1

Supplementary Information for

“Resistive switching induce by charge trapping/detrapping: A unified mechanism for

colossal electroresistance in certain Nb:SrTiO3-based heterojunctions”

Zhen Fan,1,* Hua Fan,1,* Lin Yang,1 Peilian Li,1 Zengxing Lu,2 Guo Tian,1 Zhifeng Huang,1

Zhongwen Li,1 Junxiang Yao,1 Qiuyuan Luo,1 Chao Chen,1 Deyang Chen,1 Zhibo Yan,2

Min Zeng,1 Xubing Lu,1 Xingsen Gao,1 and Jun-Ming Liu2,1

1Institute for Advanced Materials and Guangdong Provincial Key Laboratory of Quantum

Engineering and Quantum Materials, South China Normal University, Guangzhou

510006, China.

2Laboratory of Solid State Microstructures and Innovation Center of Advanced

Microstructures, Nanjing University, Nanjing 210093, China.

*Corresponding authors: fanzhen@m.scnu.edu.cn, fanhua3011@outlook.com.

Electronic Supplementary Material (ESI) for Journal of Materials Chemistry C.This journal is © The Royal Society of Chemistry 2017

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I. Supplementary figures and tables

Fig. S1 Mechanism (i): (a) electron detrapping and (b) trapping leading to the opening and

closing of the trap-assisted tunneling paths, whereas the barrier profile remains unchanged.

Mechanism (ii): oxygen vacancies within the depletion region that migrate (c) towards and

(d) away from the interface, thus modifying the barrier profile. Mechanism (iii): (e)

electron detrapping and (f) trapping at the trap states within the interfacial layer or on the

semiconductor surface, which could also modify the barrier profile. “M”, “I”, and “S”

represent metal, interfacial layer, and semiconductor (NSTO), respectively. The panels a,

c and e correspond to the low resistance states (LRS), while the panels b, d, f correspond

to the high resistance states (HRS). For mechanism (ii), the charge trapping/detrapping

within the depletion region is not shown here.

3

Fig. S2 (a) XRD θ-2θ scan, (b) (103) and (c) (113) reciprocal space mappings (RSMs) of

a ~150 nm BTO film. (d) Polarization-electric field (P-E) hysteresis loop and (e)

capacitance-voltage (C-V) curve of the ~150 nm film. The P-E and C-V measurements

were conducted with the top-to-top electrode configuration, to eliminate the significant

asymmetry caused by the Au and NSTO electrodes.1

The XRD θ-2θ scan shows that there is no impurity phase in the ~150 nm BTO film.

The RSMs further reveal that the BTO film exhibits a tetragonal phase, and the out-of-

plane and in-plane lattice constants are ~4.04 and ~4.00 Å, respectively. The tetragonality

is therefore ~1.01.

The P-E hysteresis loop is slim, which is a typical feature of the BTO thick films

grown on NSTO substrates.1 The double peaks are observed in the C-V curves. The

combined results of P-E and C-V demonstrate the ferroelectricity of the ~150 nm BTO

film.

4

Fig. S3 AFM images of (a) NSTO bare substrate, and BTO/NSTO films with the BTO

layers of (b) 2 nm, (c) 7 nm, (d) 14 nm, and (e) 21 nm in thickness. All sample surfaces are

flat with a roughness (Rq) below 150 pm. The AFM images shown in the panels a and c

were indeed taken after the electrical writing, and almost no morphological changes are

observed in the written areas, indicating that the effect of electrochemical reaction is

insignificant. No terraces are observed, because our NSTO substrates were not treated by

the etching and subsequent annealing. These treatments were shown to introduce additional

defect states near the substrate surfaces.2

5

Fig. S4 (a) Cross-sectional HRTEM image of the BTO(7 nm)/NSTO heterostructure. Fast

Fourier transform (FFT) patterns of (b) BTO and (c) NSTO taken in the areas indicated in

the panel a. The damages to the surface of the BTO layer were caused by the preparation

of TEM specimen. According to the FFT pattern, the lattice constants c and a of BTO are

calculated as 4.16 and 3.91 Å, respectively, corresponding to a tetragonality of ~1.06.

6

Fig. S5 Voltage scanning rate-dependent I-V curves measured for (a) Au/NSTO and (b)

Au/BTO (7 nm)/NSTO heterojunctions. As can be seen, when the voltage scanning rate is

reduced from 0.2 to 0.02 V/s, the I-V curves of both heterojunctions change only slightly.

This suggests that the I-V curves measured at 0.2 V/s (the scanning rate used in the main

text) can be considered as quasi-steady-state data with insignificant contribution from the

transient current.

