Enhancement of Extraordinary Size Effect on CaRuO3 Ultrathin Films

In a previous report, 25 Å periodic metal–insulator transitions dependent on the thickness of CaRuO3 ultrathin films were discovered. Compared to the conventional size effect caused by quantum wells, the rate of change is a few billions of times greater at low temperatures. Although the electrical resistivity of insulating state differs by several orders with the film thickness, the enhancement trigger was not clarified. In this study, it is clarified that the magnitude of the extraordinary size effect varies with the element supply ratio owing to precise control of the molecular beam rates of calcium and ruthenium. The supplied calcium over ruthenium ratio Ca/Ru = 1.2–1.8 during CaRuO3 deposition results in a stoichiometric ratio of Ca:Ru = 1:1 on the CaRuO3 films. Calcium‐rich elemental supply conditions result in large electrical resistivity variations. Electrical resistivity oscillations with periods of T = 23.4 and 26.3 Å are observed for the growth conditions of Ca/Ru = 1.2 and 1.6, respectively. Furthermore, a flat surface with a roughness of ≈2 Å is required to observe the size effect. Thus, the insulation of an extraordinary size effect is enhanced in CaRuO3 ultrathin films grown under the condition of calcium‐rich Ca/Ru ≈ 1.6.


Enhancement of Extraordinary Size Effect on CaRuO 3 Ultrathin Films
M. Sakoda films. [1][2][3] Size effects originating from quantum wells is a unique phenomenon observed at artificial low dimensions [4][5][6][7][8][9] in films with thicknesses of the order of de Broglie wavelengths, which corresponds to the Fermi wave length l F in crystals. For example, the period of quantum size effect is ≈400 Å in the semimetallic bismuth, and approximately angstrom in monoatomic metals such as lead and palladium. [7][8][9] Till date, the artificial low-dimensional properties of many compounds remain undeveloped. This is because growing high-quality single-crystal ultrathin films is challenging. As novel physical properties are expected to be observed in the artificial low dimensions of compounds, the fabrication of ultrathin films of compounds having novel properties is significant. This study focused on ruthenium oxides as the target compounds, which exhibit various novel properties (e.g., high-T c superconductor Ca 2 RuO 4 in thin flakes, [10] and anisotropic superconductor Sr 2 RuO 4 [11] ). The quasi-2D structures within layered perovskite compounds are considered to cause the superconductivity. We fabricated ultrathin films of CaRuO 3 (CRO), which has the basic crystal structure among the ruthenium oxides. CRO is a GaFeO 3 -type crystalline structure comprising a simple orthorhombic lattice (space group: Pbnm). [12][13][14][15][16] The RuO 6 octahedrons responsible for conduction are linked in a 3D direction. Pure CRO single crystals with a high residual resistivity ratio have been reported for bulk and thin films. [17][18][19][20][21] In particular, good epitaxiality on NdGaO 3 substrates has been reported through the observation of a clear interface via transmission electronic microscopy. [21] Therefore, high-quality CRO ultrathin films can be grown to create artificial low-dimensional electrical systems on NdGaO 3 substrates. [3] CRO exhibits non-Fermi liquid behavior, slightly heavier effective mass, and a flat energy band. [22][23][24][25][26][27][28][29][30] Owing to its positioning between the insulating and metallic phases in the Mott-Hubbard model, it is prone to physical property changes depending on various factors. CRO thin films have been reported to transform to metals or insulators under similar growth conditions via the sputtering method. [31,32] A recent study reported the alternating metal-insulator transitions depending on thickness with 25 Å period in CRO ultrathin films below using the molecular beam epitaxy (MBE) method. [3] CRO ultrathin films exhibit several orders of magnitude change in electrical resistance depending on thickness. A change in film thickness of one nanometer from 75 to 85 Å enhances In a previous report, 25 Å periodic metal-insulator transitions dependent on the thickness of CaRuO 3 ultrathin films were discovered. Compared to the conventional size effect caused by quantum wells, the rate of change is a few billions of times greater at low temperatures. Although the electrical resistivity of insulating state differs by several orders with the film thickness, the enhancement trigger was not clarified. In this study, it is clarified that the magnitude of the extraordinary size effect varies with the element supply ratio owing to precise control of the molecular beam rates of calcium and ruthenium. The supplied calcium over ruthenium ratio Ca/Ru = 1.2-1.8 during CaRuO 3 deposition results in a stoichiometric ratio of Ca:Ru = 1:1 on the CaRuO 3 films. Calcium-rich elemental supply conditions result in large electrical resistivity variations. Electrical resistivity oscillations with periods of T = 23.4 and 26.3 Å are observed for the growth conditions of Ca/Ru = 1.2 and 1.6, respectively. Furthermore, a flat surface with a roughness of ≈2 Å is required to observe the size effect. Thus, the insulation of an extraordinary size effect is enhanced in CaRuO 3 ultrathin films grown under the condition of calcium-rich Ca/Ru ≈ 1.6.

