Rectification and Amplification of Ionic Current in

Supporting Information

Rectification and Amplification of Ionic Current in Planar Graphene / Graphene-Oxide Junctions: An Electrochemical Diode and Transistor Sourav Kanti Jana1,2*, Sangam Banerjee2, Sayan Bayan2, Harish Reddy Inta1, Venkataramanan Mahalingam1* 1. Nanomaterials Lab, Department of Chemical Sciences Indian Institute of Science Education and Research Kolkata Mohanpur – 741246 West Bengal, India E-mail: [email protected], [email protected] 2. Surface Physics and Materials Science Division Saha Institute of Nuclear Physics 1/AF, Bidhannagar, Saltlake Kolkata-700064, India

Table of contents Sl. no 1 2

Name Scheme S1 Figure S1

Description Experimental section Scanning electron microscopy (SEM) images

3

EDX spectra of both GO and ERGO samples Secondary ion mass spectroscopy (SIMS) analysis of all samples

S5 S6

5

Figure S2 Figure S3 and Figure S4 Scheme S2

S7

6

Figure S5

7

Figure S6

8

Figure S7

9

Figure S8

10

Figure S9

11

Figure S10

Proposed scheme to understand the structural change before and after electrochemical reduction of GO Raman spectroscopy results and analysis of all GO and ERGO samples Impedance spectroscopy results and analysis of GO and ERGO3 samples Detailed calculation of dielectric constant of both GO and ERGO3 Mott-Schottky results of other ERGO samples (ERGO1 and ERGO2) and variation of hole to electron concentration ratio of all the samples Electrical I-V characteristics of individual GO and ERGO samples with and without electrolyte I-V characteristics of all GO-ERGO junctions without electrolyte

4

S1

Page no. S2-S4 S4

S8 S9 S9 S10-S11

S12-S14 S15

12

Figure S11

13

Figure S12

14

Figure S13

Proposed mechanism ion current rectifying characteristics of GO-ERGO3 junction Comparative study of I-V characteristics of with and without junction formed by GO and ERGO3

S16-S19 S20

Effect of pH of electrolyte the rectification and amplification of the ionic current of junction and transistor sample

S21

References

S22

15

1. Experimental Section 1.1 Synthesis of GO & ERGO GO was prepared chemically using modified Hummer’s method and the full protocol of this synthesis process has been reported elsewhere

[1-2]

. The fresh aqueous GO solution (1mg/ml)

was drop casted on SS substrates (1 cm x 1 cm) such that it is spread throughout the substrate surface. This step is followed by drying in hot furnace at 50 ºC until it was dried completely. This resulted in the formation of a thick GO film on SS. Finally, these GO films were electrochemically reduced by applying constant potential for different time in three electrode configuration. The potential was kept fixed at -0.8V and phosphate buffer solution (PBS, pH~7) was used as electrolyte during electrochemical reduction process. Here, GO coated SS substrate was used as working electrode, Pt wire as counter electrode and Ag/AgCl used as reference electrode for electrochemical reduction. Three different reduction times (1000s, 7000s, and 10000s) was maintained during preparation and accordingly the corresponding samples are named as ERGO1, ERGO2, and ERGO3 respectively.

1.2 Material characterizations Morphology of unreduced (GO) and electrochemically reduced GO (ERGO) samples was investigated through field emission scanning electron microscopy (FESEM, GEOL JSM 6390 LV). Raman Spectroscopy was used to quantify the defects in GO and ERGO samples. Room temperature Raman spectroscopy measurements were performed at a laser excitation wavelength of 488 nm line of an Argon ion laser with a spot diameter of 5 μm. All the Raman data were recorded with laser power density 0.5 mW μm−2. The spectra were collected with a LabRam HR monochromator (1800 gr mm−1 grating) equipped with a charge coupled device (CCD) detector (Jobin Yvon). S2

Electrochemical

Mott-Schottky measurements

were

performed in three

electrode

configuration adopted with GO and ERGO samples used as working electrode, platinum used as counter and Ag/AgCl used as reference electrode. The frequency maintained for the measurement was 5 KHz.

1.3 Device structure fabrication GO-ERGO 1D planar junction device was fabricated according to the scheme S1a.

(a) GO-ERGO junction PMMA

(b) GO-ERGO-GO junction

Selective chemical etching

PMMA

Selective etching of PMMA

PMMA PMMA

PMMA

ERGO GO

GO GO

GO

GO

(c)

ERGO3

ERGO GO

Scheme S1: Schematic representation for fabrication steps of planar (a) GO-ERGO, (b) GOERGO-GO junction sample, and (c) digital image of planar GO-ERGO-GO based planar n-pn transistor.

