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Mobility modulation and suppression of defect-formation in twodimensional electron systems by charge transfer management Felix Gunkel, Ronja Anika Heinen, Susanne Hoffmann-Eifert, Lei Jin, Chun-Lin Jia, and Regina Dittmann ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b00905 • Publication Date (Web): 06 Mar 2017 Downloaded from http://pubs.acs.org on March 14, 2017

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ACS Applied Materials & Interfaces

Mobility modulation and suppression of defectformation in two-dimensional electron systems by charge transfer management Felix Gunkel1,2*, Ronja A. Heinen2, Susanne Hoffmann-Eifert2, Lei Jin2,3, Chun-Lin Jia2,3, Regina Dittmann2

1

Institute of Electronic Materials (IWE2), RWTH Aachen University, 52062 Aachen, Germany 2

Peter Grünberg Institute and JARA-FIT, Forschungszentrum Jülich, 52425 Jülich, Germany 3

Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, 52425 Jülich, Germany E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT Electron mobility is one of the most-debated key attributes of low dimensional electron systems emerging at complex oxide heterointerfaces. However, a common understanding of how electron mobility can be optimized in these systems has not been achieved so far. Here, we discuss a novel approach for achieving a systematic increase in electron mobility in polar/non-polar perovskite interfaces by suppressing the thermodynamically required defect formation on the nanoscale. We discuss the transport properties of electron gases established at interfaces between SrTiO3 and various polar perovskites (LaAlO3, NdGaO3 and (La,Sr)(Al,Ta)O3), allowing for the individual variation of epitaxial strain and charge transfer among these epitaxial interfaces. As we show, the reduced charge transfer at (La,Sr)(Al,Ta)O3/SrTiO3 interfaces yields a systematic increase in electron mobility, while the reduced epitaxial strain has only minor impact. As thermodynamic continuum simulations suggest, the charge transfer across these interfaces affects both the spatial distribution of electrons and the background distribution of ionic defects, acting as major scatter centers within the potential well. Easing the charge transfer in (La,Sr)(Al,Ta)O3/SrTiO3 yields an enlarged spatial separation of mobile charge carriers and scattering centers, as well as a reduced driving force for the formation of ionic defects on the nanoscale. Our results suggest a general recipe for achieving electron enhancements at oxide heterostructure interfaces and provide new perspectives for the atomistic understanding of electron scattering in these systems.

KEYWORDS Oxide heterointerfaces, 2DEG, mobility, thermodynamics, interface chemistry, defect-formation


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Introduction Two-dimensional electron gases (2DEGs) at oxide heterointerfaces have become a major playground both for developing novel oxide electronic devices and for exploring the rich physical phenomena emerging in complex oxides in the low dimensional limit.1-3 This is because of the wide variety of novel physical properties which arise specifically because two materials are interfacing each other with atomic precision, ranging from metallicity4 to superconductivity 5 to magnetism6, 7. Typical attributes characterizing such 2DEG systems are carrier density, electron mobility and coherence length, and confinement potential. A major field of research is the control of these characteristic quantities, in order to achieve tunable electron gases at the highest possible electron mobility. This challenge is driven by the needs of classical technological applications contemplated for these electron systems8, 9 as well as by the needs of fundamental research, e.g. on quantum phenomena. 10-12 In the literature, various approaches to realize more dilute and higher mobility electron systems based on the prototypical 2DEG system, LaAlO3/SrTiO3 (LAO/STO), have been tested, particularly by varying growth parameters.

