

System for Measuring the Phase Transition Temperature of KTa_{1−x}Nb_{x}O_{3} Using Scanning Nonlinear Dielectric MicroscopyAbstractWe have developed a system for measuring the paraelectrictoferroelectric phase transition temperatureT_{C} using scanning nonlinear dielectric microscopy (SNDM). We developed a probe for samples with a huge dielectric constant and demonstrated that theT_{C} of potassium tantalate niobate (KTa_{1−x}Nb_{x}O_{3}, KTN) crystal can be measured locally using SNDM with this probe. The T_{C} measurement precision (standard deviation) is 0.09°C. This corresponds to a composition (Nb concentration x) resolution of 1.4 × 10^{−4}, which is difficult to achieve with other element analyzers. Moreover, by measuring T_{C} while changing the position, we demonstrated that we can measure the spatial distribution of the T_{C} of the KTN crystal. To reduce the time required for the operator to measure the T_{C} distribution of the KTN crystal, we developed software for fully automated operation.
1. IntroductionPotassium tantalate niobate (KTa_{1−x}Nb_{x}O_{3}, KTN) is a ferroelectric material and its dielectric constant and quadratic electrooptic (EO) constant (Kerr constant) are maximum around the paraelectrictoferroelectric phase transition temperature (T_{C}) [1]. These values are huge, so KTN is expected to reduce both the volume and driving voltage of EO devices, such as optical beam deflectors [2] and modulators [3]. In KTN, T_{C} can be adjusted by changing the composition, i.e., the Ta/Nb ratio [1]. T_{C} increases linearly with the amount of Nb (x) [4]. However, if there is a spatial change in the Ta/Nb ratio in a crystal, which may be induced by changes in the growth condition during crystal growth, T_{C} changes spatially, and the dielectric constant ε and the Kerr constant s change spatially at a given temperature. If a crystal¡Çs spatial distributions of ε and s are large (i.e., the crystal is highly inhomogeneous), it is difficult to guarantee the characteristics of an EO device manufactured from that crystal. Therefore, to guarantee the characteristics of a KTN device, it is necessary to evaluate the uniformity of a crystal¡Çs T_{C} before the device is manufactured. However, if TC has to be estimated with a precision of 0.1°C, the composition should be estimated with a precision of 1.5 × 10^{−4} [4]. This is difficult to achieve with conventional element analyzers, such as an electron probe microanalyzer (EPMA). In this paper, we describe the system for measuring the T_{C} of KTN that we developed. First, we review scanning nonlinear dielectric microscopy (SNDM) and describe the probe we developed for samples having a huge dielectric constant. Then, we describe our demonstration that the T_{C} of KTN crystal can be measured locally using SNDM with our probe. Experimental results for T_{C} measurement precision and the spatial distribution of the T_{C} of the KTN crystal are also presented. Finally, we introduce the software developed to reduce the time taken for the operator to measure the T_{C} distribution of a KTN crystal. 2. Scanning nonlinear dielectric microscopy (SNDM)2.1 Principle of SNDMScanning nonlinear dielectric microscopy (SNDM) has been developed to measure the local dielectric constant under a probe needle with high spatial resolution [5], [6]. Moreover, nondestructive measurement is possible, so a crystal that has been evaluated using SNDM can be used for manufacturing devices. A schematic diagram of SNDM is shown in Fig. 1. SNDM uses an LC (inductance and capacitance) oscillator with a probe needle. When the probe needle is far away from the sample, the resonant frequency f_{0} is , where L and C_{0} are the oscillator¡Çs inductance and capacitance (including stray capacitance), respectively. When the tip of the probe needle makes contact with the sample, the resonant frequency f_{S} is , where C_{S} is the capacitance of the sample under the probe needle. As the dielectric constant of the sample under the probe needle increases, C_{S} becomes larger and f_{S} becomes lower.
To check this, we measured the resonant frequency of several dielectric materials. The relationship between f_{S} and the dielectric constant at room temperature is shown in Fig. 2. This figure clearly indicates that the larger the dielectric constant, the lower f_{S}. Accordingly, when f_{S} is measured as a function of temperature, the local T_{C} can be obtained as the temperature that gives the lowest f_{S}. Moreover, the spatial distribution of T_{C} can be measured by changing the point touched by the probe.