Introduction
Interesting physical properties, such as high-temperature superconductivity, topological properties, and charge/spin density waves, have been discovered in low-dimensional conductive materials. The degree of freedom of electrons is artificially enclosed in low dimensions in films with a thickness of the order of nanometers. These are referred to as ultrathin the electrical resistivity by up to three and nine orders of magnitude at room and low temperatures, respectively. Moreover, compared to the conventional quantum size effect of bismuth, it exhibits a revolutionary oscillation of 10 000 times and over billions times larger at room and at low temperatures, respectively. [5,6] It is accompanied by an activation energy of 2.4 eV, which cannot be explained using the conventional mechanism based on a quantum well structure. Thus, this study proposed a mechanism of the Mott-Peierls transition owing to the anisotropy of the size effect and the nesting property in the Fermi surface. [3,[33][34][35][36][37] The metallic state of the extraordinary size effect, which is the minimum value of electrical resistivity, exhibits a similar electrical resistivity as the bulk CRO. However, the maximum resistivity at 85 Å thickness differed from that at 35 Å by eight digits at 4.2 K. Although significant differences in scaling insulation have been observed, the enhancement requirements remain unclear. This study examined the growth conditions for enhancing the insulator transition. Molecular beam supply affects the properties of thin films. The supply of the constituent elements of CRO is expected to be related to the extraordinary size effect. This study fabricated CRO ultrathin films of calcium and ruthenium through the precise control molecular beam rates using the MBE method. [38][39][40] The growth window of the Ca/Ru ratio for single crystals of CRO ultrathin films was determined to investigate the nature of the size effect depending on the respective conditions. Thus, this study aimed to identify the enhancement conditions for the scale-dependent revolutionary increase in electrical resistivity.

