Two-dimensional electron gas in SrTiO3

Two-dimensional electron gas in SrTiO3 Bharat Jalan, Susanne Stemmer Materials Department S. James Allen Department of Physics University of California, Santa Barbara SpinAge 2010 Watsonville, CA, August 30, 2010

Acknowledgements Junwoo Son, Oliver Bierwagen, Pouya Moetakef, James LeBeau Shawn Mack, David Awschalom for the PPMS Funding: ARO MURI [W911-NF-09-1-0398] DOE [DE-FG02-06ER45994]

Outline Introduction Highly-perfect SrTiO3 thin films through stoichiometry control in MBE Electrical transport properties of thin film SrTiO3 grown by MBE Nature of the 2DEG in delta-doped SrTiO3 Summary

Introduction Quantum III-V Semiconductor Structures Quantum Oxide Structures C. Weisbuch, B. Vinter: Quantum Semiconductor Structures Quantum-confined structures in III-V semiconductors have lead to a wealth of phenomena and new technologies Fundamentally different: Electrons in relatively narrow d-bands Occupy a significant fraction of the d-band Electron correlations, exchange...dominate transport Expect even richer phenomena Exploration in its infancy Very little information on the basics (band structure, band offsets, doping,...) Inherently more complex (this talk) High-quality epitaxial heterostructures to observe quantum phenomena are possible (this talk)

Defects in Oxide Thin Films Three main sources of point defects in oxide films: 1. Poor stoichiometry control during deposition (VO.., VSr, interstitials,...) 2. Impurities (H, C, transition metals,...) 3. Energetic deposition (PLD, sputtering) Regime I Regime II Regime III MBE rf sputtering PLD Cuomo et al., J. Appl. Phys. 70 1706 (1991).

Impurities in Complex Oxides Commercial SrTiO3 single crystals (Verneuil grown) www.surfacenet.de Impurity content in commercial SrTiO3 single crystals (Toplent) Charged defects deep acceptors (most likely) As-grown Total in: GaN ~ 1 ppm Si ~ ppb or better 80 80 Transmittance [%] 60 40 20 As-purchased : no absorption in the visible transparent and colorless Transmittance [%] 60 40 20 After oxygen anneal: absorption peak with wide shoulder brown color 0 500 1000 1500 2000 Wavelength [nm] 2500 0 500 1000 1500 2000 Wavelength [nm] 2500 High concentrations of impurities even in oxide single crystals

Oxide Molecular Beam Epitaxy Low intrinsic defect concentrations: High purity: evaporation from elemental metals and high purity gases; UHV conditions Low-energetic deposition Near-monolayer control of thickness, superlattices,... In-situ diagnostics Stoichiometry control?

Challenges in Oxide MBE Oxygen Stoichiometry Low growth pressures Oxygen vacancies Oxygen vacancies are believed to act as shallow donors in many transition metal oxides High oxygen pressures needed during growth Flux instability of a Ti sublimation source in a background ozone pressure of 5.0 10-5 Torr seen in the deposition rate of TiO2 Metal flux instabilities in the presence of oxygen (oxidation of sources) C. D. Theis and D. G. Schlom, J. Vac. Sci. Technol. A 14 (1996), 2677

Challenges in Oxide MBE Cation Stoichiometry MBE growth window for GaAs Below this line, solid As will not precipitate excess As desorbs in the chamber Temperature ( C) ( C) A wide MBE growth window is largely responsible for the ease and success of III-V MBE Gas Pressure (Torr) 4As(s) 4 As4(g) MBE Growth MBE Window Growth GaAs(s) Ga(l) + As(g) Window GaAs(s) Ga(l) + As(g) C.D. Theis et al., Thin Solid Films 325, 107 (1998). J. Tsao, Materials Fundamentals of Molecular Beam Epitaxy. Temperature (1000/K) Above this line, As will condense on a Ga-rich GaAs surface

