Two-dimensional electron gas in SrTiOstemmer/main_pdfs/SpinAps_workshop_short.pdf · Challenges in Oxide MBE • Low growth pressures • Oxygen vacancies • Oxygen vacancies are

Bharat Jalan, Susanne StemmerMaterials Department

S. James AllenDepartment of Physics

University of California, Santa Barbara

Two-dimensional electron gas in SrTiO3

SpinAge 2010Watsonville, 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

IntroductionC. Weisbuch, B. Vinter: Quantum

Semiconductor Structures

Quantum-confined structures in III-V semiconductors have lead to a wealth of

phenomena and new technologies

Quantum III-V Semiconductor Structures

• 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)

Quantum Oxide Structures

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)

MBErf sputtering

PLD

Regime II Regime IIIRegime I

Cuomo et al., J. Appl. Phys. 70 1706 (1991).

Impurities in Complex OxidesCommercial SrTiO3 single crystals

(Verneuil grown)www.surfacenet.de

Impurity content in commercial SrTiO3 single crystals (Toplent)

Total in:GaN ~ 1 ppm

Si ~ ppb or better

80

60

40

20

0

Tra

nsm

ittan

ce [

%]

2500200015001000500Wavelength [nm]

80

60

40

20

0

Tra

nsm

ittan

ce [

%]

2500200015001000500Wavelength [nm]

“As-purchased”:no absorption in the visibletransparent and colorless

After oxygen anneal:absorption peak with wide

shoulderbrown color

High concentrations of impurities even in oxide single crystals

As-grown

Charged defects

deep acceptors (most likely)

Outline

• Introduction




• Summary

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

• 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

• Metal flux instabilities in the presence of oxygen (oxidation of sources)

Oxygen Stoichiometry

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

C. D. Theis and D. G. Schlom, J. Vac. Sci. Technol. A 14 (1996), 2677


Cation Stoichiometry

Temperature (°C)

Temperature (1000/K)

Gas

Pre

ssur

e (T

orr)

GaAs(s) ⇔ Ga(l) + As(g)

4 As(s) ⇔ As4(g)

MBE Growth Window

Temperature (°C)

Below this line, solid As will not precipitate → excess As desorbs in the chamber

4As(s) ⇔ As4(g)

GaAs(s) ⇔ Ga(l) + As(g)

Above this line, As will condense on a Ga-rich GaAs surface

MBE Growth Window

MBE growth window

for GaAs

A wide MBE growth window is largely

responsible for the ease and success of

III-V MBE

C.D. Theis et al., Thin Solid Films 325, 107 (1998).

J. Tsao, Materials Fundamentals of Molecular Beam Epitaxy.

10-27

10-24

10-21

10-18

10-15

10-12

10-9 10

-6

P SrO

(g) [

torr

]

1.00.90.80.70.6

1000/T [1/K]


Cation Stoichiometry

Temperature (°C)1500 K

SrO(s)⇔ SrO(g)

SrO(g) + TiO2(s) ⇔ SrTiO3(s)

MBE Growth Window

Below this line, solid SrO will not precipitate: SrO will desorb in the chamber*

Above this line, SrO will condense on a TiO-rich SrTiO3 surface*

MBE growth window

for SrTiO3

No MBE growth window for most complex oxides

Assumed a sticking coefficient of one for Ti*

* C.D. Theis et al., Thin Solid Films 325, 107 (1998).


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]

Ta crucible

hole in crucible

!"#$%&'%())*%(&+,$%%-&

[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)

Novel Oxide MBE Approach

Bubbler

Gas supply (heated)

Leak valve

Baratron

Titanium tetra isopropoxide (TTIP)

Hybrid Oxide MBETitanium tetra iso propoxide (TTIP)

Ti

OTTIP source

• 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

Ti(OC3H7)4 → TiO2 + 2 C3H7OH + 2 C3H6

@ T = 350˚C

Sr cellOxygen plasma

source

!!"#$!%&'()($

*+,-./&()($

012(3$

4-,3%,1)%&$56(2%)($

78$9:(*8$;%68+$<=4=$>?@<4A$B$CCC8D-%:(86%*EF,GH121$

Metal-Organic MBE of Rutile TiO2

Ts ≈ 615 °CTTIP beam flux: 2×10-6 torr

No oxygen

• 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

B. Jalan, R. Engel-Herbert, J. Cagnon, S. Stemmer, J. Vac. Sci.

Technol. A 27, 230 (2009).

