Enhanced two dimensional electron gas charge densities at III-III/I-V oxide heterostructure interfaces

0.91 MB·English

by  Valentino R. Cooper

Enhanced two dimensional electron gas charge densities at III-III/I-V oxide
heterostructure interfaces
∗
Valentino R. Cooper
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6056
Inthispaper,densityfunctionaltheorycalculationsareusedtoexploretheelectronicandatomic
reconstruction at interfaces between III-III/I-V oxides. In particular, at these interfaces, two di-
mensional electron gases (2DEGs) with twice the interfacial charge densities of the prototypical
LaTiO3/SrTiO3 heterostructure are observed. Furthermore, a significant decrease in the band
2
effectivemassesoftheconductionelectronsisshown,suggestingthatpossibleenhancementsinelec-
1
tronmobilities maybeachievable. Thesefindingsrepresentaframework forchemically modulating
0
2DEGs,therebyprovidingaplatformthroughwhichtheunderlyingphysicsofelectronconfinement
2
can be explored with implications for modern microelectronic devices.

n
a PACSnumbers: 73.40.-c,71.28.+d,31.15.E-,81.05.Zx
J

8
1 Emergent phenomena at ABO oxide interfaces, tribution of Ti3+ cations away from the interface were
3

e.g. two dimensional electron gases (2DEGs),[1] found to be in good agreement with theoretical and ex-
]
i are paramount to understanding critical behav- perimental carrier density profiles.[6, 18–22] In a perfect
c
ior arising from electron confinement; like metal- system, the extra 1/2 electron, relative to Ti in SrTiO ,
s 3
- insulator transitions,[2] novel magnetic effects [3] and defines the intrinsic limit of 2DEG carrier densities.[23]
l
r superconductivity.[4, 5] Recent theory and experiments This electronic reconstruction is a hallmark of the ob-
t
m have sought to identify the origin of 2DEGs at insu- servedtwo-dimensionalconductivity andisaccompanied
lating oxide interfaces and surfaces in order to develop by polar distortions [18, 24, 25] (atomic displacements
.
at rules or concepts by which charge carrier densities and of the cations away from the interface) which effectively
m mobilities can be tuned. Growth under low O partial screen the electrons near the interfaces. Furthermore,
2
pressure has been shown to have (vacancy mediated) the most commonly studied 2DEGs derived from II-IV
-
d enhancements in conductivities that extend deep into (e.g. Sr2+Ti4+O ) oxides have interfacial carrier den-
3
n −
bulk regions, making these materials undesirable for sities which are intrinsically limited to 0.5 e /interface
o
examininginterfacialphysics.[6,7]Conversely,annealing unit cell.
c
[ or growth under high O2 pressure eliminates oxygen In this paper, density functional theory (DFT) calcu-

vacancies resulting in consequential increases in resis- lations are used to investigate the charge rearrangement
1
tivities; giving rise to intrinsic 2DEG behavior.[6, 7] at interfaces between I-V/III-III perovskites. The goal
v
1 In oxide heterostructures such as LaAlO3/SrTiO3 and is to apply the above insights to control the interfacial
7 LaGaO3/SrTiO3 this is understood in terms of polar- charge density by increasing the intrinsic limit of elec-
8 ization discontinuities at interfaces, i.e. the “the polar trons at an oxide heterointerface. The guiding principle
3
catastrophe” mechanism.[6, 8–12] Physically, the diver- isthattheincorporationofamultivalentcationatanin-
.
1 gence of the electrostatic potential at atomically abrupt terface, where its desired valence states are +3 and +5,
0 interfaces between insulating layered, charge-ordered should allow for an average valence of +4, thus increas-
12 III-III and a non-polar II-IV (usually SrTiO3) oxides is ing the limit of extra interfacial charge to 1 e−/interface
: compensated for by charge accumulation (in this case unit cell. By examining heterostructures comprised of
v
an extra 1/2 electron per interface unit cell) at the I-V/III-III oxides, it is confirmed that a total of 1 elec-
i
X interface. Interestinglyenough,intheseheterostructures tronperinterfaceunitcellnowpopulatestheconduction
r this only occursatTiO2 centeredinterfaces andrequires bands(twicethatofacorrespondingLaTiO3/SrTiO3su-
a relatively thick layers of LaAlO3 or LaGaO3.[10, 13] perlattice). Similar to previous observations of 2DEGs,
A chemically intuitive, δ-layer-doping, mechanism theseelectronsareprimarilyconfinedtot2g orbitalsonB
arises from the multivalent nature of transition metal cations near LaO interfaces, decay quickly into the bulk
cations, like Ti. For example, in LaTiO /SrTiO su- and are accompanied by large polar ionic distortions. In
3 3
perlattices, the local environment of Ti cations next addition, calculated decreases in electron band effective
to a “dopant”, LaO layer, splits the valence of Ti be- masses suggest that improved carrier mobilities may be
tween two possible charge states (+4 for SrTiO and achievable.
