High-sensitivity of initial SrO growth on the residual resistivity in epitaxial thin films of SrRuO$_3$ on SrTiO$_3$ (001)

The growth of SrRuO$_3$ (SRO) thin film with high-crystallinity and low residual resistivity (RR) is essential to explore its intrinsic properties. Here, utilizing the adsorption-controlled growth technique, the growth condition of initial SrO layer on TiO$_2$-terminated SrTiO$_3$ (STO) (001) substrate was found to be crucial for achieving a low RR in the resulting SRO film grown afterward. The optimized initial SrO layer shows a $c$(2 x 2) superstructure that was characterized by electron diffraction, and a series of SRO films with different thicknesses ($t$s) were then grown. The resulting SRO films exhibit excellent crystallinity with orthorhombic-phase down to $t \approx$ 4.3 nm, which was confirmed by high resolution X-ray measurements. From azimuthal X-ray scan for SRO orthorhombic (021) reflection, we uncover four structural domains with a dominant domain of orthorhombic SRO [001] along cubic STO [010] direction. The dominant domain population depends on $t$, STO miscut angle (${\alpha}$), and miscut direction (${\beta}$), giving a volume fraction of about 92 $\%$ for $t \approx$ 26.6 nm and (${\alpha}$, ${\beta}$) ~ (0.14$^{\rm o}$, 5$^{\rm o}$). On the other hand, metallic and ferromagnetic properties were well preserved down to $t \approx$ 1.2 nm. Residual resistivity ratio (RRR = ${\rho}$(300 K)/${\rho}$(5 K)) reduces from 77.1 for $t \approx$ 28.5 nm to 2.5 for $t \approx$ 1.2 nm, while ${\rho}$(5 K) increases from 2.5 $\mu\Omega$cm for $t \approx$ 28.5 nm to 131.0 $\mu\Omega$cm for $t \approx$ 1.2 nm. The ferromagnetic onset temperature ($T_c\prime$) of around 151 K remains nearly unchanged down to $t \approx$ 9.0 nm and decreases to 90 K for $t \approx$ 1.2 nm. Our finding thus provides a practical guideline to achieve high crystallinity and low RR in ultra-thin SRO films by simply adjusting the growth of initial SrO layer.


I. INTRODUCTION
The orthorhombic SRO hosts a number of intriguing physical properties, such as ferromagnetism with T c ≈ 160 K [1], Fermi-liquid behavior [2], magnetic monopole [3], and Weyl fermions [4,5]. The growth of SRO in thin-film form may open up possibilities to further tune its unusual physical properties by strain and finite-size effects. Extensive efforts have been carried out previously to grow high-crystalline SRO films on various substrates [1,[6][7][8][9], where different transport and magnetic properties were found as compared to its bulk form.
On the other hand, the issue of the critical thickness for the structural and magnetic phase transitions in ultra-thin SRO films remains a debatable issue, where the strain and substrate symmetry play important roles [10][11][12]. Theoretical outcomes infer the ferromagnetic and metallic phases in the SRO films on STO down to a thickness of about 1 nm [13,14], while experimental resolutions showed more scattered and inconclusive results due to the difficulty on maintaining high crystallinity in ultra-thin SRO films [15][16][17][18].
In the past, SRO films grown using sintered oxide targets by sputtering or pulsed laser deposition showed relatively low RRRs (< 10) [19][20][21][22][23]. On the other hand, thick SRO films grown by electron beam evaporation technique turned out to give much higher RRR (> 60) [7,8] that is approaching the value in a bulk single crystal. Such a large difference in RRR suggests a high sensitivity of the SRO stoichiometry on growth parameters, where the volatility of ruthenium oxide and thus cation deficiency turn out to be a major problem [1,24]. In this respect, an adsorption-controlled growth technique was developed for thinfilm growth of various oxides, such as PbTiO 3 , EuO, BaSnO 3 , and LuFe 2 O 4 [25][26][27][28]. We noted that similar technique was first introduced in the growth of GaAs films [29]. More recently, the growth of high-quality chalcogenide thin films also relied on this approach [30].