TTIP source

Al2O3!

TiO2!

Hybrid MBE of SrTiO3

TTIP sourceoxygen plasma source

Sr source

Tsub= 800 °Cpox= 8 × 10-6 torr

55.4

53.3

42.1

41.0

39.5

TTIP / Srflux ratio

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).

• Co-deposition (not shuttered)

• Lattice parameter as a measure of stoichiometry

• Lattice parameter increases for non-stoichiometry films (Sr rich and Ti rich)

• Excellent control over film stoichiometry

SrTiO3!

SrTiO3!

Hybrid MBE of SrTiO3: Growth Modes

after growth

substrate

• Persistent (> 180) RHEED oscillations indicate layer-by-layer 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).

SrTiO3!

SrTiO3!

Hybrid MBE of SrTiO3

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

LSAT!

SrTiO3!

DyScO3!

SrTiO3!

MBE Growth Window

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

Growth windowsGrowth windows

B. Jalan, P. Moetakef, S. Stemmer, Appl. Phys. Lett. 95, 032906 (2009).

SrTiO3!

SrTiO3!

Significance of the MBE Growth Window

B. Jalan, P. Moetakef, S. Stemmer, Appl. Phys. Lett. 95, 032906 (2009).

• 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 1020-1021 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.

Outline

• Introduction




• Summary

Electrical Transport Properties

Hall Mobilities - SrTiO3 Single Crystals

O. N. Tufte, P. W. Chapman, Phys. Rev. 155, 796 (1967)

1967 2007

G. Herranz et al., Phys. Rev. Lett. 98, 21603 (2007)

Hal

l m

ob

ilit

y (

cm2/V

s)

Hal

l m

ob

ilit

y (

cm2/V

s)

Hal

l m

ob

ilit

y (

cm2/V

s)

Temperature (K)

Temperature (K)

Temperature (K)

A. Spinelli et al., Phys. Rev. B 81, 155110 (2010)

μ = 22,000 cm2/Vs at n = 1.4×1017cm-3

2010

μ = 25,000 cm2/Vs

μ = 22,100 cm2/Vs at n = 8×1017cm-3

10 100

n-type dopants: VO

.. or Nb


1018

2

4

1019

2

4

1020

2

Car

rier

con

cent

ratio

n [c

m-3

]

1018

1019

1020

La concentration [cm-3

]

J. Son, P. Moetakef, B. Jalan, O. Bierwagen, N. J. Wright, R. Engel-Herbert, S. Stemmer, Nature Mater. 9, 482 (2010).

• 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

SrTiO3!

SrTiO3!

La:SrTiO3!Doping of MBE SrTiO3 with La

1017

2

4

6

1018

2

4

6

1019

Car

rier

con

cent

ratio

n [c

m-3

]

300250200150100500

Temperature [K]

STO 1 STO 2 STO 3

La-Doping of SrTiO3

SrTiO3!

SrTiO3!

La:SrTiO3!HAADF/STEM

La atoms

Interface

La-doped SrTiO3

nHall = 1.8×1021 cm-3

undoped SrTiO3 buffer layer


101

102

103

104

105

Ele

ctro

n m

obili

ty [

cm2 /V

s]

2 3 4 5 610

2 3 4 5 6100

2 3

Temperature [K]

4.0

3.0

2.0

1.054321

µ = 32667 cm2/Vs

n [1018

cm-3

]

µ [

10

4 cm

2 /Vs]

Hall Mobilities - MBE SrTiO3μ = 32,667 cm2/Vs at n = 7.9×1017cm-3

J. Son, P. Moetakef, B. Jalan, O. Bierwagen, N. J. Wright, R. Engel-Herbert, S. Stemmer, Nature Mater. 9, 482 (2010).

SrTiO3!

SrTiO3!

La:SrTiO3!

Magnetoresistance(Shubnikov-de Haas) oscillations

• Higher mobility than single crystals

• Most likely due to lower concentration of charged impurities, such as Al, Fe ...


Seebeck Coefficients - MBE SrTiO3

S = 980 µVK-1

• Seebeck coefficient comparable to bulk SrTiO3

• Large thermoelectric power factor of 39 µW/cmK2

• Comparable to commercial thermoelectrics

€

ZT =S2σκ

TSrTiO3!