3
+3 for LaTiO ). Therefore, an equal mixture of Ti va- DFT calculations using the local density approxima-
3
lence states (3+ or 4+) can be thought to reside at the tion with a Hubbard U (LDA+U) [26] and ultrasoft
interface giving an average valence of 3.5.[14–16] This pseudopotentials [27] as implemented in the Quantum
has been confirmed through electron energy-loss spec- Espresso simulation package [28, 29] were performed to
troscopy (EELS) measurements [17] in which the dis- study1LaXO /7KXO superlattices,whereX=Taand
3 3
2
5 1LaTiO/7SrTiO 1LaNbO/7KNbO 1LaTaO/7KTaO
4 a) b) c) d) e) 1a) 3 3 b) 3 3 c) 3 3
3
2 E
F
1
V]E
y [e -F1 eV] -1
rg -2 y [
ne -3 rg -2
E -4 ne
E
-5
-6 -3
-7
-8 ×5 ×5 ×5
-4
DOS [arb. units]
M Γ X M Γ X M Γ X M
FIG. 1. DOS for (a) bulk SrTiO3, (b) 1 LaTiO3/7 SrTiO3,
(c)1LaNbO3/7KNbO3(d)1LaTaO3/7KTaO3and(e)bulk FIG.2. Electronicbandstructurefor(a)1LaTiO3/7SrTiO3,
KTaO3. AllenergiesarerelativetotheFermilevel,EF. (The (b)1LaNbO3/7KNbO3and(c)1LaTaO3/7KTaO3 empha-
scale for the heterostructures is 5× that of the bulk struc- sizing thepartially occupied states nearthe Fermi surface.
tures.)
states, with the two lowest energy, light electron, bands
Nb. Allsuperlatticecalculationsemployedan80Rycut- coming almost entirely from dxy orbitals on the inter-
offandan8×8×1k-pointmesh. Comparisonsweremade facial Ti ions and the remaining occupied states being a
with a prototypical 2DEG system, 1 LaTiO3/7 SrTiO3. mixtureoft2g statesonalloftheTications. Moreimpor-
In all calculations, the in-plane lattice constants were tantly, in 1 LaNbO3/7 KNbO3 and 1 LaTaO3/7 KTaO3
constrainedtothe theoreticalvalue ofthe majoritycom- theseoccupiedelectronicstatessumuptoexactly2elec-
−
ponent (i.e. KXO or SrTiO ) and the out-of-plane, trons (i.e. 1 e / interface unit cell). An examination
3 3
c, lattice vector was optimized within the P4mm space of the electronic band structure shows that they con-
group with 1×1 in-plane periodicity. Simultaneously, all tribute to the Fermi surface (see Fig. 2b and c). Orbital
ioniccoordinateswererelaxeduntilallHellman-Feynman projected DOS indicate that they are derived mainly
forces were less than 8 meV/˚A. The computed bulk from the B-cation d-states (Nb/Ta) with dominant elec-
KNbO3,KTaO3,andSrTiO3cubiclatticeconstantswere tronic contributions arising from partially occupied dxy
3.951˚A,3.945˚A,and3.855˚A,respectively. (Note: these orbitals of B-cations at the LaO interface. In all three
values were obtained using standard LDA, i.e. without heterostructures light electronic bands crossing EF are
the inclusionofaHubbardU).These areintypicalLDA parabolic around Γ and heavy bands extend along the
