The Effect of Polar Fluctuation and Lattice Mismatch on Carrier

Letter pubs.acs.org/NanoLett

The Effect of Polar Fluctuation and Lattice Mismatch on Carrier Mobility at Oxide Interfaces Zhen Huang,†,‡ Kun Han,†,‡ Shengwei Zeng,†,‡ Mallikarjuna Motapothula,†,‡ Albina Y. Borisevich,§,∥,⊥ Saurabh Ghosh,§,# Weiming Lü,∇ Changjian Li,† Wenxiong Zhou,†,‡ Zhiqi Liu,○ Michael Coey,†,◆ T. Venkatesan,*,†,‡,¶,■,● and Ariando*,†,‡,● †

NUSNNI-NanoCore, National University of Singapore, 117411 Singapore Department of Physics, National University of Singapore, 117542 Singapore § Materials Science and Technology Division, ∥Institute for Functional Imaging of Materials, and ⊥The Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States # Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, United States ∇ Condensed Matter Science and Technology Institute, School of Science, Harbin Institute of Technology, Harbin 150081, People’s Republic of China ○ Department of Materials Science and Engineering, University of California, Berkeley, California 94720, United States ◆ School of Physics and CRANN, Trinity College, Dublin 2, Ireland ¶ Department of Electrical and Computer Engineering, National University of Singapore, 117576 Singapore ■ Department of Materials Science and Engineering, National University of Singapore, Singapore 117575, Singapore ● National University of Singapore Graduate School for Integrative Sciences and Engineering (NGS), 28 Medical Drive, Singapore 117456, Singapore ‡

S Supporting Information *

ABSTRACT: Since the discovery of two-dimensional electron gas (2DEG) at the oxide interface of LaAlO3/SrTiO3 (LAO/STO), improving carrier mobility has become an important issue for device applications. In this paper, by using an alternate polar perovskite insulator (La0.3Sr0.7) (Al0.65Ta0.35)O3 (LSAT) for reducing lattice mismatch from 3.0% to 1.0%, the low-temperature carrier mobility has been increased 30 fold to 35 000 cm2 V−1 s−1. Moreover, two critical thicknesses for the LSAT/STO (001) interface are found, one at 5 unit cells for appearance of the 2DEG and the other at 12 unit cells for a peak in the carrier mobility. By contrast, the conducting (110) and (111) LSAT/STO interfaces only show a single critical thickness of 8 unit cells. This can be explained in terms of polar fluctuation arising from LSAT chemical composition. In addition to lattice mismatch and crystal symmetry at the interface, polar fluctuation arising from composition has been identified as an important variable to be tailored at the oxide interfaces to optimize the 2DEG transport. KEYWORDS: Oxide interface, two-dimensional electron gas, carrier mobility, lattice mismatch, polar fluctuation

S

transferred from the LAO valence band to the STO conduction band. This electronic reconstruction creates the 2DEG at the STO side of the LAO/STO interface. The minimal thickness of the polar layer tC that is required for electronic reconstruction is tC = ε0εPΔE/eP, where εP is the dielectric constant of the polar material, ΔE is the energy gap separating the valence band of the polar layer and the conduction band of the nonpolar material, and P is the formal polarization of polar layers.10 Taking εP = 24, ΔE as STO bandgap of 3.2 eV, and P = 0.526 C m−2 for the LAO/STO (001) interface, tC is calculated to be 4

trongly correlated electrons in oxide heterostructures can exhibit various remarkable properties due to the mismatch of lattice, polarization, composition, and orbital character at the interface.1 The most famous example is the high-mobility twodimensional electron gas (2DEG) at the interface between the two insulators SrTiO3 (STO) and LaAlO3 (LAO),2 which can exhibit two-dimensional superconductivity,3 magnetic interactions,4 and electronic phase separation.5−8 The appearance of such a 2DEG is often ascribed to the polar discontinuity arising at the interface between the polar LAO overlayer and a nonpolar STO (001) substrate.2,9−11 Also, an internal electric potential V can be built up in the alternating stack of polar AlO2−/LaO+ layers on the TiO20-terminated nonpolar STO. When V exceeds the STO bandgap Eg,STO (= 3.2 eV), which is much less than that of LAO (= 5.6 eV), electrons can be © 2016 American Chemical Society