In the adsorption-controlled technique, the flux ratio of source materials and the growth temperature are key parameters to grow a stoichiometric film, and a thermodynamic phase diagram can be constructed to reveal the proper growth window for a particular structural phase.
For the adsorption-controlled growth of orthorhombic SRO films on STO, a growth window of ozone partial pressure of around 3 × 10 −6 Torr and a growth temperature ranging from about 500 o C to 800 o C was reported previously [6]. Above 800 o C, other phases of † chsu@nsrrc.org.tw ‡ wlee@phys.sinica.edu.tw 2 Sr 4 Ru 3 O 10 and Sr 2 RuO 4 become more thermodynamically favorable. Within the growth window, the supplied Ru flux forms a volatile RuO x and desorbs from the film surface. The SRO growth will happen when the RuO x combine with the SrO, and the growth rate is thus controlled by the Sr flux. With the appropriate flux ratio of Ru/Sr, the film's stoichiometry can be thermodynamically self-regulated, resulting in a high-quality and single phase SRO films on STO. However, for the adsorption-controlled growth technique, the questions in regard to the initial growth condition [31][32][33] and its influence on the follow-up SRO growth are still not well understood. In this work, we used an oxide-MBE and adopted the adsorptioncontrolled growth technique to grow SRO films with different ts on TiO 2 -terminated STO (001) c substrates, where the subscript c refers to a cubic phase. From reflection high-energy electron diffraction (RHEED) and low energy electron diffraction (LEED) analyses, we found that an optimized initial SrO layer gave a c(2 × 2) superstructure, which turned out to be a prerequisite for excellent crystallinity and low residual resistivity in the resulting SRO films.
The SRO films grown with optimized initial SrO layer showed an orthorhombic-phase down to t ≈ 4.3 nm. In addition, the structural domains in our SRO films were investigated by performing X-ray azimuthal scans across the SRO (02±1) o reflections, where the subscript o refers to an orthorhombic phase. We remark that the films grown with the optimized initial SrO layer give a significant reduction in RR as compared to films grown with unoptimized initial SrO layer. Figure 1(a) shows a schematic of the SRO film growth, where the operations of the Ru and Sr cell shutters are illustrated. Sr shutter was first opened for a certain initial growth duration (τ IGD ) for the growth of the initial SrO layer on a STO, and then Ru shutter was opened for the subsequent growth of SRO film. The resulting thickness (t) of SRO film can be well controlled by the Ru shutter opening time of τ SRO . Figure 1(b) shows the temperature dependent resistivity (ρ) with different τ IGD values for t ≈ 21.5 nm films. A practical T 2 dependence in ρ(T ) was found for all films in low temperature regime, indicating a Fermi liquid behavior as expected [2]. For convenience, we use ρ at T = 5 K (ρ(5 K)) as a measure for RR of the SRO films in the following discussions. The extracted RRRs and ρ(5 K) from the ρ(T ) curves show nonmonotonic variations with τ IGD as plotted in Fig.   3 1(c), where a maximum RRR of about 43.0 and a lowest ρ(5 K) of about 4.7 µΩcm were achieved for the film grown with an optimum τ OIGD ≈156 s. Remarkably, ρ(5 K)(RRR) becomes higher(lower) by nearly an order of magnitude for films grown with the condition of τ IGD = τ OIGD .

II. RESULTS
In order to know the structural evolution, we carefully monitored the initial growth using an in-situ RHEED. Figure 2(a) displays the RHEED pattern of the STO substrate along [110] c direction at 700 o C [34]. The time evolution of the RHEED intensity profile across the solid line in Fig. 2(a) is shown in Fig. 2(b). Upon opening Sr cell shutter, the RHEED image transformed from a spot-like pattern into a streak-line pattern. The secondary streak-lines started appearing between the primary streak-lines after τ IGD ≈ 118 s. Figure 2 nearly unchanged after then. SRO films grown with the τ IGD < τ OIGD followed the islandtype growth. In contrast, for τ IGD > τ OIGD , the streak-line feature from the initial SrO layer remains nearly unchanged after opening the Ru shutter for subsequent growth of the SRO film.
