Table Of ContentA direct view at excess electrons in TiO rutile and anatase
2
Martin Setvin,1,∗ Cesare Franchini,2,† Xianfeng Hao,1 Michael Schmid,1 Anderson
Janotti,3 Merzuk Kaltak,2 Chris G. Van de Walle,3 Georg Kresse,2 and Ulrike Diebold1
1Institute of Applied Physics, Vienna University of Technology,
Wiedner Hauptstrasse 8-10/134, 1040 Vienna, Austria
2Faculty of Physics and Center for Computational Materials Science,
Universita¨t Wien, Sensengasse 8/8-12, A-1090 Wien, Austria
3Materials Department, University of California, Santa Barbara, CA 93106-5050
A combination of Scanning Tunneling Microscopy/Spectroscopy and Density Functional Theory
(DFT+U) is used to characterize excess electrons in TiO rutile and anatase, two prototypical
2
materialswithidenticalchemicalcompositionbutdifferentcrystallattices. Inrutile,excesselectrons
canlocalizeatanylatticeTiatom,formingasmallpolaron,whichcaneasilyhoptoneighboringsites.
4
In contrast, electrons in anatase prefer a free-carrier state, and can only be trapped near oxygen
1
0 vacanciesorformshallowdonorstatesboundtoNbdopants. Thepresentstudyconclusivelyexplains
2 the differences between the two polymorphs and indicates that even small structural variations in
the crystal lattice can lead to a very different behavior.
l
u
J
The behavior of charge carriers in oxides is of key tural deformation spreads over a large number of lattice
9
2 importance in virtually all applications of these mate- sites the corresponding solution is categorized as a large
rials. Whenexcesselectronsareaddedtotheconduction polaron.
] band of an oxide, they may either retain the free-carrier Here we use the following joint theoretical and exper-
l
e character or, still assuming a defect-free crystal, couple imental approach: First, we theoretically investigate the
-
r to lattice distortions induced by its presence (electron- intrinsicbehaviorof anexcesselectron addedtotheper-
st phonon interaction). The latter case is usually referred fect crystal, i. e. stoichiometric bulk cells of anatase and
t. as to a small or large polaron, depending on the degree rutile. We establish that rutile allows polaron formation
a of electron localization [1, 2]. Polaronic effects and elec- at any Ti site, while anatase prefers a free-carrier con-
m
tronlocalizationaffectamaterials’physicalandchemical figuration. Next we inspect the effect of excess electrons
- properties, yet it remains controversial how to model it donatedbysurfaceoxygenvacancies(V s)bycomparing
d O
n appropriately from first principles [3, 4]. Here we inves- experimentalandDFT+Udata. Weusebulk-terminated
o tigate TiO2, a prototypical metal oxide. TiO2 is used rutile (110)-(1×1) and anatase (101)-(1×1) surfaces. In
c in catalysis [5–8], photoelectrochemical (Gr¨atzel) solar rutile, the excess electrons leave the V s and form po-
[ O
cells,memristors[9],andasatransparentconductiveox- larons, which can hop through the lattice. In anatase,
2 ide [10]. Two forms of TiO2 are used industrially, ru- the electrons stay trapped at the VOs. Finally, we show
v tile and anatase. The metastable anatase form is gen- thatinNb-dopedanataseelectronsarespatiallyconfined
7
erally present in nanomaterials and shows better perfor- bythedonorpotential, yettheykeeptheband-likechar-
1
manceinenergy-relatedapplicationsandinoptoelectron- acter.
8
7 ics. Even after several decades of research, a consensus For our calculations we used the VASP code [11]. On
1. on the origin of the difference between the two materi- the experimental side, low-temperature Scanning Tun-
0 als is still absent, and our aim is to resolve this issue neling Microscopy/Spectroscopy (STM/STS) was used.
4 theoretically as well as experimentally. Filled-states STM images reflect the spatial distribution
1
Stoichiometric rutile and anatase are both insulators of electrons within the bangap, and STS provides infor-
:
v with a ≈3 eV band gap. TiO2 can be turned into an mation about the electronic energy EEL (see below): Ei-
Xi n-type semiconductor by adding excess electrons by var- ther ∼ 1 eV below EF typical for small polarons [5], or
r ious means - doping, UV irradiation, or chemical reduc- ∼ 40 meV below EF for delocalized, weakly bound elec-
a tion. Electrons in the conduction band of TiO compete trons [12].