Characterization of CRO Single Crystal Films
All the CRO thin films were prepared using the MBE method. Figure 1a shows a schematic of the MBE equipment. To precisely control the amounts of supplied elements, molecular beams were detected and controlled using a fresh electron impact emission spectroscopy (EIES) filament. The grade of CRO ultrathin films was assured through an examination of their quality as crystals. First, CRO thin films with thicknesses of t = 15, 50, 100, and 200 Å were grown and CRO quality was evaluated. The supplied Ca/Ru molar ratio was optimized as 1.4-1.8 to fabricate CRO films with Ca:Ru = 1:1 as per the stoichiometric ratio ( Figure S1, Supporting Information). We evaluate the crystallinity of CRO thin film grown at the Ca/Ru elemental ratio of 1.7 as a typical condition that can fabricate pure single crystals.   Figure 1d and Figure S3b,c (Supporting Information) show the corresponding peaks that originated from CRO. The 200 Å thin CRO film exhibited pronounced XRD peaks. [21] As CRO has a crystal structure similar to that of NGO substrates, the respective peak positions were close to each other and those of CRO were slightly on the wideangle side. Electron back-scattering diffraction (EBSD) was utilized to assign CRO compound ( Figure 1e). Consequently, CRO identical Kikuchi patterns were observed, and the index of each diffraction plane was determined. CRO films grew in the (110) plane with the same orientation as the NGO (110) substrate. It has been proven that CRO films grow epitaxially along the NGO substrate lattice. The Ca and Ru element ratios Ca/Ru in the CRO films were measured using energy dispersive spectroscopy (EDS). The Ca/Ru ratios were 1.05, 1.13, 0.90, and 1.05 for CRO films with thickness of 15, 50, 100, and 200 Å, respectively. Considering the calcium-rich supplied element ratio of Ca/Ru = 1.7, the calcium elements re-evaporated from the substrate surface. Moreover, RuO x gas was shown to form under higher temperatures and stronger oxidation conditions. [21] The surfaces of CRO thin films were observed via atomic force microscopy (AFM) and scanning electron microscopy (SEM). Figure 1f and Figure S4a-c (Supporting Information) show the surface structures at each film thickness. The average surface roughness values R a were 2.39, 2.00, 1.96, and 2.04 Å for 15, 50, 100, and 200 Å film thicknesses, respectively. R a were nearly identical and independent of film thickness and thus reproducible as ≈2 Å. Figure 1g and Figure S5 (Supporting Information) show the SEM images of the corresponding surface. Owing to the high degree of flatness, no noticeable structure was observable without tilt. When the thin film was tilted 70°, a flat surface structure was observed.

Scaling Dependence of CRO Ultrathin Films Grown at Ca/Ru = 1.2
Next, the difference in the extraordinary size effect for each element supply ratio was clarified. CRO ultrathin films of various thicknesses were prepared at Ca/Ru = 1.2, 1.6, and 1.8 molecular beam rate conditions, under identical oxygen pressure and deposition temperature conditions. Consequently, the thickness dependence for each deposition condition of Ca/Ru ratio was investigated through measurements of the electrical resistivity as a function of temperature for each ultrathin film. The differences were clarified in the scale variation of electrical resistivity under the deposition conditions. The ultraviolet photoemission spectroscopy measured while etching showed that the surface (≈1 nm) was oxidized and insulated. [3] The oxide layer led to errors in this study which examined the scaling dependence on the order of angstrom. Therefore, the insulating barrier CaF 2 was deposited in situ at low temperatures to protect the surface of the CRO ultrathin films from atmospheric contamination.
First, the scaling dependence of electrical resistivity was examined by preparing CRO ultrathin films with thicknesses of 10-110 Å at Ca/Ru = 1.2 deposition conditions. Sharp RHEED patterns were observed in all thin films of 10-110 Å thicknesses ( Figure S6, Supporting Information) with good reproducibility www.advelectronicmat.de and high crystallinity. Furthermore, the streak pattern indicated a flat surface. Moreover, no differences were observed among the patterns. However, sharp semicircular point sequence patterns were observed in certain films. ( Figure S7, Supporting Information). Two rows of Laue zones accompanied with the Kikuchi line were observed. Furthermore, complete flat crystalline planes were observed in the CRO ultrathin films. Figure 2a-c shows the electrical resistivity as a function of temperature on CRO films with corresponding thicknesses prepared under the deposition condition of Ca/Ru = 1.2. CRO films with a thickness of 10 Å were insulating at low temperatures. These were induced to epitaxial strain from NGO substrates with larger lattice constants. Furthermore, the CRO ultrathin films with a thickness of 20 Å were metallic in nature similar to the bulk sample. [22][23][24][25][26][27][28][29] Whereas, those with a thickness of 25-35 Å again exhibited an upturn in electrical resistivity at lower temperatures.
