II. PRINCIPLE AND THEORY FOR SNDM AND MICROSCOPIC OBSERVATION OF THE AREA DISTRIBUTION OF FERROELECTRIC DOMAINS USING SNDM

As shown in Fig. 1, we consider the situation where there is a capacitor made of the material to be measured with nonlinearity in D–E relationship and an alternating electric field E ₃ along the z-direction (3-direction) is applied to this capacitor. Equation (1) is a polynomial expansion of the electric displacement D ₃ as a function of the electric field E ₃.

(1)

FIG. 1.

Principle of polarization detection by scanning nonlinear dielectric microscopy (SNDM).

where P _s3 is a spontaneous polarization along the same direction and ε(2), ε(3), and ε(4) are linear, lowest-order nonlinear, and one-order-higher dielectric constants, respectively (The number in the bracket denotes the rank of tensor.).

The even rank tensors, including the linear dielectric constant ε(2), are insensitive to the state of spontaneous polarization. On the other hand, the lowest-order nonlinear dielectric constant ε(3) and other higher-order odd-rank tensor nonlinear dielectric constant are very sensitive to spontaneous polarization. For example, there is no ε(3) in a material with a center of symmetry and the sign of ε(3) changes with the inversion of spontaneous polarization. Therefore, by detecting this ε(3) microscopically, we can measure the distribution of ferroelectric domains.

The capacitance C _s varies alternately owing to the nonlinear dielectric properties of the specimen caused by the application of alternating electric field E ₃ = E _pcosω _pt. The ratio of the derivative capacitance variation ΔC _s to the static value to the capacitance C _s0 is given by the following Eq. (2).

(2)

This equation shows that the alternating capacitance of different frequencies corresponds to each order of the nonlinear dielectric constant. Signals corresponding to ε(3) and ε(4) are obtained by detecting the components with a frequency equal to ω _p and 2ω _p of the applied electric field, respectively.

In the microscopy technique, we have to measure the capacitance variation in the very small portion so that we have developed a special probe for SNDM. Figure 2 shows the system setup of SNDM using an LC lumped constant resonator probe. In the figure, C _s denotes the capacitance of the specimen under the center conductor (the tip) of the probe. C _s is a function of time because of the nonlinear dielectric response under the applied alternating electric field E _p3 (=E _pcosω _pt, f _p= 5 kHz–1 MHz).

FIG. 2.

Schematic diagram of SNDM system.

This LC resonator is inserted into the positive feedback circuit of a free-running (self-excited) oscillator tuned to the resonance frequency of this resonator. Thus, this oscillator oscillates at the resonance frequency of the LC resonator. The above-mentioned electrical parts [i.e., tip (needle or cantilever), ring, inductance, and oscillator] are assembled into a small probe for the SNDM. The oscillating frequency of the probe (or oscillator) (approximately 1–6 GHz) is modulated by the change in capacitance ΔC _s(t) due to the nonlinear dielectric response under the applied electric field. As a result, the probe (oscillator) produces a frequency-modulated (FM) signal. By detecting this FM signal using the FM demodulator and lock-in amplifier, we obtain a voltage signal proportional to the capacitance variation. Thus, we can detect the nonlinear dielectric constant just under the tip and obtain fine resolution determined by the diameter of the pointed end of the tip and the linear dielectric constant of specimens. The capacitance variation caused by the nonlinear dielectric response is quite small. Therefore, the sensitivity of the SNDM probe must be very high. The measured sensitivity of the above-mentioned lumped constant resonator probe is in the range of 10⁻²² F, which is much higher than that of scanning capacitance microscopy (SCM) whose typical sensitivity is 10⁻¹⁸ F.Reference Nakagawa and Morita²¹

Originally, SNDM system was developed for the purpose of measuring ferroelectric polarization and local anisotropy of dielectrics through the detection of a third-rank nonlinear dielectric constant.