13-15

For example, a lowered growth temperature has

been reported to result in increased electron mobility13. Moreover, electric field-effects have been shown to be effective. However, these do affect both electron mobility and electron density at the same time and in an entangled manner.16, 17 As an alternative approach, novel material systems other than LAO/STO are explored. In fact, enhanced electron mobility has already been demonstrated in various cases. 13, 18-20 However, the origin of this enhancement is yet under debate and there is a lack of systematic understanding of scattering and disorder in these systems.13


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One major strategy proposed in the literature to achieve mobility enhancements is to tailor and control the epitaxial strain at the interface,21 or in thin films18, 22 thereby affecting structural distortions such as tilting and buckling of atomic planes at the interface. 23, 24 Another proposed strategy is to try to control the distribution of growth-induced extrinsic defects, in order to separate them from the mobile charge carriers.19 In this context, mainly oxygen vacancies are discussed as major scatter centers. In addition, however, for epitaxial perovskite/perovskite heterointerfaces a more complex defect structure has been suggested, involving the presence of Sr vacancy defects,25 anti-site defects 26 and cation intermixing 27in addition to oxygen vacancy defects. Moreover, the observation of increasing interface resistances

14, 15

and decreasing electron mobility

28

in

increasingly oxidized samples (i.e., in increasing absence of oxygen vacancies), suggests complex scattering processes beyond a mere oxygen vacancy scenario in these charge-transfer-based systems.20 In this study, we argue that the electron mobility at oxide heterointerfaces is directly increased by the management of the nominal charges of the atomic planes of the polar oxide, determining the amount of charge transfer occurring across polar-perovskite/non-polar perovskite interfaces. As we will elaborate, reducing the charge transfer into the interface readily results in an increased spatial separation between electrons and ionic scatter centers accumulating in the well. At the same time, the thermodynamic formation of ionic defects within the well is strongly suppressed, reducing also the total concentration of scatter centers. In contrast, the effect of epitaxial strain (i.e., lattice mismatch) is shown to have only minor impact on the electron mobility. For this purpose, we focus on the properties of the 2DEG system emerging at the epitaxial interface between the two perovskites STO and (La0.18Sr0.82)(Al0.59Ta0.41)O3 (LSAT). In agreement with a previous report18, we demonstrate a systematically enhanced electron mobility in this 2DEG,


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accompanied by an enlarged magnetoresistance (MR) compared to the standard system LAO/STO. We then discuss comprehensively the nature of this mobility enhancement and discriminate the effects of epitaxial strain and intrinsic ionic defect structure. As we show, no mobility enhancement is observed at NdGaO3/STO heterointerfaces, sharing a similar interfacial lattice mismatch with LSAT/STO, suggesting a negligible effect of epitaxial strain for establishing enhanced electron mobility in LSAT/STO. Instead, the increased electron mobility turns out to be an inherent property of the LSAT/STO material system. In order to understand the observed systematic behavior in detail, we consider the thermodynamic defect-formation processes within the well, driven by the charge transfer process29. As we discuss, the suppressed scattering rate for electrons derives from the lowered electric field required for compensation of the polarity mismatch occurring at the interface of LSAT/STO as compared to LAO/STO. Our approach highlights a general route for generating high mobility electron gases in complex oxide heterostructures by managing the involved thermodynamically required defect formation processes.

Results Fig. 1 shows typical structural properties of LSAT/STO heterostructures grown by pulsed laser deposition (PLD). During deposition, clear reflection high-energy electron diffraction (RHEED) intensity oscillations are observed indicating layer-by-layer growth mode (Fig. 1 a). As a result, after the growth the samples exhibit an atomically flat surface morphology with typical step-terrace structure (inset of Fig. 1 a). X-ray diffraction (XRD) measurements reveal clear thickness fringes (Fig. 1b) confirming a good crystallinity of the epitaxial thin film and a welldefined heterointerface between the two materials. (The position of the main film peak is hardly resolvable from the substrate peak due to the low (1%) lattice mismatch between the two


