SrTiO3 (STO) thin films of different thicknesses were deposited on MgAl2O4 (MAO) substrates to investigate the in-plane strain effect on the soft-mode frequency of the STO films. X-ray reciprocal space mapping (X-RSM) results indicate that there was no relaxation of the in-plane lattice strain of the STO films on MAO. Shifts in the soft-mode frequencies with a decrease in the film thickness were observed using terahertz time-domain spectroscopy (THz-TDS). However, despite the larger lattice mismatch between STO and MAO than that between STO and DyScO3 (DSO), the shifts in the soft-mode frequencies of the STO films on MAO were smaller than those on DSO. The results indicate that the soft-mode frequencies of the STO films on MAO are affected by the c-axis (out-of-plane) lengths.
Strontium titanate (STO) is a transition metal oxide that has a perovskite structure. Pure bulk single-crystal STO is a known quantum paraelectric that does not undergo a ferroelectric phase transition even at temperatures close to 0 K, and its permittivity is as high as 104 at low temperatures [
In this study, we measured the thickness dependence of the dielectric dispersions of STO thin films on MAO substrates using terahertz time-domain spectroscopy (THzTDS), and the in-plane lattice constants of the films were determined using X-ray reciprocal space maping (XRSM). Moreover, we measured the dielectric dispersions and lattice constants of STO films on (La0.3Sr0.7)(AL0.65 Ta0.35)O3 (LSAT) and DSO substrates for comparison to elucidate the lattice strain effect on the dielectric characteristics.
We deposited STO films with thicknesses of 60, 120, 360, and 650 nm on MAO substrates by pulsed laser deposition. STO thin films were also deposited on LSAT and DSO substrates to compare the relationship between the in-plane strain induced by the lattice mismatch and the extension or contraction of the c-axis. A q - 2q X-ray diffraction (XRD) method was used to evaluate the crystalline quality and determine the c-axis lengths of the films. Only (00l) diffraction peaks were observed in the q - 2q XRD patterns, which indicated that the films were good c-axis orientation films. Additionally, X-RSM using a Rigaku SmartLab diffractometer was used for the 360 nm thick STO film on MAO to observe the inplane lattice constant. The dielectric dispersions of the STO films were observed using a broadband THz-TDS system with a 4-dimethylamino-N-methyl-4-stilbazolium tosylate (DAST) crystal as the terahertz emitter. DAST is an organic nonlinear optical crystal that can emit broadband terahertz waves by pulsed laser irradiation except at around 1.1 THz where a large absorption peak of the DAST exists. Details of the experimental setup have been reported elsewhere [
Q||(1/Å) correspond to the a-axis (in-plane) of the STO film. The origin in Q||-axis is set at the (224) reflection of MAO. The two sharp peaks in the lower part of
We fitted the data to both the real and imaginary parts of the dielectric dispersion using a classical dampingoscillator dispersion model given by the following Equation:
where e∞ is the high-frequency dielectric constant, ∆e is the dielectric strength, wTO1 is the soft-mode frequency, and gTO1 is the damping constant. The dashed lines in
From the experimental results, it seems that not only the in-plane strain but also the c-axis length has a significant effect on the in-plane dielectric characteristics of STO films on MAO. The compressive in-plane strain in the film should induce an extension of the c-axis length in order to decrease the energy increased by the lattice deformation. This is implied by the lower-frequency shift of the soft-mode frequencies with a decrease in the film thickness as shown in
the soft mode and also an increase in the critical temperature Tc of STO thin films on MAO. Kim et al. [
STO thin films of different thicknesses were deposited on MAO, LSAT, and DSO substrates. The in-plane lattice constant of the 360 nm thick STO thin film on MAO was found to correspond to that of the MAO substrate, indicating that there was no relaxation of the in-plane strain in the film. The c-axis lengths of the STO film on MAO were determined to be longer due to in-plane compressive strain; however, the values were smaller than that expected from the trends observed in the other substrates. The soft-mode frequencies of the films shifted to lower frequencies with a decrease in the film thickness. The minimum soft-mode frequency of a STO thin film on MAO was found to be about 1.6 THz. These results indicate that the c-axis length of a STO thin film affects the in-plane dielectric characteristic of the STO film and that lattice defects prevent an increase in the Tc of the films.
The authors received technical support from T. Tanaka and T. Takehara for the X-RSM measurement. This study was supported by a Grant-in-Aid for Scientific Research (A) (No. 22246043) and the Core-to-Core Program of the Japan Society for the Promotion of Science (JSPS).