2
between free-carrier and polaronic configurations. The The energy balance for polaron formation in defect-
extent to which this happens has remained highly con- freeTiO issketchedinFig. 1(a). Theformationenergy,
2
troversial, yet strongly affects the material’s transport E , is defined as the total energy difference between
POL
properties and catalytic activity. The electrons can lo- the polaronic and fully delocalized free-carrier solution,
calize at Ti 3d orbitals, forming Ti3+ ions. This induces and results from the competition between the strain en-
relaxations of the surrounding lattice atoms by typically ergy required to distort the lattice (E ), and the elec-
ST
0.1˚A.Thequasiparticleconsistingofanelectroncoupled tronicenergygainedbylocalizingtheelectronataTisite
to the lattice relaxations in its immediate surrounding is in such a distorted lattice, E . Polarons show a com-
EL
called a small polaron [1]. When thermally activated, plexbehavior. TheelectronicenergyE =E +E
EL POL ST
small polarons exhibit hopping mobility. If the struc- is the quantity measured in photoemission spectroscopy
2
a y (arb. units) EST free-carrierEELpolaron RutileAnatase --000..42b (eV)POL tamnoneaidagtilhtotbhenroerotCifhnBigasMTsetnirleoidernxgsygeltoobiwrcobaenlirltdyaiinnlfsga.evnTloienrhraeugbasyrl,eaaccsolomaanrbfigrigeensruaurUtlaitotiinosofnrbteehaqtneuwdiferoeetrndo-
nerg EPOL UcRPA -0.6E form a polaron in anatase. The associated energy gain
E -0.8
Generalized coordinate 4 5 6 E is lower as compared to rutile.
(lattice distortion) Hubbard U (eV) EL
c rutile The most commonly used values of U for TiO2 range
6 between 2.5 and 4.5 eV [21, 22]. We calculated the U
d ,d
4 yz zx e parameter entirely from first principles using the con-
g
d-1eV, f.u.)20 anatase sofotbrrtaaaiinnneaedtdaRsaeav.nadlAuomellorPfehsUuaclsRtesPAAinp=ptrh3oe.x9ipmerVeastfeioonrntr(wuctoRirlPekAahn)ad[v2e43.]b1aeeneVdn
S (6 consistently determined using UcRPA=3.9 eV. From Fig.
O
D4 1, it is clear that UcRPA =3.9 eV suffices to stabilize the
2 d Op polaron in rutile, albeit just, whereas polaron formation
xy
0 is clearly unfavorable in a perfect anatase lattice. In ru-
-2 -1 0 1 2 3 4 5 6 7 8
Energy (eV) tile the excess electron is trapped in a Ti3+ site, forming
a small polaron; the 6 O atoms surrounding Ti3+ relax
outward by 2-4 % of the equilibrium Ti–O bond length.
FIG. 1. Calculated polaronic stability for bulk TiO rutile
2 Inanatasetheexcesselectronexhibitsafree-carrier’delo-
and anatase. a) Configuration coordinate diagram showing
calized’ character: the crystal remains unperturbed and
thepolaronic(E ),lattice(E ),andelectronic(E )en-
POL ST EL
ergiesasafunctionoflatticedistortionforthepolaronicand the excess electron is homogeneously distributed in the
delocalized solution. b) E as a function of Hubbard U crystal.
POL
in bulk rutile (orange) and anatase (blue). The vertical line STM/STS measurements for rutile (110) and
indicates the ab initio UcRPA. Orbitally decomposed density
anatase (101) are compared in Fig. 2. As in previous
of states (DOS) in rutile (c) and anatase (d), aligned with
work on rutile (110) [24, 25], we take advantage of
respect to the Ti core levels.
