dielectric properties in the microwave frequency region were measured in the TE₀₁₁ mode of a cylindrical specimen. The temperature coefficient of resonant frequency, τ_f, of MnTiO₃ was negative, and a zero coefficient was found at an intermediate composition x=0.13 in the (1-x) MnTiO₃-xTiO₂ system. In the PbTiO₃-TiO₂ system, zero τ_e composition was confirmed at low frequencies, but composition modification trials aiming to make microwave dielectric measurements possible were unsuccessful throughout the entire system.

It has been discovered that multilayer ceramic resonators, manufactured by a cofiring method at a temperature above the melting point of the inner conductor, have an improved Q-factor. The increase in Q-factor enabled the realization of an S-band multilayer low-loss bandpass filter (BPF). In this paper the insertion loss of the cofired BPFs is examined, and a relationship between firing temperature and Q-factor is established.

The first experimental observation of Cerenkov-type second harmonic generation (SHG) in an amorphous Nb₂O₅ thin-film optical waveguide on (0001) LiTaO₃ substrate is reported. The Nb₂O₅ thin films were deposited by rf magnetron sputtering on LiTaO₃ substrate. A Nd:YAG laser at 1064 nm wavelength was used as the pumping source for the SHG experiments. The conversions occurred between the fundamental (1064 nm) TE₀ guided mode and the harmonic (532 nm) TM radiation mode, and between the TM₀ guided mode and the TM radiation mode. The efficiency of both conversions was about 10^-8 for a sample with a film thickness of 788 nm. These SHG results were in good agreement with the coupled-mode theory, and the theoretical calculation revealed that the low conversion efficiencies were due to the unsuitable film thickness. It was predicted that the efficiencies could be raised to a much higher level.

In order to study the grain size dependence of optical transmittances and linear electrooptic coefficients of the ferroelectric ceramics with the composition 0.1Ba(La_1/2Nb_1/2)O₃-0.9Pb(Zr_0.5Ti_0.5)O₃, specimens having various grain sizes were prepared by the hot-pressing method under different sintering conditions, namely by varying the temperature, the time and the pressure, independently. The results obtained show that the transmittance increases as the grain size increases, and that it decreases very slightly in the phase change from the paraelectric to the ferroelectric tetragonal phase. The linear electrooptic coefficient r_c shows a slight decrease with increasing grain size.

In this paper we report the experimental and theoretical result that the photorefractive properties of pure and doped lithium niobate single crystals show a close relationship with anomalous photovoltaic (APV) current. The dopant dependence of sensitivity of two-wave mixing is discussed with the APV current in theory. The product of quantum efficiency and effective drift length ΦL_ph is obtained.

Experimental results are presented for a phase conjugate wave generation using an iron-doped lithium niobate single crystal by the degenerate four-wave mixing method. More than 300% reflection efficiency is achieved, and it is almost independent of the total incident optical intensity. The generator is then applied as a phase conjugate mirror to an all-optical associative holographic memory to reflect and amplify the diffracted beams. The retrieved output image is formed by using partial input illumination.

Field-induced antiferroelectric-ferroelectric phase transition in an antiferroelectric liquid crystal 4-(1-trifluoromethylheptyloxycarbonyl)phenyl-4'-octyloxybiphenyl-4-carboxylate (TFMHPOBC) was studied by means of microscopic observation during the switching process and the measurement of the T-E hysteresis loops. It was clarified that the threshold voltage of the switching from the antiferroelectric state to the ferroelectric state and the transmittance at the threshold voltage depend on temperature, frequency and optical purity. The optical purity is an important factor for improving the contrast of display devices.

A multiplex-driving technique for an antiferroelectric liquid crystal device has been studied. A new driving scheme is proposed, which overcomes the disadvantage of slow switching from a ferroelectric state to an antiferroelectric state. It is confirmed that the antiferroelectric liquid crystal device can be driven at a high duty ratio of 1/500 by using this scheme.

A fast electrooptic modulation in the polymer waveguide using ferroelectric liquid crystal has been proposed. In this device, the soft mode ferroelectric liquid crystal (SMFLC) is used as an active material on the passive polymer waveguide, and electrooptic switching is realized by controlling the total reflection at the polymer waveguide-liquid crystal interface. The response time is of the order of several microseconds. An analogue electrooptic modulation in the waveguide is realized using the field-induced linear molecular tilt of the electroclinic effect in SMFLC.