7

Fig. S6 Reproducibilities of the I-V curves for (a) Au/NSTO and (b) Au/BTO (7 nm)/NSTO

heterojunctions. For both heterojunctions, at least 20 devices have been tested and they all

exhibit similar RS behaviors. Here, we only show some representative results.

8

Fig. S7 I-V curves measured for the Au/NSTO heterostructures, where the NSTO

substrates were annealed using the same protocol for preparing the FJTs.

9

Fig. S8 Local I-V characteristics of the bare NSTO substrate and the BTO(7 nm)/NSTO

film measured with a conductive AFM tip. For the reverse bias conduction in the HRS, the

currents are too low and out of the measurement range.

For the FTJs, possible pinholes in the ultrathin BTO films may permanently short out

the top electrodes and substrates. If this occurs, the effective contacting areas will be

dramatically reduced and the measured currents and capacitances of the FTJs (Fig. 1 and 5

in the main text) would be several orders of magnitude smaller than those of the MSJs.

However, these exceptions are not observed in our experiments. The concern of pinholes

can be further clarified by local I-V measurements using a conductive AFM tip as the top

electrode, as shown in Fig. S8. Again, similar hysteretic I-V curves in both the MSJs and

FTJs are observed, excluding the possibility that the observed RS behaviors in the FTJs are

related to pinholes in the BTO films.

10

Fig. S9 Schematic illustration of the applied pulse train for the write voltage-dependent

resistance-voltage (R-V) loops. The voltages of write pulses (in red) vary from -Vmax to

Vmax and back to -Vmax, while the voltage of read pulses (in black) are kept at -0.2 V.

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Fig. S10 Resistance as a function of pulse width measured for (a) Au/NSTO and (b)

Au/BTO(7 nm)/NSTO junctions.

The sample was preset to the HRS (LRS) first, and then its resistance was detected at

-0.2 V after applying the write pulses with a fixed voltage of +3 V (-6.5 V) and varied

widths ranging from 1 to 106 µs. Note that the 1-µs pulse made almost no changes to the

resistance state (see Figure 2 in the main text). As can be seen from Fig. S10, both the

Au/NSTO and Au/BTO/NSTO junctions show similar switching kinetics, where the

resistance changes significantly in the time range of 1~100 µs and gradually becomes

saturated from 100 µs to 106 µs.

The applied voltages of -6.5 V and +3 V could allow the charge trapping/detrapping

process to be almost completed within ~0.01 s, which is much shorter than the

measurement time (0.5 s per data point) in our I-V measurements. In addition, the measured

I-V curves change only slightly if the voltage scanning rate is further slowed down (see

Fig. S5). These results indicate that the I-V measurements at the slow voltage scanning

rates (e.g., 0.2 V/s used in this work) may be quasi-static, and one may use quasi-static

approximation to simulate the I-V curves.

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Fig. S11 (a) SKPM, (b) PFM amplitude, and (c) phase images of the bare NSTO substrate.

(d) SKPM, (e) PFM amplitude, and (f) phase images of the BTO(7 nm)/NSTO film. The

scale bar represents the length of 1 µm. The written areas were the same as those in Fig. 3

in the main text. All images were taken after grounded-tip scanning for two times and

waiting for 30 minutes.

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Fig. S12 Current mappings taken at (a) +2 V and (b) -6 V for the NSTO substrate. Here

the applied voltages refer to the tip biases, and +2 V and -6 V can set the sample to the

LRS and HRS, respectively. Topography images taken after the voltage scans of (c) +2 V

and (d) -6 V. Note that a and c were taken in the same region, and so were b and d. However,

the region corresponding to a,c is different to that corresponding to b,d. The image in d

looks blurred due to the tip being blunt.

The conductions in both the HRS and LRS are quite uniform, and no conductive

filaments could be observed. In addition, there are no significant electrochemical reactions

because of no morphological changes, consistent with those in Fig. S3.

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Fig. S13 SKPM images taken in the Ar atmosphere for (a) NSTO substrate and (b) BTO(7

nm)/NSTO film. The signs of “+” and “-” indicate the tip biases of +2 V and -6 V for the

electrical writing.

It was previously reported that certain redox reactions (e.g., exchanging oxygen with

the ambient) might occur at the surface and they were dependent on the oxygen

atmosphere.3-5 To understand whether these redox reactions play a role, we have changed

the atmosphere from the air to the dry Ar, and then conducted the SKPM study. Fig. S13a

and b show the SKPM images taken in the Ar atmosphere for the NSTO substrate and the

BTO/NSTO film, respectively. As can been seen, the surface potential variations, i.e., the

increase (decrease) induced by the positive (negative) tip bias, are similar to those observed

in the air (Figure 3 in the main text). This also fits the scenario of charge

trapping/detrapping. However, the quantitative degrees of surface potential variations are

different as the atmosphere changes from the air to the Ar, implying that the redox reactions

may exist. Note that in the actual junctions, the NSTO and BTO are covered by the Au

electrodes (~20 nm thick); hence, the redox reactions are suppressed because the oxygen

need to penetrate the Au film and then react with the oxide surface.

