Gd-doped ceria Ce0.9Gd0.1O2−x (CGO) is a lead free compound with unusual mechanical and electromechanical properties. Off-center shift of the Ce4+ ions in the cubic oxygen environment away from oxygen vacancies under an action of the external electric field in CGO results in appearance of the “giant” electromechanical strain at low frequencies . The effective electrostriction coefficient measured by the cantilever method at low frequencies was M e = 6.47 ± 0.43 ×10−18 m2·V−2 [1, 2]. It is, therefore, attractive for micromechanical applications, if the same effect is pertinent to thin films. Cantilever technique does not have enough sensitivity, and precise laser interferometry method has to be used in order to measure sub-Angstrom electromechanical displacements in thin films. In this work, we built a simple single-beam Michelson interferometer with the high vertical resolution capable of the measurements of electrostriction effect in thin films and report for the first time the electrostriction coefficient value in the Ce0.9Gd0.1O1.95 layers of the thickness of about 1 μm.
For this study we used CGO thin films samples. Ceramic samples were prepared by the solid synthesis route as described in the earlier work [3, 4]. The surface was polished to optical quality and coated by Al electrodes via magnetron sputtering. Thin films were prepared on the 250 μm thick n-Si++ wafers via sequential RF magnetron sputtering of the 150 nm thick of Cr layer, ≈900 nm thick CGO-layer, 300 nm thick of Cr layer. Cr layers served as the top and bottom electrodes. Top electrodes were deposited via shadow masks. The diameters of the top electrodes were 2 mm.
For the measurements of the small electric field induced displacements we used a standard scheme of single-beam Michelson homodyne. interferometer as described in many publications (see e.g. [5, 6]). The schematic of the interferometer setup is shown in Fig. 1. Depending on the path length difference between the interferometer arms, small displacements of the sample surface produce a change in detected light intensity anywhere between the maximum theoretical sensitivity and zero. In order to maintain the working point between the minimum and maximum position of the photodetector, a PID-feedback system was used to stabilize the system against the slow optical path-length drift with the cut-off frequency of 5 Hz. The system compensates for the drift below 5 Hz and assumes that higher frequency is due to electric field induced displacements. The system was as compact as possible with the optical path of each arm about 1 m.
We used a single-mode stabilized solid state diode laser LCM-S-111-20-NP25 (Laser-compact, Russia) with a wavelength 532 nm and a power 20 mW, lock-in amplifier SR830 (Stanford Research, USA), multifunction data acquisition board USB-6251 (National Instruments, USA), and signal generator Agilent 33210A (Keysight Technologies, USA). For the PID-feedback loop piezo actuator P-841.01 and piezo controller E-709.SRG (Physik Instrumente (PI), Germany) were used.
The minimal displacements (interferometer resolution) are determined by the noise in the laser and in photodetector by the minimal voltage measured by the lock-in amplifier. On the top of this, the system experiences also a vibrational noise from the environment amplified by the mechanical resonances in the sample holder. In order to reduce this noise, we used a special fixture for the sample holder (Fig. 1). The thin film sample was rigidly glued to the small steel rod with the contact area of 5 mm2 in the central part. Thus, the effect of bending resonances on the vibrational noise was avoided. Also, the part of the interferometer containing both arms were isolated from the environment using a special box made of foam boards, foam rubbers, and aluminum frame. Figure 2 shows the equivalent displacement noise of the system in the range 2-15 kHz measured for the time constant of lock-in amplifier 100 ms. It is clearly seen that the vibrational noise still dominates the response and the resolution varies in the range 10−2÷ 10− 4 Å depending on frequency. Thus, the frequency dependence of the electrostrictive displacements can be measured with high enough accuracy.
