The Controlled Synthesis of Metastable Oxides Utilizing Epitaxy and Epitaxial Stabilization

1.6. ESTABLISHMENT OF RHEED-BASED COMPOSITION CONTROL METHOD WITH ABSOLUTE ACCURACY OF BETTER THAN 1% .................................................................................... 8 1.7. GROWTH OF mTASTABLE mnO3 / S R n O 3 AND B A n 0 3 / S R R 0 3 SUPERLATTICES BY MBE WITH STRUCTURAL PERFECTION COMPARABLE TO SLJPERLATI'ICES OF flI / v SEMICONDUCTORS G OWN BY MBE...............................................................................9


Executive Summary
Molecular beam epitaxy (MBE) has achieved unparalleled control in the integration of semiconductors at the nanometer level.Under the support of this DOE grant we have shown that it is possible to structurally engineer oxides with a precision that rivals the structural engineering and customization achieved in semiconductor structures.Two examples of the structural engineering that we have achieved in oxides are shown in Fig. 1 adjacent to a state-of-the-art semiconductor heterostructure.As described in Sec.2.7, all of these MBE-grown structures are metastable.
It is the broad and greatly unexplored spectrum of electronic and optical properties exhibited by oxides that makes such structural customization exciting.The ability to structurally-engineer oxides opens the door to establishing the fundamental properties of known oxide materials as a function of direction (many are anisotropic), as well as creating and probing the properties of new oxides.We did both in this DOE program.For example, we used epitaxy to establish some of the fundamental dielectric and ferroelectric properties of SrBizTa209 and SrBi2&Op-materials used in today's "smart cards" (despite the dearth of knowledge about their physical properties).We also used epitaxy and epitaxial stabilization to synthesize new phases, e.g., Srn+lT&03n+l Ruddlesden-Popper phases for n = 1 to 5, and established some of their dielectric properties.
These advances were made through the use of epitaxy, epitaxial stabilization, and a combination of composition-control techniques including adsorption-controlled growth and RHEED-based composition control that we have developed, understood, and utilized for the growth of oxides.Also key was extensive characterization (utilizing RHEED, four-circle x-ray diffraction, AFM, TEM, and electrical characterization techniques) in order to study growth modes, optimize growth conditions, and probe the structural, dielectric, and ferroelectric properties of the materials grown.The materials that we have successfully engineered include titanates (PbTiO3, BbTi3012), tantalates (SrBizTazOg), and niobates (SrBi2&09); layered combinations of these perovskite-related materials (B4Ti3012-SrTi03 and B4Ti3012-PbTi03 Aurivillius phases and metastable PbTi03 / SrTiO3 and BaTi03 / SrTiO3 superlattices), and new metastable phases (Srn+lT&03n+l Ruddlesden-Popper phases).The films were grown by reactive MBE and pulsed laser deposition (PLD).Many of these materials are either new or have been synthesized with the highest perfection ever reported.The controlled synthesis of such layered oxide heterostructures offers great potential for tailoring the superconducting, ferroelectric, and dielectric properties of these materials.These properties are important for energy technologies.

