Ramanathan Sh. (Ed.) Thin Film Metal-Oxides: Fundamentals and Applications in Electronics and Energy

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180 Y. Hikita and H.Y. Hwang

riers. One of the characteristic features of SrTiO

lies in its dielectric properties. It is

a unique material having a large relative permittivity of 300 at room temperature,

which increases to 20;000 at 4 K, driven by a ferroelectric instability frustrated by

quantum ﬂuctuations [60]. One manifestation of this property is a strongly electric

ﬁeld dependent relative permittivity [61,62].

Studies of Schottky junctions using SrTiO

as the semiconductor initially began

with reduced SrTiO

with elemental metal contacts [63]. Through these studies,

it was found that the junction characteristics are modiﬁed strongly depending on

the surface preparation conditions. After the discovery of high temperature su-

perconductivity, with a strong motivation for creating device structures, SrTiO

Schottky junctions were revisited [64], during which the surface etching technique

was developed [6,7] and detailed surface analyses were conducted [65,66]. The sur-

face preparation was found to strongly inﬂuence the I V characteristics of these

Schottky junctions [67, 68], and the electric ﬁeld dependent relative permittivity

was realized to be important in the C V characteristics of SrTiO

Schottky junc-

tions [31,32].

Due to the strong internal electric ﬁeld generated at the interface, which is a

function of the dopant concentration as evident from (5.3), the suppression of the rel-

ative permittivity is more pronounced at higher doping concentrations. Figure 5.9a

demonstrates the deviation from a linear 1=C

V response as the Nb concentration

is increased. The deduced relative permittivity plotted against the electric ﬁeld is

showninFig.5.9b[31]. The important result of this study of the electric ﬁeld de-

pendent relative permittivity of SrTiO

at Schottky interfaces is the derivation of

analytical formulae for the potential proﬁle and the C V characteristics. By incor-

porating the temperature dependence of the relative permittivity based on Barrett’s

formula [69], and the internal electric ﬁeld within the depletion region, the following

formulae were obtained:

Fig. 5.9 (a) C V characteristics at room temperature for different Nb concentrations in

1x

BiO

=NbWSrTiO

Schottky junctions. Solid (dotted) lines denote the ﬁtting curves incor-

porating the electric ﬁeld dependent relative permittivity in NbWSrTiO

with (without) an additional

interfacial layer. (b) Electric ﬁeld dependence of the relative permittivity of NbWSrTiO

at room

temperature. The circles denote the experimentally obtained relative permittivity from (a)andthe

solid and the dotted lines are calculations (From [31], by permission)

5 Complex Oxide Schottky Junctions 181



Electrostatic potential .x/

.x/ D

ab"



cosh



.W  x/



 1



(5.16)

 Electric ﬁeld E.x/

E.x/ D

a sinh



.x  W/



(5.17)

 Relative permittivity "

.x/

.x/ D

a C E.x/

a cosh

.x  W/

(5.18)

Here a and b are temperature dependent constants which have been determined

by the following empirical relations measured in Ba

1x

BiO

=NbWSrTiO

junc-

tions [32].

a.T / D



b.T /

.T; E D 0/



;b.T/D 1:37  10

C 4:29  10

T; (5.19)

.T; E D 0/ D

1635

coth



44:1



 0:937

; (5.20)

where (5.20) is Barrett’s formula [69] describing the temperature dependence of the

relative permittivity at zero electric ﬁeld. From the above formulae, an expression

for the depletion capacitance is obtained as follows:

 V/C

 V/

: (5.21)

An application of this work in understanding the unusual I V characteristics at low

temperatures has been carried out in Au=NbWSrTiO

Schottky junctions [70].

Figure 5.10ashowstheI V characteristics of an Au=NbWSrTiO

Schottky junc-

tion measured at various temperatures. The polarity is deﬁned as positive when volt-

age is applied to Au. At 300 K, the current grows steeply at an applied voltage 1 V,

while almost no reverse-bias current is observed down to 10 V. The sign of rectiﬁ-

cation is what is expected for a typical Schottky junction. However, the reverse-bias

voltage where the current starts to increase rapidly shifts to lower voltages as the

temperature is decreased. At 100 K, the I V characteristics of the junction are al-

most symmetric and at 10 K, the junction polarity is completely reversed.