Challenges in Oxide MBE Cation Stoichiometry MBE growth window for SrTiO3 No MBE growth window for most complex oxides P SrO(g) [torr] 10-6 10-9 10-12 10-15 10-18 10-21 1500 K Temperature ( C) SrO(s) SrO(g) SrO(g) + TiO2(s) SrTiO3(s) Below this line, solid SrO will not precipitate: SrO will desorb in the chamber* MBE Growth Window Assumed a sticking coefficient of one for Ti* * C.D. Theis et al., Thin Solid Films 325, 107 (1998). 10-24 10-27 0.6 0.7 0.8 1000/T [1/K] Above this line, SrO will condense on a TiO-rich SrTiO3 surface* 0.9 1.0

Challenges in Oxide MBE Additional challenges for the titanates Growth rates are limited: Very low vapor pressure of Ti Typical growth rates: < 0.2 nm/min using effusion cell [1,2] 0.7 nm/min using Ti-ball [3] (No crucible materials for molten Ti) Oxygen causes flux instability for Ti High-temperature cells heat substrate Higher growth rate with e-beam source but inherent instability of these sources requires flux monitoring and feedback control [4] [1] Z. Yu et. al., Thin Solid Films 462-463,51 (2004) [2] P. Fisher et. al., J. Appl. Phys. 103, 013519 (2008) [3] M.D. Biegalski et.al., J. Appl. Phys. 104, 114109 (2008) [4] M. Naito et.al., Physica C 305, 233 (1998); S. A. Chambers, Surf. Sci. Reports 39, 105 (2000)!"#$%&'%())*%(&+,$%%-& Ta crucible hole in crucible

Novel Oxide MBE Approach Titanium tetra isopropoxide (TTIP) Gas supply (heated) Bubbler Baratron Leak valve

Hybrid Oxide MBE Titanium tetra iso propoxide (TTIP) 56(2%)($ 4-,3%,1)%&$ 012(3$!%&'()($!!"#$ Ti *+,-./&()($ Sr cell Oxygen plasma source TTIP source O Ti(OC3H7)4 TiO2 + 2 C 3 H 7 OH + 2 C3H6 @ T = 350 C TTIP has orders of magnitude higher vapor pressures than solid Ti Scalable growth rate and stable flux No flux instabilities in presence of oxygen: higher oxygen pressure can be used Ti already comes bonded to four oxygens improved oxygen stoichiometry

Metal-Organic MBE of Rutile TiO2 No oxygen TiO 2! Al 2 O 3! TTIP source Ts 615 C TTIP beam flux: 2 10-6 torr B. Jalan, R. Engel-Herbert, J. Cagnon, S. Stemmer, J. Vac. Sci. Technol. A 27, 230 (2009). Single crystalline rutile (101) TiO2 on r-plane sapphire even without any additional oxygen TTIP source supplies oxygen Scalable growth rates as high as 125 nm/hr

Hybrid MBE of SrTiO3 TTIP / Sr flux ratio 55.4 53.3 SrTiO 3! SrTiO 3! 42.1 41.0 Sr source oxygen plasma source TTIP source T sub = 800 C p ox = 8 10-6 torr B. Jalan, R. Engel-Herbert, N. J. Wright, S. Stemmer, J. Vac. Sci. and Technol. A 27, 461 (2009). B. Jalan, P. Moetakef, S. Stemmer, Appl. Phys. Lett. 95, 032906 (2009). 39.5 Co-deposition (not shuttered) Lattice parameter as a measure of stoichiometry Lattice parameter increases for nonstoichiometry films (Sr rich and Ti rich) Excellent control over film stoichiometry

Hybrid MBE of SrTiO3: Growth Modes SrTiO 3! SrTiO 3! after growth substrate Persistent (> 180) RHEED oscillations indicate layer-bylayer growth mode [only been reported for a few systems: Si, Pt, AlAs] Transition to step-flow growth Streaky RHEED indicates atomically smooth film surface Surface reconstructions 2 along [110] (always); 4 along [110] (only for stoichiometric films after growth) Further investigations are required to understand origin of persistent RHEED oscillations. B. Jalan, R. Engel-Herbert, N. J. Wright, S. Stemmer, J. Vac. Sci. and Technol. A 27, 461 (2009). B. Jalan, P. Moetakef, S. Stemmer, Appl. Phys. Lett. 95, 032906 (2009).