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Fig. S14 PFM off-field amplitude and phase loops of (a) bare NSTO substrate and (b)

BTO(7 nm)/NSTO film. Off-field piezoresponse hysteresis loops of (c) NSTO substrate

and (d) BTO/NSTO film. (e) Off-field amplitude and phase loops of BTO/NSTO film

measured with a stiffer cantilever (32 nN/nm). In a-d, the cantilever with a small stiffness

(2.5 nN/nm) is used. In c and d, the “Normalized PR” represents the piezoresponse which

is normalized with respect to the VAC. Insets in c, d and e show the topography images

taken after the hysteresis loop measurements.

As shown in Fig. S14a and b, the butterfly-like amplitude loops and square phase

loops are observed in both the NSTO substrate and the BTO film. To understand whether

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the ferroelectric switching truly exists in the BTO film, we have studied the AC voltage-

dependent off-field piezoresponse hysteresis loops. According to the literature,6 for a

typical ferroelectric, the off-field loops almost do not change their shapes when VAC is

much smaller than the coercive voltage (Vc). However, as the VAC becomes close to or

larger than the Vc, the off-field loops deform or even collapse because the polarization is

flipped during the measurement cycle. Figure S14c and d show the VAC-dependent off-field

piezoresponse hysteresis loops. As can be seen, when the VAC is larger than 2.5 V, the off-

field loops of both the NSTO substrate and BTO film deform significantly, i.e., the loops

become narrower and their heights reduce. Such VAC dependence of loops seem to be a

feature of ferroelectrics as described above. However, since the NSTO substrate is certainly

not ferroelectric, we believe that the observed VAC dependence of loops may be attributed

to the electrostatic signals whose amplitudes increase nonlinearly with VAC. Therefore, the

technique of using VAC-dependent hysteresis loops fails to distinguish the ferroelectric

switching from non-ferroelectric factors in the NSTO-based systems. It should be noted

that the NSTO is different from some other non-ferroelectrics which exhibit linear

electrostatic behaviors, e.g., HfO2.6 For those non-ferroelectrics, the off-field loops are

largely independent of VAC, enabling the differentiation between them and the

ferroelectrics.

To reduce the tip-sample electrostatic interactions, we have replaced the cantilever

(2.5 nN/nm) with a stiffer one (32 nN/nm). Note that by using this stiffer cantilever we

have successfully measured the butterfly-like amplitude loops and square phase loops for

a standard BiFeO3 sample (results not shown here), demonstrating that this cantilever

works well for a good ferroelectric. However, Figure S14e shows that only weak amplitude

and phase hysteresis loops are observed in the BTO film at the maximum allowed DC

voltage of 8 V. There may be two possibilities:

(a) The polarization of the 7-nm BTO film may be non-switchable under the applied

voltages we have used, although it exhibits a tetragonal phase as demonstrated by

the TEM images. The weak hysteresis loops may be caused by non-ferroelectric

factors.

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(b) The polarization switching does occur in the 7-nm BTO film, but it may be too

weak to be properly detected by the stiffer cantilever.

The above spectroscopic studies by varying the VAC and using the stiffer cantilever

could still be unable to confirm whether the ferroelectric switching occurs in the

BTO/NSTO film. Nevertheless, the combined SKPM and PFM results have shown that the

charge trapping/detrapping is the dominant effect in the NSTO-based heterojunctions, and

this will not be changed by whether the ferroelectric switching exists.

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Fig. S15 Hall voltage VPN versus injected current IMO as a function of magnetic field

strength B, measured for the NSTO substrate. Inset shows the geometry of the Van der

Pauw method for Hall measurements. The electrodes M and O were used for the injection

of a constant current while the hall voltage was measured between the electrodes P and N.

The electron density nH (≈ ND) can be calculated as nH = |IMO/VPN|•B/(qd), where d is the

thickness of the substrate. By fitting, nH ≈ 1.4×1020 cm-3 is obtained. Considering the errors,

such as non-zero electrode areas and finite inter-electrode distances, our results are close

to the reported ND values of 0.7 wt% NSTO.7 To be further consistent with ref. 7, ND =

1×1020 cm-3 is adopted for the calculations in the main text.