agreement with experimental values of 4.000 ˚A, 3.988 ˚A Γ-X direction. This is a characteristic feature of 2DEGs
and 3.901 ˚A, respectively. For all heterostructure cal- and is consistent with recent angle-resolved photoemis-
culations, a Hubbard U=5 eV for B-cation d-states was sionspectroscopy(ARPES)resultsfor2DEGsatSrTiO3
found to be appropriate. Similar U values were used surfaces.[20, 30]
in previous studies of LaTiO3/SrTiO3.[18, 25] Band ef- Figure 3a displays the spatial distribution of the con-
fective masses were compute using quadratic fits of the duction electrons (i.e. arising from states between E
F
partially occupied bands. and ∼ -1.8 eV) as a function of distance away from
Figure 1 depicts the density of states (DOS) for bulk the LaO layer. Similar to previous theoretical and ex-
SrTiO , bulk KTaO , 1 LaTiO /7 SrTiO , 1 LaNbO perimental results for 2DEGs at heterointerfaces and
3 3 3 3 3
/7 KNbO and 1 LaTaO /7 KTaO superlattices. Both the SrTiO surface we find a build-up of charge of
3 3 3 3
SrTiO and KTaO , using LDA (i.e. no Hubbard U) roughly 0.22 electrons on interfacial Ti cations in the
3 3
haverelativelylargebandgapsof1.7and1.8eV,respec- 1LaTiO /7SrTiO superlattice.[6,18–22](Note: theto-
3 3
−
tively. Althoughsmallerthanexperiment,these arecon- talatomprojectedDOSaddsupto0.95e andisscaled
sistent with LDA’s underestimation of oxide band gaps. tounityinthe plots.) Thischargequicklydecaysto0.06
In agreement with previous studies, 1 LaTiO /7 SrTiO electrons in the center of the slab, indicating a decay
3 3
has occupied states just below the Fermi level, E , that length of roughly 3-4 unit cells. On the other hand, we
F
−
sum to 1 electron (or rather 0.5 e /interface unit cell). observe that the LaNbO /KNbO and LaTaO /KTaO
3 3 3 3
−
The electronic band structure plot (Fig. 2a) indicates heterostructureshave a build-up of 0.52 and 0.60 e s on
that they directly contribute to transport (i.e. cross the the interfacial Nb and Ta ions, respectively. (again the
−
Fermi level). An analysis of the orbital projected DOS projected DOS only sums to 1.8 e s and is uniformly
indicatesthatthesestatesarederivedmainlyfromTit scaledto 2.0). Surprisingly, discernible differences in the
2g
3
O La Sr/K
TABLEI.Structuralparametersandrelativeeffectivemasses
for the heterostructures studied. ao, c/a and me/m denote
B the cubic lattice parameter, c/a ratio and the relative effec-
tivemassesofthetwolowestenergypartiallyoccupiedbands,
1LTO/7STO
0.6 1LNO/7KNO respectively. Note: the curvature of the electronic structure
ns0.5 a) 1LTaO/7KTaO around Γ is symmetric. i.e. the effective mass along the Γ-X
o0.4 and Γ-M directions are essentially equal and thus only one
r
ct0.3 valueis reported for each band.