Received: November 25, 2015 Revised: February 19, 2016 Published: March 9, 2016 2307

DOI: 10.1021/acs.nanolett.5b04814 Nano Lett. 2016, 16, 2307−2313

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Nano Letters unit cells (uc) in perfect agreement with the experimental value.12 However, recent experimental results suggest that other factors, including but not limited to oxygen vacancy13,14 and chemical stoichiometry,15,16 can also influence the SrTiO3based 2DEG. So, those factors also need to be considered when estimating the critical thickness.14,17−20 A focus of current research is to improve the carrier mobility in order to make these conducting oxide interfaces more suitable for probing quantum transport21−23 and for eventual electronic device application.24 The electron mobility for the conventionally prepared LAO/STO interface is usually around 1000 cm2 V−1 s−1 at low temperatures,5,25,26 and it can be increased to 6000 cm2 V−1 s−1 by optimizing the growth condition.21 An SrTiO3/SrCuO2 cap layer on the LAO/STO heterostructure can improve the carrier mobility up to 50 000 cm2 V−1 s−1, provided the sample is prepared under high vacuum (∼10−6 mbar).25 Replacing the LAO overlayer with spinel γ-Al2O3 has been found to greatly increase the mobility to 140 000 cm2 V−1 s−1, however, the high-mobility state collapses after thermal treatment in oxygen.27 When the amorphous LAO layer is grown on the (La,Sr)MnO3-buffered STO, the mobility can reach 73 000 cm2 V−1 s−1,28 but again the mobile electrons cannot be maintained after annealing in oxygen.13 Therefore, these high-mobility 2DEG (>10 000 cm2 V−1 s−1) processes seem incompatible with other (hole-doped) functional perovskite oxides like superconducting cuprates or ferromagnetic manganites for which an oxygen-rich environment is required for film growth. The combination between the high-mobility 2DEG and hole-type conductors could provide the opportunity to integrate multiple functionalities such as superconductivity and ferromagnetism into one epitaxially grown all-oxide device. Hence, obtaining robust high carrier mobility at the conducting oxide interfaces, which can survive subsequent oxygen-rich processing condition, is of great importance and still remains a challenge. Here, we show that this can be accomplished by replacing LAO with LSAT, (La 0.3 Sr 0.7 )(Al 0.65 Ta 0.35 )O 3 or (LaAlO3)0.3(SrAl0.5Ta0.5O3)0.7. LSAT is a well-known cubic perovskite insulator with lattice constant aLSAT = 3.868 Å, dielectric constant εP,LSAT = 22, and bandgap Eg,LSAT = 4.9 eV. When grown on STO, the lattice mismatch for LSAT/STO is only 1.0%, which is only one-third of the value of LAO/STO (3.0%). Furthermore, STO and LSAT both undergo a similar cubic-totetragonal transition below 100 K,29,30 therefore the LSAT/ STO interface has a better lattice compatibility than LAO/STO from room temperature to low temperature. The sample preparation and measurement details can be found in Supporting Information (SI). Figure 1a shows the typical in situ reflection high-energy electron diffraction (RHEED) during the fabrication of the LSAT/STO (001) interface. Both the periodic RHEED oscillation and streaky RHEED pattern confirm the layer-by-layer growth. Taken together with the X-ray reflectivity data (SI Figure S1), we can identify one RHEED oscillation with the growth of one perovskite unit cell. The ex situ atomic force microscopy (AFM) image and height profile in Figure 1b exhibit one-unit-cell-high steps on the LSAT/STO (001) surface. Rutherford Backscattering Spectrometry (RBS) (SI Figure S3) reveals that the chemical composition for the LSAT film is very close to the target composition (La0.3Sr0.7) (Al0.65Ta0.35)O3, leading to an average polar charge density of ±0.3e per AO/BO2 layer along [001] axis, as illustrated in Figure 1c. Given the nonpolar nature of

Figure 1. (a) In situ RHEED oscillations of 50 uc LSAT/STO (001). The intensity is manually increased at 300 s. Insets are the streaky RHEED pattern after growth and structural scheme of perovskite LSAT. (b) Surface profile of 20 uc LSAT/STO (001). The step height is around 3.85 Å. Inset is the AFM image, where the surface profile was taken along line A−B. (c) Scheme of polar discontinuity at the LSAT/ STO (001) interface.