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materials.) Fig. 1c shows the interface region in atomic resolution obtained by high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM). Evidently, the thin film is epitaxial and exhibits a “sharp” interface with gradual intensity over only 1-2 unit cells across the heterointerface. Slight intensity fluctuations are evident in individual atomic columns (marked by arrows) in the LSAT layer, as similarly observed in the literature.18, 30 It is worth noting that in HAADF STEM, a very short dwell time (≤8 μs/pix) has to be used in order to prevent the LSAT/STO heterostructures from electron beam damage. Owing to the same reason, quantification of point defects such as vacancies on anion and cation sites and/or intermixing across the interface becomes experimentally impossible.31 After the growth, the samples turn conducting with a thickness-independent sheet resistance. At room temperature, Hall measurements yield a carrier density of about 4x10 13 cm-2 for LSAT/STO. Upon cooling, the resistance of LSAT/STO shows a metallic temperature dependence. In Fig. 2(a), we plot the low temperature sheet resistance of LSAT/STO in comparison to the one obtained for the prototypical 2DEG system LAO/STO as well as for its isoionic relative, NdGaO3(NGO)/STO. LSAT/STO shows a significantly lower residual resistance than LAO/STO and NGO/STO, which both show notably similar resistance values. At low temperature (≤ 30 K), Hall measurements reveal a non-linear Hall effect as shown in Fig. 2 (b) indicating multi channel conduction within the 2D potential well,28, 32-33 with typically two major contributions from electron populations in heavy and light mass bands.34 For LSAT/STO, the Hall resistance becomes nearly linear at fields above a few tesla, while the one obtained for LAO/STO and NGO/STO (see Figure S1) still shows significant curvature up to 9T. In a two-channel conduction model, the linear high field approximation (Rxy~(n1+n2)-1, cf. Supplement) implies that iB>>1. Here, i and ni denote the mobility and the sheet carrier density


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of the two electron populations (i=1,2). The linear behavior of Rxy at fields above about 2T hence indicates an increased electron mobility at the LSAT/STO interface as compared to the LAO/STO interface. In accordance with this, we observe a MR of almost 150% at 2K and the highest applied fields. This is again significantly higher than the MR observed for LAO/STO and NGO/STO which is in the range of 30-50% at maximum field (Fig. S1). The increased MR observed in LSAT/STO is also consistent with increased electron mobility, yet there is no indication of quantum oscillations in the investigated temperature range (down to 2 K). Using a two-channel model to fit the Hall resistance as a function of applied field (cf. Supplement), we extract i and ni in the low temperature regime as displayed in Figure 3a and 3b, respectively. We can identify a high-mobility—low-density electron population (filled symbols) and a low-mobility—high-density electron population (open symbols). For both channels, the electron mobility extracted for LSAT/STO (1≈8000 cm2/Vs, 2≈1200 cm2/Vs at 2 K) is enhanced by a factor of 4 as compared to ones extracted for LAO/STO and NGO/STO ( 1≈2000 cm2/Vs,

2≈300 cm2/Vs at 2 K). Notably, electrons in LAO/STO and in NGO/STO exhibit very similar mobility values. This is particularly remarkable since NGO provides magnetic moments (Nd 4f) in the vicinity of the interface, while LSAT and LAO do not inherently contain magnetic components. Hence, Kondo-type magnetic scattering is not a dominant factor here, consistent with the absence of a significant resistance upturn at low temperature in any of the samples (for LAO/STO, more significant resistance upturns are typically reported at higher growth pressures, apparently resulting in lower mobility and thus more defective interfaces

14-15, 28

). However, all

samples show the signature of the anomalous Hall effect (AHE), indicating the presence of weak magnetic moments in all samples.28 The AHE enters as an additional term to the Hall effect, without significantly affecting the mobility values extracted from a two-channel model.28 The


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AHE is least pronounced for LSAT/STO, while it is comparable in LAO/STO and NGO/STO (cf. Supplement, Fig. S2), indicating a similar magnetic structure in LAO/STO and NGO/STO (such as discussed in Ref. 28), and only marginal magnetism in LSAT/STO (in agreement with Ref. 35). The carrier density found for the low-mobility conduction channel is about 3-4x1013 cm-2 for all studied material systems, with the lowest value found for LSAT/STO. Interestingly, the carrier density found for the high-mobility channel is significantly increased for LSAT/STO as compared to LAO/STO and NGO/STO. Hence, LSAT/STO does not only show significantly increased electron mobility, but also an increased occupation of the high-mobility channel as compared to LAO/STO and NGO/STO, indicating a modified band structure. A similar result is found systematically for LSAT/STO samples, indicating that the mobility enhancement is a characteristic property of the 2DEG formed at the LSAT/STO interface. The systematic increase in mobility observed among the three different material systems investigated here is striking. In fact, the increase in mobility is achieved inherently when moving from LAO/STO (or NGO/STO) to LSAT/STO and does not require excessive effort, e.g. delicate optimization of growth parameters. Even more, the enhanced electron mobility appears to be an inherent property of the LSAT/STO. Albeit higher absolute mobility values have been occasionally reported for LAO/STO and in other systems13, 18, 20, the underlying physical nature of the general trend observed here still needs to be understood in detail. A mere scenario of electron scattering at oxygen vacancy defects generated during PLD growth