To further explore the surface structure prior the SRO growth, we grew a SrO layer on STO with τ IGD = τ OIGD at growth temperature of 700 o C. The secondary streak-lines were found to be stable while cooling down to room temperature, and then the sample was transferred under an ultra-high vacuum to a LEED chamber for surface structural characterizations. Figure 2(e) shows the LEED pattern with a beam energy of 88 eV. The primary spots come from the cubic STO substrate with a lattice spacing of 3.91Å. The secondary spots appeared along the lateral <110> directions halfway between the main spots. The simulated LEED pattern [35] with a c(2 × 2) structure as shown in Fig. 2(f) exhibits a close agreement with the pattern we observed. These observations confirmed a c(2 × 2) superstructure on the surface of the initial SrO layer [36]. By using the same condition of τ IGD = τ OIGD , we grew a series of SRO(t) films on STO with different t ranging from 1.2 nm to 28.5 nm. The average surface roughness of around 0.12 nm after the growth remains nearly the same as that of the STO substrate. However, we did notice some well-separated random clusters on film surface. Using an energy dispersive X-ray analyzer (SEM-EDX), we confirmed that those clusters were composed of RuO x [1]. Those random RuO x clusters on the film surface are likely coming from the excess supplied Ru during the growth. The density of the RuO x clusters can be minimized by reducing the fluxes of both Sr and Ru, while keeping the same flux ratio. But for the τ IGD = τ OIGD case, no fringes were observed, and the Bragg peak intensity was also weaker. This notable difference revealed a much better crystallinity of the SRO film grown with τ IGD = τ OIGD . We further performed CTR measurements of various off-normal SRO reflections to examine the orientation and crystalline quality of films along the lateral 5 directions. Figure 4(d) shows L-scans across the STO (204) c reflection for SRO films with t ≈ 26.6 nm and 4.3 nm. Both samples exhibit pronounced SRO Bragg peaks centered at ≈ 3.97 r.l.u. STO and intensity oscillations, and the oscillation's period agrees well with that measured from the STO (00n) c CTRs, further manifesting the excellent 3D crystalline quality of the SRO films along both normal and lateral directions.
We further moved on to the structural-phase evolution with respect to t for films grown with τ IGD = τ OIGD . Figures 5(a-d)  for the orthorhombic phase [17,38]. However, because of the similar unit cell size between tetragonal and orthorhombic phases of SRO, where the difference in lattice constants is less than 1%, diffraction peaks of the two phases are always nearby. Consequently, peak indexing and phase identification from similar RSMs become practically impossible for films thinner than ≈ 10 nm, because the SRO peaks are so broad along L due to finite size effect and the peaks associated with different rotational domains overlap seriously. Hence, we chose the orthorhombic-specific reflections, such as SRO (221) o and (021) o , as the signatures to identify orthorhombic phase. Originated from the tilt of the RuO 6 octahedra, those reflections are allowed in the orthorhombic phase but forbidden in the tetragonal phase [17].   Table 1. Table 1 summarizes the variation of volume fraction of above four domains for three SRO films with different t and (α, β).  Thickness and (α, β) dependents on domain volume fraction and RRR/ρ(5 K). β represents the miscut direction, which is defined as the angle between the terrace edge and STO We performed a thickness-dependent transport study on the films with the τ IGD = τ OIGD .  M-T curves clearly show a ferromagnetic to paramagnetic phase transition, and the T ′ c was extracted from the peak location in the derivative of the M-T curve. Inset of Fig. 7(a) shows the variation of T ′ c and T c as a function of t, where the T c values were extracted from 8 the ρ(T ) curves ( Fig. 6(a)). The T c of around 151 K for t > 9 nm decreases to around 90 K with t reducing to 1.2 nm. In the high field regime, the magnetic signal was practically linear with field strength, which was dominated by the diamagnetic background from the STO substrate. The field dependent magnetization of the SRO film can thus be obtained by subtracting a field linear component due to the diamagnetic STO, and the resulting M-H curves for a SRO film with t ≈ 28.5 nm at T = 5 K are shown in Fig. 7(b). For H SRO

III. DISCUSSION
In earlier works, the SRO stoichiometry and oxygen vacancy driven studies have been carried out, where notable changes in the RRR, ρ(5 K), film's crystallinity, and T c were reported [2,20,22,23]. We grew all the films under a similar ozone environment and within the adsorption-controlled growth regime. Hence, the significant change in RRR and ρ(5 K) with respect to the τ IGD is not likely due to either the oxygen vacancy in STO [39] or SRO stoichiometry. To further clarify the oxygen vacancy issue, we post-annealed a sample at was observed due to post-annealing. We also note that the rapid and monotonic increase of ρ(5 K) with reducing t (Fig. 6(d)) suggests the insignificance of the possible interface conduction channel between SRO and STO due to either atomic interdiffusion or charge transfer at the interface [40].