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Fig. S16 Light-induced Voc of Au/NSTO MSJs and Au/BTO/NSTO FTJs in (a) HRS and

(b) LRS. Light-induced Isc of Au/NSTO MSJs and Au/BTO/NSTO FTJs in (c) HRS and

(d) LRS. The time domains filled with yellow correspond to the periods when the light is

on. (e) Equivalent circuit model of a MIS heterojunction under light illumination,

consisting of a constant current source (Iph*), a Schottky diode (D), a shunt resistor (Rsh)

and a series resistance (Rse).

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Fig. S17 Capacitances of Au/NSTO MSJs and Au/BTO/NSTO FTJs as a function of

frequency. The increase of capacitance with decreasing frequency indicates the existence

of trap states.

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Fig. S18 Ti 2p XPS spectra of (a) the NSTO substrate and (b) the 7-nm BTO film. The

small emission peaks at the binding energies of 457~458 eV indicate the presence of

Ti3+.8

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Fig. S19 I-V curves measured with low-work-function metals In and Ti as top electrodes.

The Ti electrodes have a diameter of 200 µm while the In electrodes have an area of ~2×104

µm2. Because the In and Ti form Ohmic contacts with BTO, the information of the

BTO/NSTO contact can thus be revealed. The linear I-V curves with small resistances

indicate that the BTO/NSTO contact is Ohmic.

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Fig. S20 Experimental and simulated I-V curves of the Au/BTO/NSTO heterostructures

with the BTO layer thicknesses of (a) 2 nm and (b) 14 nm. The current jump at ~1.5 V

observed in the 2-nm BTO film may be caused by a suddenly enhanced detrapping effect

at this voltage, which can however not be simulated.

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Table S1. Fitting parameters used in Eqs. (10) and (16) in the main text

k1 V1 (V) α1 R1 (Ω) γ1

HRS 2.807 4.2 0.552 / /Au/NSTO

LRS 13.98 3.7 1.458 276 1.228

Au/BTO/NSTO HRS 11.87 4.4 1.448 / /

LRS 203.4 4.3 3.215 192 1.998

Table S2. Schottky barrier height (ΦB), tunneling transmission coefficient (θn), and

resistance for the electron drift within the depletion region in the LRS (R) used for fitting

the I-V curves of the Au/BTO/NSTO heterostructures.

BTO layer

thickness (nm)

Resistance

state

ΦB (eV) θn R (Ω) at -5 V

HRS 0.48 2.94×10-4 /2

LRS 0.43 4.45×10-2 2325

HRS 0.54 3.39×10-5 /7

LRS 0.44 3.25×10-2 4672

HRS 0.56 1.94×10-5 /14

LRS 0.49 7.81×10-3 281000

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II. Reasons for larger resistances in the MSJs than in the FTJs

With the MIS model, one can explain why the MSJs can exhibit larger resistances

than the FTJs. As discussed in the main text and Sec. IX below, the interfacial layers at the

Au/NSTO and Au/BTO interfaces are the insulating layers (also the tunneling layers),

while the BTO layer (7 nm) acts as a semiconductor depletion layer. Therefore, for both

MIS junctions, the resistances can be evaluated by Eq. (1) in the main text, where the

transmission coefficient θn and the Schottky barrier height ΦB play a major role.

Considering that the NSTO and BTO have similar band gaps (Eg_BTO ~ 3.15 versus Eg_NSTO

~ 3.22 eV)9 and electron affinities (χBTO ~ χNSTO ~ 3.9 eV),10,11 the θn and ΦB are thus largely

determined by the interfacial layers and traps. For example, the interfacial layer of

Au/NSTO may have a larger thickness and/or a higher potential barrier, resulting in a lower

θn (see Table 1 in the main text). In addition, if there are more negative charges trapped

within the interfacial layer of Au/NSTO, a higher ΦB is obtained according to Eq. (8) in the

main text (see Table 1 in the main text). Therefore, the resistances of the MSJs can be

higher than those of the FTJs.

III. Analysis of the temperature dependence of the I-V curves

Figure 4a and d in the main text shows that the reverse current increases with decreasing

temperature. This may be due to the enhanced tunneling current caused by the reduction of

barrier width at lower temperatures. It has been reported that the dielectric constant of

NSTO near the surface would decrease as the temperature becomes lower,12,13 thus giving

rise to the narrowing of barrier width (WD = [2ε0εSVbi/(qND)]0.5). On the other hand, the

forward current decreases first and then increases after the temperature reaches about 413

K. This behavior was observed previously in the Pt/NSTO MSJs12 and Pt/BFO/NSTO

FTJs.14 It is therefore deducible that in the forward bias condition, some thermally activated

processes, like thermionic emission and/or thermionic-field emission, may be involved.