36-39

is unlikely for the samples investigated here. For one, all samples studied here have

been cooled down slowly after the PLD process (10 K/min), allowing for reoxidation and ensuring a close-to-equilibrium state of the samples (following Ref. 14). Moreover, growth-induced oxygen


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vacancy formation cannot easily explain the categorical mobility variation from LAO/STO and NGO/STO to LSAT/STO observed here. Another possible cause of this characteristic increase in electron mobility discussed in the literature is the effect of lattice mismatch and epitaxial strain.18 However, comparing the three 2DEG systems, LSAT/STO, LAO/STO, and NGO/STO in detail makes this suggestion unlikely, too. Fig. 4 displays reciprocal space maps (RSMs) for the three material systems, confirming that all thin films grow under tensile strain. LSAT and NGO share an almost similar (pseudo-cubic) bulk lattice constant (3.86 Å; 3.87 Å), while the one of LAO is significantly smaller (3.79 Å). Hence, lattice mismatch and epitaxial strain are expected to be comparable and small in LSAT/STO and NGO/STO, while it is significantly larger in LAO/STO. This is illustrated in the RSM measurements by the rather large distance between substrate peak and thin film peak in outof-plane direction found for LAO/STO. In contrast to that, the peaks are close in LSAT/STO and NGO/STO. Hence, if epitaxial strain is the mobility-limiting factor here, LSAT/STO and NGO/STO should show rather identical properties and only LAO/STO should exhibit a significantly lower electron mobility – which is not the case as shown in Fig. 3a. In contrast, LAO/STO and NGO/STO identically exhibit lower electron mobility, while only LSAT/STO shows significantly enhanced mobility. Interestingly, LAO and NGO share the nominal ionic structure having trivalent cations on A- and B-site of the perovskite lattice, while LSAT nominally comprises a mixture of (La0.18Sr0.82) +2.18

on the A-site and (Al0.59Ta0.41)+3.82 on the B-site. Thus, the ionic structure of LSAT differs

from the one of LAO and NGO. Therefore, the very similar behavior of LAO/STO and NGO/STO observed in the low temperature electrical measurements clearly suggests that the nominal ionic charges of the capping layer mediate the electron mobility behavior rather than epitaxial strain. In


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fact, as shown experimentally almost similar epitaxial strain (LSAT/STO and NGO/STO) can result in significantly different electron mobility, and significantly different epitaxial strain (LAO/STO and NGO/STO) can result in very similar electron mobility. In order to understand this relation in more detail, we consider the effect of the nominal ionic structure at the interface on the development of the potential well and on the defect formation processes therein. The electron mobility at lowest temperatures is limited by scattering on crystal imperfections and defects. For oxide interfaces, these scatter centers are believed to exhibit an inhomogeneous distribution within the interface region, with a larger concentration close to the interface and a lower concentration of defects further apart from the interface.16, 28 Therefore, enhancements of the electron mobility may be achieved either by reducing the absolute concentration of defects in the potential well or by spatially separating the electrons of the 2DEG from the scatter centers. Within the polar discontinuity picture, the nominal ionic structure of the polar oxide layer determines the amount of charge that needs to be transferred into (and separated at) the interface (Fig. 5a) to level out the otherwise diverging electrical potential.27, 40 In (100)-orientation, LSAT consists of atomic planes that have the nominal charge of +/-0.18 electrons per unit cell area (e/uc2), while the atomic planes in LAO (and NGO) have a nominal charge of +/-1 e/uc2 27. This implies that a lower amount of charge, Q/A, has to be transferred into the LSAT/STO interface as compared to the LAO/STO interface. As a result, also the electric field E(0) at the interface of LSAT/STO is lower than in LAO/STO (and NGO/STO), given that E(0) and Q/A are directly connected via Gauss’ law (cf. Fig. 5a)29, 41

