Determining layer number of two-dimensional flakes of transition-metaldichalcogenides by the Raman intensityfrom substrates

Xiao-Li Li, Xiao-Fen Qiao, Wen-Peng Han, Xin Zhang, Qing-Hai Tan,Tao Chen and Ping-Heng Tan

State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academyof Sciences, Beijing 100083, People’s Republic of China

E-mail: phtan@semi.ac.cn

Received 17 October 2015, revised 11 November 2015Accepted for publication 18 November 2015Published 24 February 2016

AbstractTransition-metal dichalcogenide (TMD) semiconductors have been widely studied due to theirdistinctive electronic and optical properties. The property of TMD flakes is a function of theirthickness, or layer number (N). How to determine the N of ultrathin TMD materials is of primaryimportance for fundamental study and practical applications. Raman mode intensity fromsubstrates has been used to identify the N of intrinsic and defective multilayer graphenes up toN = 100. However, such analysis is not applicable to ultrathin TMD flakes due to the lack of aunified complex refractive index (n) from monolayer to bulk TMDs. Here, we discuss the Nidentification of TMD flakes on the SiO2/Si substrate by the intensity ratio between the Si peakfrom 100 nm (or 89 nm) SiO2/Si substrates underneath TMD flakes and that from bare SiO2/Sisubstrates. We assume the real part of n of TMD flakes as that of monolayer TMD and treat theimaginary part of n as a fitting parameter to fit the experimental intensity ratio. An empirical n,˜namely, n ,eff˜ of ultrathin MoS2, WS2 and WSe2 flakes from monolayer to multilayer is obtainedfor typical laser excitations (2.54 eV, 2.34 eV or 2.09 eV). The fitted neff˜ of MoS2 has been usedto identify the N of MoS2 flakes deposited on 302 nm SiO2/Si substrate, which agrees well withthat determined from their shear and layer-breathing modes. This technique of measuring Ramanintensity from the substrate can be extended to identify the N of ultrathin 2D flakes withN-dependent n.˜ For application purposes, the intensity ratio excited by specific laser excitationshas been provided for MoS2, WS2 and WSe2 flakes and multilayer graphene flakes deposited onSi substrates covered by a 80–110 nm or 280–310 nm SiO2 layer.

S Online supplementary data available from stacks.iop.org/nano/27/145704/mmedia

Keywords: raman spectroscopy, two-dimensional materials, transition-metal dichalcogenides,layer number, refractive index, transfer matrix formalism, multiple reflection interference

(Some figures may appear in colour only in the online journal)

1. Introduction

With the advent of graphene and the exfoliation technique forpreparing atomically thin sheets [1], layered materials (LMs)have sparked wide interest around the world [2]. Among the

LMs, transition-metal dichalcogenide (TMD) 2H-MX2

(M = Mo, W; X = S, Se) semiconductors have been widelystudied due to their distinctive electronic and optical proper-ties [3–5]. They have an X-M-X covalently bonded sandwichstructure in each layer, and the layers are weakly stacked by

Nanotechnology

Nanotechnology 27 (2016) 145704 (7pp) doi:10.1088/0957-4484/27/14/145704

0957-4484/16/145704+07$33.00 © 2016 IOP Publishing Ltd Printed in the UK1

van der Waals force. Such a stacked layer structure makes itpossible to peel off different layers from bulk. The property ofTMD flakes is a function of their thickness, or layer number(denoted as N) [3, 6–10]. For example, the band gap of MoS2,WS2 and WSe2 exhibits an indirect-to-direct transition from afew-layer to a monolayer (1L) thickness, [3, 6] enabling manyapplications in electronics and optoelectronics. Thus, how todetermine the N of ultrathin TMDs materials is of primaryimportance for fundamental study and practical applications.