IV. Reasons for the inconsistency in the fitting of ln(J/T2)-V curves

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There may be several factors causing the inconsistency in the fitting of ln(J/T2)-V

curves at very low voltages (below ~0.2 V):

(a) The contribution from tunneling to the overall current may be voltage-dependent.

At very low voltages (below ~0.2 V), the tunneling contribution is small. Hence,

both the overall current and the ideality factors are small. As the voltage increases,

the tunneling contribution increases, and then a nearly linear region of the ln(J/T2)-

V curve where the ideality factor is almost constant is reached. This region is where

we have done the fitting for the ln(J/T2)-V curves.

(b) Some other transport mechanisms may yield currents with the opposite direction,

reducing the overall current. For example, the dielectric relaxation current when the

voltage is scanned from 0.5 to -0.5 V (the sequence used in this work) has a negative

sign, opposite to the direction of current in the positive voltage regime. Such current

plays a significant role at very low voltages where the overall current is small.

V. Fitting the C-V data with a conventional Schottky junction model

In a conventional metal-semiconductor Schottky junction where no interfacial layer

is present, the C-V relationship is given by

. (1)

1

𝐶2=

2(𝑉𝑏𝑖 ‒ 𝑉)

𝑞𝜀0𝜀𝑆𝑁𝐷

The fitting of experimental C-V data to Eq. (1) gives the Vbi values of 3.54 and 2.45 eV for

the MSJs and FTJs, respectively. These values are, however, unreasonably large. The

presence of an interfacial layer therefore needs to be taken into account.15

VI. Discussion on the ideality factor n

There are many factors that could influence the ideality factor n: (i) voltage partitioning

effect, (ii) interface states, including those in equilibrium with the metal and those in

equilibrium with the semiconductor, (iii) tunneling effect, and (iv) image force lowering of

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the barrier height. For the voltage partitioning effect, the interfacial layer has a parasitic

capacitance of CIL and it can partition the applied voltage V with VIL = V(n-1)/n.

Consequently, the voltage drop across the semiconductor depletion region is VS = V/n.

Here, n is described as

. (2) 𝑛 = 1 +

𝐶𝑆

𝐶𝐼𝐿

In the C-V measurements, small-amplitude and high-frequency AC voltages were

applied. In such case, the effects (ii)-(iv) may be weak and only the voltage partitioning

effect is significant. Therefore, Eq. (2) seems to be valid for the analysis of C-V data and

has been adequately used in previous studies.12,15,16 It was further suggested that the n

values could be extracted from the HRS I-V curves in low voltage regimes using Eq. (2) in

the main text,16 which are ~2.28 and ~2.81 for the MSJs and FTJs, respectively (see Fig.

1a and c in the main text). These n values will be used throughout the analyses of C-V data

including those in LRS. The n values extracted from the LRS I-V curves are, however, not

suitable for the C-V data analysis because they are significantly influenced by the tunneling

effect and thus do not satisfy Eq. (2).

In the simulation of I-V curves, we treat the ideality factor n as a variable because the

effects (i)-(iv) can vary with the voltage. The voltage dependence of n may be described

by Eq. (10) in the main text.

VII. εS values extracted from the fitting of C-V data

By fitting experimental C-V data to Eq. (4) in the main text, the average dielectric

constants within the depletion regions of Au/NSTO MSJs and Au/BTO/NSTO FTJs are

50.9 and 27.0, respectively. These values are much smaller than the dielectric constants of

bulk NSTO (~300) and BTO (~500).9 The differences may be caused by the large built-in

field induced reduction in the dielectric constant.12,15,16 Taking the Au/NSTO MSJs as an

example, the average electric field Eavg distributed in the depletion region can be estimated

by [2qNDVbi/(ε0εS)]0.5 to be as large as 3.3 MV/cm. Further substituting Eavg into the

equation of field-dependent dielectric constant of NSTO,12,15,16 one can obtain a dielectric

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constant value of 44.3, close to the fitted value of 50.9. Note that Eq. (4) in the main text

may still be valid although the field dependence of εS is not considered, because the

scanning voltages in the C-V measurements are small.