E (0)  

1 Q .  r 0 A


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At room temperature (r~300), this corresponds to a nominal electric field of 18 MV/cm for LAO/STO (and NGO/STO) and 3.6 MV/cm for LSAT/STO. In this view, the nominal electric field established at the interface is the most notable difference between LSAT/STO on the one hand, and LAO/STO and NGO/STO on the other (Fig. 5a). The electric field established at the interface attracts electrons and is the driving force for the 2DEG formation at the interface. Typically, the screening length increases with decreasing electric field strength. Therefore, the lower nominal field in LSAT/STO causes a wider distribution of electrons into the STO substrate. Given the generally assumed inhomogeneous distribution of scatter centers, this may yield an increase in the mean electron mobility of electrons. However, in this purely electronic picture, one would expect significantly different carrier densities, nS, directly correlating with the transferred charge. This, however, is not observed experimentally (Fig. 3b). As a matter of fact, the internal electric field formed in the potential attracts not only electrons, but any defect species, ionic and electronic, that carries a negative charge, and it repels any positively charged defect from the interface. At elevated temperature (such as typically applied during the growth process of oxide heterostructures), oxygen vacancies will thus move away from the interface in response to the internal electric field. On the other hand, cation vacancies (i.e., mainly Sr vacancies as described in the literature for bare STO41-43) would accumulate in the interface region in response to the electric field. Therefore, close to equilibrium, Sr vacancies rather than oxygen vacancies are likely to be the dominant and mobility-limiting intrinsic defect in the potential well.14, 28 Comparing the different material systems discussed here, the lower electric field in LSAT/STO reflects a lower driving force for formation and accumulation of these defects, providing an additional intuitive explanation of the observed increase in electron mobility as compared to LAO/STO and NGO/STO. Due to the expected nanometer confinement at such


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interfaces and due to the vacancy nature direct evidence for the presence of Sr vacancy defects is very challenging. However, their formation at the interface as assumed follows from fundamental thermodynamic and entropic considerations (minimization of Gibbs´ free energy29). As yet, indirect indications have been provided, in particular the pO2-dependence of electron mobility in NGO/STO heterostructures

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as well as the thermodynamic stability and high temperature pO2-

dependence of the 2DEGs conductivity 14, 44-45, making this assumption well justified. For a more quantitative discussion of this scenario, we calculated the expected concentration profiles for electrons and Sr vacancy defects established at growth temperature for a given charge transfer, Q/A (Fig. 5b,c). As elaborated in detail in a previous study29 and summarized in the Supplement, we self-consistently solve in a continuum model the electrostatic equations (Poisson’s equation, Gauss´ law, and global electro-neutrality) assuming mobile ionic and electronic charge carriers (instead of electrons only46, 47) at given thermodynamic bounds, i.e. temperature, T, and oxygen pressure, pO2. For a detailed discussion, we chose the growth parameters applied for all samples (T=950 K and pO2=1x10-4 mbar) as thermodynamic bounds. (Additional pO2-dependent calculations are provided in the Supplemental, Fig. S4.) In order to represent LAO/STO (and NGO/STO), we use Q/A≈1x1014 e/cm2 (such as determined experimentally in Refs. 25, 44) and Q/A≈4x1013 e/cm2 (corresponding to 0.06 e/uc2, such as determined experimentally in the Supplement S3 and in Ref. 44). Both values are lower than the nominal ones, justified by the presence of additional screening mechanisms such as atomic displacements24, 48 effectively reducing the charge transfer. (The exact number has no significant influence on the qualitative behavior, a discussion will be provided in Fig. 5.) In fact, the very similar behavior of LAO/STO and NGO/STO indicates that the attenuated charge transfer due to atomic displacements and lattice polarization across the interface often discussed in the literature