Similarly, the electrical resistivity of CRO ultrathin films increase or decrease depending on the film thickness in Figure 2b,c. The electrical resistivity of CRO ultrathin films at 300 and 4.2 K are plotted as a function of film thickness ( Figure 2d). The minimum resistivity was in the order of 10 −5 Ω cm as previously reported. [3] However, the maximum value of electrical resistivity was enhanced to 10 −3 Ω cm. Thus, the electrical resistivity of CRO alternated between low and high values depending on the film thickness. Therefore, extraordinary size effects exhibiting tens of times changes in electrical resistivity depending on the film thickness were observed.
The characteristic feature of the film thickness alternation in electrical resistivity was that it reached maximum at ≈2 mΩ cm, as shown by the yellow dotted line. The flat ceiling maximum was not observed in the previous report. The reason is studied from the perspective of surface structure in a later section. Furthermore, a period of variation of T = 23.4 ± 0.9 Å www.advelectronicmat.de was determined from a linear fitting of the film thickness plot of electrical resistivity minima (Figure 2e). The thicknessdependent period was comparable to the previously reported T = 24.0 ± 1.2 Å. [3] 2.3. Scaling Dependence of CRO Ultrathin Films Grown at Ca/Ru = 1.6 CRO ultrathin films with thicknesses of 8-110 Å were prepared under the deposition conditions of Ca/Ru = 1.6. Subsequently, the electrical resistivity of each ultrathin film was measured to study its scaling dependence on film thickness. The sharp streak patterns of CRO ultrathin films are shown in Figure S8 (Supporting Information). They exhibited high crystallinity and good surface flatness. Figure 3a-d shows the electrical resistivity as a function of temperature on the corresponding CRO films. The CRO ultrathin film with a small thickness of 8 Å was insulating in nature, similar to the CRO ultrathin film grown at Ca/Ru = 1.2 condition (Figure 3a). With increasing film thickness, the electrical resistivity of CRO decreased stepwise (up to 15 Å thickness). Thereafter, the electrical resistivity began to increase at t = 20 Å. Insulating and metallic behaviors were observed in CRO ultrathin films with thickness above 20 Å (Figure 3b-d). The electrical resistivity of each CRO ultrathin film at 300 and 4.2 K is plotted as a function of the film thickness ( Figure 2e). The electrical resistivity was in the order of ρ = 10 −4 -10 2 Ω cm, which is a large alternation compared to the scaling dependence of CRO grown at Ca/Ru = 1.2 deposition condition. A difference of only 5 Å film thickness from 15 to 20 Å resulted in a drastic change in electrical resistivity of two and six digits at room and low temperatures, respectively. The electrical resistivity was approximately one order higher even at the minimum value compared to the thickness dependence grown at Ca/Ru = 1.2. Thus, it was proposed that CRO ultrathin films exhibited a high electrical resistivity approach applicable to the Mott insulator phase in Mott-Hubbard model. [3] The significant difference was observed in the enhancement of insulating depending on the film thickness. As all minimum values of resistivity were in the order of 10 −4 Ω cm, no significant differences appeared among the minimum resistivity values. However, the maximum of resistivity exhibited specific different values depending on the film thickness. It reached 10 2 Ω cm at room temperature in the CRO with a small film thickness of 20 Å. The electrical resistivity was as low as the order of 10 −2 Ω cm at other the maximum, that is, insulating properties were suppressed at large film thicknesses. The difference was not because of surface roughness, because no such difference was observed depending on film thickness below 200 Å shown in Figure 1f. Thus, after plotting the film thickness for each of the maxima and minima of resistivity, a period was determined as T = 26.3 ± 1.4 Å from linear fitting (Figure 2f). Therefore, the period in case of 25 Å, which is same as in the previous report, was reproduced. CRO ultrathin films were prepared under deposition conditions with a molecular beam rate ratio of Ca/Ru = 1.8. Figure S9 (Supporting Information) shows the RHEED patterns of CRO ultrathin films with thicknesses of 10-100 Å, respectively. Uneven streak patterns were observed. A few of them exhibited spotty patterns. Increased Ca supply during deposition caused suppression of flattening on film surface. All films exhibited a behavior of increasing electrical resistivity with decreasing temperature ( Figure S10, Supporting Information). High electrical resistivity of ρ > 1 mΩ cm was observed, while others yielded ρ = 10 3 Ω cm at room temperature, which is equivalent to that of typical semiconductors. The electrical resistivity of each film at 300 K was plotted as a function of thickness ( Figure S11, Supporting Information). The range of electrical resistivity was very high, on the order of ρ = 10 −3 -10 3 Ω cm at room temperature. Nevertheless, no periodic fluctuations were found owing to reduced reproducibly. Moreover, a large difference in electrical resistivity of more than five digits was observed at a film thickness of 60 Å even when attempting fabrication under the same conditions. The RHEED patterns of films with large electrical resistivity were sharp with minimal irregularity ( Figure S9n, Supporting Information). Surface flatness was necessary for insulating properties. The electrical resistivity was enhanced by six digits at room temperature compared to the electrical resistivity of CRO bulk. This shows the potential to further enhance the size effect by reproducibly growing highly planar CRO ultrathin films under conditions with large Ca rates. The details of the relationship between these CRO surface structure and the extraordinary size effect is presented in the next section.