First, poly(methyl methacrylate) (PMMA) was dissolved (30mg/ml) in toluene and SS substrate was coated with PMMA through spin coating method. Then one half of the PMMA coated SS substrate was selectively etched using acetone by ultrasonication. Subsequently, GO was deposited by simple drop cast method on the whole surface of the substrate. This resulted in one portion of GO electrically connected with SS while the other portion of GO is S3

insulated from the SS. Finally, SS connected GO films were electrochemically reduced at the same potential for different reduction times similar to above mentioned procedure. GOERGO-GO junction was also fabricated using similar protocol (scheme S1b) and digital image of it is shown in scheme S1c.

(2) Scanning Electron Microscopy analysis:

Figure S1: SEM image of (a) GO, (b) ERGO1, (c) ERGO2 and (d) ERGO3 samples.

S4

(3) EDX analysis of both GO and ERGO samples 15000

C

10000

Intensity (a.u.)

5000

O

0 12000

C

8000 4000

O

0 8000

C

6000

O

4000 2000 0 9000

C

6000

O

3000 0

0

Elements

Weight %

Atomic %

C

91.30

93.32

O

8.70

6.68

Total

100

100

Elements

Weight %

Atomic %

C

72.21

77.58

O

27.79

22.42

Total

100

100

Elements

Weight %

Atomic %

C

56.49

63.36

O

43.51

36.64

Total

100

100

Elements

Weight %

Atomic %

C

56.49

63.36

O

43.51

36.64

Total

100

100

2

4

6

Energy (keV)

Figure S2: EDX spectra of both GO and ERGO samples.

S5

ERGO3

ERGO2

ERGO1

GO

8

10

(4) Secondary Ion Mass Spectroscopy (SIMS) analysis

(a)

6

2x10

ERGO3 6

1x10

Intensity (a.u.)

C2HC2H2-

OH-

H06 2x10

C 2-

OC-CH-

(b) 4

1.4x10

ERGO2

GO ERGO1 ERGO2 ERGO3

4

1.2x10

6

0 6 4x10

Intensity (a.u.)

1x10

ERGO1

6

3x10

6

2x10

6

1x10

6

5x10

GO

6

4x10

6

3x10

4

1.0x10

COOH-

3

8.0x10

3

6.0x10

3

4.0x10

3

2.0x10

6

2x10

6

1x10

0

2

4

6

8

0.0 43.5

10 12 14 16 18 20 22 24 26 28 30

44.0

44.5

m/e

45.0

45.5

46.0

m/e

Ion intensity (a.u.)

7x10

6

6x10

6

5x10

6

4x10

6

3x10

6

2x10

6

1x10

6

O

GO ERGO1 ERGO2 ERGO3

-

(a)

0

1.0 0.9

3.0x10

5

6.0x10

5

9.0x10

5

1.2x10

6

1.5x10

Time (ms) C - (ERGO)/C - (GO) (c)

ERGO1 ERGO2 ERGO3

2

6

1.0 -

0.7 0.6 0.5

ERGO1 ERGO2 ERGO3

(b)

0.9

0.8

0.7

0.6

0.5

0.4 0.0

4.0x10

5

8.0x10

GO ERGO1 ERGO2 ERGO3

6.0x10

5

3.0x10

5

5

1.2x10

6

1.6x10

6

2.0x10

6

2.0x10

6

Time (s)

5

2

0.8

-

CERGO/CGO

9.0x10

Ion intensity (a.u.)

Normalized intensity (a.u.)

0.0

Normalized intensity (a.u.)

Figure S3: (a) SIMS finger print scan and (b) variation of carboxylic group of the unreduced and reduced samples.

(d)

0.4 0.3 0.0

0.0 5.0x10

5

1.0x10

6

1.5x10

6

2.0x10

6

Time (s)

0.0

5.0x10

5

1.0x10

6

1.5x10

6

Time (ms)

Figure S4: SIMS depth profiling for (a) O-, (b) C-, (c) C2- and (d) H- secondary ions of reduced samples with respect to unreduced sample. S6

(5) Proposed scheme of structural change of both GO and ERGO3

(a) GO OH

(b) ERGO3 OH

OH COOH

COOH OH

OH OH OH

COOH

O

O

OH

OH

OH

COOH

COOH

Scheme S2: Proposed schematic of (a) graphene oxide structure and (b) the same after electrochemical reduction with defects formed on the basal plane.