VIII. Interpretation of the photo-response results

The photovoltaic effect, namely the separation of photo-excited charge carriers by the

built-in field, is a distinct feature of a Schottky junction. By monitoring the photovoltage

(Vph) and photocurrent (Iph) responses, the information of the Schottky barrier, like barrier

profile and charge carrier transport process, can be revealed. In this study, the open-circuit

voltage (Voc) and short-circuit current (Isc) of the MSJs and FTJs in response to light

illumination were measured. The wavelength of our UV light is 365 nm, well matching the

bandgaps of NSTO (3.22 eV) and BTO (3.15 eV).9 In addition, BTO is a treated a

semiconductor depletion layer. Hence, both NSTO and BTO would contribute to the

photovoltaic effect.

Figure S16a and b show the Voc responses of the MSJs and FTJs in HRS and LRS,

respectively. The measured photovoltage Vph is calculated as Vph = |Voc (light on) – Voc (light

off)|. The Vph values of the MSJs in HRS and LRS are ~500 and ~4 mV, respectively; while

those of the FTJs in HRS and LRS are ~55 and ~0.4 mV, respectively. The reduction of

Vph upon switching from HRS to LRS has been observed in NSTO-based heterojunctions

previously.17 The changes of Vph during the RS may be caused by the barrier profile

variation and/or the modification of the tunneling process. According to the solar cell

theory,18 the ideal photovoltage Vph* (not the measured Vph) can be obtained by

, (3)𝐼 ∗

𝑝ℎ = 𝐼0[exp (𝑞𝑉 ∗𝑝ℎ

𝑛𝑘𝐵𝑇) ‒ 1]

where Iph* is the ideal photocurrent and I0 is the ideal saturation current under a reverse

bias. Iph* depends on depletion width WD and light flux density P, as

, (4)

𝐼 ∗𝑝ℎ

𝑆≈ 𝑞𝑃[1 ‒

exp ( ‒ 𝛼𝑊𝐷)1 + 𝛼𝐿ℎ

]

29

where α is the absorption coefficient and Lh is the diffusion length of minority carriers (i.e.,

holes).

We first only consider the influence of the variation of barrier profile on the measured

Vph and Iph. Taking the MSJs as an example, in HRS, Iph* might be approximated as Iph =

|Isc (light on) – Isc (light off)|, i.e., ~3.45 nA (Fig. S16c). I0 is estimated as ~2.27 × 10-2 pA

by fitting the HRS I-V curves. Vph* calculated by using Eq. (3) is ~700 mV, which seems

to be close to the HRS ΦB value (Table 1 in the main text) and also comparable to the

measured Vph of ~500 mV (Fig. S16a). Upon switching from HRS to LRS, Iph* can be

calculated by using Eq. (4) as ~3.31 nA, given that WD is known from Vbi (Table 1 in the

main text). This is still in consistence with the measured Iph of the MSJs in LRS, i.e., ~3.15

nA (Fig. S16d). However, the discrepancy lies in the calculated Vph*, which is ~468 mV as

derived from Eq. (3), given the ΦB variation of 0.23 eV for I0. The calculated Vph* is

obviously too large compared with the measured Vph of ~4 mV in LRS (Fig. S16b). Another

discrepancy can be found in the FTJs. As shown in Fig. S16c and d, the measured Iph in

HRS (~0.73 nA) is even smaller than that in LRS (~1.10 nA). This observation, in

contradiction to the fact that a wider depletion region in HRS will give rise to a larger Iph,

was also reported in ref. 11. Therefore, besides the variation of barrier profile, other factors

shall also be responsible for the observed changes in Vph and Iph upon RS. Note that the

FTJs in LRS shows a large Isc even in the dark condition (Fig. S16d), indicating that it is

not in the equilibrium state. Additionally, the positive sign of the dark Isc suggests that the

surface potential is positive in LRS, which is consistent with the SKPM results (Fig. 3d in

the main text).

In a realistic Schottky junction, the presence of charge transport processes other than

thermionic emission, like tunneling, will make the measured Vph and Iph different from their

respective ideal values determined by Eq. (3) and (4). One intuitive thinking is that when

the HRS is switched to LRS, the tunneling within either the depletion region or the

interfacial layer will be enhanced and hence less charge carriers will be recombined. The

measured Iph of LRS may therefore be larger than that of HRS. In addition, if the transport

of charge carriers in LRS relies more on tunneling, the voltage drop across the Schottky

barrier will be lowered. Therefore, the measured Vph of LRS can become much smaller

30

than that of HRS. To reflect the above effects, the Schottky junction may be described by

an equivalent circuit model as schematically shown in Fig. S16e. In this model, Rsh and Rse

are the shunt resistance of the depletion region and the series resistance of the interfacial

layer, respectively. The output current I under an applied voltage V is

. (5)𝐼 = 𝐼0{exp [𝑞(𝑉 ‒ 𝑅𝑠𝑒𝐼)