2.2 Probe for keeping contact force constantIn crystals with a huge dielectric constant, such as KTN, f_{S} depends strongly on the contact force that the probe needle exerts on the sample. The reason for this is as follows: when the probe needle is in point contact with a sample having a huge dielectric constant, the electric field is concentrated in a very small area just under the tip of the probe needle [7], and f_{S} depends on the capacitance of that very small area. When the contact force is stronger, the contact area is larger due to deformation, and f_{S} depends on the capacitance of the larger area and is lower; namely, f_{S} depends on both the dielectric constant and the contact force. In the work described here, we developed a probe that keeps the contact force constant during the measurement of T_{C}. A schematic diagram of the probe is shown in Fig. 3(a). The probe consists of a conductive tube and a conductive needle that can move up and down in the tube, which has a stopper to prevent the needle from falling out. When the tip of the probe is not in contact with a sample, the needle is held by the stopper, as shown in Fig. 3(b). On the other hand, when the tip is in contact, the sample pushes the needle upwards, as shown in Fig. 3(c). With this design, the contact force is equal to the force of gravity acting on the needle and can be kept constant.
3. Experimental results3.1 Measurement of T_{C} of KTNThe resonant frequency f_{S} is plotted as a function of temperature T in Fig. 4 when the probe needle (Aucoated, tip radius: 500 µm) came into contact with a KTN single crystal (6 × 5 × 0.5 mm^{3}, x ≈ 0.4). We estimated T_{C} to be about 35°C because domains appeared or disappeared at this temperature. The f_{S} was about 1214 MHz when the probe needle was kept far away from the sample; namely, C_{S} = 0. We used a Peltier device and a controller to sweep the temperature and we collected data during the cooling phase. The sweep rate was not constant, but the average rate was about 0.3°C/s. As shown in the figure, f_{S} was minimum at around 35°C. This indicates that SNDM can measure the T_{C} of KTN.
3.2 T_{C} measurement precisionWe evaluated the precision of this method. We performed the T_{C} measurement N times, where N = 101. A histogram of T_{C} is shown in Fig. 5. Here, for T_{C}, we used the temperature at which df_{S}/dT was the smallest because it changes drastically around T_{C}, as shown in Fig. 4. This large change is induced by an abrupt change in the dielectric constant. The mean value of T_{C}, _{C}, was 35.6°C, and the standard deviation was 0.09°C. If we use the standard deviation as the precision, then the precision of this method is 0.09°C, which corresponds to a composition resolution of 1.4 × 10^{−4}, using the empirical equation T_{C} = 676x + 32 measured in kelvin, where x is the amount of Nb [4]. This precision for the composition is difficult to achieve with other element analyzers, such as an EPMA.
3.3 Spatial distribution of T_{C}Next, we evaluated the T_{C} distribution of the crystal. We measured T_{C} at 20 (= 5 × 4) points with a spacing of 1 mm. The distribution is shown in Fig. 6. For this crystal, T_{C} is higher in the top left of the figure. The maximum and minimum T_{C} values were 35.37 and 34.7°C, respectively. Here, T_{C} = 35.37°C corresponds to x = 0.4091 and 34.7°C to x = 0.4081, where x is the amount of Nb. Therefore, the variation in T_{C} in this crystal was 0.67°C, which corresponds to a variation in composition of about 0.001 using the above empirical equation [4].
4. Measurement systemTo reduce the time required for the operator to evaluate the T_{C} distribution of the KTN crystal, we automated the measurement and data processing. A window of the software we developed is shown in Fig. 7. After the measurement condition (measurement spacing and number of points etc.) has been assigned and the sample has been set, the measurement is finished in a fully automated manner. Moreover, to eliminate manual data processing after the measurement, the software detects T_{C} by a differential calculation, as discussed in section 3.2 and records it.
5. ConclusionWe described our system for measuring the phase transition temperature T_{C} of KTN using SNDM and a newly developed probe designed to keep the contact force constant during the temperature sweep. The precision (standard deviation) is 0.09°C, which corresponds to a composition resolution of 1.4 × 10^{−4}. By measuring T_{C} while changing the position, we demonstrated that we could measure the T_{C} distribution of the KTN crystal. We also developed software capable of measuring the T_{C} distribution of the KTN crystal in a fully automated manner. This measurement system will enable the uniformity of KTN crystals to be evaluated, so it will be possible to guarantee the characteristics of KTN devices made from KTN crystals. 6. AcknowledgmentsWe thank Professor Yasuo Cho of Tohoku University for fruitful discussions about SNDM. References
