Synthesis science of SrRuO 3 and CaRuO 3 epitaxial films with high residual resistivity ratios

Epitaxial SrRuO 3 and CaRuO 3 ﬁlms were grown under an excess ﬂux of elemental ruthenium in an adsorption-controlled regime by molecular-beam epitaxy (MBE), where the excess volatile RuO x ( x = 2 or 3) desorbs from the growth front leaving behind a single-phase ﬁlm. By growing in this regime, we were able to achieve SrRuO 3 and CaRuO 3 ﬁlms with residual resistivity ratios ( ρ 300 K / ρ 4 K ) of 76 and 75, respectively. A combined phase stability diagram based on the thermodynamics of MBE (TOMBE) growth, termed a TOMBE diagram, is employed to provide improved guidance for the growth of complex materials by MBE. © 2018 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons

The ruthenates host a myriad of exotic electronic and magnetic phenomena, including odd-parity superconductivity, 1 quantum criticality, 2 and electronic nematicity. [2][3][4] In many ruthenates, even very small amounts of disorder can mask the true ground state. For instance, the odd-parity superconductivity of Sr 2 RuO 4 is the most disorder-sensitive superconductor known, where impurity concentrations in the range of only hundreds of ppm 5 or structural disorder 6 can destroy the superconducting ground state. In the case of CaRuO 3 , only recently have films with very low residual resistivities helped to reveal a Fermi liquid ground state below 1.5 K, where previous studies suggested non-Fermi liquid behavior. 7 Moreover, the properties of ruthenates are known to respond dramatically to dimensionality, [8][9][10] strain, [11][12][13] and pressure, 14,15 making them an ideal system for exploring the effects of biaxial strain and dimensional confinement in epitaxial thin films. Therefore, the ability to synthesize ruthenate thin films with extremely low amounts of disorder will be crucial for understanding how their emergent properties and ground states can be manipulated and controlled in thin film form.
A significant issue during the growth of ruthenate thin films is the loss of ruthenium in the form of RuO x (x = 2, 3, or 4). [16][17][18] The growth temperature at which this loss occurs depends on oxygen activity, but is typically above about 700 • C. [19][20][21] The films so produced contain ruthenium vacancies and have high residual resistivities. [19][20][21][22][23][24][25][26][27] In extreme cases, SrRuO 3 films exhibit semiconducting behavior in electrical transport measurements with dρ/dT < 0 with a concomitant reduction in ferromagnetic T c and an expansion in volume per formula unit. [19][20][21][22][23][24][25][26][27][28] One approach to maintaining film stoichiometry is to grow at a low substrate temperature where the volatility of ruthenium (in the form of RuO x ) is negligible. Unfortunately significant structural disorder exists in such films, which limits their residual resistivity. The highest residual resistivity ratio (RRR), (ρ 300 K /ρ 4 K ), reported for SrRuO 3 grown from a stoichiometric flux is 8.4. 29 Another approach is to grow at high substrate temperature where ruthenium volatility is significant and flood the growing film with excess ruthenium. This approach is analogous to the way in which high quality films of compound semiconductors with volatile constituents such as GaAs are grown. [30][31][32][33][34][35][36][37][38] The advantage of such an approach is that thermodynamics can be employed to automatically control film stoichiometry. The high growth temperature reduces disorder, and the automatic composition control provided by thermodynamics, within a range of growth conditions called a "growth window," can be harnessed to synthesize single-phase thin films with excellent electrical properties.