Establishment and Thermodynamic Understanding of Adsorption-Controlled Growth Regime for PbTiO3 and BidTi3012 by MBE
We have investigated the use of an adsorption-controlled growth mechanism to accurately and reproducibly control film stoichiometry during the growth of oxides by MBE.Adsorptioncontrolled growth was first utilized for the MBE synthesis of epitaxial GaAs thin films over 30 years ag0.4-7This growth mechanism relies on the volatility of the group V component and has been explained using thermodynamics.*-"In the growth of oxides, the oxygen incorporation is controlled by an adsorption-controlled growth mechanism, but we have established and understood (using thermodynamics) that in addition to oxygen, the incorporation of lead and bismuth may also be controlled by an adsorption-controlled growth mechani~m.'~.'~For example, PbTiO3 and BhTi3012 can be grown in a regime where it is only necessary to accurately control the titanium flux.Within a wide range of lead, bismuth, and oxygen fluxes (the "growth window" for the adsorption-controlled growth of these phases), phase-pure PbTiO3 and BbTi3012 films may be realized with the growth rate entirely controlled by the titanium flux.We have demonstrated fiom measured fjlm thickness, RBS composition measurements, monitoring of RHEED half-order intensity oscillations during growth, and in situ flux measurements using atomic absorption spectroscopy (AA), that at suitable temperature and ozone pressure the titanium sticking coefficient approaches one and the excess lead or bismuth desorbs.12*13 In Fig. 2 we show the results of our thermodynamic calculations where we contrast the adsorption-controlled growth window for the synthesis of GaAs with that for PbTiO3 and BbTi3012.Because PbO (and As2) is the dominant vapor species that exists when PbTiO3 (or GaAs) is heated in the temperature-pressure region pl~tted,'~ the axis of the ordinate in Fig. 2(a) can be plotted as simply a function of pressure.However, as many BixOy species with comparable partial pressure are created when BbTi3012 is heated, the ordinate axis in Fig. 2(b) is the total flux of bismuth (or arsenic) atoms.Like GaAs, it can be seen that a growth window exists for the adsorption-controlled growth of PbTiO3 and BbTi3012.In comparison to GaAs, however, the   between the two dashed lines.For PbTi03, the growth window for phase-pure PbTiO3 growth as a function of reciprocal temperature and PbO pressure exists between the two solid lines in (a).For BbTi3012, the growth window for phase-pure BbTi3012 growth as a function of reciprocal temperature and bismuth flux (&om all of the BixOy species in the vapor phase) exists between the two solid lines in (b).

3
The use of adsorption-controlled growth has proven to be extremely effective for the MBE growth of 111-V and 11-VI semiconductors, 11*15~1' PbTiO3 and BbTi3012 (our which has since been confirmed by others17), Bi2Sr2Cu06,I8 and to a lesser degree the growth of (Rb,Ba)Bi03.19 We anticipate that adsorption-controlled MBE growth will be applicable to many other multicomponent oxide materials containing a volatile metal-oxide constituent.20

Adsorption-Controlled Growth of SrBizTa209 and SrBiflbzO9 by PLD
Like BbTi3012, these structurally-related Aurivillius compound^^'-^^ also grow in an adsorption-controlled growth regime with bismuth oxide species being analogous to arsenic in the GaAs system.In other words, a constant overpressure of the volatile bismuth oxide species must be maintained in the system to stabilize epitaxial, phase-pure growth.To fully exploit this phenomenon, we have explored the use of non-stoichiometric, bismuth-rich targets as source materials for the growth of SrBizTa209 and SrBi2mO9 by PLD.To maintain this appropriate overpressure, particular attention must be paid to the PLD growth conditions (substrate temperature, oxidant pressure, laser fluence, and laser pulse rate) as they each play a significant role in determining an optimized growth window.We have optimized the growth conditions of SrBizTa209 and SrBi2m09 films by PLD by exploring a wide range of bismuth-rich target compositions and corresponding growth conditions.26This optimization of adsorption-controlled growth conditions has allowed us to grow epitaxial iilms of these materials with unparalleled perfection and establish several of their fundamental properties, as described below.