SrTiO3 (001), a polar-discontinuity-induced 2DEG is expected at the LSAT/STO (001) interface. In order to minimize the effect from oxygen vacancy,13,14 the annealed LSAT/STO interface was obtained by ex situ annealing the as-grown interface at 600 °C in 1 bar oxygen for 1 h. In Figure 2, the transport properties of the as-grown and annealed interfaces are compared. Figure 2a shows the typical sheet resistance RS as a function of temperature for 12 uc (001) LSAT/STO interfaces. Both the as-grown and

Figure 2. (a) Sheet resistance, (b) carrier density, and (c) carrier mobility are shown as a function of temperature for as-grown (red) and annealed (blue) 12 uc LSAT/STO interfaces. The carrier density is calculated from Hall measurement from −1 to 1 T. 2308


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Figure 3. Sheet conductance, GSheet, carrier density, nS, and carrier mobility, μS, at 2 K are shown as a function LSAT thickness for the LSAT/STO (001) interface in (a), (110) in (b), and (111) in (c). The carrier mobility of (001) LAO/STO (orange) prepared under the same growth parameters is also shown in (a) for comparison.

5 uc where the 2DEG is established and the other is around 12 uc where the mobility is greatest. On the other hand, this high mobility 2DEG is also observed at the annealed (110)- and (111)-orientated LSAT/STO interfaces, which is similar to the LAO/STO interface with different orientations.26,31 But unlike LSAT/STO (001) interface, both the (110) and (111) interfaces show only a single critical thickness at 8 uc, as shown in Figure 3b,c. At 2 K, the carrier density for all three annealed LSAT/STO interfaces is around 1−2 × 1013 cm−2, and the carrier mobility for (110) and (111) interfaces is around 6000 cm2 V−1 s−1. When compared to LAO/STO interfaces, the (110) and (111) LSAT/STO interfaces show much more robust metallicity. For example, our data show that the high-mobility 2DEG can be maintained in the LSAT/STO (110) and (111) interfaces with a 50 uc thick LSAT layer, while the LAO/STO (110) and (111) interfaces show low-temperature insulating behavior when LAO thickness is beyond just 10 uc.26 Therefore, two major differences between LSAT/STO and LAO/STO interfaces can be found in Figure 3. One is the much higher carrier mobility and more robust metallicity at the LSAT/STO interface, and the other one is the observation of two critical thicknesses at (001) LSAT/STO interface but not at the (110) and (111) LSAT/STO or all LAO/STO interfaces. This high carrier mobility and robust metallicity of LSAT/ STO can be ascribed to the small structural mismatch between the oxides. Such structural mismatch includes the nominal lattice mismatch calculated from lattice parameters, and the crystal symmetry mismatch related to octahedral rotation/ tilting. The nominal lattice mismatch can induce the octahedral distortion and thus influence the orbital structure and bond length; while the mismatch of crystal symmetry can change the connectivity of octahedral network and modify the bond angle at the hetero interface.32,33 For the conventional LAO/STO interface, the lattice mismatch is 3.0% at room temperature, three times of that of the LSAT/STO interface. This large