A detailed study of dielectric and optical properties in ferroelectric liquid crystal (R)-4^'-3(-methoxycarbonyl-2-propoxycarbonyl)phenyl 4-(4-(n-octyloxy)phenyl)benzoate (3MC2PCPOPB) has been carried out. It has been found that the anomalous temperature dependence of the dielectric constant in 3MC2PCPOPB is due to the antiferroelectric property. In the antiferroelectric phase, five stable states are observed in voltage dependence of apparent tilt angle, and on the basis of those measurements the T(temperature)-E(electric field) phase diagram is obtained. In a thin cell (<3 µm), both ferroelectric and antiferroelectric domains are simultaneously observed at the same temperature over a wide temperature range. Although the ratio of the area of antiferroelectric domains to that of ferroelectric domains gradually increases with decreasing temperature, a complete antiferroelectric phase does not appear even at low temperature.

This paper proposes new types of one and two-dimensional electrooptic (E-O) lenses of simple structure. The two-dimensional lens is composed of two one-dimensional E-O lenses which are arranged to converge light beams perpendicular to each other. The refractive index distribution of the lens is calculated using the finite-element method, and ray tracing is performed by solving the ray equation for each one-dimensional lens. Parameters of the E-O lens, such as electrode width and gap, and crystal thickness, are optimized. One and two-dimensional lenses are demonstrated, and the focusing and temporal characteristics are studied experimentally.

Electrooptic ceramics of (Pb, La)(Zr, Ti)O₃ were fabricated by a combination of the partial-coprecipitation and doctor-blade methods. The PLZT powder, with particles of submicron size that were excellently dispersed, was prepared by (Zr, Ti)O₂ solid-solution powder and PbO and La₂O₃ oxide powders. The large-scale PLZT ceramics with the dimension of 10×10∼20 cm and thickness of 1.5 mm were molded by the doctor-blade method and then conventionally sintered at 1200∼1250°C for 20∼60 h under the controlled condition of PbO and oxygen atmosphere. The fabricated PLZT ceramics with 0.5 mm thickness showed the transmittance of 65∼67% in the range of wavelength greater than 600 nm, and the quadratic electrooptical coefficient of 4.5×10^-16 O²/V².

The moving grating method was applied to a photorefractive Bi₁₂SiO₂₀ crystal in order to enhance the light amplification factor γ₀ in the two-wave mixing process and the reflectivity R of the phase conjugate wave in the four-wave mixing process. It was found that γ₀ and R exhibited maximum values when the interference pattern moved inside the Bi₁₂SiO₂₀ crystal at an optimum velocity. We achieved 65% reflectivity of the phase conjugate wave at that velocity. The response time of the photoinduced refractive index grating was determined with varying incident beam intensity, external electric field and grating spacing.

Optical gyration studies on Co₃B₇O₁₃I and Cu₃B₇O₁₃Cl were conducted by the high accuracy universal polarimeter (HAUP) method. Temperature dependences of the gyration tensor g₁₂ manifested sharp peaks at improper ferroelectric transition points. The electrogyration coefficient of Co₃B₇O₁₃I also exhibited a sharp peak at the transition point. Taking our previous work of Fe₃B₇O₁₃I into account, it was concluded that peculiar temperature dependences of gyration and the electrogyration coefficient are a common nature of ferroelectric boracite crystals.

Optical properties of La-modified lead zirconate titanate (9/65/35) in the intermediate phase were studied by the HAUP (high accuracy universal polarimeter) method. It was found that this material is optically inactive under electric fields. On the other hand, temperature dependence of the quadratic electrooptic coefficient was measured after careful corrections using the HAUP method.

Birefringence Δn_c of the improper ferroelectric Gd₂(MoO₄)₃ was accurately measured by using the HAUP (high accuracy universal polarimeter) method as a function of temperature and electric field. Electric field dependence of Δn_c was found to show unique behaviour in the vicinity of T_c. It is of importance that the linear electrooptic coefficient r₆₃ changes its sign and manifests a sharp peak in the close vicinity of T_c. This result coincides qualitatively with the result reported by Kobayashi and Miyazaki, but disagrees with other reports.

N-type ZnO thin films with a crack- and columnar-free structure were successfully prepared on p-type Si substrates by the sol-gel process. The current-voltage (I-V) characteristics of the heterojunction of n-ZnO/p-Si show a rectification, and the capacitance-voltage (C-V) characteristics show an approximately linear C^-2-V relationship in the reverse bias condition. In the ZnO thin film, two gap states located at 0.054 eV and 0.12 eV below the conduction band were measured by isothermal capacitance transient spectroscopy (ICTS).