surface O vacancies (V ) that readily form under
O
standard preparation conditions [5] to provide excess
charge (donors). At anatase (101), V s migrate to the
O
(PES) or STS, as the lattice atoms are “frozen” within
bulk at temperatures as low as 200 K, but surface V s
O
thetimescaleoftheexperimentalprobe[2,5,13]. Forthe
can be created non-thermally [26]. Here subsurface V s
O
purposeofelectricalconductivity,however,activationen-
were pulled to the surface using the field of the STM tip
ergies are typically ∼tens of meV. This is indicative of
as shown in ref. [27].
either a low barrier for hopping between neighboring po-
For rutile [Fig. 2(c)] the filled local density of states
laronic configurations, or a small excitation energy from
(LDOS) directly at the V is small; most of the cur-
O
the polaronic to the free-carrier state [13].
rent comes from the rows of 5-coordinated surface Ti
5c
Figure1(b)illustrateswhytheoreticalmodelingofthe atoms. Thisisevenmoreapparentwhenscanningatvery
polarons in TiO2 and other oxides remains a challeng- closetip-sampledistances(seelowerpartoftheimagein
ing and controversial issue. Standard DFT always yields Fig. 2(c), and the Supplement for details). In contrast,
delocalized solutions. Electrons can be localized by ap- the electrons stay at the vacancy at anatase [Fig. 2(d)],
plying a Hubbard U; the value of U, and thus EEL, as suggested by the vanishing LDOS at the rest of the
will then determine whether the polaronic solution will surface.
be stable [14–18]. The situation is equally critical with Point tunneling spectra were measured at various dis-
hybrid functionals, where EEL depends on the amount tances from the surface VOs on rutile and anatase, see
of exact exchange incorporated in the DFT functional Figs. 2(g,h). The STS peak positions agree well with
[4, 13, 19, 20]. photoemission spectra taken from our samples as well as
From Fig. 1(b) we infer that E is 0.4 eV larger other published data [5, 28]. The CBM is located just
POL
in rutile than anatase, and that a larger U is required above E , as expected for reduced TiO ; band bending
F 2
to form a small polaron in anatase (U > 5 eV) than in does not play a significant role. In STS on rutile, the
rutile (U > 3.5 eV). We find that both materials have polaronicband-gap-stateisfound0.7±0.1eVbelowE ;
F
a similar E (0.41 eV); the difference in E origi- again, the spectra are very similar when taken either di-
ST POL
nates from the electronic energy E . The formation of rectlyatthevacancyorattheTi rows. Onanatase,the
EL 5c
a polaron involves the depletion of the conduction band gap state is found at 1.0±0.1 eV below the Fermi-level
minimum (CBM), which has a different character in the [28], and it is strictly localized at the vacancy. When
two TiO polymorphs. Figure 1 c,d shows that the con- the point spectrum is measured away from the V s at
2 O
duction band in anatase is 1 eV wider than in rutile, anatase (101), this gap state is not detected.
3
a b a PsLubVO PsRub PsurfVO Psurf
b
V
O
V
O
P
surf
1]
110] [10
[
[001] 1177 [010] 5697 PsLub
VSAMPLE = + 1.0 V, 7x7 nm2 VSAMPLE = + 0.8 V, 7x7 nm2 c
c 1180 5697 d
V
O
V
O
V
O 1181 5697 d VO e
V = - 1.4 V (top); -0.6 V (bottom) V = - 1.0 V
SAMPLE SAMPLE
e f
V
A] O
I [n PsLLLub PsRub
0 1 2 3 0 1 2 3
x [nm] x [nm]
g
V)/(I/V)64 SSUTTPSSS Tv[aai .cruoa.w]nscy 64 SSUTTPSSS Tv[aai .cruoa.w]ncsy h f VO P VO g
d2 2 surf
dI/ PL PR
(0 0 sub sub
-3 -2 -1 0 1 -3 -2 -1 0 1
V [V] V [V]
SAMPLE SAMPLE
FIG. 2. Local electronic structure of rutile (110) (left) and FIG.3. Surfacecalculationsofexcesselectronsinrutile(110)
anatase(101)(right)surfacesdopedbysurfaceoxygenvacan- and anatase (101) donated by a surface V . In rutile, small
O
cies. Constant-height scanning tunneling microscopy images polaronscanassumemanyenergeticallyalmostequivalentpo-
of (a, b) empty states and (c, d) filled states of the same ar- sitions. a) Configurations with two subsurface polarons P
sub
eas. VOmarkssurfaceoxygenvacancies;theyarealsomarked (top) and one Psub plus one surface polaron Psurf (bottom).
