Electron transport through asymmetric ferroelectric tunnel junctions: current-voltage characteristics

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by  Natalya A. Zimbovskaya

Electron transport through asymmetric ferroelectric tunnel junctions:
current-voltage characteristics
Natalya A. Zimbovskaya
Department of Physics and Electronics, University of Puerto Rico,
100 CUH Station, Humacao, PR 00791, and Institute for Functional Nanomaterials,
University of Puerto Rico, San Juan, PR 00931
(Dated: January 3, 2010)
Wehavecarriedoutcalculationsofcurrent-voltagecharacteristicsfortheelectrontunnelcurrent
0 throughajunctionwithathininsulatingferroelectricbarrierassumingthatinterfacetransmissions
1 fortheleftandrightinterfacesnoticeablydifferduetodissimilarityoftheinterfaces. Obtainedcon-
0 ductancevsvoltageandcurrentvsvoltagecurvesexhibitwelldistinguishableasymmetrichysteresis.
2 Weshowthattheasymmetryinthehystereticeffectscouldoriginatefromtheasymmetricbiasvolt-

n ageprofileinsidethejunction. Inparticular,weanalyzethehysteresisasymmetriesoccurringwhen
a the bias voltage distribution is low-sensitive to the spontaneous polarization reversal.
J
3 PACSnumbers: 73.23.-b,85.50.-n

]
i Ferroelectric materials attract significant interest of mostly concentrated on studies of zero bias conductance
c
s the research community due to their potential useful- of FTJs. However, the theoretical analysis of current-
- ness in various technological applications [1]. In the bias voltage (I − V) relationships is also important
l
r past decade it was repeatedly shown in the experiments for it provides more thorough characterization of the
t
m thatferroelectricitycouldbemaintainedinfilmsofsome electron transport through FTJs. As shown in Ref.
. perovskite oxides with thickness of the order of a few [13], the polarization reversal in the ferroelectric films
t
a nanometers [2–6]. These experimental observations were causes a hysteretic behavior of both current-voltage and
m corroborated by first-principles computations predicting conductance-voltage characteristics. Especially interest-
- the critical film thickness for ferroelectricity to persist in ing hysteretic effects may occur in asymmetric FTJs
d
perovskite films to be as thin as a few lattice parame- where the interfaces are dissimilar. The dissimilarity
n
ters [7–10]. Thus, both experimental and theoretical re- couldoccurwhentheleadsaremadeoutofdifferentmet-
o
c sults indicate that ultrathin ferroelectric films exist and als [14, 18]. Also, it could originate from the atomic and
[ may be used as barriers in ferroelectric tunnel junctions electronicstructureofthejunction[19]. Wheninterfaces

(FTJ). A ferroelectric tunnel junction consists of two differ, the effects of the polarization reversal also may
1
v conducting electrodes (leads) separated by a nanometer- differ depending on the specific properties of the inter-
8 thick ferroelectric film. Electrons can tunnel across the faces. This may result in asymmetry of tunnel electrore-
0 filmthusmaintaininganonzeroconductanceofthejunc- sistance(TER)versusbiasvoltagecurvesandofhystere-
4
tion. Specificnatureoftheferroelectricbarriersaddnew sis loops in current-voltage characteristics. In strongly
0
functional properties to FTJs [11] Such junctions could asymmetricFTJsbothTERandhysteresiscouldbewell
.
1
serve as essential components in manifold nanodevices pronounced for a certain bias voltage polarity and sig-
0
such as binary data storage memories and switches [12]. nificantly reduced on the polarity reversal. The asym-
0
1 Themostimportantfeatureofferroelectricsisthepres- metricTERandhystereticeffectswererecentlyreported
v: enceofspontaneouspolarizationwhichcouldbereversed forasymmetricjunctionsincluding BaTiO3 [20,21]and
i by an applied electric field. The polarization switch- Pb(Zr0.2Ti0.8)O3 [22] ferroelectric barriers.