e
el0.2
# 0.1 System ao [˚A] c/a me/m
0.0 1 2
0.25 b) 1 LaTiO3/7 SrTiO3 3.885 8.117 0.49 0.59
0.20 1 LaNbO3/7 KNbO3 3.951 8.085 0.35 0.41
Å]0.15 1 LaTaO3/7 KTaO3 3.945 8.009 0.30 0.35
g [0.10
n0.05
eri0.00
nt c) a representative 2 dimensional projection of the atomic
e
c0.25 structure of a 1/7 heterostructure). Similar to previ-
-
Off0.20 ous DFT results we find that the magnitude of SrTiO3
0.15 off-centering is 0.18 ˚A and 0.13 ˚A for the A- and B-
0.10
cations near the interface, respectively.[18, 25] Figure 3b
0.05
and c show that the magnitudes of the B- and A-
0.00
-4 -3 -2 -1 0 1 2 3 4 cation off-center displacements in the LaXO /KXO
3 3
Relative z-coordinate
structures are all appreciably larger than those in
LaTiO /SrTiO . These larger polar distortions are con-
FIG.3. (coloronline)[top]Representative2-dimensionalpro- 3 3
sistentwiththeneedforlargerinterfacialpolarizationsto
jectionofarelaxedsuperlattices. (a)Chargedistributionand
(b)magnitudeofB-and(c)A-cation off-centeringasafunc- adequately screen the interfacial charges. Unexpectedly,
tionofrelativez-coordinateforthesuperlatticesstudied. All the LaTaO3/KTaO3 superlattice while having the larger
distances are relative to LaO planes. interfacial charge exhibits smaller polar distortions than
LaNbO /KNbO . Although the difference in the com-
3 3
puted interfacialchargemay be a consequence of scaling
decay of charge away from the LaO interface are seen. of the charge densities, it may also be a direct indica-
In LaNbO /KNbO , there is still roughly 0.15 e−/unit tor of the magnitude of charge screening in these two
3 3
cell area in the bulk region, whereas the charge density materials arising from the differences in their respective
in LaTaO /KTaO drops off much more sharply, falling dielectric constants - with the lower dielectric constant
3 3
to less than 0.1 e−/unit cell area. This deviation may material being more strongly screened. A second expla-
be linked to differences in dielectric constants. Theoret- nationisthatKNbO3,unlikeKTaO3,hasapolarground
ical calculations have demonstrated that a larger dielec- statewhichmaybemorefavorabletoinducingpolardis-
tric constant can result in a greater spread of electrons tortions. In which case, the polar nature of the KNbO3
awayfromtheinterface.[31,32]KTaO andSrTiO have structure may be more advantageous as recent studies
3 3
very similar dielectric constants,[33, 34] while KNbO have proposed the use of an electric field as a switch for
3
hasamuchstrongerdependenceofdielectricconstanton controlling interface conductivity.[24, 36]
phase.[35]Infact,KNbO3 canhaveadielectricconstants Finally,TableIliststherelativebandeffectivemasses,
that is a few orders of magnitude greater than SrTiO3 me/m,ofthetwolowestenergypartiallyoccupiedbands
and KTaO3, making the observed behavior reasonable. (seeFig.2). Remarkably,thecomputedme/mvaluesfor
Regardless,theseresultsclearlyindicateasignificanten- SrTiO , are in excellent agreement with ARPES mea-
3
hancement in the concentration of electrons near the in- surements performed for SrTiO surface 2DEGs (0.5 -
3
terface for III-III/II-IV heterostructure relative to the 0.6m /m).[30]Whiletheoriginofthe2DEGsatSrTiO
e 3
III-III/I-V system, with thelowerdielectric constantma- surfaces is almost certainly due to a different mecha-
terialsbeingmoreconducivetoconfiningelectronstothe nismthantheδ-dopedstructures,thisresultissuggestive
interface. of characteristic electronic structure features. It should
In accordance with the observed interfacial electronic be pointed out that La doped SrTiO has considerably
3
reconstruction we find considerable polar distortions of higher effective mass (m /m > 1) and that the band
e
the A- and B-cations away from the LaO layer. These effective masses predicted here neglects correlation ef-
off-center displacements gradually return to zero in the fects. Moreover, the 1 LaXO /7 KXO structures were
3 3
center of the SrTiO /KXO layers. (See Fig. 3 [top] for foundto havesignificantdecreasesinm for thesebands
3 3 e
4
(which dominate the electron density at the interfaces), sion,OfficeofBasicEnergySciences,U.S.Departmentof
implyingpossibleincreasesincarriermobilitiesintheIII- Energy. ThisresearchusedresourcesoftheNationalEn-
III/I-V superlattices. Of course, semiconductor physics ergyResearchScientificComputingCenter,supportedby
tells us that increases in charge densities (as observedin the Office of Science, U.S. Department of Energy under
the 1 LaXO /7KXO basedheterostructures)areoften Contract No. DEAC02-05CH11231.
3 3
accompanied by decreases in carrier mobilities. Typi-
cally increased carrier densities arise from increases in
dopant concentrations, which act as scattering centers
thereby reducing the mean free path of the carriers. In
∗ [email protected]
the above materials the LaO layers could be considered
[1] A. Ohtomo, D. A. Muller, J. L. Grazul, and H. Y.
dopants (i.e. δ-doped layers). Since the concentration
Hwang, Nature419, 378 (2002).
of La remains constant at the interface there may be
[2] S.Thiel,G.Hammerl,A.Schmehl,C.W.Schneider, and
little change in the scattering lifetimes, τ. Hence, devia- J. Mannhart, Science 313, 1942 (2006).
tions in electron mobilities, µe, may be more affected by [3] A. Brinkman, M. Huijben, M. van Zalk, J. Huijben,
changesinm (whereµ =eτ/m ). Furthermore,recent U. Zeitler, J. C. Maan, W. G. van der Wiel, G. Rijn-
e e e
dynamical-mean-field calculations of oxide heterostruc- ders, D. H. A. Blank, and H. Hilgenkamp, Nat. Mater.