S7

(6) Raman Spectroscopy analysis of GO and ERGO samples The Raman spectra of GO and ERGO is shown in Figure S5. Both GO and ERGO samples show two main characteristic peaks (D and G). The G band (1590 cm -1) is a result of in-plane vibrations of sp2 bonded carbon atoms in the hexagonal ring whereas the D (1331 cm-1) band is due to out of plane vibrations assigned to the presence of structural defects [3]. The 2D band is appeared at ~2660 cm-1 which is a second-order two-phonon process and exhibits a strong frequency dependence on the laser excitation. The intensity ratio (ID/IG) of D and G bands measures the defect density present in the respective samples. The GO sample has both sp 3 hybridized carbon region and unoxidized domain of sp2 hybridized carbon atoms. The density of sp3 domains is higher than the sp2 domains yielding lowest ID/IG ratio exhibited by GO sample. This ratio increases with increase in the reduction of the GO indicating the removal of oxygen functional groups from the basal plane of ERGO samples. 500

(a)

GO

D

D

300

G

250

300

Intensity (a.u.)

ERGO1

(b)

350

G

400

400

ID/IG~ 1.19

ID/IG~ 1.4

200

200

150 100

100

2D

2D

50 0

0 0

500

1000

1500

2000

2500

250

(c)

3000

ERGO2

D

0

3500 250

500

1000

(d)

1500

2000

2500

3000

3500

ERGO3

D

200

200

G

150

G

150

ID/IG~ 1.57

100

ID/IG~ 1.6

100

50

50

2D

2D 0

0 0

500

1000

1500

2000

2500

3000

3500

0

500

1000

1500

2000

2500

3000

-1

Raman shift (cm ) Figure S5: Raman spectra of (a) GO, (b) ERGO1, (c) ERGO2 and (d) ERGO3. S8

3500

(7) Impedance spectroscopy results: Nyquist plot of both GO and ERGO3 8.0k

-Zimaginary (Ohm)

GO ERGO3 6.0k

4.0k

2.0k

0.0 0

1k

2k

3k

Zreal (Ohm) Figure S6: Nyquist plot of both GO and ERGO3 (8) Dielectric constant calculation of both GO and ERGO3 from impedance spectroscopy results: The dielectric constant can be written as a complex number [4] 𝜖 = 𝜖 ′ − 𝜖 ′′ 𝑍 ′′ . 𝑙

With, 𝜖 ′ = − 2𝜋𝑓𝜖

0

𝐴𝑍 2

𝑍′. 𝑙

and 𝜖 ′′ = 2𝜋𝑓𝜖

0 𝐴𝑍

2

Where, where 𝑍 ′ and 𝑍 ′′ are the real and imaginary parts of samples of the impedance Z measured at frequency f, ϵo is permittivity in the free space, A is the area and l is the thickness of the samples. 7

3.5x10

GO ERGO3

7

3.0x10

7

2.5x10

7

'

2.0x10

7

1.5x10

7

1.0x10

6

5.0x10

0.0 1000

10000

100000

Frequency (Hz) Figure S7: Variation of dielectric constant of both GO and ERGO3. S9

(9) Mott-Schottky (M-S) theory and results 2.0

1.4

(a)

(b)

ERGO3

1.2

1.6 1.0

1.2

p/n

0.8

0.8

2

-2

4

9

1/Csc(F cm x10 )

ERGO1 ERGO2

ERGO2 0.6

0.4

ERGO1

0.4 0.2

GO 0.0

0.0

-0.6

-0.4

-0.2

0.0

0.2

0.4

0

2000

4000

6000

8000

10000

12000

Electrochemical reduced time (s)

Potential (V, vs. SHE)

Figure S8: (a) Mott-Schottky plots of all ERGO1 and ERGO2 samples and (b) variation of p/n ratio of all pristine GO and electrochemical reduced GO samples.