The performance of the interferometer was validated by measuring the displacements in a standard ceramic PZT5A pellet . The frequency response within the range of 1 to 10 kHz (Fig. 3a, red curve) was almost flat with a small number of spurious resonances that prevented accurate measurements in a broad frequency range. In comparison, strong resonance behavior was observed in the film in a standard configuration, i.e. when it was glued by entire surface (black curve). It demonstrates effective suppression of the bending effect in bulk ceramics. Measured piezoelectric coefficient of PZT5A was 374 ± 5 pm/V. This value is in a good agreement with the table value for the piezoelectric coefficient d33 of PZT5A . To verify the linearity of the setup, we measured the AC-voltage dependence of displacements in congruent lithium niobate (CLN) sample (Z-cut) that has negligible own non-linearity. Figure 3b demonstrates that the amplitude of the displacement is linear with the amplitude of applied voltage up to 5 V. The resulting piezoelectric coefficient of CLN sample d33 was 6 pm/V, which also corresponds to the table value . The minimum displacement measured in this case was 2·10−2 Å (signal to noise ratio 1).
The results of the electrostriction measurements in CGO thin film samples are shown in Figure 4. Measurements were done in the frequency range 5-30 kHz (second harmonic) and voltage amplitudes up to 6 V. The frequency dependence was almost flat with a tendency to decrease up to a clear resonance at 20.1 kHz. This peak is attributed to the extensional resonance of substrate that cannot be avoided in the present setup. The measured effective electrostriction coefficient was M33 = 4.3 · 10−21 m2/V2 at frequency 13.49 kHz (Fig. 4a, b). This value is much lower than that reported in Ref. , measured in ceramics at low frequency. Measurements below 1 kHz are difficult in our setup because of the increase of vibrational noise from the nearby machines and natural limit due to the cut-off frequency of the feedback system. Low value of M33 can be also attested to the clamping effect of the substrate and smaller grain size as compared to ceramics.
For the interferometric studies, the surfaces of the ceramic samples were polished and the reflecting Cr-electrodes were sputtered using Edwards Auto 500 electron-beam evaporation system. Measurements of the electrostrictive coefficient M33 were performed by applying AC voltage with frequency f, and the surface displacement was measured at 2f using the corresponding feature of the lock-in. The time constant of the lock-in was always 300 ms.
In our setup, we could also measure a transverse electrostriction coefficient M13. In this case, 700 nm CGO thin film was allowed to bend during DC voltage application of 4.9 V. In this case, bending moment develops, which translates into the displacement of the top surface of the film (see schematic in Fig. 5a). The effective electrostriction coefficient M13 can be calculated from this data using the Stoney formula  (Fig. 5b) that is generally used to calculate the residual stress value:
where Y s is the Young's modulus of substrate (179 GPa), ν s is the Poisson's ratio (27), t s is the thickness of the substrate (250 um), t f is the thickness of the film (700 nm), and ΔR is the change of the curvature radius of the bent sample (1.25 m). Then, the stress value can be used in calculation of M13 coefficient:
where γ 13 is the stress coefficient (σ·E−2, ≈600 kPa·kV−2·cm−2), Y f is the Young's modulus of film (190 GPa), and ν f is the Poisson ration of the film (43). The estimated electrostrictive coefficient was M13 = 1.7·10−16 m2/V2, which is very close to the value reported in Refs. [1, 2]. We should take into account that this value is measured at DC (i.e., at zero frequency) in the partially clamped conditions. That effective electrostriction coefficient is determined not only by the intrinsic mechanism due to ionic displacements and bond stretching, but can also depend on the competition between intragrain conductivity and Schottky behavior of the electrodes; large difference between the DC and high frequency measurements is not a surprise. Further measurements need to clear out the electrostriction mechanism in the CGO films.
Highly sensitive single beam interferometer to measure electrostrictive displacements was developed in this work. Resolution of the interferometer varied in the range 10−2÷ 10− 4 Å depending on frequency and the minimum displacement measured was 2·10−2 Å. Gd-doped ceria Ce0.9Gd0.1O1.95 (CGO) thin films have been investigated to get both M33 and M31 coefficients. Interferometric measurements showed relatively low electrostrictive coefficients at high frequency (M33 = 4.3·10−21m2/V2) possibly due to elevated impedance of electrodes at high frequencies. Applying the DC voltage to the film provided giant displacement in thin film and the calculated transverse electrostrictive coefficient was M13 = 1.7·10−16 m2/V2.
The equipment of the Ural Center for Shared Use “Modern Nanotechnology” of the Ural Federal University was used. The research was made possible by Russian Foundation for Basic Research (grant 15-52-06006-MNTI_a) and by government of the Russian Federation (Act 211, Agreement 02.A03.21.0006).