Adsorption-controlled growth of complex oxides 39-72 provides a pathway for achieving thin films with very low residual resistivities by mitigating defects resulting from cation non-stoichiometry. Indeed, SrVO 3 thin films with exceptionally low residual resistivities have been demonstrated using a metal-organic precursor for vanadium. Ruthenates, on the other hand, do not require a metalorganic precursor to access an adsorption-controlled growth window due to the high volatility of RuO x species. [16][17][18] To date, the highest RRRs, (ρ 300 K /ρ 4 K ), reported for thin films are ∼80 for an 80 nm thick SrRuO 3 film and 39 for a 78 nm thick CaRuO 3 film, respectively. 7,73 For comparison, the highest RRRs, (ρ 300 K /ρ 4 K ), reported for single crystals of SrRuO 3 and CaRuO 3 are 162 and 38, respectively. 74,75 In general, the RRRs of perovskite ruthenate thin films have been low, likely due to the presence of ruthenium vacancies and more generally due to a lack of clear guiding principles for the growth of high-quality perovskite ruthenate thin films.
In this manuscript, we outline a thermodynamic growth window for the growth of SrRuO 3 and CaRuO 3 thin films in an adsorption-controlled regime utilizing high-purity elemental sources. Adsorption-controlled growth is critical for avoiding defects related to cation non-stoichiometry, which can be detrimental to electrical transport properties. SrRuO 3 and CaRuO 3 epitaxial thin films were grown using a Veeco GEN10 molecular-beam epitaxy system. Strontium and calcium were evaporated from low-temperature effusion cells while an electron beam evaporator was used for ruthenium. All of the elemental source materials-strontium, calcium, and ruthenium-had a purity of 99.99%. Oxidation was achieved using either the output from a commercial ozone generator (∼10% O 3 + 90% O 2 ) or distilled ozone (∼80% O 3 + 20% O 2 ). The ozone + oxygen mixture was introduced through a water-cooled, electropolished 316L stainless steel tube with a 4.6 mm inner diameter pointed at the substrate with an angle of inclination of 40 • from the normal of the substrate and that terminates at a distance of 9.6 cm from the center of the substrate. The tube provides an enhancement in the local oxidant pressure by a factor of ∼4× over the background chamber pressure. Substrate temperature was measured using a pyrometer. (110) NdGaO 3 substrates, from CrysTec GmbH, were etched using HF-NH 4 OH and then annealed at 950 • C in flowing oxygen to yield a GaO 2 -terminated surface. 76 (100) SrTiO 3 substrates were etched in buffered HF and annealed at 950 • C in flowing oxygen to yield a TiO 2 -terminated surface. 77 Figure 1(a) illustrates the pressure-temperature window under which different members of the Sr n+1 Ru n O 3n+1 Ruddlesden-Popper (RP) series [78][79][80] are thermodynamically stable. The thermodynamic data for Sr n+1 Ru n O 3n+1 are from electrochemical cell measurements, 81 while the thermodynamic data for ruthenium oxides are from Rard. 17 Note that Fig. 1(a) is a combination of two types of phase diagrams. The solid lines in the bottom half of Fig. 1(a) are the typical Ellingham diagram applied to the Sr-Ru-O ternary system with three solid phases in equilibrium with each other. Along those lines, the partial pressures of all species in the system are a function of temperature including the partial pressure of oxygen plotted in the diagram. In contrast, the dashed lines in the top half of the diagram denote the equilibria between two solid phases under a flux balance equation given as follows: where Φ Ru is the excess flux of ruthenium arriving at the substrate, k is the Boltzmann constant, T s is the substrate temperature, p RuO 2 and p RuO 3 are the partial pressures of RuO 2 (g) and RuO 3 (g), respectively, and m RuO 2 and m RuO 3 are the molecular masses of RuO 2 (g) and RuO 3 (g), respectively. This flux balance is established by considering that the incoming excess flux of ruthenium to the substrate is balanced by the flux of ruthenium leaving the substrate in the form of RuO x (g). In this diagram, the blue, purple, gold, and red lines represent the change of stability of SrRuO 3 (s), Sr 4 Ru 3 O 10 (s), Sr 3 Ru 2 O 7 (s), and Sr 2 RuO 4 (s), respectively. This combined phase stability diagram is very useful in guiding the growth of complex phases by molecular-beam epitaxy (MBE). For oxygen partial pressures below the dotted black and dotted green lines, solid ruthenium or RuO 2 cannot be fully vaporized, and the conventional Ellingham diagram can be used to describe the phase relations as a function of temperature and oxygen partial pressure. At oxygen partial pressure above the dotted black and dotted green lines, however, solid ruthenium or RuO 2 is no longer stable with respect to the gas phase and is thus fully vaporized. Thermodynamic stability during MBE is consequently dictated by the equilibrium among species in the gas phase under a given overall ruthenium flux as dictated by Eq. (1). We call this combined phase stability diagram based on the thermodynamics of MBE (TOMBE) growth a TOMBE diagram.