We performed measurement of a lead zirconate titanate (PZT) film sample using SNDM. The result is shown in Fig. 3. From this image, we can confirm that SNDM can resolve in great detail of a domain structure of PZT. The tip used in this measurement was a metal-coated conductive cantilever with a tip radius of 25 nm. This image is of an epitaxial PZT thin film (400 nm)/La-Sr-Co-O/SrTiO₃ substrate.Reference Ganpule, Nagarajan, Li, Ogale, Steinhauer, Aggarwal, Williams, Ramesh and De Wolf²² The strip shaped 90° a–c domain pattern is clearly seen in the figure.

FIG. 3.

SNDM image of an epitaxial lead zirconate titanate thin film on La-Sr-Co-O/SrTiO₃.

III. SNDM FOR 3D OBSERVATION OF NANOSCALE FERROELECTRIC DOMAINS (3D-SNDM)

The other advantage of SNDM in investigation of ferroelectric materials is that it is possible to measure the polarization components both perpendicular (vertical) and parallel (lateral) to the specimen surface by selecting the direction of the applied electric field.Reference Odagawa and Cho^13–Reference Sugihara and Cho¹⁵ The 3D measurement of ferroelectric polarization is quite important because many ferroelectric materials have 3D domain structures.

In ferroelectric materials, the sign of the lowest-order component of the nonlinear dielectric constant (third-rank tensor) changes with an inversion of the polarization direction. Hence, by measuring the sign of the nonlinear dielectric constant, we can obtain the polarization direction. As explained the principle in Fig. 4, in vertical measurement, we apply alternating electric field along the polarization direction and measure the capacitance variation along the same direction, thus SNDM detects the component of polarization perpendicular to the specimen surface [ε(3) component]. On the other hand, in lateral measurement, we apply alternating electric field along the polarization direction too; however, we measure the capacitance variation perpendicular to the polarization direction so that it can detect the parallel component polarization (ε ₃₁₁ component).

FIG. 4.

SNDM principle in vertical and lateral measurements.

Figure 5 shows a schematic diagram of an SNDM system designed to measure in both the vertical and lateral polarization directions. In vertical measurement, the bottom electrode is used to apply an alternating electric field in the vertical direction. In lateral measurement, an alternating electric field is generated by applying an alternating voltage to four electrodes denoted as A, B, C, and D on the electrode plate. By producing a 90° phase shift between the applied voltages, V _A−B (=2V ₁cosθ) and V_C−D (=2V ₁sinθ), a rotating electric field is generated parallel to the specimen surface. By using the rotating electric field, the phase output of the lock-in amplifier directly indicates the lateral azimuth angle of polarization.

FIG. 5.

Schematic diagram of three-dimensional type of SNDM system.

In this experiment, lateral measurement was carried out in the x-cut plane of a multidomain congruent LiTaO₃ single crystal with a thickness of 200 μm, which has a lateral polarization component only.

Figure 6(a) shows a phase image obtained for lateral measurement in the x-plane of the LiTaO₃ crystal. Antiparallel polarization orientations are clearly distinguished in this image. This image further reveals that the c–c domains do not penetrate along the Z-axis contrary to the usual expectation, i.e., ferroelectric polarization is expected to penetrate through the crystal along the polarization direction. In other words, the multidomain structure of the congruent LiTaO₃ crystal generated by the depolarization process was found to be composed of numerous charged domains. Figure 6(b) also shows a phase image in the x-plane of the LiTaO₃ crystal, in which the specimen has been physically rotated by 90°. In these images, where the azimuthal polarization angles are indicated by arrows on the color scale, it can be seen that the phase signals shift by around 90° in accordance with the rotation of the specimen.

FIG. 6.

(a) Phase image in x-cut plane of multidomain LiTaO₃ substrate by lateral measurement; (b) phase image by lateral measurement after physical rotation of specimen by 90°.