annealed interfaces can maintain the metallicity (dRS/dT > 0) from 300 to 2 K. However, as shown in Figure 2b, the carrier density of the as-grown interface decreases during cooling, while the annealed interface exhibits a temperature-independent carrier density. The “carrier frozen” phenomenon of the asgrown interface can be ascribed to the oxygen vacancy. The energy level of oxygen vacancy is slightly lower than the bottom of conduction band in STO, therefore, the oxygen-vacancyinduced carriers become localized at low temperatures.14 By contrast, the annealed interface is fully oxidized and the polardiscontinuity-induced carriers locate within the STO conduction band (above Fermi level), hence the carrier density is less dependent on temperature. Moreover, the carrier mobility is unchanged at both as-grown and annealed interface as shown in Figure 2c, suggesting the ex situ annealing can effectively remove the oxygen vacancy without changing the carrier mobility. The thickness-dependent transport data at 2 K for the annealed LSAT/STO (001), (110), and (111) interfaces are summarized in Figure 3a−c, respectively. In Figure 3a, the (001) interface becomes conducting when covered by a LSAT layer with thickness t ≥ 5 uc. Furthermore, the low-temperature sheet conductance of LSAT/STO increases with t, reaching its highest value at t ≈ 12 uc. This conductance improvement is not caused by any increases of carrier density, but it is brought about by a great enhancement of carrier mobility μS, which reaches its peak of 35 000 cm2 V−1 s−1 at t = 12 uc. And this high carrier mobility is about 30 times larger than that of LAO/ STO interfaces, which are prepared under the same growth parameters (in Figure 3a and SI Figure S2) or reported in previous studies.5,25,26 Also, we note that clear Shubnikov−de Haas conductance oscillations can be observed at 2 K below 9 T for (001) interfaces with high carrier mobility in SI Figure S4. In addition, the transport data clearly show that there are two critical thicknesses for the LSAT/STO (001) interface: one is at 2309


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Nano Letters lattice mismatch can induce distortion of the BO6 octahedra at STO surface, especially when LAO layer is thick. The tetragonal-like distortion has also been observed at the STO surface even in the coherently grown heterostructure.34 The break of cubic symmetry in STO layer would greatly reduce the carrier mobility.35 Moreover, the LAO/STO interface suffers from a rhombohedral/cubic symmetry mismatch, whereas both the LSAT and STO are cubic. So, the crystal symmetry mismatch and the octahedral tilting which are expected in the few STO layers near the LAO/STO interface36 should not arise for LSAT. In the case of CaTiO3 (despite a lower lattice mismatch with LAO), the orthorhombic, octahedral tilting at the LaAlO3/CaTiO3 interface reduces the Ti−O−Ti bond angle and results in carrier localization.37 Furthermore, the structural compatibility between STO and LSAT is maintained at low temperatures, because both oxides undergo a cubic-totetragonal structural transition below about 100 K.29,30 Hence, by replacing LSAT with LAO, the structural mismatch is greatly reduced at the interface, resulting in the observed high carrier mobility at the LSAT/STO interfaces. Following this idea, we can anticipate that the transport difference between LSAT/STO and LAO/STO, arising from the structural mismatch at the interface, will be even larger when the LAO and LSAT films are thicker. In Figure 4, the LSAT/STO and LAO/STO interfaces with a thick polar overlayer (∼100 uc) are compared. Figure 4a shows that the 100 uc LSAT/STO interface can still preserve the metallic behavior with μS = 6500 cm2 V−1 s−1 at 2 K, while the LAO/ STO interface becomes insulating below 50 K. This suppression of conducting 2DEG in thick LAO/STO samples is also reported elsewhere.26,38 In Figure 4b of XRD θ-2θ scans, well-defined thickness fringes can be observed for LSAT/STO interface, but no such fringes are seen for the LAO/STO interface. Moreover, by comparing reciprocal space mapping (RSM) around the (103) reflection in Figure 4c,d, the structural reflection of LAO/STO is much worse than that of LSAT/STO. The LAO (103) reflection is diffusive and is divided into two parts, one of which, indicated by red arrow, shows structural relaxation tendency of the LAO to its bulk value. By contrast, the 100 uc LSAT/STO interface can still maintain the coherent growth with a sharp LSAT (103) reflection, showing less structural mismatch and hence higher carrier mobility. Furthermore, the lattice mismatch at the interface can also explain the suppression of carrier mobility in the thicker samples. As shown in Figure 3a, LAO/STO samples (10−25 uc) show a faster decrease of mobility with thickness than LSAT/STO samples (12−25 uc) but both of them exhibit a similar tendency of mobility suppression with thickness. This drop of mobility with thickness should hence be ascribed to the lattice mismatch strain effect. With increasing the film thickness, the film would gradually relax to its bulk lattice. Given the connectivity between the on-top film and STO surface, the strain effect from the on-top film to STO surface is enhanced by increasing the film thickness, resulting in more defects and larger lattice deformation at the STO surface with the lower carrier mobility. Now, we are trying to explain why the conducting LSAT/ STO (001) interface exhibits two critical thicknesses, whereas for all LAO/STO, LSAT/STO (110) and (111) interfaces, there is only one. It must be noted that the growth-induced nonstoichiometry, oxygen vacancy, and interface interdiffusion can influence the interface conductivity.13−20 However, these effects cannot quantitatively explain the thickness-dependent

