Free Electrons Holes and Novel Surface Polar Order in Tetragonal BaTiO 3 Ground States Y. Watanabe12 D. Matsumoto1 Y. Urakami1 A. Masuda1 S. Miyauchi1 S. Kaku1 S.-W. Cheong3 M. Yamato1 and E. Carter3

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Free Electrons Holes and Novel Surface Polar Order in Tetragonal BaTiO3 Ground States

Y. Watanabe1,2*, D. Matsumoto1, Y. Urakami1, A. Masuda1, S. Miyauchi1, S. Kaku1, S.-W. Cheong3,

M. Yamato1, and E. Carter3

1University of Hyogo, Himeji, Japan, 2Kyushu University, Fukuoka, Japan, ATT Bell Lab, Murray Hill, NJ, USA

*watanabe@phys.kyushu-u.ac.jp

We find novel polar orders that yield electron (e-) and hole (h+) gas and depend on surface terminations,

using density functional theory (DFT) that, unlike existing reports, relaxed all the ion positions of

ATiO3 having spontaneous polarization PS (A: alkali earth metal). By the experiments of atomic-

oxygen cleaned surfaces of BaTiO3, we find both e- and h+ gas that are proven to originate from PS and

constrain electrostatic potential, which has been missing. These experiments that remarkably agree

with the DFTs of defect free BaTiO3 reveal the properties of PS-originated e-h+ and, for ferroelectric

basics, an e-h+-posed intrinsic constraint on depolarization field arising from PS in proper time ranges.

Built-in fields in insulators accumulate interests for functional two-dimensional (2D) electrons

(e-) and holes (h+) gases [1-3]. In particular, depolarization field (Ed) arising from spontaneous

polarization (PS) of insulating ferroelectrics is expected to form 2D e- and h+ in novel geometries [4-

8]. Theoretically, these e- and h+ (abbreviated as e-h+) exist on positive PS (P+) and on negative PS (P)

faces, respectively, accompanying the potential difference between these faces



that is close to

ferroelectric bandgap Eg (Fig. 1(a)) [6-8]. Therefore, we conjecture that the e-h+ constrains the

existence-form of Ed [7] that is considered as a basis underlying ferroelectric properties [9-14]. The

validation of this conjecture, yet unaccepted, requires the experimental proof of intrinsicality, which

is missing.

When polaronic trapping is negligible, the 2D conductance of these layers ~ PS



is theoretically

close to the minimum 2D metallic conductance [15] (



~ 1 cm2/Vs [16]), and the free carrier density

n is approximately PS/eleh ~ 1020-21 cm-3 or PS/e ~ 1014 cm-2 (e: elementary charge, leh: thickness of the

layer ~ 1nm) [8, 17-19]. Such metal-like n makes Schottky-barrier unimportant [20] to yield ohmic

current-voltage (IV) characteristics down to low field. Contrarily, nonohmic (nonlinear) conductance

in insulators is due to nonequilibrium carriers injected from electrode or excited from traps [21],

suggesting that the equilibrium n in the conduction path is negligibly small (SM-1; SM-# denote

Section# in Supplemental Material).

Such e-h+ is considered to form at P+ to P+ (P+P+) and P to P (PP) domain boundaries

(DB) and ferroelectric surfaces and interfaces (Fig. S1; Fig. S# is in Supplemental Material) [8,18-19,

22-28], where enhanced conductance at these DBs is reported as evidence. However, these DBs show

either e- or h+, non-ohmicity, no enhanced conductance at low field, and low n (7500 cm-2 at high field

[22]. Some semiconducting ferroelectrics show ohmicity with n < 1016 cm-3 at high field but only h+

conduction modestly larger at DBs than at bulk parts [23,24]).



~ Eg is not reported. These

characteristics disagree with the aforementioned theoretical expectations of defect-free ferroelectrics

[6-8, 17-19]. Further, these measurements are conducted with field sufficiently high to induce

resistance switching [29-31] and the migration of the ions/defects [32] that become e-h+-suppliers and

closely resemble resistance switching [18]. These experimental properties might be explained by small

polarons [18,21] but are consistent with defect-PS complexes, i.e. defects at these DBs proposed by

studies including electron microscopy and density functional theory (DFT) [33-37]. This interpretation

is fortified by the defect-induced drastic reduction in n and Ed and disappearance of h+ (Fig. S1(b)).

Here, by resolving these issues, experiments and DFTs with/without electron correlation (and

hybrid functional) for polaron reveal the PS-originated e-h+ and non-contact controls of PS as a

functional field effect. The DFTs that unlike the literature relaxed all the ion positions of ferroelectric-

phase disclose polar orders determined by BaO- and TiO2-terminations, which explains experimental

n and the location of e- that are different those of h+.