IV. NONCONTACT SCANNING NONLINEAR DIELECTRIC MICROSCOPY

Recently, we have developed NC-SNDM operating under UHV conditions.Reference Ohara and Cho¹⁶ As shown in Fig. 7, NC-SNDM utilizes the signal from higher-order nonlinear dielectric constant ε(4) to control the noncontact state (tip–sample gap control) and simultaneously detect the lowest-order nonlinear dielectric constant ε(3). Thus, NC-SNDM can be used to observe the topography and dielectric properties of materials.

FIG. 7.

Brock diagram of noncontact scanning nonlinear dielectric microscopy (NC-SNDM) operated under the ultrahigh vacuum condition.

Equation (2), using the dielectric constant, is a somewhat macroscopic description. However, even if a very localized situation is considered, for example, atomic resolution in mind, because the localized dipole moment also causes capacitance variation, Eq. (2) is still applicable by replacing the macroscopic dielectric constant ε with the local polarizability factor ε _local of a single dipole moment as a matter of form.

In the actual measurements, the ambient condition should be UHV because adsorbed water, which has a relatively high-dielectric constant of the order of 80, on the specimen surface causes the electric field under the tip to broaden under such an atmosphere condition.Reference Ohara and Cho²³ Therefore, an UHV-type SNDM was developed. In this study, the specimen and probe were in a vacuum chamber in which the degree of vacuum was below 1.0 × 10⁻¹⁰ Torr.

To confirm the atomic resolution, a well-established standard sample is required. Therefore, Si(111) was chosen as a representative specimen. In this experiment, an alternating voltage of 3 V_p-p at 30 kHz was applied. Figure 8 shows a simultaneously measured topographical image {image of the height control signal applied to the Z-axis piezoscanner to maintain a constant ε _local (4) signal [Fig. 8(a)]} and the image of the ε _local (3) signal distribution [Fig. 8(b)]. In the topography, the Si(111)7 × 7 atomic structure is clearly recognized; therefore, it is confirmed that the atomic resolution was achieved by NC-SNDM. Moreover, it is also confirmed that the distribution of the ε _local (3) signal was obtained simultaneously. Because the ε _local (3) image has a contrast that corresponds to individual Si adatoms, this image includes information on the dipole moment of single Si adatoms. This is the first successful demonstration of the achievement of atomic resolution in a dielectric microscopic technique.

FIG. 8.

(a) Topography of Si(111)7 × 7 atomic structure observed by NC-SNDM [ε _local(4) feedback]; (b) simultaneously measured dipole moment image by ε _local(3) (−0.5 V bias application).

This technique, which is used to detect dielectric properties and topography, is applicable not only to semiconductors but also to both polar and non-polar dielectric materials. Thus, it is expected that NC-SNDM will contribute to the study of electric dipole moment distribution in insulating materials on the atomic level.

We also succeeded to resolve fullerene (C₆₀) molecule deposited on Si(111)7 × 7 surface by NC-SNDM. In this measurement, at first, we fabricated a C₆₀ thin film with a thickness of one monolayer on Si(111)7 × 7 surface. The measured result is shown in Fig. 9. This image is an ε(3) (1ω _p) amplitude image with the inset of the expanded image in which the fine internal structure of C₆₀ molecule is clearly resolved.

FIG. 9.

Internal structure of C₆₀ molecule observed by NC-SNDM [ε(3) amplitude image].

Next the Si(111)7 × 7 surface covered with 0.37 ML of C₆₀ molecules by NC-SNDM is shown in Fig. 10. To obtain the topological image by the NC-SNDM, the ε(4) signal was utilized for the feedback parameter to maintain the gap between the tip of the probe and specimen. The Si(111)7 × 7 surface could be clearly recognized under the C₆₀ molecules. The origin of the SNDM signal for the Si(111)7 × 7 surface has been previously reported.Reference Cho and Hirose¹⁸

FIG. 10.