6, 493 (2007).
ture 2DEGs suggest that correlation effects are least af-
[4] K. v. Klitzing, G. Dorda, and M. Pepper,
fectedbydopantconcentrationsandthatthe bandeffec-
Phys. Rev.Lett. 45, 494 (1980).
tive masses have the most deviations.[37]
[5] T. Ando, A. B. Fowler, and F. Stern,
In summary, using first principles methods, it Rev. Mod. Phys. 54, 437 (1982).
is demonstrated that superlattices comprising I-V [6] W. Siemons, G. Koster, H. Yamamoto, W. A. Harrison,
(K1+[Nb/Ta]5+O ) and III-III (La3+[Nb/Ta]3+O ) per- G. Lucovsky,T. H.Geballe, D.H.A.Blank, andM. R.
3 3
Beasley, Phys. Rev.Lett. 98, 196802 (2007).
ovskiteshavetwice the interfacialchargedensities ofIII-
[7] A. Kalabukhov, R. Gunnarsson, J. B¨orjesson,
III/II-IV(SrTiO /LaTiO ) superlattices. Here, the flex-
3 3 E. Olsson, T. Claeson, and D. Winkler,
ibility of multivalent cations, like Nb and Ta, leads to Phys. Rev.B 75, 121404 (2007).
−
an intrinsic limit of 1 e per interface unit cell, twice [8] A. Ohtomoand H.Y. Hwang, Nature427, 423 (2004).
the limit of previously studied III-III/II-IV and I-V/III- [9] N. Nakagawa, H. Y. Hwang, and D. A. Muller, Nat.
III [24, 38] superlattices. Also, changes in electron ef- Mater. 5, 204 (2006).
fective masses (with no change in dopant levels) imply [10] R. Pentcheva and W. E. Pickett,
Phys. Rev.Lett. 102, 107602 (2009).
that further enhancements in mobilities may be achiev-
[11] N. C. Bristowe, E. Artacho, and P. B. Littlewood,
able. As such, this research highlights a viable path for
Phys. Rev.B 80, 045425 (2009).
enhancing the properties of 2DEGs. In addition, devia-
[12] M. Stengel and D. Vanderbilt,
tions in polar distortions and charge redistribution em- Phys. Rev.B 80, 241103 (2009).
phasize the need for a better understanding of the rela- [13] P. Perna, D. Maccariello, M. Radovic, U. S. di Uccio,
tionship between dielectric constant and electronic and I.Pallecchi,M.Codda,D.Marr,C.Cantoni,J.Gazquez,
atomic reconstructions. In agreement with other theo- M. Varela, S. J. Pennycook, and F. M. Granozio,
Appl. Phys.Lett. 97, 152111 (2010).
reticalmodels,[31,32]theseresultssuggestthatlowerdi-
[14] G. A. Baraff, J. A. Appelbaum, and D. R. Hamann,
electric constantmaterials (e.g. KTaO ) should be more
3 Phys. Rev.Lett. 38, 237 (1977).
idealfor realizingtruly two-dimensionalelectronicgases.
[15] W.A.Harrison,E.A.Kraut,J.R.Waldrop, andR.W.
Alternatively,polaroxideslikeKNbO3maybemoresuit- Grant, Phys. Rev.B 18, 4402 (1978).
able for applications where it is necessary to switch the [16] H. Chen, A. M. Kolpak, and S. Ismail-Beigi,
charge carrier concentrations. Naturally, synthetic lim- Adv.Mater. 22, 2881 (2010).
itations related to effectively reducing ions like Ta5+ to [17] H. W. Jang, D. A. Felker, C. W. Bark, Y. Wang, M. K.