Growth of SrBi~Taz09 and SrBim209 Films with Highest Structural Perfection and Highest Remanent Polarization Ever Reported
Although they are now widely used in "smart cards," little is known about the fundamental properties of the layered ferroelectric materials SrBizTa209 and SrBizNbZO9.For example, prior to our work the spontaneous polarization of these materials was unknown, as was the anisotropy in the dielectric constants, coercive fields, and fatigue resistance.The critical property that was known about these materials that has enabled the smart card application is that polycrystalline SrBi2Ta209 and SrBi2mO9 films were capable of withstanding repeated ferroelectric switching cycles (in excess of 10l2 in polycrystalline films) without The layered structure of SrBi2Ta209, SrBi2mO9, and other Aurivillius phase^^'-^' that show similar fatigue-resistance, was argued to be responsible for this advantageous property.To get a more detailed understanding of what makes these materials fatigue resistant, it is desirable to measure the anisotropy in the properties of SrBi2Ta209 and SrBi2m09 films.For example, are these materials fatigue resistant in all directions, e.g., perpendicular to as well as parallel to their Bi202 planes?In addition, spontaneous polarization is a key parameter of all ferroelectrics.
To investigate the anisotropy in the dielectric and ferroelectric properties of SrBi2Ta209 and SrBi2PO9 f i l m s , we have grown epitaxial films of these materials on (OOl), (1 lo), and (1 11) SrTiO3 substrates and studied their orientation, perfection, and electrical properties with four-, circle x-ray dfiaction, AFM, RBS, TEM (both planar view and cross-sectional views), polarization-electric field (P-E), and capacitance-voltage (C-V) measurements.The epitaxial orientation relationship on all substrates can be described as one involving a local continuation of the perovskite sublattice and is schematically shown in Fig. 3. Four-circle x-ray diffraction, RBS (Xmi ,, = 12% for SrBi2Ta209 and x m i n = 5% for SrBi2m09),2691 and TEM32*33 analyses indicate that the epitaxial films grown under our optimized adsorption-controlled conditions have the highest structural perfection and phase purity reported to date for these materials.
The three orientations of epitaxial SrBiZTa209 and SrBizm09 films have been used for three different purposes.The SrBi2Ta209 and SrBi2mO9 films on (001) SrTiO3 substrates are free of growth twins (see Fig. 3), making them ideal for the study of two types of domains in these films using TEM: (1) out-of-phase and (2) ferroelectric domains.34 We recently reported the first observation of ferroelectric domains in SrBi2mO9 films.34 The ferroelectric domains are unusual in these films both in their small size, -50 nm, and in the non-faceted nature of the ferroelectric domain walls.We believe that the latter results from the incredibly small anisotropy (~0.02%) in the a and b lattice constants of SrBi2mO9, as a and b are equal to five significant digits (a = b = 5.5094This is in considerable contrast to the widely studied ferroelectrics BaTiO3 and Pb(Zr,Ti)Os, where the difference in lattice constants is 1.1% and up to 6.4%, respectively, and the domain walls are high faceted.With the miniscule anisotropy in its a and b lattice parameters, the ferroelastic strain energy associated with 90" ferroelectric domain boundaries in SrBizmO9 is much smaller than in more conventional ferroelectrics and we believe that this is why the domain walls curve to such a degree.34 By growing SrBi2Ta209 and SrBi2m09 films on (1 11) SrTiO3 substrates (with an underlying epitaxial SrRuO3 electrode), we achieved what at the time was the highest remanent polarization reported for SrBi2mO9 or SrBi2Ta209 ijlrr~s,'~ 15.7 pC/cm'.
Because the spontaneous polarization of SrBi2Ta209 and SrBi2mO9 exists entirely along its a axis, an increase in remanent polarization is associated with f i l m orientations in which a larger component of the a axis lies pardel to the direction in which the electric field is applied.From Fig. 3 it is evident that of the three orientations studied, growth on (1 11) SrTiO3 will have the largest remanent polarization for the standard parallel plate capacitor geometry, and it does.Finally, the SrBi2TazO9 and SrBi2m09 films grown on (1 10) SrTiO3 have been used to establish the spontaneous polarization in these compounds, as described below.

Establishment of Lower-Bound of Spontaneous Polarization of SrBiflb209
A lower-bound for the spontaneous polarization, P,, of SrBi2Nb209 was established by epitaxially growing SrBizm09 on (1 10) SrTiO3 s~bstrates.~'Unlike other potentially interesting epitaxial orientations, this orientation is special because of the specific angular relationship between the P, and remanent polarization, Pr, vectors.Here, the four types of twins (the two growth twins shown in Fig. 3 and an additional two twins generated within each of those during cooling through the Curie temperature (transformation twins) due to a-b twinning) are equivalent in terms of their contributions to the remanent polarization because the projection of the P, vector along the direction of the applied electric field is identical for all four twins (i.e., always involves two rotations of 45").This is a key simplification, since quantification of the a-b twinning (at least in this orientation) is not required to estimate P,.Additionally, details concerning the switching nature (through either 90" or 180" reorientation of the polar axis) of the spontaneous polarization can be ignored since both a 90" or a 180" reorientation would result in the same effect on the remanent polarization.Thus, this orientation is special because many of these still unanswered fundamental questions are rendered immaterial to the establishment of P,.From the measured remanent polarization and an understanding of the epitaxial geometry, a lower bound of 22.8 pC/cm2 was determined for Ps.30This is a lower bound for this fundamental value, since our t , calculation assumes that the entire f i l m is switching and that the film is entirely phase-pure.That the film is free of second phases and hlly crystalline is supported by TEM (performed on the same f i l m ) and x-ray diffraction results.However, although the P, value is taken from a fully-saturated hysteresis loop, it cannot be concluded that 100% of the f i l m is actually switching.For this reason, our value of 22.8 pC/cm2 is a lower bound on the Ps of SrBi2m09.