SrTiO3!

La:SrTiO3!

300 K

300 K

10-1

100

101

102

103

104

σ [

Scm

-1]

1017

1018

1019

1020

1021

1022

n [cm-3

]

1000

800

600

400

200

0

|S| [

µVK

-1]

|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.)

40

30

20

10

0

S2 σ [µ

W/c

mK

2 ]

1017

1018

1019

1020

1021

1022

n [cm-3

]

B. Jalan, S. Stemmer, Appl. Phys. Lett. 97, 042106 (2010).

Outline

• Introduction




• Summary

Two-dimensional electron gases with SrTiO3

*Y. Kozuka et al., Nature 462, 487 (2009).

• Delta-doping: thin highly doped layer sandwiched between undoped layers

• Shubnikov-de Haas oscillations and 2DEG behavior have been observed*

delta-doped layer

SrTiO3

SrTiO3

Ener

gy

Depth

EF

E0

E1

E2

• 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

• Only perpendicular component of B-field determines SdH → 2D

• Fourier transform indicates two frequencies → two subbands or is this something else?

MBE film, La-delta doped layerShubnikov-de Haas oscillations

FT a

mpl

. (a.

u.)

100806040200

Frequency (T)

27 T54 T

! R

xx

[a.u

.]

0.240.200.160.120.08

1/B [ T-1]

0.410 K 0.8 K 1.2 K 1.8 K 2.5 K 3.0 K

B. Jalan, S. Stemmer, S. Mack, S. J. Allen, Phys. Rev. B 82, 081103(R)(2010).

SrTiO3

SrTiO3

La:SrTiO3


Fourier transform indicates two frequencies → two subbands?

FT a

mpl

. (a.

u.)

100806040200

Frequency (T)

27 T54 T SrTiO3

SrTiO3

La:SrTiO3


!Rxx

[a.u

.]0.240.200.160.120.08

1/B [ T-1

]

Experiment Two subband model

• Experiment fit to standard 2DEG equation with two subbands [1]:

• 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).

!

"Rxx

= 4R0 exp #2s$ 2k

BT

D/!%

c( )s=1

&

'2s$ 2

kBT !%

c

sinh 2s$ 2k

BT /!%

c( )cos

2$s "1 B( )B

#$s

(

) * *

+

, - - !

!

"c

= eB m#!

?

Two-dimensional electron gas in SrTiO3

Analogy with hole 2DHGs in III-V

quantum well potential lifts k=0 degeneracy

Anti-crossing

Need to also consider strong non-parabolicity:

C. Weisbuch, B. Vinter: Quantum Semiconductor Structures

D. A. Broido, and L. J. Sham, Phys. Rev. B 31, 888 (1985).

U. Ekenberg, and M. Altarelli, Phys. Rev. B 32, 3712 (1985).

• 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


• 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.

• 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



• Use three-dimensional equation [1], because it includes spin-splitting (applicable here because of weakness of the oscillations):

[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).

!

"Rxx

R0

=5

2b

s

s=1

#

$ cos2%E

F

!&c

s '%

4

(

) *

+

, - !

!

2"nh

2eB!

two-dimensional case

!

bs ="1( )

s

s

!#c

2EF

$

% &

'

( )

1 2

2* 2skBT !#c

sinh 2* 2skBT !#c( )+ exp "

2* 2skBTD

!#c

$

% &

'

( ) cos

*sgm,

2me

$

% &

'

( ) !

relative strength of weak and strong

minima

SdH periodicity

s = 1,2

TD, R0, g, period (Δ1/B) as fit parameters to data at 0.4 K

!

"1 B = 2e nh( )

One subband + spin splitting model

temperature dependence is

determined by m*



0.250.200.150.101/B (T

-1)

0.41 K 0.8 K 1.2 K 1.8 K 2.5 K 3.0 K

! 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, ...

One subband + spin splitting model

• Carrier concentration is 1.3×1012cm-2, about 4% of the Hall concentration (3×1013cm-2).

• 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 (~1017 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

Documents

Two-dimensional electron gas in SrTiOstemmer/main_pdfs/SpinAps_workshop_short.pdf · Challenges in Oxide MBE • Low growth pressures • Oxygen vacancies • Oxygen vacancies are