According to the Mott-Schottky (M-S) theory [5], the space charge capacitance per unit area at the electrode and electrolyte interface is given by the following equation. 1 2 𝑘𝑇 =± [𝑉 − 𝑉𝑓𝑏 − ] 2 (𝑒𝜀𝜀𝑜 𝑁) 𝑞 𝐶𝑠𝑐

Where, e is electronic charge, ε is dielectric constant of the samples, ε o is the permittivity of free space, N is charge density (and it should be either Na, acceptor or Nd donor charge density depending upon the electronic conductivity of the sample.) in the samples, Vfb is the extent of band bending in depletion layer, k is the Boltzmann constant, and T is the absolute temperature. The ‘+’ and ‘-’sign indicate the electrode is n type and p type respectively and the charge concentration of the electrodes can be determined by the slope (M=2/e0N) of the above Mott-Schottky equation. From the Mott-Schottky plot (Figure S8a), it is confirmed that the conductivity of GO is ntype and ERGO3 is p type. Moreover the value of positive slope of GO (MGO~1.7) and

S10

negative slope of ERGO3 (MERGO3~1.65) is almost the same. Therefore the ratio of majority charge carriers of both GO and ERGO3 (electron and hole) can be estimated from the positive and negative slope of the Mott-Schottky plots of the GO and ERGO3 samples. The calculation is depicted as follows. MERGO3 = ε

Thus,

2

N+ ERGO3 N− GO

&

+ ERGO3 .ε0 .e.NERGO3

= (ε

εGO ERGO3

MGO

) ∗ (M

ERGO3

MGO = ε

2 − GO .ε0 .e.NGO

)

Since MGO and MERGO3 are almost same, therefore hole and electron concentration ratio (NERGO3+/NGO-) of ERGO3 and GO depends upon only the relative change of the dielectric constant of the samples. GO has high dielectric constant compared to the ERGO3. Hence at any value of GO, hole density in ERGO3 is higher than electron density of GO. The variation of charge concentration of all the samples is shown in Figure S8b.

S11

(10) Electrical I-V characteristics of individual GO and ERGO samples with and without electrolyte We fabricated GO-ERGO3 based junction by selective electrochemical reduction of GO film as shown in Scheme 1a. The details of the fabrication process have been described in the experimental section. Before making the junction we measured the I-V characteristics (as shown in Figure S9) of individual GO and ERGO samples in the presence and absence of aqueous electrolyte. The non-linear I-V characteristics (measured in the solid state) of GO confirms the Schottky contact formed between semiconducting samples and Ag paste, while the linear I-V characteristic of ERGO3 sample attributes to the formation of Ohmic contact. This verifies ERGO3 sample is semi-metallic in nature. However, in presence of electrolyte ERGO3 shows non-linear I-V characteristics. The non linear I-V response of GO-ERGO3 junction sample attributes to the Schottky junction formed between them (shown in Figure S10). The potential barrier formed at the Schottky junction between GO and ERGO3 restricts the carrier transport through the sample from one contact to another (without electrolyte).

S12

2

Current density (mA/cm )

GO

(a)

0.008 0.004 0.000 -0.004 -0.008 -0.012 -1.2

Solid state Electrochemical -0.8

-0.4

0.0

0.4

0.8

1.2

Potential (V)

2

0.04

ERGO2

(c)

0.02

0.00

-0.02

-0.04 -1.2

Solid state Electrochemical -0.8

-0.4

0.0

0.4

4 ERGO1

(b)

2

0

-2

Solid state Electrochemical

-4-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

Potential (V) Current density (A/cm )

2

2 Current density (A/cm ) Current density (mA/cm )

0.012

0.8

1.2

Potential (V)

1.0

ERGO3

(d)

0.5

0.0

-0.5

-1.0 -1.2

Solid state Electrochemical -0.8

-0.4

0.0

0.4

0.8

1.2

Potential (V)

Figure S9: I-V characteristics of both GO and ERGO samples measured with and without electrolyte (Na2SO4). Electric field induced electron transport in GO is increased in presence of electrolyte as shown in Figure S8a. As the two silver contacts were made on the same GO electrode which is highly resistive in nature, therefore there is potential barrier formed between GO and Ag which restricts the planar electron transport resulting very low current observed in the solid state I-V measurement. However, the enhancement of current in presence of electrolyte is observed due to the electrolysis of water as H2 is generated at one contact and O2 at other. Here, two potential barriers might be considered (one is Schottky barrier formed between Ag and GO and other one is between GO and electrolyte) during I-V measurements of individual GO samples in presence of electrolyte. As a result there are two segments in I-V characteristic of GO in presence of electrolyte, one current profile is observed between -0.5V S13