Observation of Spiral Growth in e-axis Oriented BidTijO~p SrBi2Ta20% and SrBi2Nb209
Films Grown by MBE and PLD AFM images of the surfaces of (001) BhTi3012 films grown by MBE36 on (001) SrTiO3 as well as of (001) SrBi2Ta20g and (001) SrBi2NbZOg films grown by PLD26*3' on (001) SrTiO3 reveal the presence of a high density (lo8 to lo9 per cm2) of growth spirals emanating from dislocations with screw component.Such growth spirals also occur in the growth of other layered perovskite thin m, e.g., ( O O ~) Y B ~~C U ~O ~-~~~-~~ and indicate that growth occurs by the incorporation of the deposited species at the steps that emanate from dislocations having a screw component, i.e., spiral Unfortunately, the surfaces of oxide films that grow by spiral growth tend not to be smooth because the growth spirals contain several winds, making the peakto-valley roughness over a square micron region typically at least 10 run As smooth surfaces are a prerequisite to the growth of high quality superlattices, we have investigated the growth of c-axis oriented BiQTi3012, SrBi2Ta209, and SrBi2m09 films on substrates of varying lattice mismatch.By growing on substrates better lattice-matched to BhTi3012 than (001) SrTiO3, e.g., (001) LaAl03-Sr2AlTaO6 (LSAT) or (110) NdGaO3, we have been able to grow films free of growth spirals.36This avoidance of spiral growth enabled us to grow smooth BhTi3012 f i l m s and subsequently higher n Bi2(Bi,Pb,Sr),lTi,,O3,, 3 Aurivillius phases (which can be considered as a superlattice of alternating formula units of BhTi3012 and SrTiO3 or PbTi03).43

Establishment of MEED-Based Composition Control Method with Absolute Accuracy of Better than 1%
The growth of high quality multicomponent oxide thin films by reactive MBE requires precise composition control.In some cases, e.g., the growth of PbTi03 or BhTi3O12 described above, it is possible to use adsorption-controlled growth conditions to automatically limit the incorporation of volatile constituents.In many other cases, however, such fortuitous automatic composition control is not possible.SrTiO3 and BaTiO3 are examples where adsorptioncontrolled growth conditions are not possible for practical substrate temperatures.Although we use the best of today's commercially-available techniques for in situ composition control, i.e., atomic absorption spectroscopy (AA) and a quartz crystal microbalance (QCM), one of the major obstacles to the controlled synthesis of metastable oxides is the lack of adequate composition control.To this end we have developed an in situ =ED-based composition control method for the stoichiometric deposition of SrTi03 (100) from independent strontium and titanium sources.44By monitoring changes in the RHEED intensity oscillations as monolayer doses of strontium and titanium are sequentially deposited, the Sr:Ti ratio can be adjusted to within 1% of stoichiometry.These shuttered RHEED oscillations differ from the conventional RHEED oscillations that occur when species are codeposited; they are analogous to the RHEED oscillations that occur during the growth of GaAs f i l m s a t low temperatures by the sequential deposition of gallium and where fractional coverage results in a modulation of the RHEED intensity oscillation envelope.46Furthermore, the presence of a beat frequency in the intensity oscillation envelope allows the * , adjustment of the strontium and titanium fluxes so that a full monolayer of coverage is obtained with each shuttered dose of strontium or We have found this technique to have an absolute accuracy of better than 1%.44 Its use, coupled with epitaxy and epitaxial stabilization, has allowed us to grow the new and metastable oxides described below.