with circles in c. e, f) Line profiles along the lines in a) and b) The only stable configuration at the anatase surface, with
b), respectively. STS measured above VO and above regu- both excess electrons bound to the surface VO. c) Polaron
lar 5-fold coordinated Ti5c surface atoms of g) rutile and h) dynamics in rutile (orange) and anatase (blue) and corre-
anatase. Photoemission spectra (hν =120 eV, dashed lines) sponding statistical analysis for rutile. The small polarons
are included for comparison. Rutile at T =78 K, anatase at stay mostly in the subsurface (S-1) below the vacancy and
T =6 K. at surface (S) Ti sites. (d)-(g) Calculated STM images for
5c
empty (d, e) and filled (f, g) states in rutile (left, the three
most frequent polaronic configurations according to the MD
analysis) and anatase (right, the electron is always trapped
Previouscalculationsonrutileshowedthatmanypola-
at the surface V ).
ronic configurations have almost identical total energies O
[Fig. 3(a)] [16, 29, 30]. In our first principles Molecu-
lar Dynamics (MD) calculations, closely following Ref.
16, the polarons also hop rapidly among lattice Ti sites laronic configurations, where both the surface and the
[Fig. 3(c)]. Mostly (∼75% of the time) they stay in the subsurface small polarons contribute. Below T = 20 K,
first subsurface layer; occasionally (∼25%) they move to we observed the complete absence of conductivity sug-
the surface Ti sites [16]. Calculated empty- and filled- gesting that the polarons freeze in.
5c
states images for three such configurations are shown in In stark contrast to rutile, however, a surface V on
O
Figs. 3(d,f). The polaron position does not affect the anatase gives rise to immobile electrons pinned at Ti
empty-states image, whereas it is apparent when imag- sites just at the V [21] with a high E of ∼ 1 eV
O EL
ing filled states [crosses in Fig. 3(f,g)]. In STM on rutile [Figs. 3(b,c)]; these electrons are observed in filled-states
at T = 78 K, we measure a weighted average of the po- STM(compareFigs.2dand3g). Intotal-energycalcula-
4
a b SpatiallyresolvedSTS[Fig.4(c)]imagesrevealapeakat
(−40±10) meV and the absence of any gap state at −1
eV. The bright regions shown in Figs. 4(a,b) are stable
in time and do not migrate within a temperature range
from 6 to 78 K, suggesting that the electron is stabilized
at the positively-charged subsurface donor, most likely
VSAMPLE = + 0.3 V, 13x11 nm2 8426VSAMPLE = - 0.5 V (DFT) 8426 Ncrbea.tFesiga. 4q(uda)nsthuomwswaelsli,mwphleermeotdheel.elTechteroionnoizcecdupdioensoar
c 0 1 2 IΨI2 d single energy level. The electron wave function is spread
+0.1 over several unit cells around the donor, and is modu-
0.0 E lated by the periodic potential of the crystal lattice; a
F
Shallow donor
-0.1 calculated STM image of a slab with a Nb impurity [in-
level
[V]MPLE--00..32 sseeteFthige.S4u(pbp)]leamgreenets.wInelrlewcietnhttAhReePxEpSermimeaesnut.reFmoerndtest[a1i2ls]
VSA-0.4 + Dpootneonrt ial asimilarpeakat(40±10)meVbelowEF wasattributed
to a ”large polaron”. The distinction between a shal-
-0.5
low,delocalizeddonorlevelandalargepolaronissubtle.