Hybrid MBE of SrTiO3 SrTiO3! DyScO3! SrTiO3! LSAT! LSAT = (La0.3Sr0.7) (Al0.65Ta0.35)O3 XRD rocking curve AFM B. Jalan, R. Engel-Herbert, N. J. Wright, S. Stemmer, J. Vac. Sci. and Technol. A 27, 461 (2009). B. Jalan, P. Moetakef, S. Stemmer, Appl. Phys. Lett. 95, 032906 (2009). LSAT* substrates for rocking curve measurements On LSAT substrates, narrow rocking curve widths, similar to that of substrate (34 arcsec) Atomically smooth film surfaces on all substrates

MBE Growth Window Growth windows TTIP desorption leads to a growth window at practical substrate temperatures and fluxes Stoichiometry is self-regulating within the growth window No need for precise flux control Shift to higher TTIP/Sr flux ratios with increasing temperatures shows that desorption of TTIP is responsible for growth window B. Jalan, P. Moetakef, S. Stemmer, Appl. Phys. Lett. 95, 032906 (2009). SrTiO 3! SrTiO 3!

Significance of the MBE Growth Window Without an MBE growth window, stoichiometry control requires precise flux control Only possible to 0.1-1 % *,** * M. E. Klausmeier-Brown, J. N. Eckstein, I. Bozovic, and G. F. Virshup, Appl. Phys. Lett. 60, 657 (1992). ** J. H. Haeni, C. D. Theis, and D. G. Schlom, J. Electroceram. 4, 385 (2000). Corresponds to defect concentrations of 10 20-10 21 cm -3 Conventional MBE with all solid sources for Sr and Ti does not have a growth window. Hybrid MBE approach with TTIP: desorption leads to a growth window at practical substrate temperatures and fluxes. Stoichiometry is self-regulating within the growth window, no need for precise flux control. Volatility of TTIP is the reason for the growth window. B. Jalan, P. Moetakef, S. Stemmer, Appl. Phys. Lett. 95, 032906 (2009).

Electrical Transport Properties Hall Mobilities - SrTiO3 Single Crystals μ = 22,000 cm 2 /Vs at n = 1.4 10 17 cm -3 μ = 25,000 cm 2 /Vs μ = 22,100 cm 2 /Vs at n = 8 10 17 cm -3 Hall mobility (cm 2 /Vs) Hall mobility (cm 2 /Vs) Hall mobility (cm 2 /Vs) 10 100 Temperature (K) Temperature (K) O. N. Tufte, P. W. Chapman, Phys. Rev. 155, 796 (1967) Temperature (K) G. Herranz et al., Phys. Rev. Lett. 98, 21603 (2007) 1967 2007 A. Spinelli et al., Phys. Rev. B 81, 155110 (2010) n-type dopants: VO.. or Nb 2010

Electrical Transport Properties Doping of MBE SrTiO3 with La La:SrTiO 3! SrTiO 3! SrTiO 3! Carrier concentration [cm -3 ] 2 10 20 4 2 10 19 4 2 10 18 10 18 10 19 10 20 La concentration [cm -3 ] Carrier concentration [cm -3 ] 10 19 6 4 2 10 18 6 4 2 10 17 0 50 100 150 200 Temperature [K] STO 1 STO 2 STO 3 250 300 1:1 correspondence of La-concentration and free carrier concentration over several orders of magnitude Excellent control over doping concentration of unintentional defects below doping level Metallic (degenerate) for all doping levels J. Son, P. Moetakef, B. Jalan, O. Bierwagen, N. J. Wright, R. Engel-Herbert, S. Stemmer, Nature Mater. 9, 482 (2010).