𝑛𝑘𝐵𝑇 ] ‒ 1} +𝑉 ‒ 𝑅𝑠𝑒𝐼

𝑅𝑠ℎ‒ 𝐼 ∗

𝑝ℎ

One may assume that I0 is small and thus the first term on the right side of Eq. (5) may

be neglected. By letting V = 0 and I = 0, one can obtain

, (6)𝐼𝑉 = 0 =

𝑅𝑠ℎ

𝑅𝑠ℎ + 𝑅𝑠𝑒𝐼 ∗

𝑝ℎ

and

, (7)𝑉𝐼 = 0 = 𝑅𝑠ℎ𝐼 ∗𝑝ℎ

respectively. Here, IV=0 and VI=0 may represent the measured Iph and Vph, respectively.

On the basis of Eq. (6), the measured Iph of the FJTs in LRS being larger than that in

HRS can be well understood. From HRS to LRS, although Iph* becomes smaller due to the

reduction of the depletion width, the Rsh/(Rsh+Rse) ratio may become larger and even

overcompensate the reduction of Iph*. The product IV=0, corresponding to the measured Iph,

may thus become larger in LRS.

According to previous analyses based only on the variation of barrier profile, the ratios

of Vph* (LRS) versus Vph

* (HRS) are ~0.67 and ~0.81 for the MSJs and FTJs, respectively.

On the other hand, if one assumes that there is no barrier variation, Iph* will be unchanged.

VI=0 calculated with Eq. (7) is thus proportional to Rsh. If Rsh scales with the RS ratios, the

VI=0 (LRS) versus VI=0 (HRS) ratios can be smaller than 0.001 in both the MSJs and FTJs.

The measured ratios of Vph (LRS) versus Vph (HRS), as shown in Fig. S16a and b, are

~0.008 and ~0.007 for the MSJs and FTJs, respectively. One may therefore deduce that the

huge decrease of the measured Vph from HRS to LRS is largely caused by the reduction of

31

Rsh related to the enhanced tunneling effect in LRS14. The effect of the variation of barrier

profile seems to be less significant in this case.

The combined results of Vph and Iph therefore suggest the concurrence of variation of

barrier profile and modification of tunneling process, as summarized as follows. (i) The

measured Iph of LRS is lower than that of HRS in the MSJs while the situation is reversed

in the FTJs. How the measured Iph varies from HRS to LRS depends on the competition

between the reduced depletion width and the enhanced Rsh/(Rsh+Rse) ratio. (ii) The

measured Vph decreases by about two orders of magnitude from HRS to LRS in both the

MSJs and FTJs. This may be largely caused by the reduction of Rsh related to the enhanced

tunneling effect in LRS, while it is less influenced by the variation of barrier profile.

IX. Discussion on the nature of the interfacial layer and the ultrathin BTO layer.

It is known that an interfacial layer can be formed at the metal/oxide interface from

various origins. The extrinsic origins include carbon contamination,16 metal deposition-

induced damage and/or disorder,19 inter-diffusion and/or reaction between metal and

oxide,20 and accumulation of oxygen vacancies.8 Some intrinsic origins, such as atomic

rearrangement,21 reduction of inter-dipole interactions at the interface,22 strain gradients

due to lattice mismatch,23 and depolarization effect,24 have also been proposed. It remains

an issue which origin(s) is (are) responsible for the interfacial layers in our samples, and

the properties of these interfacial layers (thickness, composition, etc.) are also unknown;

nevertheless, the existences of interfacial layers at both the Au/NSTO and Au/BTO

interfaces could not be denied in view of the C-V results. The interfacial layers are actually

the tunneling layers,25 even for the FTJs. This can well explain why the FTJs shows larger

transmission coefficients θn than the MSJs (see Table 1 in the main text). If the whole BTO

layer (~7 nm) is assumed to be the tunneling layer,14,26 θn would be very small because θn

decreases exponentially with the tunneling layer thickness.

Indeed, the ultrathin BTO layer is a semiconductor depletion layer. This is because

the BTO layer can become semiconducting due to the presence of unintentionally

32

introduced defects/impurities. The defects/impurities can be easily introduced into the

BTO films during the PLD process, allowing for the facts such as oxygen-deficient growth

atmosphere, non-perfect stoichiometry of the target, and interdiffusion between the BTO

films and substrates. Previous studies revealed the existence of defects in high-quality BTO

films that were grown layer-by-layer on the NSTO substrates.8,9 We have also investigated

the defect chemistry of our BTO films using X-ray photoemission spectroscopy (XPS).