Several optical techniques have been developed toidentify the N of the TMD flakes, such as photoluminescence(PL) and optical contrast [5]. PL can be used to distinguish 1Lfrom multilayer (ML) because of its strong and narrow PLpeak [3]. Optical contrast is not sensitive to the flake qualityand the stacking structure of 2D flakes [11–13], and thus ithas been widely used to identify the N of graphene flakes bycomparing the experimental value with the theoretical one fordifferent N thanks to almost identical complex refractiveindex (n) from 1L graphene (1LG) to ML graphene (MLG)[13, 14]. However, quantitative analysis of the optical contrastof ultrathin TMD flakes on SiO2/Si substrate is difficultbecause there exist abundant features associated with opticaltransitions in the wavelength (λ) dependent n for TMD flakesand the n of TMD flakes itself significantly depends on N dueto the indirect-to-direct transition from ML to 1L [15, 16].

Ultra-low Raman spectroscopy has been used to reliablydetermine N for MLG, TMD flakes and 2D alloy flakes[8, 17, 18]. However, this technique requires expensiveadapters and a nonstandard equipment setup. Therefore, it isessential to look for the technique of N identification only bythe standard Raman system. Recently, Raman mode intensityfrom substrates has been used to identify N of intrinsic anddefective MLGs up to N = 100 [19]. This technique is dif-ficult to apply to TMD flakes due to the lack of unified n forTMD flakes from 1L to ML. However, the calculation ofRaman mode intensity from substrates only requires n at thewavelengths of the laser excitation and the scattered photon,and thus, in this paper, we try to extend this technique for Ndetermination of TMD flakes deposited onto the SiO2/Sisubstrate. By fitting the experimental data of the intensityratio between the Si peak from SiO2/Si substrates underneathTMD flakes and that from bare SiO2/Si substrates, weobtained empirical n,˜ namely, n ,eff˜ for ultrathin MoS2, WS2and WSe2 flakes at different laser excitation wavelengths. Thefitted neff˜ of MoS2 has been used to determine the N of MoS2flakes on Si substrate covered by 302 nm SiO2, which agreeswell with that determined from their shear and layer-breathingmodes [8].

2. Experimental details

Ultra-thin MoS2, WS2 and WSe2 flakes were mechanicallyexfoliated from bulk MoS2, WS2 and WSe2 (purchased from2d Semiconductors, Inc), and transferred onto Si substratescovered with SiO2 film with different thickness (h ,SiO2

100 nm, 89 nm or 302 nm). Raman measurements were per-formed at room temperature using a Jobin-Yvon HR800

micro-Raman system equipped with a liquid nitrogen-cooledcharge couple detector (CCD), a ×50 objective lens with anumerical aperture (NA) of ∼0.45 and a 1800 lines mm–1

grating. The excitation energies ( Le ) are 2.09 eV from aHe–Ne laser, 2.34 eV and 2.54 eV from a Kr+ laser. Plasmalines were removed from the laser beam by BragGratebandpass filters. Measurements down to 5 cm−1 are enabledby three BragGrate notch filters with optical density 3 andwith full width at half maximum (FWHM) of 8 cm−1 [8].Both BragGrate bandpass and notch filters are produced byOptiGrate Corp. The typical laser power is about 0.4 mW toavoid sample heating.

3. Results and discussion

3.1. ~neff of MoS2 flakes fitted from N-dependent Si modeintensity

We denote a N-layer TMD flake as NL-TMD, such as NL-MoS2, NL-WS2 and NL-WSe2, and thus monolayer MoS2 isdenoted as 1L-MoS2. 1–10L MoS2 flakes were pre-estimatedby the Raman measurements of the ultra-low-frequency shear(C) and layer-breathing (LB) modes, as previously done forMoS2 and MoWS2 flakes [8, 18]. Figure 1(a) shows the high-frequency Raman spectra of 1–10L MoS2 along with Si modefrom substrate which were measured by Le of 2.34 eV.Because of the different symmetry between even and odd NL-TMDs and bulk TMDs, the corresponding two Raman-activemodes E g2

1 and A g1 in bulk TMDs should be assigned as theE′ and A1¢ in odd NL-TMDs and the Eg and A g1 modes in evenNL-TMDs [5, 20], respectively. However, to see the evol-ution from 1L to NL (N > 1), hereafter the two modes forall cases are simply labeled as E g2