Surface Structure of CRO Ultrathin Films
Obvious differences appeared in the thickness-dependent behavior of the electrical resistivity for element supply ratio Ca/Ru = 1.2, 1.6, and 1.8. The RHEED patterns showed that the surface of the CRO films was related to the enhancement of resistivity. We characterized the surface state of CRO ultrathin films with thickness of 30 Å grown at Ca/Ru = 0.8-2.4 by AFM to clarify the differences. Although the RHEED patterns exhibited sharp streaks for Ca/Ru ≤ 2.0, its sharpness was reduced at Ca/Ru = 2.4 ( Figure S12, Supporting Information). The average surface roughness R a of the CRO ultrathin films was measured by AFM and plotted in Figure 4a as a function of Ca/Ru growth condition. The Ra at Ca/Ru = 1.4 was the flattest as 1.48 ± 0.10 Å, which is comparable to the Ra of the NGO substrate of 1.3 Å. The CRO films contained elements of Ca:Ru = 1:1 stoichiometric ratio owing to the reevaporation of Ca around growth condition of Ca/Ru ≈ 1.4 ( Figure S2, Supporting Information).
The Ra increase was obtained as R a = 2.36 ± 0.21 and 3.07 ± 0.83 Å for Ca/Ru = 1.6 and 1.8, respectively. The R a corresponding to the uneven streak patterns at growth condition of Ca/Ru = 1.8 are shown in Figure S9 (Supporting Information). The R a was ≈4.66 ± 2.18 Å at Ca/Ru = 2.0. It became rougher with increase in the Ca/Ru ratio under the deposition condition of Ca/Ru ≥ 1.4. Accordingly, the size dependence was not observed with growth condition of Ca/Ru = 1.8 because www.advelectronicmat.de the surface roughness suppressed the size effect ( Figure S11, Supporting Information). The CRO film grown at Ca/Ru = 1.8 contained various thicknesses. When certain areas of the thin film were insulators, they also contained metallic areas with different thicknesses, resulting in a reduction in the clarity of the metal-insulator transitions. Thus, a small roughness of R a ≈ 2 Å was required for the extraordinary size effect.
However, the roughness of the film surface dramatically increased at growth condition of Ca/Ru ≤ 1.2. The roughness was R a = 7.86 ± 1.94 Å at Ca/Ru = 1.2. The films grown at Ca/Ru = 1.0, 0.8 also exhibited similar surface roughness. Moreover, the scaling dependence (shown in Figure 2d) was observed in films grown at Ca/Ru = 1.2, despite the large R a . However, there was poor reproducibility in terms of the insulating properties for the films grown at Ca/Ru = 1.8, which produced a thin film with a smaller R a . Differences in thickness in the order of angstroms in CRO ultrathin films cause metal-insulator transitions.