Pure and Mn-doped NaNbO₃ crystals have been investigated dielectrically between 380 and 20 K. Below room temperature, no phase transition is observed in pure sodium niobate. With increasing Mn content, a structural phase transition is induced around 140 K. The dielectric constant shows a maximum for the sample with 0.7 wt.%, and shows large thermal hysteresis. In the low-temperature region, ferroelectric activities could not be detected in either pure or lightly doped NaNbO₃. The phase diagram of T_c vs the concentration of Mn is obtained. Domain motion associated with this phase transition is observed around the transition temperature. This evidence proved that the low-temperature phase is induced by light doping with Mn ions. The uniaxial stress decreases T_c; dT_c/dσ=-80 K/kbar on heating and -600 K/kbar on cooling.

Optical properties of LiNH₄C₄H₄O₆·H₂O (LAT) were studied by means of a high-accuracy universal polarimeter (HAUP). The temperature dependences of the gyration tensor components were obtained. The elastogyration coefficients were determined. Rotation of the indicatrix takes place only around the b axis in the low-temperature phase. The rotation angle of the gyration surface was found to be three orders of magnitude larger than that of the indicatrix.

Humidity dependence of the surface resistivity and the dielectric properties of adsorbed-water layers on the surfaces of LiNbO₃ and LiTaO₃ single crystals were examined. Experiments were carried out for the specimens with various cuts of the crystals to investigate the mechanism and the origin of the logarithmic dependence of the surface resistance on humidity.

Optimum conditions to form ferroelectric BaMgF₄ films on GaAs substrates are investigated. It has been found in vacuum evaporation of BaMgF₄ sources that combination of low-temperature deposition and subsequent high-temperature annealing is effective for forming BaMgF₄ films that do not contain BaF₂ and MgF₂ crystallites. The optimum deposition and annealing temperatures obtained thus far are 300°C and 600°C, respectively. Crystallinity and electrical properties of the optimum films are characterized.

A compensation for ferroelectric hysteresis loop distortion has been developed and applied to some ferroelectric or antiferroelectric phase transitions. The distortion of loop has been numerically synthesized on the basis of an equivalent circuit and subtracted from the measured signal; in the calculation, nonlinearity of the circuit can be taken into account as necessary. Successful results were obtained in ferroelectrics near the second-order phase transition and in antiferroelectrics which show nonlinear conductivity or a nonlinear dielectric constant.

Simulations of step-type and pulse responses have been performed using a two-dimensional lattice model in ferroelectrics in which latent nuclei are randomly distributed. Polarization and current responses under the step-type applied field and the narrow applied pulse field shorter than switching time t_sw are described. The critical pulse width t^*, for which the system returns to the initial polarization state after the narrow applied pulse field is removed, is obtained, and it is found that the value of t^* depends on the applied field and the interaction between neighboring dipole moments.

The phase transition behavior in the systems of (1-x)Pb(Mg_1/3Nb_2/3)O₃-xPbTiO₃ (PMN-PT) and 0.99Pb_1-yLa_2y/3TiO₃-0.01MnO₂ (PLT) relaxor ferroelectrics has been investigated to explore the nature of diffused phase transitions (DPT) in these materials. All the dielectric constant (ε)-temperature (T) characteristics for these materials above the Curie point have been found to be described by the equation (1/ε-1/ε_m)^1/n=(T-T_m)/C^', where ε_m is the maximum dielectric constant of a material, T_m is the temperature giving ε_m, and n and C^' are constants changing with composition. In the system PMN-PT, the value of n was found to change continuously from 1.0 for PT to 2.0 for PMN without any irregularity. The value of n for the materials of the system PLT also shows a similar variation with La content, and moreover, two C^' versus T_m plots obtained for the two systems PMN-PT and PLT show substantially the same behavior. The nature of DPT is considered to be closely connected with compositional and structural variations, which determine the spatial size and morphology of ferroelectric domains below the Curie point.