-0.6
DFT+U calculations reproduce the measured STM im-
-0.7 Lattice potential
position (dI/dV)/(I/V)
age only when lattice relaxations (polaronic effects) are
taken into account. In STM images the density distribu-
tion has an anisotropic shape, with spatial extensions of
FIG. 4. Shallow donor state at Nb-doped anatase (101). a) ∆r[010]=12−25˚A and∆r[101]=4−8˚A.Thisagrees
Empty- and b) filled-states STM images taken at T = 6 K
well with Fr¨ohlich’s model for large polarons [1], from
(constantheight). Thebrightareasareinthevicinitytosub-
whichweobtain∆r[010]=19.0˚A, and∆r[101]=3.5˚A
surface dopants. The inset “DFT” in b shows a calculated
STM image of the large polaron. The large polaron wave- related to the anisotropy of the screening and effective
function is more extended along the [010] (12-25 ˚A), then masses (see Supplement). Thus, this state is similar to a
alongthe[101](4-8˚A)direction. c)Spatiallyresolvedplotof large polaron, but cannot move through the crystal like
(dI/dV)/(I/V) along the blue dashed line. (Note the differ- a true polaron.
entenergyscaleascomparedtoFig. 2.) d)Modelofa”large
Ourstudyillustratesthebasicprinciplesofexcesselec-
polaron”, stabilized at the subsurface donor atom.
tron behavior in the model oxide TiO . The different
2
stacking of octahedrally-coordinated Ti in the two poly-
morphs, and the resulting subtle differences in the elec-
tionsanyattempttomovetheelectrontoadifferentbulk tronic structure around the CBM, provide for a higher
Ti lattice site resulted in an unstable, high-energy con- energy gain upon small polaron formation in rutile than
figuration. The electron localization close to the anatase in anatase. Filled-states STM clearly shows the various
surface VO is facilitated by high local structural flexibil- cases: Smallpolaronsthatreadilyhopinrutile,electrons
ity of the lattice near the vacancy, decreasing the strain trappedatsurfaceV sinanatase,andspatiallyextended
O
energy EST. shallow donor states in Nb-doped anatase. STS also
Whenelectronsareintroducedviaadopantthatmod- shows distinct signatures, with an apparent deep (∼eV)
ifies the lattice structure only slightly (See SI), polaron polaronic state for rutile, yet a much shallower state (40
formation remains favorable in rutile, whereas spatially meV) at dopants of anatase. The latter shows spectro-
moreextendedsolutionsarepreferredinanatase. Thisis scopic similarities with recent ARPES results [12] and
reflected in the 4 orders of magnitude larger conductiv- its lateral extension is well-described by Fr¨ohlich’s the-
ity of Nb–doped anatase compared to Nb–doped rutile: ory for large polarons. These experimental results prove
anatase exhibits metal–like temperature-dependence of electron de/localization for anatase/rutile surfaces. Re-
theconductivity,whereasrutileretainsasemiconductor- centEPRdata[3]indicatethesamebehaviorinthebulk
like character [10, 31]. Our DFT+U calculations suggest of these materials, in agreement with the calculations in
that the higher conductivity in Nb–doped anatase is due Fig. 1(b).
totheabsenceoflocalizedsmallpolarons,whereasinru- Polaronsarecentraltotheoftenexoticbehaviorofox-
tile – with the same U – small polarons are formed. The ides[32]aswellastheirtechnologicalapplications. Inthe
STM results are again entirely consistent with this pre- specific case of TiO , anatase is used as an electrode in
2
diction. In an anatase sample doped with ∼1% Nb [27], photoelectrochemical solar cells. Band-like charge trans-
fairly extended bright regions in the STM images with a portandthelackofsmallpolaronformationisthekeyre-
measurable density of states below E (Fig. 4) are vis- quirement for increasing the cell efficiency. On the other
F
ible. The Nb dopants were distributed unevenly in our hand,theformationofsmallpolaronsinrutileisanasset
sample. Fig. 4 shows a region with low concentration. incatalysis,asthepolaronformationismorefavorableat
5
surfaces than in the bulk, facilitating an efficient charge laronsandBipolaronsinHigh-TcSuperconductivityand
transfer to catalyzed species [6]. In mixtures of the two Related Materials (Cambridge University Press, Cam-
TiO phases, anatase provides a good electron conduc- bridge, 1995).
2
[33] D. O. Scanlon, et al., Nature Materials 12, 798 (2013).
tor that transports charge carriers to the interface with
rutile, where they are trapped [33].
This work was supported by the ERC Advanced Re-
search Grant ‘OxideSurfaces’, and by the Austrian Sci-
ence Fund (FWF). Computing time provided by the Vi-
enna Scientific Cluster is gratefully aknowledged.
∗ [email protected]
† [email protected]
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