ε(3) (1ω _p) phase image (upper left) and topography (upper right) by NC-SNDM. Dipole moment induced from C₆₀ molecule to threefold symmetric site (lower left and lower middle). Absorption probabilities of C₆₀ molecule on Si(111)7 × 7 surface (lower right).

Adsorption site of C₆₀ molecules on Si(111)7 × 7 surface was well established by STM.Reference Wang, Hashizume, Shinohara, Saito, Nishina and Sakurai^24, Reference Hou, Jinlong, Haiqian, Qunxiang, Chanhhan, Hai, Wang, Chen and Qingshi²⁵ For small surface coverage, C₆₀ molecules prefer threefold symmetric sites due to the highly symmetric characteristic of C₆₀ molecular structure.

Simultaneous phase image of ε(3) (upper left of Fig. 10) and the topography by ε(4) (upper right of Fig. 10) are shown. The tendency of phase reversal can be recognized on almost all the C₆₀ molecules, even though phase reversal does not occur on the Si(111)7 × 7 surface.Reference Hirose, Ohara and Cho^17, Reference Cho and Hirose¹⁸ The site on the Si(111)7 × 7 surface at which phase reversal occurs was investigated to understand the relationship between the position of the C₆₀ molecule and phase reversal. The circles drawn in Fig. 10 correspond to C₆₀ molecules where phase reversal did not occur, judging from the unit cell for the Si(111)7 × 7 surface corresponding to the orange dotted triangles drawn in Fig. 10 (upper right). The green circles correspond to C₆₀ molecules on the corner holes, whereas the red circles correspond to C₆₀ molecules on twofold symmetric sites. The yellow circles correspond to C₆₀ molecules whose position cannot be defined due to poor resolution. Surprisingly, no phase reversal for C₆₀ molecules on twofold symmetric sites and corner holes can be recognized, and phase reversal only occurred for C₆₀ molecules on threefold symmetric sites. This is because the electric dipole moment originating from charge transfer from a Si adatom was only induced on threefold symmetric sites.Reference Kobayashi and Cho¹⁹

Therefore, an electric dipole moment cannot be induced on twofold symmetric sites and corner holes because charge transfer does not occur for C₆₀ molecules at these locations.

The ratio of the number of C₆₀ molecules on threefold symmetric sites with phase reversal and the total number of C₆₀ molecules on twofold symmetric sites and corner holes with no phase reversal is similar to that of the number of C₆₀ molecules on the three sites on an Si(111)7 × 7 surface as estimated by STM (as shown in Fig. 10 lower right).Reference Wang, Hashizume, Shinohara, Saito, Nishina and Sakurai²⁴ Therefore, no phase reversal occurs on the twofold symmetric site and corner hole. Thus, it is considered that the phase of ε(3) signal in NC-SNDM reflects whether an electric dipole moment is induced at the interface between the C₆₀ molecule and an individual site.

This means that NC-SNDM can only detect the electric dipole moment induced at the interface between C₆₀ molecule and threefold symmetric site.

Since the technique is applicable not only to semiconductors but also to both polar and non-polar dielectric materials, SrTiO₃ and TiO₂ surfaces were observed by NC-SNDM. Figures 11(a) and 11(b) show the topography and polarization on Nb-doped SrTiO₃(100) surface, respectively. This sample was annealed at 1150 °C for 10 min in UHV condition. In the topography, periodic atomic structure was clearly observed. In the polarization [ε(3)] image, upward polarization was observed. From this result, the surface of this sample is terminated with TiO₂ layer. Next, we also have measured widegap semiconductor TiO₂(100) surface as shown in Fig. 12. This sample was fabricated by heat treatment at 1000 °C for 5 min in UHV condition, too. From the topography [Fig. 12(a)], it is confirmed that one surface structure contains three layers denoted using the symbols XYZ. We think that the microfaceted topography of (110) surface was measured.Reference Hardman, Parkash, Muryn, Raikar, Thomas, Prime, Thornton and Blake²⁶ As shown in the polarization image of Fig. 12(b), upward polarization was detected. We think the signal originates from a Ti cation.