X In the present work we theoretically analyze transport
ing inherent to ferroelectric materials alters the sign of
r characteristics of an asymmetric FTJ. We simulate the
polarization charges at the electrode/barrier interfaces
a
FTJ by a ferroelectric film of thickness d sandwiched
thuschangingtheelectrostaticpotentialprofileinsidethe
between two semi-infinite metal electrodes. We assume
junction. Also, the polarization switching shifts ions in
that the film is uniformly polarized in the direction per-
ferroelectric unit cells and changes lattice strains in the
pendiculartotheelectrodeplanes, whichisthedirection
filmaffectingtheelectronbandstructureofthejunction.
of “z” axis within the chosen coordinate system. At
As a result, transport characteristics of a FTJ may be
small values of the applied bias voltage the conductance
significantly modified. The effect of the polarization re-
of a tunnel junction per area A could be described by
versal on FTJ conduction was predicted in earlier works
the following expression [23]:
(see e.g. Refs. [13–15]) and observed in experiments
on Pt/Pb(Zr0.52Ti0.48)O3/SrRuO3 FTJ [15], on junc- G 2e2 d2k
tions with La0.1Bi0.9MnO3 tunnel barrier [16] and on A = h Z (2π)|2|T(E,k||) (1)
Pt/SrTiO3/Pt junctions [17].
Currently, theoretical and computational efforts are where k istheprojectionofthetunnelingelectronwave
||
2
vector to the electrode’s plane, and E is the tunnel en- computations we do not include in our model the effect
ergy,whichtakesonvaluesclosetotheFermienergy E . ofanintrinsicelectricfieldthroughoutthebarrier,which
F
The transmission function T(E, k ) may be factorized appears due to the difference in the electrostatic dipoles
||
and presented in the form [24]: attheinterfaces,aswellasthestraineffectsduetopiezo-
electricity.
T(E,k )=t (E,k )exp −2κ(E,k )d t (E,k ) (2)
|| L || || R || To estimate the current through the junction we use
Here, t (E,k ) and t (E(cid:8),k ) are the i(cid:9)nterface trans- the expression:
L || R ||
mission functions for the left and right electrodes, re- J 2e d2k
spectively,and κ(E,k||) isdeterminedbytheheightand A = h Z dE(fL−fR)Z (2π)|2|T(E,k||). (5)
shape of the potential barrier in the tunnel junction and
by the energy-momentum relation of a tunneling elec- Here,thetransmissionfunction T(E,k ) isgivenbyEq.
||
tron. Generally speaking, it also depends on the bias (2)and f areFermidistributionfunctionswithchem-
L,R
voltage but one may disregard this at small values of V. icalpotentials µ . Thechemicalpotentialsareshifted
L,R
Employing a simple form for the energy-momentum re- with respect to E when a nonzero bias voltage V is
F
lation: applied across the junction, namely:
~2k2 ~2k2 µ =E +ηeV; µ =E −(1−η)eV. (6)
E = || + z (3) L F R F
2m 2m
The division parameter η shows how the voltage V is
where m is the effective mass of the tunneling electron, distributed in the junction. The expression (5) resem-
we may approximate: bles the well known Landauer formula for tunnel current
through molecular junctions and/or quantum dots cou-
1 d 2mΦ(z)
κ(E,k )= +k2dz (4) pled to the conducting leads [25]. It could be derived
|| dZ0 r ~2 || using surface Green’s functions formalism presented in
the earlier work [26]. We have grounds to belive that η
Here, Φ(z) is the overall potential profile seen by the
takesonvaluesdependingontherelationoftheinterface
tunneling electrons. At zero bias voltage the potential
transmissions t and t . Calculating the current den-
Φ(z) is a superposition of the potential, which deter- L R
sitywehypothesizethat η =t /(t +t ), whichresem-
mines the positions of conduction bands in metal elec- R L R
bles the expression for the division parameter commonly
trodes with respect to the Fermi energy, and the bar-
used in the theory of electron tunnel transport through
rier potential occurring due to the presence of the insu-
molecularbridgesandquantumdots. Inthattheory η is
lating ferroelectric film. Also, the overall potential in-
describedbythesimilarexpressionwheretheparameters
cludes a contribution created by surface charges on the
determining the coupling of a molecule/quantum dot to
surfaces of the ferroelectric film and screening charges
the left and right leads take on the parts of the interface
appearing on the electrode surfaces. The simplest ap-
transmissions.