The electrostatics of the polarization charge 



P) at P+P+ and PPDBs, surfaces, and

insulator/ferroelectric is virtually identical [38]. While PS terminates stably at surfaces even without

defects, these DBs are unstable without defects and, hence, exist at defects [31-37]. Therefore, we

study the free surfaces with minimal defects of BaTiO3 single crystals (SM-2(Methods)). Further, we

applied only low external fields without contacting the surfaces in order to eliminate extrinsic

conductance and contamination, e.g. from the cantilever of the scanning probe microscope (SPM) [32].

Atomically flat BaTiO3 surfaces were electroded (Fig. 1(b)). To keep clean surfaces, all the

measurements were done in an ultrahigh vacuum (UHV) in darkness. Because conventional cleaning

of UHV-heating (> 1100 K) creates countless oxygen vacancies (O-vacancies), sample surface is

cleaned at 300 K by atomic O of which the oxidation capability is equivalent to 1010 atm O2 (Fig. 1(c))

[39] and an electrostatic method (Fig. S2). The stable outermost layer of the [001] [100] surfaces of

ATiO3 (A: Ba, Sr) is AO in an oxidizing atmosphere and TiO2 in a reducing atmosphere and air [40-

42], and buckling of the TiO2 is reported for paraelectrics [42,43]. The PS in the gap between two

electrodes, T1 and T2, was oriented by applying 80 V~160 V/mm between T1 (T2) and the bottom

electrode B (Figs. 1(d) and S3). This field was the maximum applied field in the experiments and not

on the surface conduction path. Such low applied field in the gap and the large width of the gap (0.012~

0.3 mm) prohibited migration of ions and defects into the main part of the gap. That is, the PS-

orientation was controlled without contacting the target surface, thereby eliminating conductance

unrelated with PS. The poled states as shown in Fig. 1 were obtained by performing poling while

cooling the sample from TC (~ 400 K) to 300 K, which is a slightly reducing condition, and the surface-

terminations of BaTiO3 in Fig. 1 is considered as TiO2 [40-42].

The orientation of PS (// c-axis) was monitored by polarization microscopy, piezoelectric

response microscopy (PFM), and the nonlinear capacitance (Fig. S4). To retain cleanness, the surface

potential and topography were measured in true non-contact mode that uses Van der Waals force. To

avoid contacting the surface, the domains were mainly identified from the potential images perfectly

agreeing with the PFM images (Fig. S5). Capacitance C and IV curves for determining the conductance



between T1 and T2 (



T-T, current IT-T, Fig. 1(e)), T1 and B (



T-B, current IT-B), and T2 and B (



T-B,

IT-B) were acquired; here,



T-B is the bulk conductance



bulk (Fig. S6). Carrier type identification was

supplemented by chemistry [44,45] (Fig. S7). TC was detected using polarization microscopy and from

the T-dependence of C. The maximum applied voltage and the field for the IV measurements were 0.5

V and 1 ~ 40 mV/m, respectively to avoid carrier injection and resistance switching. Because the

BaTiO3 was 105 times thicker than the thickness of e-h+ layers [8,17],



T-T due to bulk appeared at high

T (Fig. 1(e), SM-3).

Figures 1(f)-1(j) show the polarization microscopy images, IV hysteresis curves of each state, and

corresponding T-dependences of



T-T and PS (by Ginzburg-Landau theory). The initial state was

unpoled and ac domained; the P and P+ states formed subsequently and were measured. After an

additional P+ poling, the IV curves and



T1-T2 (P++) were measured (Figs. 1(g) and 1(j)). The ohmicity

down to low fields proves that conductance was due to the equilibrium carriers.



T-T of the unpoled

states (



T-Tunpoled) was the same in UHV and air wherein free e-h+ at surfaces disappeared by adsorbates

(Fig. S8). Therefore,



T-Tunpoled was due to the thick bulk, and



surface





T-T 



T-Tunpoled (This means

also



surfaceunpoled = 0), where



surface denotes the surface conductance. Alternatively,



surface



≈



T-T 



T-

B, because the bulk conductance



T-B approximately equaled



T-Tunpoled (Figs. 1(h) and 1(j)). Therefore,

below T* of Fig. 1(j),



T-T of all of the poled states was



surface, which applies also to IT-T.



surfaceunpoled = 0 and the disappearance of



surface (=



T-T 



T-Tunpoled) above TC that coincided

with that of PS prove that



surface was induced by PS (Fig. 1(i)); the approach of



T-T of the P++ state to



T-Tunpoled was insufficient because we did not wait for the slow approach. Furthermore, in the repeated

formation of different states, only P, P, or unpoled determined



T-T, whereas the number of vacuum

heatings to 410 K, which would have increased O-vacancy, did not affect



T-T (Fig. S9, SM-4, SM-5).