1 and A ,g1 as is commonlydone in the literature [5, 7, 21]. With increasing N, thepeak position difference between the E g2

1 and A g1 modes,

Δω (A-E) = Pos(A g1 )-Pos(E g21 ), increases from 17.4 cm−1 for

1L to 25 cm−1 for 10L, following the formula ofΔω (A-E) = 25.8 − 8.4/N [5]. The peak area of the E g2

1 and

A g1 modes, I(E g21 ) and I(A g1 ), increases with N up to N = 4

and then gradually decreases with N, as shown in figure 1(b),after being normalized by the peak area of the Si mode(I0(Si)) from bare substrate that is not covered by MoS2flakes. Obviously, I(E g2

1 )/I0(Si) and I(A g1 )/I0(Si) cannot beused to identify N for few-layer MoS2.

Figure 1(a) shows that the peak area of the Si mode,I2D(Si), from the substrate underneath MoS2 flakes mono-tonously decreases with increasing N. Now we focus onI2D(Si) itself. To exclude the effect of crystal orientation onthe Raman intensity, I2D(Si) is normalized by I0(Si). Themaximum of I0(Si) can be obtained by rotating the Si waferand adjusting the focus of the laser beam onto the Si substrate,then, we directly moved the laser spot to MoS2 flake tomeasure I2D(Si) to ensure a good signal-to-noise ratio ofI2D(Si)/I0(Si). Figures 1(c), (d) and (e) depict the N-depen-dent I2D(Si)/I0(Si) (squares) for NL-MoS2 flakes on SiO2/Sisubstrate (hSiO2

= 100 nm) excited by Le of 2.54 eV, 2.34 eV

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Nanotechnology 27 (2016) 145704 X-L Li et al

and 2.09 eV, clearly showing the monotonous decrease inintensity with increasing N. The laser beam to Si substrate isinitially adsorbed by the MoS2 flake and the Raman signalfrom Si substrate is adsorbed again by the MoS2 flake, similarto the case of MLGs [19, 22]. This makes I2D(Si)/I0(Si)sensitive to N of MoS2 flakes, implying its possibility of Nidentification for MoS2 flakes.

I2D(Si) can be calculated by using the multiple reflectioninterference method and transfer matrix formalism for mul-tilayered structures [19], which can be expressed in air/NL-MoS2/SiO2/Si four-layer structure as the following equation:

I

F z F z

z

Si

, , , ,

sin cos d d sin cos d d d , 1

h

i s p p j s p p

i j

2D0 0

arcsin NA

0

2

0

arcsin NA

0

2

, , , ,L R

2

Si

( ) ( )( )

( )

( ) ( )

ò ò ò ò òå å q j q j

q q q j q q q j

µ

¢ ¢

´ ¢ ¢ ¢ ¢

p p

= = ¢ ¢ ¢^ ^

where the Raman intensity is given by integrating over thesolid angle (arcsin (NA)) of microscope objective ( ,q j forthe laser beam and ,q j¢ ¢ for the Raman signal) and the

penetration depth of laser excitation into Si layer(h 2 mSi m» ). Different from the case of normal incidencewhere , , ,q j q j¢ ¢ = 0, the s-polarization (transverse electricfield, E,

perpendicular to the NL-MoS2 c-axis) and the

p-polarization (transverse magnetic field, H ,

associated toelectric field by H nE˜=

) field components are considered

separately for the oblique incidence, which are involved in thelaser excitation enhancement factor FL and Raman scatteringenhancement factor FR. FL and FR are calculated by usingtransfer matrix formalism, in which complex refractive index(n) and thickness (h) of each medium should be known inadvance. I0(Si) can be obtained by setting the thickness ofMoS2 flakes to be zero. The detailed derivation process can befound in the supplementary data stacks.iop.org/NANO/27/145704/mmedia.