proximation for Φ(z) appropriate for a symmetric FTJ
Regardless of symmetry/asymmetry of a FTJ, the
is a trapezoid barrier with a thickness d and heights
transmission coefficients t and t differ, and the dif-
Φ(0) = U +ϕ(0), Φ(d) = U +ϕ(d) where ϕ(z) is the L R
ference in their values may be significant. For instance,
potential induced by the surface charges. The relative
heights of the barrier at z = 0 and z = d are deter- it was reported that in a Pt/BaTiO3/Pt junction one
mined by the potential difference ϕ(0)−ϕ(d). The dif- of the transmission coefficients was approximately three
times greater than another one [10]. One may expect
ferencechangesitssignwhenthepolarizationinthefilm
even greater difference in the interface transmission for
reversescausingthehysteresisintheconductionthrough
the FTJ studied by Maksymovich et al [22], where recti-
theFTJtooccur. InasymmetricFTJsthechangeinthe
fying current-voltage characteristics were reported. One
complex band structure induced by the left-right asym-
reason for the disparity in the transmission functions is
metry of the ferroelectric displacements in the barrier
the trapezoid-like profile of the potential barrier. The
maynoticeablychangetheaveragebarrierheights U for
barrier height decreases along the polarization direction,
two polarization states, as was theoretically shown for
therefore t should exceed t when the polarization
a SrRuO3/BaTiO3/SrRuO3 junction basing on first R L
points to the right and vice versa. In symmetrical FTJs
principles computations [19]. The difference in the bar-
with identical interfaces one may expect the transmis-
rier heights for different polarization directions may be
sion coefficients simply interchange their values on the
of the same order or greater than that induced by the
polarization reversal:
potential ϕ(z). In the following transport calculations
we take into account both the effect of depolarizing field t→ =t←; t→ =t← (7)
L R R L
corresponding to the potential ϕ(z) and variations in
the barrier height appearing due to the junction asym- where an arrow indicates the polarization direction. In
metry. However, to avoid extra complications in further such a case the bias voltage division parameter η in the
3
Eq. (6) is to be replaced by 1−η when the polarization
direction is reversed. Accordingly, the current-voltage
curves associated with different polarization states (al-
though asymmetric by themselves duetothe asymmetry
in the bias voltage distribution across the junction) are
arrangedinthe V−I planeinsuchawaythathysteretic
features remain symmetrical. The TER versus voltage
curve must be symmetrical upon bias voltage reversal,
as well.
In asymmetric FTJs the relationship between the
transmissions t and t fordifferentpolarizationdirec-
L R
tions is more complicated. Due to an asymmetric defor-
mation of the ferroelectric potential profile the relations
(7)donotholdanymore. Besides,dissimilarityinthein-
terfaces may affect the transmissions due to the reasons FIG.1: (Coloronline)Conductance G = 1 dI ofthemodel
A AdV
unrelated to ferroelectric properties of the film linking asymmetric FTJ vs bias voltage for the paraelectric (dash-
the electrodes. Even within the simple one-dimensional dotted line) and ferroelectric (solid and dashed lines) states
model of a FTJ employed in the present work, one must ofthefilm. ThecurvesareplottedusingEqs. (1)-(6)at T =
takeintoaccountspecificfeaturesofthecontactbetween 30K, d = 1.8nm, U = 0.6eV (low resistance ferroelectric
state), U = 0.8eV (high resistance ferroelectric state), for
theelectrodesandthefilm, whichcouldsignificantly dif-
tL =3tR (left panel) and tR =3tL (right panel).
ferontheleftanfrightsidesofthejunction. Forinstance,
in the case when the electrodes are made out of differ-
ent metals, this may significantly influence the interface
transmissions. Also, FTJs studied in the recent works ity to the polarization reversal. Accordingly, we accept
[20, 22] consisted of an epitaxial ferroelectric film grown that tL/tR remains the same regardless of the polariza-
on the top of conducting electrode and a sharp metal tip tion direction.
serving as another electrode. We may expect a nonepi- Computingtheconductanceandcurrentforourmodel
taxial contact between the tip and the film to notably FTJ we used the results reported in Ref. [10] for
modifythecorrespondinginterfacetransmissionforboth Pt/BaTiO3/Pt junctions. So, we assumed that d =
polarization directions. Some other effects, which could 1.8nm, and zero bias conductances per unit cell area
modifyinterfacetransmissionsinasymmetricFTJs(and, takeonvalues G/A≈17.0×10−5e2/h (fortheparaelec-
in consequence, the bias voltage distribution across the tric state of the film) and G/A ≈ 2.9×10−5e2/h (for
junctions) are discussed elsewhere (see e.g. Ref. [22] its low resistance ferroelectric state), respectively [27].