The IV hysteresis curve of the P+ surface after a long-time poling exhibited ohmic conductance

with a conductivity of 0.1 -1cm-1 for leh ~ 2 nm (Fig. 2(a)) and persisted for at least 15 h (Fig. 2(b)).

This conductivity is 1/80th the theoretical conductivity of a continuous atomically flat surface for



1 cm2/Vs [16]



and close to the minimum metallic conductance [15]. Subsequently, the BaTiO3 was

exposed to N2 gas, whereby the adsorbates in the N2 were expected to diminish Ed, produce traps of

e-h+, and thereby reduce



surface. After the exposure,



T-T decreased to 1/500th its value before the

exposure (Figs. 2(b) and S10). However, it was still 100 times higher than



T-B (



≈



T-Tunpoled). Because



surface



≈



T-T 



T-B, this shows that the surface conduction layer survived after the exposure and

demonstrates its robustness.

Figure 3 shows potential



and



T-T of each poled state of another BaTiO3, where no

measurements of the T-dependence were conducted to minimize the formation of O-vacancy. BaTiO3

in Figs. 3(a)-3(e) experienced no vacuum heating, while BaTiO3 in Figs. 3(f)-3(j) experienced vacuum

heating to 410 K. The initial state directly after O irradiation (Fig. 3(a)) was a multi-domained one

consisting of P+ and P domains; the green areas on the left of the white dashed lines in the images

are grounded electrodes. All the experiments were performed in non-contact except for PFM at 4 points.

First, we will examine Figs. 3(f)-3(j), which depict properties after vacuum heating and hence

are probably of the TiO2 surface as in Fig. 1. By positive and negative poling at 300 K,



of the free

surface immediately became uniformly positive and negative with respect to the electrode, respectively

(Figs. 3(g)-3(i)), and



surface appeared. These surfaces of positive and negative



were P+ and P

surfaces, respectively (Fig. S5), which was confirmed by PFM at the four points of Fig. 3(h). Therefore,

the ohmic IV curves in blue and red (Fig. 3(j)) are of P and P+ surfaces, respectively, and closely

resemble the IV curves in Fig. 1(h) except for the conductance lower than those in Fig. 1(h) (because

of the inferior surface flatness).



| in Figs. 3(g)-3(i) was 100 times lower than the unscreened |



| by Kittel theory [9] that yields

a lower bound on |



| for vortex domains [10] (Fig. S11, SM-6). This means that negative (positive)

charges moved to the P+ (P) surface. These charges had high mobility because the screening occurred

within milliseconds (Fig. 3(f)). The difference in e



between the P+ and P surfaces, e



, was close

to Eg of BaTiO3 (Fig. 3(i)).



T-T of the P+ and P states became higher down to 0 V than



T-Tunpoled

(Fig. 3(j)), showing the emergence of



surface



(This



T-Tunpoled was estimated from



T-Tunpoled of Fig. 3(e),

because



T-Tunpoled was independent of vacuum heating (Fig. S9)). Similar poling repeatedly formed P+

and P surfaces, their



surface’s correlated completely with



(Figs. 3(i) and 3(j)), and the potential

profiles obeyed those estimated by e-h+ depletion theory (Figs. 3(i) and S12, SM-7). These observations

consistently show that e- and h+ appeared on P+ and P surfaces, respectively, through Ed (Fig. 1(a)).

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FreeElectronsHolesandNovelSurfacePolarOrderinTetragonalBaTiO3GroundStatesY.Watanabe1,2*,D.Matsumoto1,Y.Urakami1,A.Masuda1,S.Miyauchi1,S.Kaku1,S.-W.Cheong3,M.Yamato1,andE.Carter31UniversityofHyogo,Himeji,Japan,2KyushuUniversity,Fukuoka,Japan,ATTBellLab,MurrayHill,NJ,USA*watanabe@phys.kyushu-u.ac.jpWe...

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Free Electrons Holes and Novel Surface Polar Order in Tetragonal BaTiO 3 Ground States Y. Watanabe12 D. Matsumoto1 Y. Urakami1 A. Masuda1 S. Miyauchi1 S. Kaku1 S.-W. Cheong3 M. Yamato1 and E. Carter3.pdf

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Free Electrons Holes and Novel Surface Polar Order in Tetragonal BaTiO 3 Ground States Y. Watanabe12 D. Matsumoto1 Y. Urakami1 A. Masuda1 S. Miyauchi1 S. Kaku1 S.-W. Cheong3 M. Yamato1 and E. Carter3

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