By examining the forward-bias I V characteristics in a semi-logarithmic plot,

an unusual temperature dependence can be seen below 75 K (Fig. 5.11a). Be-

tween 300 and 75 K, the onset of the exponentially increasing current shifts to

182 Y. Hikita and H.Y. Hwang

Fig. 5.10 (a) I V and (b) C V characteristics of an Au=NbWSrTiO

junction at various tempera-

tures. Simulated temperature dependence of the (c) relative permittivity and (d) the barrier potential

proﬁle in the depletion region. (e) The simulated I V characteristics for various temperatures

(From [70], by permission)

Fig. 5.11 (a) I V characteristics on a semi-logarithmic scale between 300 and 10 K. Bold,

dashed,anddot-dashed curves correspond to the data at 10, 25, and 50 K, respectively. Higher

temperature data are shown by thin curves. Linear ﬁtting is shown by the bold lines.(b)

cosh

=kT



 1=E

plot between 300 and 10 K. The bold line is a linear ﬁt for the

temperature region between 300 and 100 K (From [70], by permission)

5 Complex Oxide Schottky Junctions 183

higher voltages, whereas below 75 K a ﬁnite non-exponentially dependent current

ﬂows at smaller voltages where no signal current was observed above 75 K. An

increase in the forward-bias current with decrease in temperature implies a de-

crease in the barrier. Since the SBH is typically weakly temperature dependent (as in

Fig. 5.8), the barrier width must be evolving signiﬁcantly with temperature. Since

classical thermionic emission depends only on the SBH and not on the barrier width,

non-thermal transport processes, such as tunneling, must be responsible for the tem-

perature dependence in the I V characteristics in the low temperature regime.

The C V characteristic at 300 K in Fig. 5.10b shows a linear 1=C

V relation,

which gradually becomes non-linear below 100K. The bending of the curves at

low temperature indicates the importance of the electric ﬁeld dependent relative

permittivity, and can be analyzed using (5.21).

To clarify the origin of the polarity reversal and the sharp transition in the

junction transport mechanism around 100 K, the experimentally obtained I V

characteristics were analyzed within the framework of thermionic-ﬁeld emission.

First, the band bending was calculated based on (5.16) incorporating the elec-

tric ﬁeld dependent relative permittivity of SrTiO

. The SBH was estimated from

the I V characteristics by plotting ln ŒJ

cosh .E

=kT/=T  vs. 1=E

using the

data between 300 and 100 K where a systematic trend was observed (Fig. 5.11b).

Figure 5.10c shows the calculated relative permittivity using (5.18) as a function

of the distance from the interface inside NbWSrTiO

for different temperatures.

While the bulk relative permittivity of SrTiO

monotonically increases with de-

creasing temperature, the relative permittivity within 5 nm from the interface

monotonically decreases with decreasing temperature. Accordingly, the Schottky

barrier width is reduced, giving a large tunneling current at lower temperatures. In

Fig. 5.10e the calculated IV characteristics are presented reproducing the polarity

switching behavior of the junction with decrease in temperature.

5.3.2 SrRuO

=Nb:SrTiO

Junction – The Canonical Complex

Oxide Heterojunction

In contrast to the disordered interface between Au and NbWSrTiO

; SrRuO

a good heteroepitaxial metal because it is highly conducting in the absence of

chemical substitution and it is well lattice matched to SrTiO

(SrTiO

D 0:391 nm,

pseudocubic SrRuO

D 0:393 nm) [71]. Furthermore, the interface between

SrRuO

and SrTiO

is free from a polar discontinuity which can be a signif-

icant source of interface states [12]. Therefore, among the range of perovskite

heterojunctions, the SrRuO

=NbWSrTiO

(001) interface may be relatively electron-

ically clean. Also, this is the system in which the SBH has been characterized most

comprehensively, namely by I V , C V , IPE, and PES.

