A two-dimensional electron gas (2DEG) in SrTiO3is created via modulation doping by interfacing undoped SrTiO3with a wider-band-gap material, SrTi1xZrxO3, which is doped n-type with La. All layers are grown using hybrid molecular beam epitaxy. Using magnetoresistance measurements, we show that electrons are transferred into the SrTiO3, and a 2DEG is formed. In particular, Shubnikov-de Haas oscillations are shown to depend only on the perpendicular magnetic field. Experimental Shubnikov-de Haas oscillations are compared with calculations that assume multiple occupied subbands

Cain, Tyler A.

Kajdos, Adam P.

Ouellette, Daniel G.

Stemmer, Susanne

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UC Santa BarbaraUC Santa Barbara Previously Published WorksTitleTwo-dimensional electron gas in a modulation-doped SrTiO3/Sr(Ti, Zr)O3 heterostructurePermalinkhttps://escholarship.org/uc/item/76h8g79fJournalApplied Physics Letters, 103(8)AuthorsKajdos, Adam P.Ouellette, Daniel G.Cain, Tyler A.et al.Publication Date2013-08-23DOI10.1063/1.4819203 Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaTwo-dimensional electron gas in a modulation-doped SrTiO3/Sr(Ti, Zr)O3heterostructureAdam P. Kajdos,1 Daniel G. Ouellette,2 Tyler A. Cain,1 and Susanne Stemmer11Materials Department, University of California, Santa Barbara, California 93106-5050, USA2Department of Physics, University of California, Santa Barbara, California 93106-9530, USA(Received 30 June 2013; accepted 9 August 2013; published online 23 August 2013)A two-dimensional electron gas (2DEG) in SrTiO3 is created via modulation doping by interfacingundoped SrTiO3 with a wider-band-gap material, SrTi1xZrxO3, which is doped n-type with La. Alllayers are grown using hybrid molecular beam epitaxy. Using magnetoresistance measurements, weshow that electrons are transferred into the SrTiO3, and a 2DEG is formed. In particular, Shubnikov-deHaas oscillations are shown to depend only on the perpendicular magnetic field. ExperimentalShubnikov-de Haas oscillations are compared with calculations that assume multiple occupiedsubbands. VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4819203]Two-dimensional electron gases (2DEGs) at interfacesbetween SrTiO3 and other complex oxides exhibit unique phe-nomena, including superconductivity,1 Rashba spin-orbit cou-pling,2 and magnetism.3–7 Most studies thus far have focusedon 2DEGs at polar/nonpolar interfaces, such as LaAlO3/SrTiO3,8–10 LaTiO3/SrTiO3,11,12 and GdTiO3/SrTiO3.13,14Mobile carriers in these heterostructures arise from a polardiscontinuity at the interface, which gives rise to extremelyhigh carrier densities on the order of 3 1014 cm2(LaAlO3/SrTiO3 interfaces typically have lower densities, forreasons that are not yet well understood9). An alternative routeto high-mobility 2DEGs is modulation doping, originallydeveloped for III–V heterostructures,15 leading to devicessuch as high-electron mobility transistors,16,17 and scientificdiscoveries, such as the fractional quantum Hall effect.18 Thisapproach spatially separates the mobile charge from the ion-ized dopants by transferring it into an undoped layer. A heter-ostructure that has suitable conduction band alignments istherefore essential for modulation doping.Here, we show that a 2DEG in SrTiO3 can be created bymodulation doping. We use SrTi1xZrxO3 as the doped,wider band gap perovskite, i.e., the analog of AlGaAs inGaAs/AlGaAs structures. SrTi1-xZrxO3 is a solid solutionof cubic SrTiO3 and orthorhombic SrZrO3. The band gap ofSrZrO3 (5.6 eV (Ref. 19)) is substantially larger than that ofSrTiO3 (3.2 eV). The band alignment between SrTiO3 andSrZrO3 is Type I, with a conduction band offset, DEc, of1.9 eV.20 Given the large DEc, reasonable band offsetsshould be achievable even for small x, which serve to reducethe substantial lattice mismatch between SrTiO3(a¼ 3.905 Å) and SrZrO3 (pseudocubic unit cell, a 4.1 Å),and facilitate doping, which would likely be difficult in awide band gap material such as SrZrO3.Figure 1 shows a sketch of a modulation doped SrTiO3/SrTi0.95Zr0.05O3 heterostructure, along with a band diagram ofthe conduction band edge, Fermi level and the electron density,as calculated using a 1D Poisson solver.21 