Domain structures in tetragonal Pb(Zr_xTi_1-x)O₃ (PZT) single crystals etched by HF+HCl solution were observed by means of a scanning electron microscope. The relationship between the etch patterns of pseudocubic {100} faces and spontaneous polarization vectors was examined using micro-Raman spectroscopy and electron channeling patterns. Both the a-face and the positive c-face are quickly etched, but the former results in a rough surface while the latter results in a smooth one. The negative c-face is rather slowly etched. Another type of etch pattern with a wedge-shaped section was observed; this is usually observed in PZT ceramics but has not been reported in BaTiO₃. This pattern can be explained by the difference in etch rates between various {100} faces and the peculiar domain structures which consist of a single domain region with narrow or wedge-shaped 90° domains. It is assumed that such a domain structure is, although unstable under electrical stress, stable under mechanical stress.

Strong nonlinear behavior was observed in a LiNbO₃:Fe piezoelectric resonator with a photorefractive periodic grating. The resonator is a y-cut plate with Au electrodes totally or partially deposited on both faces. The current-voltage and the admittance-frequency characteristics show nonlinear behavior such as hysteresis only near the resonance frequency. In some conditions, the current changes negatively with the voltage. These characteristics depend on the Q-value of the resonator. The present nonlinear phenomena do not occur when the Q-value is too large, while they occur at larger values of Q in usual resonators. We found that the Q-value of the resonator with the photorefractive grating varied when the resonator was annealed or when the period of the grating was changed.

Unknown dielectric stiffness constants in elastic Gibbs free energy for Pb(Zn_1/3Nb_2/3)O₃ were estimated by fitting the calculated phase diagram with the experimental one for the Pb(Zn_1/3Nb_2/3)O₃-PbTiO₃ (PZN-PT) solid solution, and by considering the discontinuity of the dielectric constant at the rhombohedral-tetragonal morphotropic phase boundary in the (1-x)PZN-(x)PT system, x>0.105. The calculated PZN=PT phase diagram using the newly estimated values was in good agreement with the experimental PZN-PT one. The dielectric constants, lattice parameters and piezoelectric constants of the PZN-PT system could be calculated at a given composition and temperature. On comparison with experimental data, this method was found to be effective for material design.

This paper describes the H-type vibratory gyroscope used as an angular rate sensor. The vibrational displacements of the gyroscope are analyzed by the finite element method, and a new structure of the gyroscope, which can be supported at a zero-displacement point, is clarified. This H-type gyroscope is expected to be an angular rate sensor with a high quality factor and high stability.

Powder materials having the composition Pb_0.88Ba_0.12(Zn_1/3Nb_2/3)_0.30(Mg_1/3Nb_2/3)_0.50Ti_0.20O₃ were prepared by a two-step calcination method. All the constituent oxides, except for PbO, were precalcined, and then the resulting mixtures were postcalcined with PbO to obtain powders having the desired composition. A series of experimental studies of the powder and the ceramic showed that samples fabricated by the present method had better properties in terms of perovskite phase purity, sinterability, breakdown voltage and dielectric constant, compared to those prepared by the conventional method using one-step calcination.

DC dielectric breakdown strength Eb of grain-oriented Bi₄Ti₃O₁₂ ceramics fabricated by the hot-forging method and the cold-uniaxial pressing method has been studied. In the hot-forging sample with the X-ray orientation factor of 0.84, Eb was about 22 MV/m, when electric field was applied parallel to the pressing axis of the grain-oriented ceramics. On the other hand, Eb was about 16 MV/m, when the field was perpendicular to the pressing axis. It was found that grain orientation is effective in increasing Eb parallel to the pressing axis.

The measurement accuracy of complex permittivity in the dielectric rod resonator method has been investigated. The measurement error of relative permittivity is 0.05% (standard deviation), which is permissible for the applications of resonators. The dielectric loss was measured by setting conducting plates at both ends of the dielectric resonator. The frequency dependence of the conductivity due to the surface roughness of the plates was investigated using three kinds of standard rod resonators. It is concluded that the measurement error of tan δ can be reduced to 1.5×10^-6 (standard deviation) for a dielectric specimen with ε_r=30.2 at 10 GHz by using the high-Q standard dielectric rod resonators which are placed between conducting plates with surface roughness less than the skin depth at the measurement frequency.

The fiber-optic measurement and evaluation of piezoelectric vibration of circular rod and disk ceramics are described. The values corresponding to the piezoelectric d- and g-constants can be obtained locally by measuring amplitude and Q-value at the first-resonance frequency under appropriate electric conditions. The results are analyzed numerically by using the theory of coupled resonance.