In the TOMBE diagram [ Fig. 1(a)], the light-green shaded region is the adsorption-controlled growth window for SrRuO 3 , where solid SrRuO 3 is in equilibrium with RuO x (x = 2 or 3) in the gas phase. Within this growth window, any excess ruthenium will desorb from the surface of the film as RuO x (g) (x = 2 or 3), leading to the phase-pure epitaxial growth of SrRuO 3 . Indeed, pausing growth within this window with the strontium shutter closed and the ruthenium shutter open results in a steady state situation where the SrRuO 3 film is stable and no phases are growing (neither SrRuO 3 nor any other phases). In the absence of an A-site cation (strontium or calcium), all of the incident ruthenium atoms are converted to RuO x (g), which readily desorbs from the surface. This is analogous to the adsorption-controlled growth window for III-V compound semiconductors where the excess group V species desorb from the growth front. [30][31][32][33][34][35][36][37][38] This adsorption-controlled growth window for SrRuO 3 [shaded in green in Fig. 1(a)] is bounded by various reactions. The dotted black line, representing the reaction of ruthenium metal with oxygen to form RuO x (g), delineates the low oxygen pressure boundary below which excess ruthenium will precipitate as ruthenium metal. On the high-temperature side, it is bound by the dotted blue line beyond which SrRuO 3 will decompose into Sr 4 Ru 3 O 10 and RuO x (g). Similar breakdown under highly oxidizing conditions has been reported to occur at the surface of SrRuO 3 thin films. 82 On the low-temperature side, bounded by the dotted green line, excess ruthenium will precipitate as RuO 2 (s).
The dashed lines, representing phase equilibria between various Sr n+1 Ru n O 3n+1 RP phases with RuO x (g), shift toward the upper left hand corner of the TOMBE diagram with increasing RuO x (g) partial pressure. The RuO x (g) partial pressure is determined by the excess ruthenium flux, which is another parameter that can be tuned to navigate around the thermodynamic growth window. The adsorption-controlled window for the other Sr n+1 Ru n O 3n+1 RP phases, for example, Sr 2 RuO 4 , which is stable between the dashed red and dashed gold lines, is much narrower likely due to the very similar free energies of formation of these RP phases as is the case for Sr n+1 Ti n O 3n+1 RP phases. 83 During MBE growth, it is straightforward to provide an excess flux of ruthenium since ruthenium and strontium are evaporated from separate independent sources. Excess ruthenium flux is critical for accessing this adsorption-controlled growth window for ruthenates.
A similar TOMBE diagram [ Fig. 1(b)] was calculated for the Ca n+1 Ru n O 3n+1 RP series. The thermodynamic data for Ca n+1 Ru n O 3n+1 are from electrochemical cell measurements, 84 while the thermodynamic data for ruthenium oxides are from the work of Rard. 17 In Fig. 1(b), the blue, gold, and red solid lines represent the equilibrium of CaRuO 3 (s), Ca 3 Ru 2 O 7 (s), and Ca 2 RuO 4 (s) with Ru(s), respectively. The dotted versions of the corresponding lines represent equilibria between the same phases and RuO x (g).