Figure 4. (a) RS(T) curves for 100 uc LAO/STO (001) and LSAT/ STO (001) samples. (b) XRD θ−2θ scans around (002) for LAO/ STO and LSAT/STO. (c) RSM around (103) for 100 uc LAO/STO (001) sample. (d) RSM around (103) for 100 uc LSAT/STO (001) sample. The red line indicates the coherent growth with the same inplane lattice constants for the film and the substrate. The green line indicates the LAO bulk (fully relaxed). The red arrow in (c) indicates the structural relaxation in LAO film. It should be noted that the unitcell volume of LSAT film is increased by ∼2%, which is slightly larger than 1.5% that is expected in a conventional perovskite oxide with Poisson ratio around 0.25. This implies that some point defects might present in the film due to a very slight nonstoichiometry beyond our RBS resolution and/or polar discontinuity.17

transport property shown in Figure 3. Moreover, our experimental data suggest these effects should not be dominant in our LSAT/STO samples. For example, no clear stoichiometric deviation was observed in our RBS data in SI Figure S3. The frozen-out carriers, which are induced by oxygen vacancy in STO,14,39 were not seen in the annealed LSAT/STO sample in Figure 2. Also, the thickness of interdiffusion area is around 2−2.5 nm, as shown in SI Figure S5. In this thickness range, even the “50% well-mixed” La0.5Sr0.5TiO3 film would be either insulating (RS > 107 Ω) or with the low carrier mobility ∼1000 cm2 V−1 s−1.40 Such a thin intermixing layer is unlikely to induce the high-mobility carriers as we observed at the LSAT/ STO interface. Hence, a possible model is proposed based on polar discontinuity and polar fluctuation. On the basis of the chemical composition, the LSAT lattice consists of 30% LAO and 70% SrAl0.5Ta0.5O3 (SATO) sublattices. As shown in Figure 5a, if grown on TiO2-terminated STO (001) the formal polarization of these 30% LAO sublattice P0 will point from the surface to the interface and can be calculated to be 0.523 C/m2. On the other hand, for the 70% SATO sublattice the formal polarization can be either parallel or antiparallel to P0 depending on the position of Al and Ta (±P0 with an equal probability), leading to an average 2310


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Figure 5. (a) The LSAT layer contains 30% LAO sublattice (P0) and 70% SATO sublattice (±P0) on TiO2-terminated STO (001). (b) Different formal polarizations for different columns, which are formed by randomly mixing 30% LAO and 70% SATO sublattices in the 6 uc LSAT/STO (001), leading to 2DEG in STO beneath for Column A and B, or localized positively charged holes for Column C. (c) On the basis of the binomial distribution, the LSAT formal polarization P, which is characterized by Pμ ± σP, is shown as a function of LSAT thickness. When the LSAT layer is 5 uc (t1), LSAT formal polarization P with a positive fluctuation Pμ + σP is beyond the PC, starting to form 2DEG at the interface. When the LSAT layer is above 11 uc (t2), LSAT formal polarization Pμ − σP is above zero, indicating the absence of the localized holes that scatter the 2DEG carriers.