La-Doping of SrTiO3 HAADF/STEM La:SrTiO 3! SrTiO 3! SrTiO 3! La atoms La-doped SrTiO3 nhall = 1.8 10 21 cm -3 Interface undoped SrTiO3 buffer layer

Electrical Transport Properties μ = 32,667 cm 2 /Vs at n = 7.9 10 17 cm -3 Hall Mobilities - MBE SrTiO3 La:SrTiO 3! SrTiO 3! SrTiO 3! 10 5 µ = 32667 cm 2 /Vs Magnetoresistance (Shubnikov-de Haas) oscillations Electron mobility [cm 2 /Vs] 10 4 10 3 10 2 10 1 µ [10 4 cm 2 /Vs] 4.0 3.0 2.0 1.0 1 2 3 4 5 6 2 3 4 5 n [10 18 cm -3 ] 2 3 4 5 6 10 Temperature [K] 100 2 3 J. Son, P. Moetakef, B. Jalan, O. Bierwagen, N. J. Wright, R. Engel-Herbert, S. Stemmer, Nature Mater. 9, 482 (2010). Higher mobility than single crystals Most likely due to lower concentration of charged impurities, such as Al, Fe...

Electrical Transport Properties ZT = S2 σ Seebeck Coefficients - MBE SrTiO3 La:SrTiO 3! SrTiO 3! κ T SrTiO 3! S [µvk -1 ] 1000 800 600 400 200 S, film (this work) S, single crystal (Okuda et al.) S, single crystal (Frederikse et al.) σ, film (this work) σ, single crystal (Okuda et al.) S = 980 µvk -1 300 K 0 10 17 10 18 10 19 10 20 10 21 10 22 n [cm -3 ] 10 4 10 3 10 2 10 1 10 0 10-1 σ [Scm -1 ] S 2 σ [µw/cmk 2 ] 40 30 20 10 300 K 0 10 17 10 18 10 19 10 20 10 21 10 22 n [cm -3 ] Seebeck coefficient comparable to bulk SrTiO3 Large thermoelectric power factor of 39 µw/cmk 2 Comparable to commercial thermoelectrics B. Jalan, S. Stemmer, Appl. Phys. Lett. 97, 042106 (2010).

Two-dimensional electron gases with SrTiO3 SrTiO3 SrTiO3 delta-doped layer Delta-doping: thin highly doped layer sandwiched between undoped layers Shubnikov-de Haas oscillations and 2DEG behavior have been observed* *Y. Kozuka et al., Nature 462, 487 (2009). EF Energy Depth E2 E1 E0 Know the origin of the carriers (unlike LAO/STO) Potential well and subband formation Electrons in highest subbands are spread-out and have higher mobility Significant scatter from the dopants; however, it allows for the study of 2DEGs

Two-dimensional electron gas in delta-doped SrTiO3 MBE film, La-delta doped layer Shubnikov-de Haas oscillations SrTiO3 La:SrTiO3 SrTiO3 FT ampl. (a.u.) 27 T 54 T 0.410 K 0.8 K 1.2 K 1.8 K 2.5 K 3.0 K 0 20 40 60 Frequency (T) B. Jalan, S. Stemmer, S. Mack, S. J. Allen, Phys. Rev. B 82, 081103(R) (2010). 80 100! R xx [a.u.] Only perpendicular component of B-field determines SdH 2D 0.08 0.12 0.16 0.20 0.24 Fourier transform indicates two frequencies two subbands or is this something else? 1/B [ T -1 ]

Two-dimensional electron gas in delta-doped SrTiO3 FT ampl. (a.u.) SrTiO3 Experiment La:SrTiO3 27 T Two subband model 54 T SrTiO3?!R xx [a.u.] 0 20 40 60 Frequency (T) Fourier transform indicates two frequencies two subbands? 80 100 0.08 0.12 B. Jalan, S. Stemmer, S. Mack, S. J. Allen, Phys. Rev. B 82, 081103(R)(2010). 0.16 1/B [ T -1 ] 0.20 0.24 Experiment fit to standard 2DEG equation with two subbands [1]: & ( ) "R xx = 4R 0 ' exp #2s$ 2 k B T D /!% c s=1 2s$ 2 k B T!% c ( ) sinh 2s$ 2 k B T /!% c ( ) ( 2$s "1 B cos* )* B + # $s-,-! " c = eb m #! Use experimentally determined electron mass (1.56 m0)! The frequencies! (21 and 54 T) do not correspond to the experimental frequencies The SdH oscillations are not well-matched [1] A. Isihara, and L. Smrcka, J. Phys. C 19, 6777 (1986).