The light-green shaded region in Fig. 1(b) is the adsorption-controlled growth window for CaRuO 3 within which solid CaRuO 3 is in equilibrium with RuO x (x = 2 or 3) gas. The adsorptioncontrolled growth window for CaRuO 3 is much narrower than that for SrRuO 3 . This is due to the greater difference in Gibbs formation energy between SrRuO 3 and RuO 2 than between CaRuO 3 and RuO 2 . A similar growth window has been proposed for the growth of Sr n+1 Ir n O 3n+1 RP phases. 85 We use ozone as an oxidant due to its high oxidation potential, which enables us to access high oxygen activity regions of the TOMBE diagram without exceeding a chamber background pressure of 10 6 Torr. Total chamber pressures exceeding 10 6 Torr can oxidize the source materials inside effusion cells causing flux instabilities. 86 The following equation describes how the ozone partial pressure at the substrate can be converted to an equivalent partial pressure of molecular oxygen, 90 p O 2 , where p O 3 is the ozone partial pressure at the substrate, ∆G 0 is the standard free energy of formation of ozone from oxygen, and T s is the substrate temperature (where ozone decomposition occurs): The cyan lines in the TOMBE diagrams [ Figs. 1(a) and 1(b)] are ozone oxidation potential lines for a range (10 11 to 10 5 Torr) of ozone partial pressures. Note that we have not included RuO 4 (g) in the RuO x (g) gas phase in our thermodynamic calculations for Figs. 1(a) and 1(b). The effect of including RuO 4 (g) on the TOMBE diagrams of the Sr n+1 Ru n O 3n+1 and Ca n+1 Ru n O 3n+1 RP phases are depicted in Figs. S5(b) and S6(b) of the supplementary material, respectively. Figure  This contradicts our demonstrated ability to grow these phases by MBE (as is shown, for example, in Fig. S4 of the supplementary material). Excluding RuO 4 (g) in the calculations can be further justified by the fact that RuO 4 (g) is likely formed by the oxidation of RuO 3 (g) in the gas phase. 18,91 Therefore, it is unlikely that RuO 4 (g) will be a significant component of the RuO x (g) gas phase under the low pressure conditions encountered during MBE growth where interaction between species in the gas phase is minimal due to the long mean free paths.
Having established the thermodynamic basis for the adsorption-controlled growth of SrRuO 3 and CaRuO 3 , we now turn to the growth and characterization of optimized films. We grew a 32 nm thick SrRuO 3 thin film on a (100) SrTiO 3 substrate at a temperature of 700 • C and a chamber background pressure of 10 6 Torr of (∼80% O 3 + 20% O 2 ). We used a strontium flux of 1.5 × 10 13 atoms/cm 2 s and a ruthenium flux that was 2.3 times the strontium flux. We also grew a 38 nm thick CaRuO 3 thin film on a (110) NdGaO 3 substrate at a substrate temperature of 685 • C and a chamber background pressure of 10 6 Torr of (∼10% O 3 + 90% O 2 ). We used a calcium flux of 2 × 10 13 atoms/cm 2 s and a ruthenium flux that was 2.6 times the calcium flux. These conditions fall within the growth window indicated in Fig. 1(a) for SrRuO 3 . In the case of CaRuO 3 , however, our growth conditions fall outside the calculated growth window [ Fig. 1(b)] for CaRuO 3 on the higher temperature and higher oxygen pressure side of the TOMBE diagram. In this region of the TOMBE diagram, CaRuO 3 decomposes through successive oxidation to higher n members of the RP-series with the final decomposition product being CaO and RuO x (g). We believe that CaRuO 3 growth is possible outside the thermodynamic window due to the relatively low growth temperature, which kinetically suppresses the oxidative decomposition of CaRuO 3 . This is similar to the epitaxial growth of metastable alloys at low substrate temperatures to kinetically suppress thermodynamic phase separation. [92][93][94][95][96][97][98][99][100][101][102] The growth window outlined above works well provided there is a sufficiently high oxidant flux to avoid any oxidation kinetics issues. 69 At the end of the film growth, the strontium/calcium and ruthenium shutters were closed simultaneously and the samples were rapidly cooled under the same ozone pressure as that used during growth until the substrate temperature was below 250 • C.