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24, 48-49

mainly arises in response to the ionic structure and the electric field, too, rather than from

lattice mismatch-induced epitaxial strain. In Fig. 5b and c, we compare the electric potentials and the corresponding depth profiles of electrons and Sr vacancies received from the model calculations. In LSAT/STO, we observe a lower interface potential (Fig. 5b) associated with an overall lower electron concentration profile than in LAO/STO or NGO/STO (Fig. 5c). At the same time, in LSAT/STO the potential well spreads wider into the bulk than in LAO/STO (Fig. 5b). As indicated by the dashed lines, 90% (99%) of the 2DEG electrons are confined to 7nm (25nm) in LSAT/STO, while they are confined to 3nm (12nm) in LAO/STO. Hence, the larger the charge transfer at the interface, the stronger is the confinement of the electrons of the 2DEG, in agreement with classical semiconductor models. At same time, the accumulation of ionic species, i.e., Sr vacancy defects that are attracted by the electric field at the interface is significantly reduced in LSAT/STO in our model (Fig. 5c). Hence, the density of scatter centers within the space charge layer is greatly reduced. The established depth profile of Sr vacancy defects is very steep in the near-interface region providing the inhomogeneous defect structure within the potential well, such as generally assumed in the literature.16-17, 50 Thus, electrons close to the interface are experiencing much more scattering events, than electrons moving further apart. Hence, our model calculations consistently confirm a widening of the electron confinement for LSAT/STO as compared to LAO/STO (and NGO/STO), with a beneficial effect for the electron mobility (Fig. 5e). Due to the electric-field dependence of the dielectric constant of STO evident at low temperature,47, 51 this effective separation of electrons and ionic scatter centers becomes even more pronounced upon cooling. Additionally, a widening of the potential affects also the energy splitting of the subband structure in the well,32 which in turn controls the subband occupation observed at low temperature. Hence, the different


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confinements may explain the increasingly occupied high-mobility subband in LSAT/STO as compared to LAO/STO and NGO/STO (Fig. 3b). Furthermore, localization of electrons (i.e., localized Ti3+ states) 35, 52 is particularly favored under strong confinement, i.e. rather in LAO/STO and NGO/STO than in LSAT/STO, which is consistent with literature, too.35 Interestingly, the integrated sheet electron densities obtained from the model calculations yields ns,calc=2.4x1013 cm-2 for LSAT/STO and 4.1x1013 cm-2 for LAO/STO. Thus, there is a discrepancy between the 2D electron density and the assumed total charge transfer (Q/A). This is because the missing charge is accommodated by accumulated ionic Sr vacancy defects. In both systems, the Sr vacancy concentration increases steeply towards the interface reaching values as high 7x1020 cm-3 in the LAO/STO (and NGO/STO) case and 3x1019 cm-3 in the LSAT/STO, while it drops quickly into the bulk. Averaged over the first unit cell from the interface, this corresponds to a concentration of 1uc =3.7x1020 cm-3~ 2.2at% of vacancies formed right at the interface in the LAO/STO case. In the second unit cell from the interface, we obtain a mean concentration of only 0.7 at% of vacancies. In the LSAT/STO case, the concentration in the first unit cell from the interface is already well below 1at%. Hence, these concentrations are hardly detectible in a direct manner, e.g. by means of imaging as well as electron spectroscopy such as shown in Fig. 1c. This is 1) because of their vacancy nature, 2) because of their low concentration and 3) because of the presence of electron beam damage. Note, however, that spectroscopically the required counter part of Sr vacancy formation, i.e., the segregation of SrO on the nanoscale has been reported for LAO/STO and NGO/STO, in good agreement with our model.

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Moreover, the

presence of ancillary negative charge next to electrons has been proposed in the literature,50 hinting towards the presence of additional ionic defects that are not of oxygen vacancy-type, too.