to +0.7V which might be due to the Schottky barrier and another profile is bellow -0.5V and greater than +0.7V. The second profile is likely to be responsible for water electrocatalysis. In case of ERGO samples (ERGO1 and ERGO2), the trend of non linearity of I-V response is minimized with the reduction time of GO (Figure S9b and Figure S9c). On the hand, ERGO3 being semi-metallic nature attributes to the linear I-V response in the solid state. Thus there is no barrier formed between Ag contact and ERGO3 yielding ballistic electron transport through the basal plane of ERGO3 in solid state I-V profile. However, in presence of electrolyte, I-V response is almost same with solid state I-V profile as the two contacts are on same ERGO plane. Moreover, in presence of electrolyte there is a chance to form slight band bending (because of the very small flat band voltage ~ +0.03V at the interface and thereby it shows the slightly non-linear I-V characteristics with little reduction of current because of semiconducting property of ERGO3 in the presence of electrolyte. Therefore, the I-V response of ERGO3 in electrochemical state shows similar response with slight non-linearity (Figure S9d)).

S14

(11) I-V characteristics of GO-ERGO3 junction without electrolyte

40

GO-ERGO3

20

Current (nA)

0 -20 40 -40

GO-ERGO2

20 0 -20 -40 40

GO-ERGO1

20 0 -20 -40 -1.0 -0.8 -0.6 -0.4 -0.2

0.0

0.2

0.4

0.6

0.8

1.0

Potential (V) Figure S10: I-V characteristics of different junctions measured without electrolyte.

S15

(12) Proposed mechanism ion current rectifying characteristics of GO-ERGO3 junction As GO is n-type and ERGO3 is p-type, at the electrolyte interface there is space charge composed of both positive and negative sides, respectively. In the absence of applied potential across the device, due the electrostatic attraction a large number of positive counter ions (H+) get adsorbed at the ERGO3 surface than the adsorption of negative ions (OH-) on GO surface (case 1 of Figure S11). This led to the formation of Helmholtz double layer (HDL) at the interface of both GO and ERGO3. As the negative space charge density of ERGO3 is higher than the positive space charge density of GO (due to more charge carriers on the p-type), the width of the HDL charge in ERGO3 is expected to be higher than GO side. Therefore we observed an upward band bending at the electrolyte interface in the GO side while in ERGO side it shows downward bending. This difference in the width of the HDL layer on both GO and ERGO3 resulted in a gradient in the charge layer at the electrolyte interface. When reverse bias is applied (case 2) to the device (i.e. positive terminal of source is connected to the n-type GO and negative terminal is connected to p-type ERGO3), the width of double layer on the both GO and ERGO3 increases because of bias dependent electrons and holes attract electrostatically more counter ions from the bulk electrolyte to the surfaces of the respective electrodes. The potential dependent variation of interfacial double layer capacitance of GO-ERGO3 junction is shown in Figure 2c. The interfacial capacitance at this potential sweep is depicted in Figure 2d which signifies that HDL acts as potential barrier for electron conduction through the basal plane of the device. Thus both upward and downward band bending in GO and ERGO side increase, respectively. Therefore no current conduction is observed in negative potential sweep from -1 to 0 V. However, during 0 to 1V potential sweep (in case 3, i.e. negative terminal of the source is connected to the n-type GO and positive terminal is connected to p-type ERGO3) causes decreasing of band bending through minimization of the space charge on both electrodes. As