Reflection high-energy electron diffraction (RHEED) was used to monitor the film growth. The RHEED pattern recorded at the end of growth (Fig. S1 of the supplementary material), while the film was still at growth temperature, consisted of spots on an arc (the Laue zone) for both the SrRuO 3  X-ray diffraction (XRD) measurements were carried out in a Rigaku SmartLab high-resolution diffractometer. The indices given for SrRuO 3 , CaRuO 3 , and NdGaO 3 all correspond to the nonstandard Pbnm setting of space group #62, where the c-axis is the longest axis of the unit cell. The θ-2θ XRD scans of a SrRuO 3 film grown on (100) SrTiO 3 and a CaRuO 3 film grown on (110) NdGaO 3 are shown in Figs. 2(a) and 2(b), respectively. These XRD patterns are free of spurious peaks indicating that the films are single-phase. The presence of Laue oscillations [insets to Figs. 2(a) and 2(b)] show that the films have good crystallinity and smooth interfaces. Rocking curve measurements in ω around the 220 reflections of SrRuO 3 [ Fig. 2(c)] and CaRuO 3 [ Fig. 2(d)], respectively, indicate that the rocking curve full width at half maximum (FWHM) of the films is comparable to the substrates upon which they are grown. Specifically the SrRuO 3 film had a FWHM of 40 arc sec compared to the 38 arc sec FWHM of the underlying SrTiO 3 substrate. Similarly, the CaRuO 3 film exhibited a FWHM of 13 arc sec compared to the 11 arc sec FWHM of the NdGaO 3 substrate upon which it was grown. These values confirm that the films have high structural perfection.
XRD φ scans [ Fig. S2(b) of the supplementary material] confirm that the CaRuO 3 film grown on (110) NdGaO 3 is untwinned with respect to the in-plane c-axis orientation of the film and follows the in-plane crystallographic orientation of the isostructural substrate. This is further confirmed by imaging the RuO 6 octahedral rotations using annular bright-field scanning transmission electron microscopy (ABF-STEM). 104   Cross-sectional transmission electron microscopy specimens were prepared using the standard focused ion beam (FIB) lift-out process on an FEI Strata 400 FIB equipped with an Omniprobe AutoProbe 200 nanomanipulator. Following sample preparation, the TEM specimens were imaged on an aberration-corrected 300 keV FEI Titan Themis with a probe convergence semi-angle of 30 mrad. High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images were acquired with inner and outer collection angles of 68 and 340 mrad, respectively, from both the 32 nm thick SrRuO 3 film grown on the SrTiO 3 substrate [ Fig. 3(a)] and the 38 nm thick CaRuO 3 film grown on the NdGaO 3 substrate [ Fig. 3(b)]. As electrons scattered to high angles are collected in the HAADF detector, atomic columns occupied by a higher atomic number (Z) appear brighter whereas those with a lower Z show darker contrast.
The uniform growth of the SrRuO 3 film on the SrTiO 3 substrate can be seen from the HAADF-STEM image in Fig. 3(a). Due to the higher Z of the B-site ruthenium in the film than the B-site titanium in the substrate, the film appears brighter. Furthermore, while the HAADF intensities from ruthenium (Z = 44) and strontium (Z = 38) in the SrRuO 3 film are rather difficult to distinguish by eye due to their similar Z, a line profile along the film's growth direction clearly displays the alternating intensities arising from the occupancy of ruthenium and strontium as shown in Fig. S7 of the supplementary material. Similarly, the uniform growth of CaRuO 3 on NdGaO 3 can be confirmed from the HAADF-STEM image in Fig. 3(b) as the contrast between the Aand B-site cations are reversed for CaRuO 3 and NdGaO 3 arising from the B-site ruthenium having a higher Z than the A-site calcium in CaRuO 3 , while in NdGaO 3 the A-site neodymium has a higher Z than the B-site gallium.