It was also pointed out that step-flow growth mode is more favorable for achieving atomically smooth surface in SRO thin films [1,31,32]. In a simplified model [31], two relevant time scales are considered. One is the lifetime of an adatom diffusing on a terrace with width L before being absorbed on the surface, namely τ lif e = L 2 /2D, and D is the diffusion constant. The other time scale represents the time elapsed between two consecutive atoms to land on the surface, and it can be described by τ land = a 2 /L 2 F , where F and a are the deposition flux and the surface lattice constant, respectively. The condition for step-flow growth regime requires τ life < τ land . The additional periodicity from the initial SrO layer with a c(2 × 2) superstructure ( Fig. 2(e)) not only provides ordered nucleation sites for SRO growth but also imposes a much shorter length scale as compared to the terrace width L in the τ life term, which prevents the island formation and promotes the step-flow growth.
As a result, the SRO film grown with the τ IGD = τ OIGD gives rise to an excellent crystallinty and reduces(increases) the ρ(5 K)(RRR) by about an order of magnitude as compared to the films grown with τ IGD = τ OIGD .
One disadvantage for the adsorption-controlled growth technique is the random RuO x clusters on SRO films due to the excess Ru flux during the growth process. Nevertheless, our growth condition is well within the thermodynamic growth window for an equilibrium state of SRO solid phase and RuO x gas phase [6]. We thus argue that those random RuO x clusters mostly precipitated on the film surface and did not significantly influence the crystallinity of SRO films underneath, which is supported by the observations of pronounced intensity oscillations in the CTR and off-normal L-scans on our SRO films. Moreover, RuO x clusters are well separated by more than few microns, which is not likely to influence the transport properties of SRO. But, in the magnetization measurement, the RuO x clusters may give an additional contribution to the background signal.
Previous studies of SRO films on STO have revealed the presence of structural domains that is sensitive to the STO's α and β parameters [41,42], which mostly relied on analyses of

IV. CONCLUSION
Using an oxide-MBE and adsorption-controlled growth technique, we grew SRO(t) films on STO (001) c and studied their thickness-dependent structural, transport, and magnetic properties. Our results revealed that within the adsorption-controlled growth regime, a control on the initial SrO growth parameters is crucial to achieve a low RR. The initial SrO layer with τ IGD = τ OIGD results in a c(2 × 2) superstructure, which serves as a proper template for the growth of SRO films with high-crystallinity and low RR. substrate was heated to a growth temperature of around 700 o C that was measured using a pyrometer. In order to avoid the oxygen loss in the STO, distilled ozone was supplied into the growth chamber whenever substrate temperature was above 150 o C. Ozone partial pressure was maintained at around 3 × 10 −6 Torr throughout the growth process. Sr and Ru was evaporated using a standard effusion-cell and e-beam, respectively. The atomic fluxes of both Sr and Ru were precalibrated using a quartz crystal microbalance. Sr flux was about 9.29 × 10 12 cm −2 s −1 and the Ru/Sr flux ratio was kept around 2.2. The Sr-cell shutter was opened first for certain duration, and then Ru shutter was opened as illustrated schematically in Fig. 1(a). The growth process was in-situ monitored via a RHEED. A LEED was used to identify the surface atomic structure. AFM and SEM-EDX were used to investigate the surface morphology and the film composition, respectively. High resolution X-ray scattering characterizations were carried out at beamlines TPS 09A and TLS 07A of the NSRRC, Taiwan. The transport measurements were performed using a superconducting magnet system with a variable temperature insert. The magnetic properties were studied using the commercial Quantum Design magnetic properties measurement system.