and references therein). So, the bias voltage distribu- We did carry out calculations for t /t = 3 (η = 0.75)
R L
tion across an asymmetric FTJ for different polarization and t /t = 3 (η = 0.25) for ferroelectric states of
L R
orientations could hardly be predicted basing on some the film. For the film in the paraelectric state we as-
generalconsiderations. ForeachparticularFTJtherela- sumed t = t . Using these values we estimated the
L R
tion of the interface transmissions (which greatly affects interface transmissions for paraelectric and ferroelectric
the bias voltage distribution) must be separately estab- barriers in the junction. As shown in the Fig. 1, the
lished, and the results may significantly vary depending conductance through the junction with the ferroelectric
ontheFTJcharacteristics. Forinstance,weremarkthat barriershouldexhibitratherwelldistinguishablehystere-
in the asymmetric FTJ whose transport properties were sis. The hysteresis is asymmetric with respect to V =0,
studiedbyGruvermanetal[20], tL <tR forbothpolar- and we observe the significant asymmetry in the TER.
ization directions. This follows from the reported shape At t = 3t the TER is small at positive bias volt-
L R
of the I−V characteristics. age but it significantly increases upon the reversal of the
In summary, various asymmetric features in the hys- bias voltage polarity, as shown in the left panel of the
teretic behavior of the tunnel current and conductance figure. When t = 3t the TER is much better pro-
R L
in asymmetrical FTJs originate from asymmetries in the nounced at positive bias voltage (see the right panel of
tunnel barrier profile for different polarization directions the Fig. 1). Basing on the experimental results of Gar-
andfromspecificsofthebiasvoltagedistribution(deter- cia et al [21] for thin BaTiO3 films, we may roughly
mined by the relationship between the interface trans- estimate the coercive voltage V for our model FTJ as:
c
missions). The relative effects of these two factors could V ∼1.0−1.5V. Therefore,thedifferenceintheTERval-
c
vary but neither one should be disregarded on general uesat V =±V , whichoccursduetothespecificsofthe
c
grounds. Here, we concentrate on the analysis of trans- bias voltage profile across the junction may reach values
port properties of a strongly asymmetric FTJ where the of the order of 102 −103. The current-voltage charac-
biasvoltagedistributionexhibitsarelativelylowsensibil- teristics are presented in the Fig. 2. We see asymmetric
4
man,O.Auciello,P.H.Fuoss,andC.Thompson,Science
304, 1650 (2004).
[4] C. Lichtensteiger, J. M. Triscone, J. Junquera, Ph.
Ghosez, Phys. Rev. Lett. 94, 047603 (2005).
[5] A. Petraru, H. Kohlstedt, U. Poppe, R. Waser, A. Sol-
bach, U. Klemradt, J. Student, W. Zander, and N. A.
Pertsev, Appl. Phys. Lett. 93, 072902 (2008).
[6] C.L.Jia,V.Nagarajan,J.-Q.He,L.Houben,T.Zhao,R.
Ramesh, K. Urban, R. Waser, Nat. Mater. 6, 64 (2007).
[7] N. Sai, A. M. Kolpak, and A. M. Rappe, Phys. Rev. B
72, 020101(R), (2005).
[8] C.-G.Duan,S.S.Jaswal,andE.Y.Tsymbal,Phys.Rev.
Lett. 97, 047201 (2006).
[9] G. Gerra, A. K. Tagantsev, N. Setter, and K. Parlinski,
Phys. Rev. Lett. 96, 107603 (2006).
[10] J. P. Velev, C.-G. Duan, K. D. Belashchenko, S. S.
FIG.2: (Coloronline)Current-voltagecharacteristicsforthe Jaswal,andE.Y.Tsymbal,Phys.Rev.Lett.98,137201
model ferroelectric tunnel junction. The curves are plotted (2007).
using Eqs. (1)-(6) The parameters take on the same values [11] E. Y. Tsymbal and H. Kohlstedt, SCience 313, 181
as in the Fig. 1. (2006).
[12] M. Dawder, K. M. Rabe, and J. F. Scott, Rev. Mod.