FIG. 11.

Topography (a) [ε(4) feedback] and dipole moment (b) [ε(3) image] on Nb-doped SrTiO₃(100) surface by NC-SNDM.

FIG. 12.

Topography (a) [ε(4) feedback] and dipole moment (b) [ε(3) image] on widegap semiconductor TiO₂(100) surface by NC-SNDM.

V. NEXT GENERATION ULTRAHIGH-DENSITY FERROELECTRIC DATA STORAGE BASED ON SNDM

With the advances in information processing technology, the importance of high-density data storage is increasing. Studies on thermal fluctuation predict that magnetic storage, which plays a major role in this field, will reach a theoretical limit in the near future; thus, a novel high-density storage method is required.

Ferroelectrics can hold bit information in the form of the polarization direction of individual domains. Moreover, the domain wall of typical ferroelectric materials is as thin as the order of a few lattices, which is favorable for high-density data storage. Therefore, we have been studying ferroelectric high-density data storage based on SNDM.

In this section, we describe the fundamental studies of artificially formed ferroelectric nanodomains to obtain the information needed for memory applications. First, we investigated how small nanodomain dots were actually formed. As shown in Fig. 13, at this stage, the smallest artificial nanodomain single dot formed was 2.8 nm in diameter.Reference Tanaka, Kurihashi, Uda, Daimon, Odagawa, Hirose, Hiranaga and Cho²⁷ This single dot was formed by the application of an 8.0 V, 10 ns pulse with a direct current offset of 0.5 V on a congruent lithium tantalate (CLT) thin plate with a thickness of 30 nm. If we can form many bits and maintain this domain dot size, the corresponding memory density will reach 82 Tbit/inch². However, unfortunately, this goal is somewhat difficult to achieve. When we form bit in the vicinity of another bit, the two bits merge with each other. Therefore, it is very important to evaluate how close domain dots can be formed to each other. We formed a nanodomain dot array composed of bits “1” and “0” varying the bit size and spacing. We then obtained an artificial nanodomain dot array with a bit size of 7 nm as shown in Fig. 14.Reference Tanaka, Kurihashi, Uda, Daimon, Odagawa, Hirose, Hiranaga and Cho²⁷ Because the 7-nm ϕ dots in the array are sufficiently resolvable for practical data storage, it is expected that, with further refinements, the system will be applicable as a storage technology. However, it also should be noted that with the current quality of ferroelectric recording media and the level of technology,these very small domain dots can be formed only in a very small area on the medium. As mentioned above, although we have reported that ferroelectric data storage at a density of above 1 Tbit/inch² is possible in principle, this does not necessarily mean that actual information storage, requiring an abundance of bits to be packed together at high density, is easy to achieve. To facilitate actual storage, a large medium of sufficient surface quality and homogeneity is needed. Therefore, demonstration of actual data storage at above 1 Tbit/inch² using ferroelectric materials is important to show whether the technology is really achievable. Figure 15 shows an SNDM image of a 64 × 64 data bit array written on a 30-nm-thick CLT recording medium. The data bits of “1” and “0” were recorded as +z and −z domains, respectively. The bit spacing was 12.8 nm, which is equivalent to an areal data storage density of 4 Tbit/inch².Reference Tanaka and Cho²⁰ Thus, real information storage at above 1 Tbit/inch² was definitely demonstrated with ferroelectric medium.

FIG. 13.

Smallest artificial nanodomain single dot formed was 2.8 nm in diameter.

FIG. 14.

Artificial nanodomain dot array with a bit spacing of 7 nm formed by 8.5 V, 5 nsec pulses applied with a direct current offset of 0.5 V.

FIG. 15.

Actual information recorded at a bit spacing of 12.8 nm (areal recording density: 4 Tbit/inch²). 64 × 64 bit data written on a congruent lithium tantalate (CLT) single crystal formed on a 30-nm-thick CLT plate.