Growth of Metastable PbTiOJ / SrTiO3 and BaTiO3 1 SrTiO3 Superlattices by MBE with Structural Pe~ection Comparable to Superlattices of III / V Semiconductors Grown by MBE
Using reactive MBE and the composition control methods described above (adsorptioncontrolled growth for PbTi03 and RHEED-based composition control for SrTi03 and BaTiOs), we have grown PbTiO3 / SrTiO3 and BaTi03 / SrTiO3 superlattices on (001) SrTi03 substrate^.^'^Both of these systems form a solid solution over their entire composition range.47i48Thus, PbTiO3 / SrTiO3 as well as BaTiO3 / SrTiO3 layered heterostructures are metastable; it is energetically favorable for these oxides to dissolve into each other forming (Pb,Sr)Ti03 and (Ba,Sr)Ti03 solid solutions.The metastability of PbTiO3 / SrTiO3 and BaTi03 / SrTi03 heterostructures is analogous to the situation for AlAs / GaAs heterostructures, which also form a solid solution over their entire composition range.49 As can be seen in the cross-sectional TEM images in Fig. 1, the interface abruptness and layer thickness control of our PbTiO3 / SrTiO3 and BaTiO3 / SrTiO3 superlattices are comparable to what has been achieved for AlAs / GaAs superlattices grown by MBE' and MOCVD" (not shown).The PbTi03 and BaTiO3 layers in these superlattices were grown to have thicknesses less than the critical thickness for the formation of interfacial misfit dislocations, leaving the entire superlattice fully coherent with the substrate.Indeed TEM revealed that the interfaces in both the PbTiO3 / SrTiO3 and BaTiO3 / SrTiO3 superlattices are fully-coherent; no misfit dislocations or  , other defects were observed in the superlattices by TEM.2s3The PbTi03 and BaTiO3 layers are oriented with their c-axis parallel to the growth direction.The dimensional control and interface abruptness achieved in these oxides indicate that MBE is a viable method for constructing oxide multilayers on a scale where enhanced dielectric effects are e~pected.~'To probe the regularity in the periodicity of these superlattices over macroscopic dimensions, $28 x-ray diffraction scans were performed.Figure 4 shows the 828 scan of the same PbTiO3 / SrTi03 superlattice whose TEM is shown in Fig. 1.The high degree of uniformity in the structural order of the superlattice over macroscopic dimensions is revealed by the presence of all of the superlattice peaks and by the narrowness of these peaks.The full width at halfmaximum (FWHM) of these peaks is comparable to the FWHM of the PbTiO3 peaks arising from the 50 nm thick PbTiO3 buffer layer and overlayer that encapsulate the superlattice.
In addition to superlattices, we have also prepared digitally-graded structures in which the average composition is varied by changing the fraction of occurrence of pure layers of the two constituents.Digital grading is commonplace in the growth of compound semiconductors by MBE." Figure 5(a) shows an example of digital grading in oxides on a comparable length scale to that used in advanced semiconductor structures.In the example shown, the composition is digitally graded from pure SrTiO3 to pure BaTiO3 by linearly increasing (in 10% increments) the fraction of BaTi03 unit-cell-thick layers that occur in each segment of the structure.52The grading from pure SrTi03 begins by depositing a one unit-cell-thick (in the c-axis direction) BaTi03 layer followed by a SrTi03 layer nine unit cells thick (in the c-axis direction).Then comes a two unitcell-thick BaTiO3 layer followed by a SrTiO3 layer eight unit cells thick.Next a three unit-cellthick BaTiO3 layer followed by a SrTi03 layer seven unit cells thick, . .., until a ten unit-cell-thick BaTi03 layer is deposited, completing the digital grading from pure SrTiO3 to pure BaTiO3.Just like their oxide su'perlattice counterparts, these digitally-graded BaTiOs / SrTiO3 structures are also metastable; the equilibrium state is a (Ba,Sr)TiOs solid solution.However, the  , rate of cation interdiffusion between the Ba-sites and Sr-sites (both A-sites) in these perovskites is slow.This is apparent from Fig. 5(b), which shows an HRTEM image of a piece of the same film shown in Fig. 5(a) after it was annealed for 2 hours at 1000 "C in 1 atm of pure oxygen.Significant interdifhsion is only just beginning to occur under these conditions.Being able to anneal these metastable structures at such high temperatures in oxygen is advantageous in exploring the intrinsic dielectric, ferroelectric, and optical properties of such customized oxide heterostructures.In their as-grown state, the electrical properties of our layered titanate f i l m s have significantly higher leakage (and dielectric loss) than after annealing.We attribute this behavior to a reduction in the concentration of oxygen vacancies.