Phys. 77, 1083 (2005).
hysteretic behavior of the tunnel current. As well as for [13] H.Kohlstedt,N.A.Pertsev,J.RodriguezContreras,and
R. Waser, Phys. Rev. B 72, 125341 (2005).
conductance, the asymmetry in the hysteresis loops to a
[14] M.Ye.Zhuravlev,R.F.Sabirianov,S.S.Jaswal,andE.
considerable degree originates from the bias voltage pro- Y. Tsymbal, Phys. Rev. Lett. 94, 246802 (2005).
file in the junction. We remark that the I −V curves
[15] J. Rodriguez Contreras, H. Kohlstedt, U. Poppe, R.
in the right panel of the Fig. 2 resemble those recently Waser, C. Buchal, N. A. Pertsev, Appl. Phys. Lett. 83,
reported in the work [20]. 4595 (2003).
In conclusion, we have demonstrated that current- [16] M.Gajek,M.Bibes,S.Fusil,K.Bouzehouane,J.Fontcu-
voltage and conductance-voltage characteristics of an berta, A. Barthelemy, and A. Fert, Nat. Mater. 6, 296,
(2007).
asymmetric FTJ may exhibit a pronounced hysteretic
[17] J. Son, J. Cagnon, and S. Stemmer, Appl. Phys. Lett.
behavior of a special kind whose distinctive feature is 94, 062903 (2009).
a well pronounced asymmetry in the hysteresis loops for [18] Y. Zheng and C. H. Woo, Nanotechnology, 20, 075401
different bias voltage polarities. The asymmetry in the (2009).
hysteresis largely originates from the asymmetric bias [19] J.P.Velev,C.-G.Duan,J.D.Burton,A.Smogunov,M.
voltage division in the junction. In strongly asymme- K.Niranjan,E.Tosatti,S.S.Jaswal,andE.Y.Tsymbal,
tryc junctions the dissimilarity of the interfaces may af- Nano Lett. 9, 427 (2009).
[20] A. Gruverman, D. Wu, H. Lu, Y. Wang, H. W. Jang,
fect interface transmissions so much that the effects of
C. M. Folkman, M. Ye. Zhuravlev, D. Felker, M. Rz-
the polarization reversal may be surpassed. In this case, chowski, C.-B. Eom, and E. Y. Tsymbal, Nano Lett. 9,
the relationship between the transmissions is low sen-
3539 (2009).
sitive to the polarization revesal, and the bias voltage [21] V.Garcia,S.Fusil,K.Bouzehouane,S.Enouz-Vedrenne,
distribution across the junction rather weakly depends N.D.Mathur,A.Barthelmy,andM.Bibes,Nature460,
on the polarization direction. Our results give grounds 81 (2009).
to expect that the bias voltage reversal in the consid- [22] P.Maksymovych,S.Jesse,P.Yu,R.Ramesh,A.P.Bad-
dorf, S. V. Kalinin, Science 324, 1421 (2009).
ered strongly asymmetric FTJs should bring significant
[23] C. B. Duke, Tunneling in solids (Academic, New York,
changes to their transport characteristics, and this could
1969).
be used in designing of nanodevices.
[24] K.D.Belashchenko,E.Y.Tsymbal,M.vanSchilfgaarde,
Acknowledgement: AuthorthankJ.P.Velevforhelpful D. Steward, I. I. Oleinik. S. S. Jaswal, Phys. Rev. B 69,
discussion and G. M. Zimbovsky for help in manuscript. 174408 (2004).
[25] See e.g. S. Datta, Quantum transport: Atom to Transis-
tor (Cambridge University Press, Cambridge, England,
2005).
[26] J. Kudrnovsky, V. Drchal, C. Blaas, P. Weinberger, I.
Turek, and P. Bruno, Phys. Rev. B 62, 15084 (2000).
[1] T. M. Shaw, S. Trolier-Mckinstry, and P. C. McIntyre,
Annu. Rev. Mater. Sci. 30, 263 (2000). [27] ItwasshowninRef.[10]thatthe BaTiO3 filmwiththe
thickness of 1.8nm could exist in both paraelectric and
[2] T. Tybell, C. H. Ahn, and J. M. Triscone, Appl. Phys.
Lett. 75, 856 (1999). ferroelectric states.
[3] D.D.Fong,G.B.Stephenson,S.K.Streiffer,J.A.East-