S16

a result the number of surface adsorbed ions gets minimized on both sides of the planar junction. At a certain potential, the surface charge of the GO approaches to zero which is the flat band potential of it. However, at the same potential on the ERGO3 side, there will be slight excess negative charges (OH-) which might lead to the subsistence of HDL layer. We believe this might be the reason for the observed higher interfacial capacitance upto 0.25 V. Above 0.25 V (case 4), there is accumulation of bias dependent negative charges on the GO surface which is the inversion band bending of n-type GO and at the same time the surface charge of ERGO3 moves towards zero yielding the flat band condition of ERGO. This causes interfacial capacitance of the GO-ERGO3 junction suddenly drops at 0.25V. Capacitance curve from -1 to 0.25 V gives a slope (~0.68 µF/V.cm2) which indicates the potential dependent surface charge variation of the GO-ERGO3 device. At potential just above 0.25 V, an electrocatalytic half cell reaction in GO side starts through reduction of H+ ions and produces H2. This particular potential might be called “inversion potential” (Vinv) of this electrochemical device. Upon further increase of the bias potential (case 5), there is no double layer charge at the electrolyte interface on both sides of the junctions and a accumulation or inversion band bending of p-type ERGO is formed. Moreover, at the same time we believe another half cell reaction occurs through the oxidation of OH- ions in ERGO side and produces both H+ ions and O2 gas. Thus these H+ ions further enhance the reduction current in GO side resulting in sharp rise in the observed current and in fact we observed a huge bubble on GO side. Hence these simultaneous electrocatalytic processes in each side of the junctions yield a unidirectional ionic current flow through the device. It is observed that surface capacitance (Figure 2c) in GO-ERGO3 is much higher compared to the other devices. Since there is hardly any charge carrier difference between GO and ERGO1, therefore surface capacitance of GO-ERGO1 junction does not have any variation even at Vinv. Hence we did not observe large forward current compared to GO-ERGO3 junction.

S17

Case 1: No bias applied

Case 2: Reverse bias -2 to 0 V

Case 3: Forward bias 0 to +2 V

Case 4: At V=Vinv

Case 5: At V>Vinv

S18

Figure S11: Mechanism of charge carrier transport on the basal plane of GO-ERGO3 at the electrolyte interface. Charge layer distribution at the electrode-electrolyte interface and the proposed band diagram at electrolyte interface when, case1: there is no potential applied across the junction (depletion of space charges), case2: potential variation with positive terminal of power supply is connected with GO and negative terminal is connected with ERGO, case3: potential variation with positive terminal is connected with ERGO and negative terminal is connected with GO, case4: applied potential is just at certain potential called “Vinv”, case5: applied potential is greater than “Vinv” (accumulation of negative and positive charges separately on GO and ERGO3 surface respectively).

S19

(13) Comparative I-V characteristics with junction and without junction formed by GO and EROGO3 0.30

GO-ERGO3 not junction GO-ERGO3 junction

0.25

Current (A)

0.20 0.15 0.10 0.05 0.00 -0.05 -3

-2

-1

0

1

2

3

Potential (V) Figure S12: I-V characteristics of GO and ERGO3 which are not connected but on the same plane of the substrate.

S20

(14) Effect of pH of electrolyte the rectification and amplification of the ionic current of junction and transistor sample 0.6

4

H2SO4

2

1

0

(b)

Na2SO4

0.5

NaOH

Current (mA)

Current (mA)

Na2SO4 3

H2SO4

(a)

NaOH 0.4

0.3

0.2

0.1

Vinv(pH~2) V (pH~7) V (pH~12) inv inv 0.0

-1 -1.0

-0.5

0.0

0.5

1.0

0.0

0.2

0.4

0.6

0.8

1.0

Potential (V)

Pontential (V)

Figure S13: (a) I-V characteristics of the diode, and (b) transistor characteristics (I-V response one junction (V21) by keeping constant potential of 0.2 V applied at other junction) measured in 0.5 M H2SO4 (pH~2), Na2SO4 (pH~7), and NaOH (pH~12).

S21

(15) References [1] Bagani, K.; Ray, M. K.; Satpati, B.; Ray, N. R.; Sardar, M.; Banerjee, S. Contrasting magnetic properties of thermally and chemically reduced graphene oxide. J. Phys. Chem. C 2014, 118, 13254-13259. [2] Hummer, W. S.; Offeman, R. E. Preparation of Graphitic Oxide. J. Am. Chem. Soc. 1958, 80, 1339. [3] Cancado, L. G.; Jorio, A.; Martins Ferreira, E. H.; Stavale, F.; Achete, C. A.; Capaz, R. B.; Moutinho, M. V. O.; Lombardo, A.; Kulmala, T. S.; Ferrari, A. C. Quantifying Defects in Graphene via Raman Spectroscopy at Different Excitation Energies. Nano Lett. 2011, 11, 3190-3196. [4] Lanfredi, S.; and Rodrigues, A. C. M. Impedance spectroscopy study of the electrical conductivity and dielectric constant of polycrystalline LiNbO3. J. Appl. Phys 1999, 86, 22152219. [5] Albery, W. J.; O'Shea G. J.; Smith, A. L. Interpretation and use of Mott–Schottky plots at the semiconductor/electrolyte interface. Faraday Trans., 1996, 92, 4083-4085.

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