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Our model calculations allow for a systematic variation of the charge transfer yielding a simple way to estimate the expected defect structure for a given Q/A. In Fig. 5e, we plot the integrated sheet densities of Sr vacancies (red bars) and electrons (black bars) as a function of Q/A at the given pO2 and T, providing a measure of the expected weight of ionic and electronic charge compensation depending on the electrostatic bounds of the system. These consideration reveal a systematic trend. For large Q/A, such as in LAO/STO (and NGO/STO), electrons and Sr vacancies almost equally contribute to charge compensation. Hence, not only the 2DEG electron density is large, but also the amount of ionic Sr vacancies. In contrast to this, for reduced Q/A, such as in LSAT/STO, mainly electrons contribute to charge compensation. Hence, in LSAT/STO, the favored charge compensation mechanism is the formation of a rather clean electron gas, since the intrinsic driving mechanism for defect formation is suppressed. In fact, further reduction of Q/A, e.g. to 1x1013 e/cm2 and below systematically suppresses the accumulation of ionic defect species, so that cleaner and cleaner interfaces are expected to be formed the more the required charge transfer at the interface is reduced (Fig. 5e). In other words, the electrostatic boundary conditions in polar-perovskite/STO heterointerfaces require a defined amount of charge to be transferred across the interface. Therefore, when aiming for dilute electron gases with reduced carrier density, these systems have to pay the cost of the missing electronic charges by the formation of ionic defects29, namely Sr vacancies25, which then limit the electron mobility.14,

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Therefore, it is desirable to ease the

electrostatic bounds by reducing the nominal charge of the atomic planes as compared to LAO. This is achieved e.g. by replacing LAO with LSAT, as discussed here. Furthermore, a continuously cleaner interface forms as one moves towards lower and lower charge transfer. In practice, this means heterostructures with polar oxides that have even smaller polarity than LSAT. Thus, a


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heterostructure specifically designed following this approach is expected to show further increased electron mobility. As a limiting case, a 2DEG system with canceling electric field is expected to show a greatly increased electron mobility. This may be provided by a 2DEG relying on a quenched profile of excess oxygen vacancies, instead of charge transfer driven by electrostatic bounds, as in this case the driving force for Sr vacancy formation is absent. In fact, high mobility values has been reported for -Al2O3/STO55 as well as for amorphous LAO/STO heterostructures, both suggested to rely on oxygen vacancy formation only.19-20, 44, 56 A second option is the kinetical suppression of the formation and/or distribution of Sr vacancy defects within the space charge layer, by exploiting the sluggishness of Sr diffusion in STO at lower growth temperatures. Hence, by avoiding high temperature treatments, Sr vacancy formation may be limited to the very interface region or even suppressed completely.29 Indeed, low-temperature growth of LAO/STO has been reported to provide increased mobility values, too.13, 57 The scenario based on Sr vacancy defects suggested here is hence consistent with experimental observations of mobility enhancements reported in the literature, and furthermore may well serve as a physical explanation of these.

Conclusions In summary, it has been derived that the LSAT/STO interface readily exhibits a lower amount of ionic defects within the space charge region, resulting in a cleaner interface in which electron scattering is strongly reduced. As a result, a systematically increased electron mobility is accessible in low temperature transport experiments using LSAT/STO instead of the LAO/STO standard. The difference in epitaxial strain between LSAT/STO and LAO/STO cannot justify the difference in electron mobility, as shown on the example of NGO/STO, sharing the same strength


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of epitaxial strain with LSAT/STO, but the same electron mobility with LAO/STO. In contrast, we argue that the observed behavior in LSAT/STO is the result of a two-fold process: 1) a widening of the potential well which spatially separates Sr vacancy impurities (having a sharp depth profile) from the electrons of the 2DEG; and 2) a lowering the electro-chemical driving force for ionic defect formation by reducing the interfacial electric field. Both effects stem from the altered ionic structure and in particular from the low nominal charge of the atomic planes in LSAT. Therefore, it may be beneficial to seek dilute 2DEGs at oxide interfaces that have an even smaller, but finite electrical dipole at their interface. The use of such low-polarity oxides may represent a systematic future direction yielding mobility enhancements in oxide heterostructures. Experimental PLD growth: 25 unit cells of LSAT (LAO, NGO) were deposited on TiO2-terminated SrTiO3 single crystals (CrysTec GmbH, Germany) by pulsed laser deposition at a growth temperature of 950 K and a growth pressure of 1x10-4 mbar oxygen. In all cases, a laser fluence of 1.9 J/cm2 was applied to single crystalline targets (CrysTec GmbH, Germany) at a frequency of 1 Hz and a targetto-substrate distance of 60 mm. All samples were cooled down at a rate of 10 K/min in deposition pressure. The slow cooling rate is required to allow for the reoxidation of oxygen vacancies