Figure 5.12a shows room temperature I V characteristics of 100 nm SrRuO

on NbWSrTiO

(001) for two different concentrations of Nb (0.01 and 0.5 wt%),

showing typical rectifying behavior in both cases [72]. In the C V characteristics,

184 Y. Hikita and H.Y. Hwang

Current Density (10

-3

A/cm

)

-1.0 -0.5 0.0 0.5 1.0

Voltage (V)

Nb = 0.01 wt %

Nb = 0.5 wt %

T = 300 K

1 / 2

-12

(A/photon)

1 / 2

-12

(A/photon)

1 / 2

54321

Photon Energy (eV)

Nb = 0 .01 wt %

Nb = 0.5 wt %

T = 300 K

2.52.01.51.0

Photon Energy (eV)

Nb = 0.01 wt %

Nb = 0.5 wt %

T = 300 K

1/C

(10

)

1/C

(10

)

-6 -4 -2 0 2

Voltage (V)

Nb = 0.01 wt %

Nb = 0.5 wt %

T = 300 K

Fig. 5.12 (a) I V and (b) C V characteristics of SrRuO

=NbWSrTiO

junctions for Nb D 0:01

and 0.5 wt%. (c) The full IPE spectra and (d) the magniﬁed spectra from which the SBH were

evaluated. The bold lines are the ﬁts using Fowler’s relation. All measurements were taken at room

temperature (From [72], by permission)

a difference in the 1=C

 V plot is evident between the two Nb concentrations

(Fig. 5.12b). For Nb D 0:01 wt%, a linear relation is observed, and V

deduced

from the voltage intercept is 1:35 ˙ 0:01 V. The uncompensated donor concentra-

tion N

evaluated from the slope of the plot is 1:6  10

3

, which is smaller

by more than an order of magnitude in comparison with the nominal value of

3:3  10

3

. Bulk Hall effect measurements of the substrate gives N

1  10

3

, implying uniform (given the linearity of 1=C

) partial passiva-

tion of the near surface donors. Similar deviations from nominal Nb concentrations

have also been reported by other groups in the same system where the Nb con-

centration from Hall measurements gives smaller values than those characterized

by inductively coupled plasma emission spectroscopy analysis at Nb concentrations

lower than 0.1 at%, as shown in Fig. 5.13 [73].

5 Complex Oxide Schottky Junctions 185

Fig. 5.13 (a) The temperature dependent resistivity of NbWSrTiO

with varying Nb concentration.

(b) The carrier concentration determined from Hall measurements plotted against the chemically

measured Nb concentration in SrTi

1x

by inductively coupled plasma emission spec-

troscopy (From [73], by permission)

In the case of Nb D 0:5 wt%, nonlinear behavior is observed in the 1=C

 V

plot due to the electric ﬁeld dependence of the relative permittivity in SrTiO

[62].

Fitting (5.21)toNb D 0:5 wt% C V data, and taking a and b parameters from

[32], V

of 1:40 ˙ 0:1 VandN

of 2:7  10

3

are obtained, in reasonable

agreement with the nominal value 1:7 10

3

and the bulk Hall effect value of

2:9  10

3

As can be noticed from Fig. 5.13a, NbWSrTiO

is a degenerate semiconductor;

therefore the correction for the energy difference between the SBH and the V

./

should be calculated not based on Boltzmann statistics but taking into account the

electrons residing in the conduction band where the band is bent, which is dependent

on the density of states [74]. By applying a parabolic band approximation for the

conduction band in NbWSrTiO

, the correction term is reduced to 0:4 compared

with the non-degenerate case [75]. The calculated  is 0.8 (117) meV for 0.01wt%

(0.5 wt%), assuming a single parabolic band with an effective mass of 1:3m

[76],

and using N

deduced from the C V slope, the SBHs





are calculated as

1:35 ˙ 0:01 eV .1:35 ˙ 0:1 eV/ for Nb D 0:01 wt% (0.5wt%) concentrations.

As described in the previous section, IPE is one of the most reliable methods

in characterizing the SBH. The details of the measurements are given in [72].

Figure 5.12c shows the photon energy dependence of the square root of the pho-

toyield

Y . Two principle features can be seen in the wide scan spectra. Above

3.2 eV, the energy gap of SrTiO

;

Y sharply increases corresponding to the photo-

generation of electron-hole pairs in NbWSrTiO

. The second feature is the gradual

onset of

Y between 1.3 and 2.4 eV (Fig. 5.12d). The linear response obtained over

a wide spectral range strongly suggests that current generation is due to electron

excitations from the metal to the semiconductor, and not from excitation of elec-

trons from localized in-gap states, which would signiﬁcantly deviate from linearity.