The Ti 2p XPS spectra of both BTO and NSTO show small emission peaks at the binding

energies of 457~458 eV (Fig. S18), suggesting the presence of Ti3+.8 This may be

associated with oxygen vacancies and other native point defects, providing evidence that

our BTO films are doped semiconductors. Additionally, the FTJs show similar rectifying

I-V behaviors as the MSJs, suggesting that the BTO films (7 nm) are n-type

semiconductors.

In addition, BTO and NSTO have similar bandgaps (Eg) (Eg_BTO ~ 3.15 versus Eg_NSTO

~ 3.22 eV)9 and electron affinities (χ) (χBTO ~ χNSTO ~ 3.9 eV),10,11 and the band offset

between BTO and NSTO revealed by the XPS is smaller than 0.22 eV.9 The BTO/NSTO

interface is therefore close to an Ohmic contact, as demonstrated by previous transport

studies.27,28 To confirm this, low-work-function metals of In and Ti were used as top

electrodes to form Ohmic contacts with BTO, and then the I-V characteristics were

measured. As shown in Fig. S19, both In/BTO/NSTO and Ti/BTO/NSTO heterostructures

show linear I-V behaviors with small resistances, indicating that the BTO/NSTO contact is

Ohmic. Therefore, from the perspective of band alignment, BTO in the NSTO-based FTJs

is more like a semiconductor depletion layer rather than a wide-gap insulating layer for

electron tunneling. Due to the small band offset between BTO and NSTO,9 the potential

profile within the whole depletion region is thus largely continuous while the discontinuity

at the BTO/NSTO interface may be neglected.

With the above understanding, a unified MIS model can therefore be used to describe

both the MSJs and FTJs.

X. Fitting of I-V curves for the FTJs with different BTO layer thicknesses

33

First of all, we would like to mention that in our MIS model, the ultrathin BTO layer

is approximated as a semiconductor depletion layer similar to the NSTO. In fact, the

material properties of the BTO (e.g., donor concentration Nd and bulk resistance Rbulk) are

different from those of the NSTO. Therefore, the inconsistency between the MIS model

and the actual Au/BTO/NSTO heterostructure will increase as the BTO layer becomes

thicker. Consequently, the reliability of the I-V curve fitting based on the MIS model

becomes poorer in the thicker BTO films.

Although one can hardly know the upper limit of the thickness below which the MIS

model is still valid, there may be an empirical method to predict whether the MIS model

can be applied. If the current increases steeply (i.e., near-exponentially) with the applied

voltage under forward bias condition, the MIS model may still be applicable. Otherwise,

the Schottky barrier theory is violated because the insulating property of BTO will play a

significant role in the charge transport. Based on this empirical method, it may be

appropriate to fit the I-V curves of the BTO films below 14 nm.

The simulated I-V curves of the 2-nm and 14-nm BTO films are shown in Fig. S20,

while that of the 7-nm film is shown in Figure 6 in the main text. As can be seen, relatively

good agreement between the simulated and experimental data can be achieved. The major

fitting parameters of the BTO films with different thicknesses are summarized in Table S2,

which may be interpreted as follows:

(a) The Schottky barrier height (ΦB) in a specific resistance state (HRS or LRS)

increases as the BTO layer thickness increases. According to the C-V results in

Figure 5 in the main text, the 1/C2-V slope of the Au/BTO/NSTO junction is slightly

larger than that of the Au/NSTO junction, which may suggest that the BTO has a

smaller donor concentration Nd than the NSTO. Therefore, the depletion region may

need to be extended farther away from the interface (i.e., a larger depletion width

WD) to maintain the charge neutrality in the thicker BTO films. Because the built-

in voltage Vbi (and consequently ΦB) scales with the product Nd·WD2 where WD

plays a greater role, the ΦB thus increases as the BTO layer thickness increases.

(b) The tunneling transmission coefficient (θn) in a specific resistance state (HRS or

LRS) decreases as the BTO layer becomes thicker. In our MIS model, the θn

34

depends on the interfacial layer thickness dIL and tunneling barrier height in the

interfacial layer (ΦT), as θn ∝ exp[-dIL(ΦT)1/2]. The dIL and ΦT have been shown to

be interface quality-dependent.16 As the BTO layer grows thicker, its surface

roughness slightly increases (see AFM images in Fig. S3), thus reducing the quality

of the Au/BTO interface. As a result, the dIL and/or ΦT may increase as the BTO

layer thickness increases, leading to a decreasing trend of θn.

(c) The resistance for the electron drift within the depletion region in the LRS (R) at a

specific voltage (e.g., -5 V) increases as the BTO layer thickness increases. Due to

the high resistivity of the BTO layer in the depleted state, the thicker the BTO layer

is, the higher the resistance for the electron drift will be.

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