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potentially formed during the PLD growth process. X-ray diffraction and reciprocal space mapping: X-ray diffraction data ( -2) was recorded using a Philips X´pert PW 3200 diffractometer (Cu K,1/2). RSM data was provided by PANalytical GmbH, Germany. Note that differing substrate intensities and RSM resolution stem from varying integration times and step width used during the measurement, without affecting the determination of the lattice parameters and strain state.


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Scanning transmission electron microscopy: Lamellar specimens for STEM investigations were prepared by focused ion beam milling using an FEI Helios Nanolab 400s dual-beam system

58

.

HAADF STEM imaging was performed in an FEI Titan 80-300 microscope equipped with a probe spherical aberration corrector, running at an acceleration voltage of 300 kV 59. The inner collection angle of HAADF was 70 mrad. Transport measurements: Transport measurements were performed between 2 K and 300 K in a Physical Property Measurement System (PPMS, Quantum Design). The interfaces were contacted using Al-wire bonding in a mimicked Hall bar structure (cf. Ref. 28). Numerical simulations: Thermodynamic simulations were performed using a custom C++ code. We self-consistently solve Poisson’s equation, fixing the input field (associated with the parameter Q/A) at the interface and satisfying a flat potential in the bulk (global charge neutrality). Within the space charge region an equilibrium of electrons, electron holes, oxygen vacancies and strontium vacancies is assumed.


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Figure 1. (a) RHEED intensity oscillation obtained during growth of 25 unit cells of LSAT on STO. The inset shows the resulting surface morphology. (b) X-ray diffraction of LSAT/STO. (c) Atomic-resolution HAADF-STEM image of the LSAT/STO interface region. Arrows mark occasional intensity fluctuations in individual columns.


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Figure 2. (a) Temperature-dependence of the sheet resistance obtained for LSAT/STO in comparison to LAO/STO and NGO/STO. (b) Hall resistance obtained for LSAT/STO at selected temperatures. (c) Corresponding MR vs. applied magnetic field (+/-9T).


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Figure 3. (a) Low temperature Hall mobility obtained from non-linear Hall characteristics. (b) Corresponding electron density.


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Figure 4. Reciprocal space maps (-103) obtained for LSAT/STO, NGO/STO, and LAO/STO. Note that differing substrate intensities and RSM resolution stem from varying integration times and step width used during the measurement without affecting the determination of the thin films´ strain state.


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Figure 5. (a) Schematic of the electric field established at the LSAT/STO and LAO/STO interface. (b) Electrostatic potential obtained in thermodynamic equilibrium at growth conditions (T=950 K, pO2=1x10-4 mbar) for LSAT/STO and LAO/STO. (c) Corresponding concentration profiles of electrons and Sr vacancy defects. (d) Schematic of electron scattering in near the interface of LSAT/STO and LAO/STO heterointerfaces. (e) Sheet concentrations of electrons and Sr vacancy defects accumulated in the interface region as a function of charge transfer, Q/A.


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Supporting Information. Collection of Hall and MR data; detailed description of numerical simulations; pO2-dependent simulation results Author Contributions F.G. performed numerical simulations and supervised the research project. R.A.H. performed transport experiments and fabricated the samples. L.J. and C.L.J. provided TEM analysis. F.G., S.H.-E., R.W., and R.D. discussed the results and contributed to the manuscript. Funding Sources R.D. acknowledges funding from the W2/W3 program of the Helmholtz association. ACKNOWLEDGMENT F.G. and S. H-E. thank PANalytical GmbH for RSM characterization. Doris Meertens is thanked for the STEM sample preparation. REFERENCES 1. 2. 3. 4. 5.

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