A DEc of 95 meVwas estimated using Vegard’s law. The SrTi0.95Zr0.05O3 layer isn-type, doped with La to a carrier density of 2 1019 cm3. A2DEG resides in the SrTiO3.Experimentally realizing this structure requires thegrowth of epitaxial, stoichiometric SrTiO3 and SrTi1xZrxO3thin films, to ensure high mobility, avoid charge trapping,and allow for doping of the SrTi1xZrxO3. Here, we usehybrid molecular beam epitaxy (MBE), previously devel-oped for high-mobility SrTiO3.22,23 In this approach, both Tiand Zr are supplied from high-purity (99.999%) metal-organic precursors, titanium tetra isopropoxide (TTIP), andzirconium tert-butoxide (ZTB), respectively.The SrTi0.95Zr0.05O3/SrTiO3 heterostructure discussedin this paper consists of a 120 nm undoped SrTiO3 layergrown on (001) SrTiO3, followed by growth of a 30-nm-thick La-doped SrTi0.95Zr0.05O3 layer (see Fig. 1). ForSrTi1-xZrxO3, both precursors were co-evaporated, andthe beam equivalent pressures were adjusted relative toFIG. 1. Schematic of a modulation-doped SrTi0.95Zr0.05O3/SrTiO3 hetero-structure and corresponding band diagram. The conduction band offset wasestimated using experimental values for SrZrO3/SrTiO3 (Ref. 20) andassuming Vegard’s law. The conduction band edge (Ec), Fermi level (Ef),and carrier density (n) were calculated using a 1D Poisson solver.21 The dop-ant density in the SrTi0.95Zr0.05O3 and the surface pinning potential wereassumed to be 2 1019 cm3 and 0.1 eV, respectively. The SrTiO3 layer isnominally undoped with 1016 cm3 residual donor-type defects (an upperlimit established by doping studies for these high-quality MBE films).0003-6951/2013/103(8)/082120/4/$30.00 VC 2013 AIP Publishing LLC103, 082120-1APPLIED PHYSICS LETTERS 103, 082120 (2013)that of Sr to give A:B site stoichiometric films (where A¼Srand B¼Ti or Zr) of the desired Zr content (x). Growth opti-mization to obtain the correct A:B site ratio closely followedour approach for SrTiO3,23 and details will be reportedelsewhere. Oxygen was supplied by an rf plasma source. Thesubstrate temperature was 900 C as measured by thermo-couple. La was evaporated from a solid source effusioncell to obtain a carrier concentration of 2 1019 cm3.Doping calibrations were carried out using thick, uniformlydoped layers, which confirmed n-type doping of theSrTi0.95Zr0.05O3 layers, but showed much lower mobilitiesthan the modulation doped samples investigated here. In-situreflection high-energy diffraction (RHEED) patterns werestreaky during and after growth for all films and showed per-iodic oscillations in intensity at the beginning of growth,indicating layer-by-layer growth.24 2h-x x-ray diffractionscans in the vicinity of the SrTiO3 002 reflection showed asingle, separate 002 peak for the SrTi1xZrxO3 film andclearly defined Laue oscillations.24 The composition x wascalibrated by comparing the unstrained unit cell volume,obtained from lattice parameter measurements, to that ofbulk SrTi1xZrxO3.25 The sample was post-growth annealedin a rapid thermal annealing furnace in 1 atm of oxygen at800 C for 30 s to ensure oxygen stoichiometry. Hall andlongitudinal resistance measurements at temperaturesbetween 300 K and 2 K and magnetic fields (B) up to 14 Twere performed in van der Pauw geometry using a PhysicalProperties Measurement System (Quantum Design). Ohmiccontacts (40 nm-Al/20 nm-Ni/400 nm-Au) were deposited byelectron beam evaporation through a shadow mask onto thecorners of a square sample. The longitudinal magnetoresist-ance was measured using a standard lock-in technique in aHe3 cryostage at temperatures ranging from 0.45 K to 3 K.Data at low B showed positive magnetoresistance at lowtemperatures, with a sharp dip near B¼ 0, possibly due toweak antilocalization. Magnetoresistance measurements as afunction of the angle h that B makes with the surface normalwere performed at 2 K using a horizontal sample rotatorstage (h¼ 0 indicates that B is perpendicular to theinterface).To confirm the existence of a 2DEG and to probe thedimensionality of the electron system in the SrTi0.95Zr0.05O3/SrTiO3 heterostructure, we investigate Shubnikov-de Haasoscillations that appear in the longitudinal magnetoresistancein a quantizing magnetic field. In particular, for a 