Growth of n = 1 to 5 Sr,,+ITi,,Oj,,+l Phases, Including Metastable Ones, by MBE
We have used reactive MBE to create new materials by atomic-layer engineering.An example is the phase-pure growth of the n = 1 to 5 members of the Sr,,+lTiO3,,+1 homologous series, whose crystal structures are shown in Fig. 6.These compounds are known as Ruddlesden-Popper phases after the researchers who discovered the n = 1 (Sr2Ti04) and n = 2 (Sr3Ti207) members of this ~e r i e s .~~. ~~ SrTiO3, the n = m member of this homologous series, consists of alternating Ti02 and SrO layers.The n = 1 (Sr2Ti04) compound has a double SrO layer disrupting the perovskite network along the c-axis.Subsequent members of the series have an increasing number (n) of perovskite blocks separating the double SrO layers.As the $28x-ray diffraction patterns in Fig. 7 (and cross-sectional TEM images in Fig. 8) show, it is possible to grow single-phase epitaxial f i l m s with specific n values, even though nearby phases have similar formation energies.The example shown is the synthesis of the first five members of the Sr,,+lTi,,O3,,+~ Ruddlesden-Popper homologous series.55These structures, shown in Fig. 6, are analogous with the Sr,,+lRunO3,,+l series.X-ray diffraction is an excellent probe for spotting non-periodicity (i.e., intergrowths) in the stacking sequence in the c-direction.
Intergrowths cause certain peaks to broaden, shift, or split in 28.56-58A l l of the peaks in Fig.Using reactive MBE and a combination of AA and RHEED-based composition control we have grown the first five members of the Srn+lTit03n+l Ruddlesden-Popper homologous series: Sr~Ti04, Sr3Ti207, Sr4Ti3O1o, Sr5T&013, and Sr6Tis016.~~X-ray difli-action (Fig. 7) and high-resolution TEM images (Fig. 8) confirm that these f i l m s are epitaxially oriented and contain relatively few intergrowths.Dielectric measurements indicate that the dielectric constant tensor coefficient €33 increases from a minimum of 44k4 in the n = 1 (Sr2Ti04) film to a maximum of 26332 in the n = 00 (SrTiO3) film.55Detailed investigations using quantitative high-resolution TEM methods reveal that the films have the expected n = 1-5 structures of the Ruddlesden-.Popper Sr,+lTi,,O3,+1 homologous series.Among these films, SrzTi04, Sr3Ti207, and Sr4Ti3010 thin films are nearly free of intergrowths, while Sr5Tj4013 ahd Sr6Ti~O16 thin films contain noticeably more anti-phase boundaries in their perovskite sheets and intergrowth defect^.'^We have shown that these results are consistent with what is known about the thermodynamics of Sr,+1Ti~03~+1 phases, including the metastability of Sr,+lTi,03n+l phases with 3 F n <

Understanding of why Epitaxial Sr&Og Films are not Superconducting
Sr2Ru04, which is isostructural to the high-T, cuprate superconductor Lal,Sr,Cu04, is the only known Cu-free layered perovskite superconductor.66Rice and Sigrist predicted that the pairing state of SrzRu04 is odd-parity, possibly p -~a v e .~~ However, phase-sensitive measurements similar to those carried out on high-7'' cuprates to establish their d-wave paring ~tate,~*-~' are lacking for SrZRuO4.To facilitate such experiments on SrzRu04, an important step is the growth of superconducting epitaxial films of this material.Although epitaxial SrzRu04 fjlms have been superconductivity has not been achieved.From single crystal work it is known that both impurities (e.g., as little as 300 ppm of aluminum)8o and "structural disorder"81 can quench superconductivity in Sr2RuO4.To date, there has been very little characterization of structural defects in SrzRu04 single crystals and films.Consequently, the particular type of structural defects that suppress superconductivity in Sr2Ru04 is not established.
We grew epitaxial Sr2Ru04 thin f i l m s by PLD from high-purity (99.98%)Sr2RuO4 targets on (001) LaA103 and found them not to be superconducting down to 0.4 K.A correlation was observed between higher resistivity ratios in electrical transport measurements and narrower x-ray diffraction rocking curve widths of the SrzRu04 Nms.This correlation implicated structural disorder as being responsible for the lack of superconductivity in these epitaxial Sr2RuO4 films.
High-resolution TEM was used to investigate the structural defects in these films.The dominant structural defects, i.e., the defects leading to the observed variation in rocking curve widths in the films, are (011) planar defects, with a spacing comparable to the in-plane superconducting coherence length of Sr2RuO4 (see Fig. 9).These results imply that minimizing structural disorder is the key remaining challenge to achieving superconducting Sr2RuO4