The question that arises is why the size effect appeared in the films grown at of Ca/Ru = 1.2 despite large R a . We observed the details of each surface structure with AFM to elucidate the reason (Figure 4b-i). The surface roughness of the CRO ultrathin film increased over the entire surface with increasing calcium supply ratio for Ca/Ru ≥ 1.4. In contrast, the www.advelectronicmat.de structure was clearly divided into flat areas and dented valleys at Ca/Ru ≤ 1.2. Thus, there was a large difference between high and low areas in a film. The cross-sectional roughness of the film surface grown with Ca/Ru = 1.2 was measured for certain areas to investigate the details of the structure. As shown by the blue lines in Figure S14a,b (Supporting Information), the crosssectional roughness in the highlands was flat as R a = 0.8 and 1.6 Å. The flat surfaces were in the order of 100 nm in size. The highlands caused by the Laue zone of RHEED are shown in Figure S7 (Supporting Information). In contrast, the roughness values of the cross section across the valley were R a = 11.9 and 11.2 Å, as shown in Figure S14c,d (Supporting Information), respectively. Practically, the CRO ultrathin films grown in the Ca/Ru = 0.8-1.2 contained 10-100 nm sized valleys on the surface, where tough RHEED patterns appeared excellent owing to very sharp Laue zone and streaks. These ultimately flat highlands of ≈1 Å caused the extraordinary size effect on electrical resistivity although the valley structure on surface caused the ceiling characteristics of the electrical resistivity alternation below 2 mΩ cm, as shown in Figure 2d. At film thicknesses where the highlands were insulated by the 25 Å period size effect, the valley part was not insulated because it was ≈10 Å thinner. The image is consistent with the suggested density wave stage where in charge or spin achieves commensurability at the thickness of 25 Å. Although the flat area becomes commensurate and insulating, the deep valleys are incommensurate to have current paths ( Figure S15, Supporting Information). Accordingly, the whole film cannot be insulated.
Although such differences in electrical resistivity which are observed in micro-areas of convexity and concavity on thin-film surfaces have been confirmed by scanning microwave microscopy, [41] no size effect was observed on the thin films with an overall surface roughness of a few nanometers. Consequently, as the valleys become current paths, the electrical resistivity was not fully enhanced, as shown in Figure 2d. The periodicity of size effect, surface roughness, and RHEED patterns are summarized in Table 1 for the CRO ultrathin films grown with the molecular supply ratio Ca/Ru = 1.2, 1.6, and 1.8.

STEM Observations
The structure of the RuO 6 octahedron in ruthenium oxides is dominant for physical properties. [13,[42][43][44][45] This study clarifies the changes in the structure of the RuO 6 octahedron contained in CRO at the interface above the substrate. The structure and composition of the samples were investigated via atomic-solution inverse contrast annular bright-field (ABF)/ high-angle annular dark field (HAADF)-STEM imaging. Figure 5a shows a schematic of CRO structure while Figure 5b-e shows the ABF and HAADF imaging of the films grown at Ca/Ru = 1.2 and 1.6, respectively. The elements in Figure 5b-e are observed at the same position. Ca and Ru are visible in the HAADF image, whereas O, a lighter element, is visible using ABF. [43][44][45] The periodic arrangement of Nd, Ga, Ca, and Ru can be seen in the vicinity of the interface from HAADF imaging in Figure 5c,e and Figure S16 (Supporting Information). The projected angle θ (defined in Figure 5f inset) between the Ru and O atoms in Figure 5d was measured and plotted at the Ru and Ga sites above and directly below the interface indicated by the dotted line, respectively (Figure 5f). The Ga site at the interface deviates significantly, although the deviation is within the expected tilt angle of ±16.4° of the NGO substrate below the interface. In contrast, the absolute value of θ at the Ru site tends to be smaller when farther from the vicinity of the interface. Since the NGO (110) substrate is +0.4% and +0.6% larger than the CRO for the in-plane [110] and [001] directions, respectively, the substrate interface is subjected to stronger tensile strain. Atomic positions reported for the bulk sample represent the tilt angle as large as θ = 15.5°. The slope is large up to the first to fourth layer, indicating that it is heavily influenced by the substrate. At the fifth to seventh layer, the slope is within the range of angles expected in the bulk. Above the eighth layer, the tilt angle is smaller than the bulk value.