Two-dimensional electron gas in SrTiO3 Analogy with hole 2DHGs in III-V quantum well potential lifts k=0 degeneracy Need to also consider strong non-parabolicity: D. A. Broido, and L. J. Sham, Phys. Rev. B 31, 888 (1985). U. Ekenberg, and M. Altarelli, Phys. Rev. B 32, 3712 (1985). Anti-crossing C. Weisbuch, B. Vinter: Quantum Semiconductor Structures Degeneracy of VB and surface electric field combine to couple strongly to parallel and perpendicular transport highly non-parabolic subbands field-dependent cyclotron mass Lifting of two-fold spin degeneracy due to lack of interface inversion symmetry and strong spin-orbit coupling two distinct subbands

Two-dimensional electron gas in delta-doped SrTiO3 Lack of understanding of the bulk electronic structure of SrTiO3: Tetragonal splitting (how large?) Spin-orbit split off band (how much?) Experiments needed! Theory quite complicated Nevertheless, realize the following (in analogy with hole gases in III-V): The effective mass (~ 1-2 m0) and effective Landé factor, g, (~2) are comparable Landau and spin splittings in the magnetic field are likely comparable Cannot use equation with g = 0 Use model with one subband + spin splitting.

Two-dimensional electron gas in delta-doped SrTiO3 One subband + spin splitting model Use three-dimensional equation [1], because it includes spin-splitting (applicable here because of weakness of the oscillations): "R xx R 0 = 5 2 ( $ cos 2%E F s ' % + * - )!& c 4, # b s s=1 two-dimensional case 2"nh 2eB SdH periodicity ("1 B = 2e nh) ( b s = "1 ) s s $!# c ' & ) % 2E F ( s = 1,2 1 2 2* 2 sk B T!# c ( ) sinh 2* 2 sk B T!# c $ 2* 2 sk + exp " B T ' $ ' & D ) cos & *sgm, ) %!# c ( % 2m e ( TD, R0, g, period (Δ1/B) as fit parameters to data at 0.4 K relative strength of weak and strong minima temperature dependence is determined by m* [1] L. M. Roth, and P. N. Argyres, in Semiconductors and Semimetals Vol. 1, edited by R. K. Williardson, and A. C. Beer (Academic Press, New York, 1966). B. Jalan, S. Stemmer, S. Mack, S. J. Allen, Phys. Rev. B 82, 081103(R)(2010).

Two-dimensional electron gas in delta-doped SrTiO3 One subband + spin splitting model! R xx (a.u.) Experiment Calculation Fit to 0.4 K data yields experimentally determined frequency (27 T) Temperature dependence and SdH period is well described Only the highest lying subband, with the highest mobility, gives rise to SdH Spin-related effects important Series of possible g factors: 0.698, 1.86,... Carrier concentration is 1.3 10 12 cm -2, about 4% of the Hall concentration (3 10 13 cm -2 ). 0.10 0.15 1/B (T -1 ) 0.41 K 0.8 K 1.2 K 1.8 K 2.5 K 3.0 K 0.20 B. Jalan, S. Stemmer, S. Mack, S. J. Allen, Phys. Rev. B 82, 081103(R)(2010). 0.25 A small fraction of the electrons in one subband in a large number of electrons in the delta-doping potential The electron density in that subband is likely not constant (note different frequencies at low B-fields) in exp. and calc.

Summary Novel oxide MBE approach allows for high purity, low-energetic deposition of complex oxides (titanates) with excellent stoichiometry control MBE growth window allows for stoichiometric films without being limited by precision of flux control Low carrier concentrations (~10 17 cm -3 ) and 1:1 correspondence of dopant and carrier concentrations indicate low intrinsic defect concentrations Very low defect concentrations allow for record electron mobilities 2DEG in SrTiO3 obtained through delta-doping exhibits 2D quantum oscillations 2DEGs in SrTiO3 contain all the complications of 2DHGs of conventional semiconductors Showed that quantitative description of DEGs in SrTiO3 can be obtained provided effects from spin-splitting are taken into account Spin-related effects are important in DEGs in SrTiO3