186 Y. Hikita and H.Y. Hwang

By extrapolating the linear portion of

Y with respect to the incident photon

energy, the barrier height is obtained. This extrapolation gives the SBH



IPE



1:47 ˙ 0:01 eV and 1:31 ˙ 0:01 eV for Nb D 0:01 and 0.5 wt%, respectively. The

SBH values deduced from the two techniques, IPE and C V , are in reasonable

agreement with one another; ˆ

IPE

is 9% larger than ˆ

for 0.01wt% Nb, and

3% smaller for 0.5 wt% Nb. Indeed, the independent measure of the SBH by IPE

gives considerable support for the quadratic model for 1=C

used to incorporate

dielectric nonlinearities in the 0.5 wt% NbWSrTiO

junction – a linear extrapolation

would signiﬁcantly underestimate the SBH. The remaining discrepancies may arise

from interface states, although the detailed interface electronic structure is not cur-

rently known.

The experimentally determined values for ˆ

IPE

can be compared with the SBH

estimated from the Schottky–Mottmodel





[38]. The work function of SrRuO

is 5.2 eV [77], and the electron afﬁnity of SrTiO

is 3.9 eV [78], giving ˆ

1:3 eV, which is in relatively good agreement with the experimentally determined

IPE

, particularly considering the simplicity of the Schottky–Mott framework. This

is evidence that the formation of the SBH in SrRuO

=NbWSrTiO

is likely domi-

nated by the electron afﬁnity rule. This relation is also supported by barrier height

characterization of the same junction by means of vacuum photoemission [79].

In Fig. 5.14a, the measured work functions of SrRuO

thin ﬁlm and the

NbWSrTiO

substrates are shown, which give the value of 5:2 ˙0:1 and 4:1˙0:1 eV

respectively in good agreement with previously reported values. From the Ti-2p

core-level shifts (Fig. 5.14b), the obtained SBH



PES



is 1:2 ˙ 0:1 eV which is

in good agreement with the calculated value based on the Schottky–Mott relation.

This contrasts with the case for La

0:6

0:4

MnO

in which the SBH calculated from

the Schottky–Mott relation (0.7eV) is smaller than the SBH obtained from the

Fig. 5.14 (a) Secondary electron emission spectra of a SrRuO

thin ﬁlm (thick solid), a

0:6

0:4

MnO

thin ﬁlm (thin solid), and NbWSrTiO

substrate (dashed). The arrows indicate the

work function of each material. (b) Plot of the energy shift of the Ti 2p core-level peaks as a

function of SrRuO

(open circles)andLa

0:6

0:4

MnO

(ﬁlled triangles) over layer thickness. The

lines are guides for the eye (From [79], by permission)

5 Complex Oxide Schottky Junctions 187

core-level shift (1.2 eV) by 0.5 eV, indicating a signiﬁcant contribution from the

interface dipoles, as discussed later. From the above systematic characterization of

the SBH in SrRuO

=NbWSrTiO

, we can conclude that: (1) the SBH follows the

Schottky–Mott rule, (2) for higher concentration of Nb dopants in NbWSrTiO

,the

electric ﬁeld dependent relative permittivity of SrTiO

must be taken into account,

and (3) for smaller concentration of Nb in NbWSrTiO

, the Nb ratio of ionized

dopants decreases from the nominal concentrations.

5.3.3 Schottky Barrier Height Dependence on the Chemical

Composition in La

1x

=NbWSrTiO

Junctions

Metallic conductivity in perovskites often emerges in materials which have their

A-site cations substituted by heterovalent cations. Examples include La

1x

TiO

[80], La

1x

[81], and La

1x

MnO

[82]. In such cases, the het-

erovalent dopants, in these cases Sr, act as acceptors reducing the chemical

potential. By forming Schottky junctions using such metals, it is expected that

the SBH changes systematically as a function of doping unless a phase transi-

tion is induced. A systematic investigation has been carried out in the system

1x

M O

=NbWSrTiO

.M D Mn; Fe; Co; Ni/ which follows the chemical

potential shift characterized by I V and C V methods [83]. Although not all of

the investigated materials are metallic in the whole doping region, the slope of the

shift in the chemical potential as a function of x overlaps in all cases (Fig. 5.15).