Next, we measured the lattice distances using θ-2θ scan ( Figure S17a, Supporting Information) to investigate the crystal structure. The (220) peak of the CRO fabricated under the growth condition of Ca/Ru = 1.0 appeared at the high angle of the substrate as reported previously. The length of RuO 6 sites to the growth direction was almost the same d = 3.845 Å under Ca/Ru = 1.0 condition compared to d = 3.847 Å estimated from the bulk samples. The (220) peaks of the CRO films grown at Ca/Ru = 1.2 and 1.6 were observed at a lower angle than the substrate peak, and their lattices were d = 3.915 and 3.891 Å extended by 1.8% and 1.2% compared to the bulk, respectively.
When a film achieves tensile epitaxial strain in-plane, the lattice generally shrinks in the vertical direction. The pseud perovskite SRO vertically extends/shrinks under compressive/ tensile strain on various substrates, respectively. [45] However, the CRO films grown under Ca-rich conditions are elongated in the plane-perpendicular direction despite the tensile strain from the NGO substrate. Similarly, the CRO film on STO (001) substrates is extended to out of plane as well as in-plane. [31] We consider the RuO 6 octahedral as the cause of the lattice expansion of CRO to both in-plane and perpendicular. Considering the STEM observations, the CRO lattice can expand to both inplane and out-of-plane ( Figure S18, Supporting Information). The RuO 6 octahedron in the CRO bulk has a large tilt angle, and the small tilt of the RuO 6 extends in both in-plane and perpendicular directions. The shape of a single RuO 6 octahedron is not easily distorted because Ru and O atoms are covalently bonded. The expansion phenomenon appears only in CRO with large slopes compared to SrRuO 3 .
Finally, we discuss the relation of the increase in CRO volume on the extraordinary size effect. CRO located in the quantum critical region is known to exhibit transition to Fermi  Figure S11, Supporting Information). The CRO film with high electrical resistivity has at large lattice of d = 3.978 Å ( Figure S17b, Supporting Information). In contrast, no peak was observed on the low angle side for the CRO films with low electrical resistivity. The lattice expansion contributes to the increase in electrical resistivity. The result indicates that the Mott transition is related to the insulation of the extraordinary size effect, i.e., the location of the CRO in the Mott-Hubbard model is to induce a larger size effect as it approaches the Mott-insulated phase.

Conclusion
This study investigated the thickness dependence of the electrical resistivity of CRO ultrathin films that exhibit the extraordinary size effect prepared at each element supply ratio. The sharp RHEED patterns were observed through the precise control of calcium and ruthenium molecular beams. Consequently, extraordinary size effects were observed under the growth condition of Ca/Ru = 1.2 and 1.6. The variation was enhanced by up to 1-7 digits compared to the size effect caused by quantum wells. Furthermore, it was clarified that the insulation was enhanced when increasing the Ca/Ru supply ratio.