Ta3+ may exist. A feasible route may be to substitute Niranjan,C.T.Nelson,Y.Zhang,D.Su,C.M.Folkman,
S.H.Baek,S.Lee,K.Janicka,Y.Zhu,X.Q.Pan,D.D.
interfacial Ta cations with a cation, like V, that is more
Fong,E.Y.Tsymbal,M.S.Rzchowski, andC.B.Eom,
easily reduced. Ultimately, these results presenta chem- Science 331, 886 (2011).
ically intuitive framework(in the absence offactors such [18] S. Okamoto, A. J. Millis, and N. A. Spaldin,
as O vacancies) through which intrinsic carrier concen- Phys. Rev.Lett. 97, 056802 (2006).
trations, and perhaps even carrier mobilities, of oxide [19] S. Okamoto and A. J. Millis, Nature428, 630 (2004).
heterostructure 2DEGs can be tuned and may be use- [20] A. F. Santander-Syro, O. Copie, T. Kondo, F. Fortuna,
S.Pailhes, R.Weht,X.G.Qiu,F.Bertran,A.Nicolaou,
ful in device engineering[39] andin controllingquantum
A. Taleb-Ibrahimi, P. Le Fevre, G. Herranz, M. Bibes,
phenomena due to electron confinement.
N. Reyren, Y.Apertet, P. Lecoeur, A. Barthelemy, and
V.R.C. would like to acknowledge helpful discussions M. J. Rozenberg, Nature 469, 189 (2011).
with C. Bridges, C. Cantoni, H. N. Lee, S. Okamoto, D. [21] C. Cantoni, J. Gazquez, F. M. Granozio, M. P. Oxley,
Parker, W. Siemons and D. Xiao. This work was sup- M.Varela,A.R.Lupini,S.J.Pennycook,C.Aruta,U.S.
ported by the Materials Sciences and Engineering Divi- diUccio,P.Perna, andD.Maccariello, (2011),(Unpub-
5
lished). [31] S. Okamoto and A. J. Millis,
[22] M. Takizawa, S. Tsuda, T. Susaki, H. Y. Hwang, and Phys. Rev.B 70, 075101 (2004).
A.Fujimori, arXiv:1106.3619v1. [32] S.S.KancharlaandE.Dagotto,Phys.Rev.B74,195427
[23] J. S. Kim, S. S. A. Seo, M. F. Chisholm, R. K. Kremer, (2006).
H.-U.Habermeier,B.Keimer, andH.N.Lee,Phys.Rev. [33] M. D. Agrawal and K. V. Rao, J. Phys. C: Solid State
B 82, 201407(R) (2010). Phys. 3, 1120 (1970).
[24] Y.Wang,M.K.Niranjan,S.S.Jaswal, andE.Y.Tsym- [34] G. Rupprecht and R. O. Bell,
bal, Phys. Rev.B 80, 165130 (2009). Phys. Rev.135, A748 (1964).
[25] D. R. Hamann, D. A. Muller, and H. Y. Hwang, [35] G. Shirane, H. Danner, A. Pavlovic, and R. Pepinsky,
Phys.Rev.B 73, 195403 (2006). Phys. Rev.93, 672 (1954).
[26] V. I. Anisimov, J. Zaanen, and O. K. Andersen, Phys. [36] A. D. Caviglia, S. Gariglio, N. Reyren, D. Jac-
Rev.B 44, 943 (1991). card, T. Schneider, M. Gabay, S. Thiel, G. Hammerl,
[27] D.Vanderbilt,Phys. Rev.B 41, 7892(R) (1990). J. Mannhart, and J. M. Triscone, Nature 456, 624
[28] M. Cococcioni and S. de Gironcoli, (2008).
Phys.Rev.B 71, 035105 (2005). [37] S. Okamoto, Phys. Rev.B (Rapid) 84 (2011).
[29] P. Giannozzi, et al., J. Phys.: Cond. Matt. 21, 395502 [38] E. D. Murray and D. Vanderbilt,
(2009). Phys. Rev.B 79, 100102 (2009).
[30] W. Meevasana, P. D. C. King, R. H. He, S. K. Mo, [39] J. Mannhart and D. G. Schlom,
M. Hashimoto, A.Tamai, P.Songsiriritthigul, F.Baum- Science 327, 1607 (2010).
berger, and Z. X.Shen, Nat.Mater. 10, 114 (2011).