The resistivity of the same SrRuO 3 and CaRuO 3 samples was measured in a van der Pauw geometry as a function of temperature. The results are shown in Fig. 4. With RRRs of 76 for SrRuO 3 and 75 for CaRuO 3 , the advantage of growing ruthenate films under adsorption-controlled conditions is evident. The transport properties of ruthenates are highly sensitive to structural disorder induced by cation non-stoichiometry including point and planar defects. 19 This is usually reflected in the low RRR of films grown under non-optimized conditions. Growth under optimized conditions, outlined earlier, resulted in films with high RRRs likely due to a reduction in defects related to cation nonstoichiometry.
Note that adsorption-controlled growth conditions are not synonymous with perfect composition control. Adsorption-controlled growth conditions access the single-phase region of SrRuO 3 and CaRuO 3 , but depending on how wide the composition range is of single-phase SrRuO 3 and CaRuO 3 and from which side it is approached (in our case the ruthenium-rich side)-factors that change with growth temperature and chemical potentials-the stoichiometry of the resulting film will change  though it will always remain single phase. This is analogous to the growth of III-V compound semiconductors, where this behavior is utilized to controllably alter point defect concentrations, e.g., the EL2 defect in GaAs. 108 It is evident from Fig. 4(b) that the CaRuO 3 films grown on NdGaO 3 exhibit anisotropic electrical transport in the in-plane directions. Although the room temperature resistivities [ Fig. 4(b)] are similar along the [001] and [110] directions, the RRR along the [001] direction is significantly higher than that along the [110] direction. This is likely due to the highly anisotropic Fermi surface of CaRuO 3 , which has been revealed by angle-resolved photoemission spectroscopy (ARPES) measurements on our CaRuO 3 /NdGaO 3 (110) thin films. 109 Similar anisotropy in electrical transport has been observed for CaRuO 3 /NdGaO 3 (110) films grown using pulsed-laser deposition (PLD). 110 The RRR of 75 measured along [001] for our CaRuO 3 film is the highest of any CaRuO 3 films reported to date. For SrRuO 3 , our film has a comparable RRR to that of the highest report. 73 In summary, we have employed a combined phase stability diagram (TOMBE diagram) pertinent to MBE growth and outlined a thermodynamic growth window for the reproducible growth of SrRuO 3 and CaRuO 3 thin films with high RRR. Although the exact growth parameters might not be directly transferable from one growth chamber to another, the thermodynamic window outlined can be used as a guide while tuning synthesis conditions to grow ruthenate perovskite thin films with high RRR. The effects of moving into and out of the desired growth window can be seen directly in RHEED as shown in Figs. S3 and S4 of the supplementary material.
See supplementary material for more details on the reactions taken into account for constructing the TOMBE diagrams together with additional characterization of the films shown in Fig. 2  Similarly Eqs. (S12) -(S17) were considered for calculating the TOMBE diagrams for the Can+1RunO3n+1 Ruddlesden-Popper series. Figure S1: RHEED images of the same SrRuO3 and CaRuO3 films measured in   overlaid with the RHEED images taken along the <100>p azimuth during growth under various growth conditions. RHEED in combination with this TOMBE diagram enables the growth space to be navigated to achieve desired Srn+1RunO3n+1 phases. Figure S4: TOMBE diagram for Can+1RunO3n+1 phases (the same as Fig. 1(b)) overlaid with the RHEED images taken along the <100>p azimuth during growth under various growth conditions. RHEED in combination with this TOMBE diagram enables the growth space to be navigated to achieve desired Can+1RunO3n+1 phases. Note that the conditions under which we grow Ca2RuO4 films fall in the region for CaO(s) + RuOx(g) in the TOMBE diagram. We believe that we are able to achieve Ca2RuO4 epitaxy due to kinetic suppression of decomposition of Ca2RuO4 into CaO(s) and RuOx(g).