Experimental Section
Film Growth: CRO ultrathin films were grown in a customerdesigned MBE chamber with basal pressure of ≈1 × 10 −5 Pa. All of Ca, Ru, and CaF 2 were evaporated by the electron beam by using the Hydra e-guns (Thermionics Laboratory, Inc.). The typical emission currents were 15, 100, and 10 mA for Ca, Ru, and CaF 2 , respectively, with acceleration voltage of 80-100 kV. Molecular beams of ruthenium and calcium were controlled by EIES. The EIES sensors are calibrated against the quartz crystal microbalance, which were inserted at the substrate holder position with the substrate holder swung up. The molecular beam of barrier material CaF 2 was detected by a quartz crystal microbalance method in a constant power mode. The target www.advelectronicmat.de rates of the calcium molecular beam were 0.25-0.64 Å s −1 for the supplied molecular ratio of Ca/Ru = 0.8-2.0. The target rates of the molecular beams of ruthenium and calcium fluoride were 0.1 and ≈1 Å s −1 , respectively. The CRO films were entirely grown at rate of 25 Å min −1 . The film thickness was estimated from the deposition time to measure molecular beam rate by EIES. It is proven that the estimation is in phenomenal agreement with actual film thicknesses to compare the AFM observation. [3] The oxides were grown by supplying ozone O 3 using a conventional ozonizer as a concentration of ≈14%. The partial pressure of oxygen p O2 was measured by using a quadrupole mass electrometer (Q-mass). The growth condition was p O2 ≈ 4 × 10 −4 Torr for all CRO films. The growth temperature was 800 °C. The details of the home-made MBE system are shown elsewhere. [38][39][40] The substrate was neodymium gallate with (110) surface of a typical size of ≈2 mm × 5 mm. The surface roughness of the NGO substrate was ensured to be below 2.5 Å. NGO substrates were annealed in situ at 800 °C for 1 h before the deposition.
CRO with (110) surface was grown on a substrate of NGO with (110) surface. [46,47] As the crystal structure of CRO is very similar to that of NGO substrate, the CRO films were grown epitaxially along the crystal orientation on substrates. The growth surface of CRO (110) on the NGO (110) substrate was determined by EBSD. Furthermore, the excess calcium supplied reevaporated from the surface of substrates owing to the high calcium vapor pressure. Accordingly, CRO autoregulated compounds to stoichiometric ratios on the NGO substrate. Highly crystalline and flat CRO ultrathin films were reproducibly grown using home-made MBE equipment. A calcium fluoride (CaF 2 ) insulator layer with thickness of 50 Å was deposited on CRO ultrathin films below 200 °C to protect the surface of films from oxidization. However, as this makes the surface of films insulating in the atmosphere, [3] the barrier is necessary to measure the properties of ultrathin films. The surface of the films was observed in situ based on RHEED. Typical patterns of NGO substrates and CaF 2 barrier layer are shown in Figure S19 (Supporting Information).
Measurements: The crystal structure of CRO was assigned by θ-2θ scans of the XRD. EBSD was also performed to assign crystal structure and direction of growth on CRO. An AFM (SPA-400) was used to study the roughness of surface on CRO films. Furthermore, field emission-SEM (JSM-7000F, JEOL) was performed to observe the surfaces of the CRO films. EDS was performed to determine the ratio of the elements Ca and Ru in the sample in the same equipment as SEM. The temperature dependence of electrical resistivity above 4.2 K was measured using the conventional two-and four-probe methods for insulators and metals, respectively ( Figure S20, Supporting Information). However, the distance between terminals in the two-probe method was shortened to <0.2 mm to obtain the current value to measure insulating films. Furthermore, the direction of the current was parallel to c-axis in all samples. The lattice spacing of the CRO (110) surface was measured through X-ray diffraction (XRD) using SmartLab (Rigaku Co., Ltd.).
STEM Observations: The samples were quarried from thin films and thinned using a focused ion beam milling with Ga + ions (JIB-4601F Multi Beam System; JEOL Co., Ltd.). The specimens were further thinned via energy of 0.3-1 keV Ar-ion gentle milling (IV-8; Technoorg Linda Co., Ltd.). STEM experiments were performed at room temperature on an electron microscope (JEM-ARM 200F; JEOL Co., Ltd.). The instrument was equipped with double spherical aberration correctors and a coldfield emission gun. The microscope was operated at an acceleration voltage of 200 kV for all experiments. The STEM images were collected with a 14-17 mrad convergent angle (20 µm condenser aperture). The collection angles were 12-24 and 68-280 mrad for ABF and HAADF imaging.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.