by PC = ε0εPEg,STO/et. As shown in Figure 5c, for LSAT (001) with formal polarization P = Pμ ± σP there is an intersection between PC and Pμ + σP between 4 and 5 uc. It indicates the LSAT polar layer can stabilize a 2DEG on STO (001) when its thickness is above 5 uc, consistent with our observation on the first critical thickness (t1) at 5 uc for the appearance of the 2DEG. Moreover, as the thickness increases beyond 5 uc, P has reduced its negative formal polarization component (Pμ − σP) leading to an increasing mobility, which peaks at 10−11 uc (t2) where the negative formal polarization goes to zero. Beyond 10−11 uc, P is always positive and the mobility cannot increase further. This is consistent with the observed second critical thickness where the mobility peaks at 12 uc. Beyond 12 uc, the mobility decreases due to lattice strain, albeit at a slower rate compared to LAO/STO. By contrast, for (110) and (111) orientations, the direction of SATO formal polarization cannot be changed by switching Al and Ta position, always pointing from O2−4 to Sr(Al,Ta)O+(3−4) layer along (110) orientation, and from SrO3−4 to (Al,Ta)+(3−4) layer along (111) orientation. Hence, there is no positively charged scattering center and only one critical thickness for 2DEG is observed in the (110) and (111) interface. Therefore, our model can nicely explain all the observations in Figure 3, suggesting the important role of polar fluctuation at the LSAT/STO interfaces. In summary, when the lattice mismatch of conducting oxide interface on STO is reduced from 3.0% to 1.0% and the symmetry mismatch is minimized by replacing the polar layer LAO with cubic LSAT, the carrier mobility of 2DEG can be greatly improved (∼35000 cm2 V−1 s−1 at 2 K), almost 30 times larger than the conventional LAO/STO prepared under the same conditions (∼1000 cm2 V−1 s−1). Further this mobility is robust under different oxygen processing conditions. Moreover, the observation of two critical thicknesses for the LSAT/STO (001) interface but not the (110) and (111) interfaces (one for

formal polarization of 0.3P0 for LSAT. Therefore, if randomly mixing together the 30% LAO sublattice of P0, 35% SATO sublattice of P0 and 35% SATO sublattice of −P0 to form the 6 uc LSAT layer on TiO2-terminated STO (001) as shown in Figure 5b, the formal polarization for LSAT layer will be different from column to column. In Figure 5b, the formal polarization for LSAT layer is P0 in Column A, 0.3P0 in Column B, or −0.4P0 in Column C, and the ratio of possibility among Column A, B, and C is 1:2:1. In other words, the LSAT (001) with the same chemical composition exhibits polar fluctuation−various values of formal polarization P for different sublattices, leading to the potential fluctuation that can explain the observed variations on valence band offset at the (001) STO/LSAT interface.41 On the basis of polar discontinuity model,13 electrons (holes) must be created to compensate P0 (−P0). Hence, a mobile 2DEG will be created in STO under Column A and B, whereas localized holes will exist under Column C, which can scatter the mobile electrons thereby lowering carrier mobility. A statistical model is built to evaluate the polar fluctuation of LSAT/STO (001) interface, by assuming that one LSAT (001) monolayer could have 65% chance for producing an electric dipole moment as P0V or 35% chance for −P0V, where V is the volume for one LSAT (001) monolayer. By applying the binomial distribution (SI Note S2), the mean value of formal polarization Pμ is 0.3P0 and the standard deviation of formal polarization σP is (0.91/t)0.5P0, where t is the LSAT thickness (uc). Hence, the LSAT formal polarization P can be characterized by Pμ ± σP with a polar fluctuation σP, which varies with LSAT film thickness. In other words, the actual value of the formal polarization will lie between Pμ − σP and Pμ + σP. If we define the critical formal polarization PC as the minimal formal polarization required for the polar layer with a given thickness t to create 2DEG on STO, PC can be calculated 2311


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the appearance of 2DEG at 5 uc and the other for optimum carrier mobility at 12 uc) can be ascribed to the polar fluctuation in LSAT (001). Further improvement in the carrier mobility of the 2DEG induced in STO by polar discontinuity of the interface is likely if the structural mismatch and polar fluctuation can be avoided.

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b04814. Additional characterization, sample preparation, and statistical model. (PDF)

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Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Author Contributions

Z.H. and K.H. contributed equally to this work. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank H. Hilgenkamp, S. Saha, Q. He, and C. G. Li for the discussion. This work is supported by the National University of Singapore (NUS) Academic Research Fund (AcRF Tier 1 Grant No. R-144-000-346-112 and R-144-000-364-112) and the Singapore National Research Foundation (NRF) under the Competitive Research Programs (CRP Award No. NRF-CRP 8-2011-06 and CRP Award No. NRF-CRP10-2012-02).

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The Effect of Polar Fluctuation and Lattice Mismatch on Carrier

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