2DEG, theperiodicity of these oscillations, which are due to quantiza-tion into Landau levels, should only depend on the compo-nent of B that is normal to the interface.Figure 2 shows the longitudinal magnetoresistance atdifferent temperatures. At 0.45 K, Shubnikov-de Haas oscil-lations are observed for B> 5 T. Oscillations persist totemperatures up to 3 K. The oscillating component of themagnetoresistance, DRxx, was obtained by subtracting thenon-oscillating background using multiple polynomial fits.Figure 3(a) shows DRxx as a function of 1/B [DRxxð1=BÞ] at0.45 K. A Fourier transform (FT) of DRxxð1=BÞ is shown inthe inset and exhibits multiple peaks, which will be furtherdiscussed below. Figure 3(b) shows Shubnikov-de Haasoscillations for different h, measured at 2 K and plottedagainst ðB cos hÞ1. Resistance maxima and minima appearat the same values of ðB cos hÞ1 for h up to 60, confirmingthe two-dimensionality of the electron system. Therefore, assuggested by the band diagram in Fig. 1, a 2DEG has beencreated on the SrTiO3-side of the interface.Shubnikov-de Haas oscillations allow for the extractionof important characteristics, including the effective masses(m*) for the subbands and the quantum scattering time (sq)or Dingle temperature (TD). For 2DEGs with a singlesubband, values for m* and TD are determined from thedecay in the amplitude of oscillations with increasing tem-perature and by constructing a Dingle plot at a fixed tem-perature, respectively. Multiple subbands (or spin splitting)complicate such analyses, since oscillations contain contri-butions from several components. Therefore, we fit theexperimental data, DRxxð1=BÞ, at 0.45 K to the standardequation26FIG. 2. Longitudinal magnetoresistance (Rxx) measured at temperaturesbetween 0.45 K and 3 K.FIG. 3. (a) Shubnikov-de Haas oscillations, DRxxð1=BÞ, measured at 0.45 Kand h¼ 0. The inset shows a Fourier transform of the data. Approximatepositions for four peaks are labeled. (b) Shubnikov-de Haas oscillationsmeasured at 2 K at various tilt angles h (the angle between B and the inter-face plane normal) and plotted as a function of the inverse perpendicularcomponent of the magnetic field, ðB cos hÞ1.082120-2 Kajdos et al. Appl. Phys. Lett. 103, 082120 (2013)DRxxR0¼Xli¼12Ai exp 2p2kBTD;ihxc XsinhðXÞ cos2pfiBþ p ;(1)where i is the subband index, l is the number of occupiedsubbands, Ai are amplitude factors associated with intrasub-band scattering probabilities, kB is the Boltzmann constant,TD,i is the Dingle temperature of each subband, h is thereduced Planck’s constant, xc is the cyclotron frequency, fiare the oscillation frequencies (in 1/B), and X ¼ ð2p2kBTÞ=ðhxcÞ. Figure 4 shows experimental and calculatedDRxxð1=BÞ at temperatures between 0.45 K and 3 K for l¼ 4.The temperature-dependence was calculated and the m*’sadjusted to match the experimentally observed behavior. Theparameters obtained from the fits and the extracted sheet car-rier density (ns), sq, and quantum mobility (lq) for each sub-band are shown in Table I. The frequencies are in goodagreement with those obtained in the FTs shown in Fig. 3(a).The lowest value for m* (0.95 m0, where m0 is the free elec-tron mass) is consistent with a dxy-derived subband.27–30 Spin-orbit coupling can hybridize dxy-derived with dxz/dyz-derivedsubbands.29 This results in a heavier in-plane mass.Theoretical calculations support multiple occupied subbandsat this carrier density.29 Alternative models and fits to theexperimental Shubnikov-de Haas oscillations were alsoexplored (see Ref. 24), including whether multiple frequen-cies could arise from two spin-split subbands. A goodqualitative match with the data could be obtained, and atpresent, we cannot distinguish between these models.24These uncertainties place limitations on the accuracy ofthe extracted values in Table I. The extracted lq’s of around2000 cm2V1s1 are consistent with the onset of magnetore-sistance oscillations around 4–5 T, i.e., when lqB > 1.The total sheet density estimated from Table I is approx-imately 8.4 1012 cm2, which is only 19% the Hall density,ns,H¼ 4.46 1013 cm2, measured at 300 K. The remainingcarriers can be reasonably assumed to reside in the La-dopedSrTi0.95Zr0.05O3 layer. Carrier distributions calculated inFig. 