Growth of Superconducting Sr2RuO4 Films by MBE
As described in Sec.2.9, Sr2Ru04 (Tc = 1.5 K in single crystals)83 is unique in several ways, To enable including increasing evidence that it is an unconventional superconductor.phase-sensitive measurements to establish its pairing symmetry, a crucial step is the growth of superconducting films of Sr2RuO4.In Sec.2.9, we described our identification of crystallographic shear defects as the dominant defects in epitaxial Sr2RuO4 films.82A cross-sectional TEM image showing such defects is shown in Fig. 9.Note that the spacing between the planar defects is not significantly greater than the in-plane superconducting coherence length of Sr2Ru04, &,(0) 66 mg3 In all images covering a sufficiently large area, at least one such defect was observed over any a-b plane interval of &,(0).And, since any lattice defect can be a pair-breaker in an odd-parity superconductor, these planar defects that disrupt the RuO2 planes are very likely responsible for the suppression of superconductivity in these high-purity Sr2Ru04 films.A schematic of how we believe these defects are generated is shown in Fig. 10.

Fig. 2 .
Fig. 2. The thermodynamics of adsorption-controlled growth.For GaAs growth, the growth window for phase-pure GaAs growth (as a function of reciprocal temperature and As2 pressure in (a) or as a function of reciprocal temperature and arsenic flux in (b)) exists

Fig. 3 .
S r B i 2 m 0 9 and SrBi2Ta209 grow epitaxially on (001) SrTiO3 with the c-axis parallel to the substrate surface normal, on (1 10) SrTiO3 in a two-fold twin structure with the c-axes tilted by 245" fiom the surface normal, and on (1 11) SrTiO3 in a three-fold twin structure with the c-axes tilted by 57" away fiom the surface normal.

Fig. 4 .
Fig. 4. 8 2 8 x-ray dfiaction scan of a [(PbTiO3)10 / (SrTi03)10]15 superlattice in which aPbTiO3 layer 10 unit cells thick (in the c-axis direction) is grown on top of a SrTi03 layer 10 unit cells thick (in the c-axis direction) and this bilayer is repeated 15 times.The OO! superlattice reflections, the 001 reflection of the thick PbTi03 buffer layer and overlayer, and 001 reflection of the SrTiO3 substrate are labeled.The x-ray diffi-action data indicate that this superlattice has a periodicity of 8.37 f 0.02 nm. b

Fig. 5 .
Fig. 5. HRTEM images of a digitally-graded BaTiO3 / SrTiO3 layer that goes from pure SrTiO3 to pure BaTi03 in unit-cell-thick increments.(a) The as-grown sample (Tsub = 660 "C) and (b) after annealing at 1000 "C for 2 hours in oxygen.The BaO monolayers in each unit-cell-thick layer of BaTiO3 are marked with arrows.As can be seen in (b), the nano-engineered layering is stable to relatively high temperatures.

Fig. 8 . 2 (
Fig. 8. Cross-sectional HRTEM images (from left to right) of the n = 1 (SrzTiOr), n = 2 (Sr3Ti207), n = 3 (Sr4Ti3010), n = 4 (SrsT&013), and n = 5 (Sr6Ti5016) m.A model of the crystal structure of the n = 1 and n = 5 members are adjacent to the corresponding images showing the position of the SrO double layers and perovskite layers.The arrows mark the position of the interface of the films with the homoepitaxial SrTiO3 buffer layer.

Fig. 10 .
Fig. 9. Anm arrowe closely lack of LTEM :d regi than super image of a high-purity c-axk SrzRu04 film grown by PLD I on is a crystallographic shear defect.These planar defects a~ the in-plane superconducting coherence length of SrzRu04, conductivity in these films.[Ref.821.-e spaced explainin
-latter growth windows are considerably narrower.Nonetheless, the adsorption-controlled growl