The trend is in good agreement with the previously obtained photoemission results

of these materials [84–86] indicating that the band offsets at these interfaces follow

the systematic trend of the afﬁnity rule.

5.3.4 Termination Control of the Schottky Barrier Height

Unlike the case for SrRuO

=NbWSrTiO

,theLa

1x

M O

=NbWSrTiO

heterojunc-

tions just described have an additional degree of freedom at the interface. The het-

erointerface between two (001)-oriented perovskites with different cations can have

two different interface terminations (Fig. 5.16). Given the partially ionic nature of

oxides, the different terminations could have signiﬁcantly different interface dipoles,

thus changing the band lineup across the interface, which has been investigated ex-

perimentally at an interface between the ferromagnetic metal La

0:7

0:3

MnO

and

the n-type semiconductor NbWSrTiO

.BygrowingaLa

0:7

0:3

MnO

ﬁlm directly

on TiO

-terminated NbWSrTiO

,anMnO

=La

0:7

0:3

O=TiO

interface is formed

(Fig. 5.16a). Alternatively, by ﬁrst growing 1 unit cell (uc) of SrMnO

before

0:7

0:3

MnO

deposition, the MnO

=SrO=TiO

interface is formed (Fig. 5.16b),

which is equivalent to the deposition of La

0:7

0:3

MnO

on the SrO-terminated

NbWSrTiO

surface [87]. The deposition of a fractional unit cell of SrMnO

allows

the study of the evolution of the SBH between these endpoints.

188 Y. Hikita and H.Y. Hwang

Fig. 5.15 (a)TheSBH(ﬁlled squares)andV

(ﬁlled circles) as a function of doping x in

1x

M O

=NbWSrTiO

and (b) chemical potential shifts of the La

1x

M O

referenced to

the respective chemical potential level of each La

1x

M O

with x D 0:5.Theinset shows the

schematic band alignment (From [83], by permission)

Figure 5.17 shows typical room temperature I V , C V , and IPE characteristics

for samples with different SrMnO

coverage. Clear rectifying behavior was

observed in all cases with forward-biased current density systematically decreasing

with increase in SrMnO

coverage. The barrier height obtained from the I V

characteristics





was calculated based on thermionic emission by ﬁtting the

forward-biased region of the I V characteristics. The SBHs obtained from the

three independent measurements are summarized in Fig. 5.17d, exhibiting a sys-

tematic increase in the SBH as a function of SrMnO

coverage at the interface. The

barrier heights extracted from V

determined by C V measurements ˆ

have

been corrected for the energy difference between the conduction band minimum and

the Fermi level in the NbWSrTiO

which is a small correction in this case .8:1 mV/.

Neither the simplest Schottky–Mott model nor the classical Fermi level pinning

mechanism based on surface states of semiconductors proposed by Bardeen [43]ofa

5 Complex Oxide Schottky Junctions 189

[001]

La, Sr

SrMnO

Fig. 5.16 The two different possible interfaces between the perovskites La

0:7

0:3

MnO

and

SrTiO

joined in the [001] direction: (a)TiO

-terminated, and (b) SrO-terminated SrTiO

(From

[87], by permission)

800

600

400

200

1/C

(10

)

-2 -1 0 1

-1

-3

-5

-7

| Current Density | (A/cm

)

-1.5 -1.0 -0.5 0.0 0.5

Voltage (V) Voltage (V)

x = 0.0

x = 0.3

x = 0.6

x = 1.0

x = 0.0

x = 0.3

x = 0.6

x = 1.0

x = 0.0

x = 0.3

x = 0.6

x = 1.0

1.5

1.0

0.5

0.0

(V)

1.00.80.60.40.20.0

IPE

Dipole

1/2

-12

(A /photon)

1/2

2.01.51.0

Photon Energy (eV) SrMnO

Coverage (uc)

Fig. 5.17 (a) I V characteristics, (b) C V characteristics, and (c) IPE spectra of

0:7

0:3

MnO

=.SrMnO

=NbWSrTiO

junctions at room temperature. (d) Summary of the ob-

tained barrier heights from I V (circles), C V (squares), and IPE (triangles) measurements.

The dotted line indicates the variation of the screening dipole in a simple ionic model (From [87],

by permission)