1 confirm this picture qualitatively. Using reasonableassumptions for the mobilities and carrier densities in bothlayers, a Hall coefficient can be calculated from a multi-carrier model and compared with experimentally measuredvalues. Good agreement is found.24 The two spin-split sub-band interpretation of the data (see Ref. 24) results in lowercarrier densities. Prior studies of 2DEGs in SrTiO3 foundupwards of 60%–95% of carriers in the 2DEG to not giverise to oscillations,14,31–34 which is likely due to disorderlimiting the mobility of a significant fraction of the carriers,preventing oscillations to be resolved for all subbands.Discrepancies exist between calculated and experimen-tal DRxx in all models. One possible explanation is intersub-band scattering,35,36 which was neglected in Eq. (1). Theenergy spacing between subbands, DE, is very smallDE ¼ qhDfm; (2)where Df is the difference in oscillation frequencies betweenany two subbands, and q is the elementary charge. FromTable I, DE ranges from 0.15 meV to 5 meV. Intersubbandscattering may thus be significant. It is generally more signif-icant at low B35,36 and could thus potentially affect finer fea-tures that would otherwise appear in the measuredresistance. At present, a complete theory of magnetoresist-ance oscillations of 2DEGs in SrTiO3 is still lacking.In summary, we have shown that modulation dopingprovides an alternative route to 2DEGs in SrTiO3. Futurestudies should be dedicated to a complete understanding ofthe quantum oscillations, and to further improving the mobil-ity in these structures. For example, remote ionized impurityscattering can be mitigated by inserting an undopedSrTi1-xZrxO3 spacer. Lower-density 2DEGs can be obtainedby optimizing the doping and Zr content of the SrTi1-xZrxO3,which determine the band offsets.FIG. 4. (a) Temperature-dependent Shubnikov-de Haas oscillations,DRxxð1=BÞ, measured at h¼ 0 and at temperatures between 0.45 K and 3 K.(b) Calculated [Eq. (1)] Shubnikov-de Haas oscillations for temperaturesbetween 0.45 K and 3 K, using the parameters listed in Table I.TABLE I. Parameters extracted from fits of the experimental Shubnikov-de Haas oscillations measured at 0.45 K to a four-subband model [Eq. (1)]. Alsoshown are the sheet carrier densities (ns), quantum scattering times (sq), and quantum mobilities (lq) of each subband extracted from the fits. The effectivemass m* is determined from the cyclotron frequency xc ¼ eB=m, sq is calculated from sq ¼ h=ð2pkBTDÞ, and ns is calculated from f ¼ nh=2q, where h isPlanck’s constant.Subband index i R0A (X) f (T) m* (m0) TD (K) ns (cm2) sq (s) lq (cm2V1s1)1 0.8 68.4 1.2 0.8 3.30 1012 1.52 1012 22252 6.5 43 1.5 1.1 2.08 1012 1.10 1012 12883 2 41.2 1.4 0.8 1.99 1012 1.52 1012 19074 2 21.2 0.95 0.9 1.02 1012 1.35 1012 2496082120-3 Kajdos et al. Appl. Phys. Lett. 103, 082120 (2013)The authors thank David Awschalom for making availablethe equipment for magnetotransport measurements and JimAllen, Guru Khalsa, and Allan MacDonald for helpful discus-sions. A.P.K. and T.A.C. received support from the NationalScience Foundation through a Graduate Research Fellowship(Grant No. DGE-1144085) and the Department of Defensethrough a NDSEG fellowship, respectively. Experimental costs(A.P.K.) were supported by the UCSB MRL, which is supportedby the MRSEC Program of the National Science Foundationunder Award No. DMR-1121053 and (T.A.C.) by the Center forEnergy Efficient Materials, an Energy Frontier Research Centerfunded by the DOE (Award No. DESC0001009). The work alsomade use of the UCSB Nanofabrication Facility, a part of theNSF-funded NNIN network.1N. Reyren, S. Thiel, A. D. Caviglia, L. F. Kourkoutis, G. Hammerl, C.Richter, C. W. Schneider, T. Kopp, A. S. Ruetschi, D. Jaccard et al.,Science 317, 1196 (2007).2A. D. Caviglia, M. Gabay, S. Gariglio, N. Reyren, C. Cancellieri, and J.M. Triscone, Phys. Rev. Lett. 104, 126803 (2010).3A. Brinkman, M. Huijben, M. Van Zalk, J. Huijben, U. Zeitler, J. C.Maan, W. G. Van der Wiel, G. Rijnders, D. H. A. 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Two-dimensional electron gas in a modulation-doped SrTiO3/Sr(Ti, Zr)O3 heterostructure

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