I2D(Si)/I0(Si) is expected to be sensitive to N, NA of theobjective used, Le and hSiO2

, as demonstrated in the case ofMLGs [19]. A variation of 10 nm for can introduce a changeon the N-dependent I2D(Si)/I0(Si) [19], therefore, a precisedetermination of hSiO2

is very important for N identification ofNL-MoS2 flakes on SiO2/Si substrates by I2D(Si)/I0(Si). As a

Figure 1. (a) Raman spectra of NL-MoS2 with N from 1 to 10 in the range of the E ,g21 A g1 and Si modes for Le = 2.34 eV, where N is

determined by the C and LB modes of the flakes. (b) N-dependent I(E g21 )/I0(Si) and I(A g1 )/I0(Si) and the corresponding theoretical curves

calculated from n .eff˜ The experimental (Exp., squares) and theoretical (Theo., solid, dashed and dash-dotted lines) data of I2D(Si)/I0(Si)related with NL-MoS2 flakes as a function of N for the excitation energies of (c) 2.54 eV, (d) 2.34 eV and (e) 2.09 eV. hSiO2 = 100 nm. Thedashed, dash-dotted and solid lines are calculated based on the n for 1L-MoS2 and bulk MoS2 and the fitted neff˜ for NL-MoS2, respectively.

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Nanotechnology 27 (2016) 145704 X-L Li et al

simple, fast and nondestructive technique, optical contrastmeasurement can be used to determine with a typical micro-Raman confocal system [14]. It is found that an effectiveNA must be used to calculate optical contrast of multilayergraphene deposited on SiO2/Si substrates once the commonlyused 100 × objective with NA of ∼0.9 is used for the opticalmicroscope [12, 13, 19]. In this work, the 50 × objective withNA of 0.45 is used to measure I2D(Si)/I0(Si). In fact, asshown in the supplementary data stacks.iop.org/NANO/27/145704/mmedia, it is found that I2D(Si)/I0(Si) is not sensitiveto NA when NA � 0.5 and N � 10 for NL-MoS2 flakes onSiO2/Si substrates.

The unified n = n ik- for MoS2 flakes from 1L to MLis necessary to calculate N-dependent I2D(Si)/I0(Si), where nand κ are the real and imaginary parts of n,˜ respectively.However, both n and κ for MoS2 flakes are found to besensitive to N in the visible region [15, 16]. λ-dependent n of1L-MoS2 and bulk MoS2 are obtained according to theircomplex dielectric functions [15] using a formula of n .2˜ e=If we apply n of 1L-MoS2 or bulk MoS2 to all the NL-MoS2flakes, I2D(Si)/I0(Si) can be calculated for the three ,Le asshown in figures 1(c), (d) and (e) by dash-dotted and dashedlines, respectively. Either of them fits well to the experimentaldata. When Le = 2.54 eV and 2.34 eV, the experimental datalie in-between the two theoretical curves. However, when

Le = 2.09 eV excitation, the experimental data are larger thanthe two theoretical ones because they are under the near-resonant condition with the B exciton [3, 10].

In order to identify N by I2D(Si)/I0(Si), it is necessaryto adopt an empirical n,˜ namely ñeff, for MoS2 flakes, tominimize the difference between the theoretical and exper-imental data. If we do not consider the multiple reflectioninterference effect, the difference between I2D(Si) and I0(Si)results from the adsorption of the laser beam and Ramanbeam when they pass through the MoS2 flakes, which ismainly dominated by the imaginary part (κ) of n of MoS2,but not by the real part (n) of n of MoS2. Thus, we assumethe real part of ñeff, namely, neff, of MoS2 flakes as n of 1L-MoS2. Also, as an approximation, we neglect the differenceof neff˜ between the wavelengths of laser excitation andRaman beam. Finally, we can obtain the imaginary part ofñeff, namely κeff, of MoS2 flakes by fitting the experimentalI2D(Si)/I0(Si) by the theoretical ones for each excitationwavelength. We found that, indeed, the fitted κeff can makethe theoretical I2D(Si)/I0(Si) agree well with the exper-imental ones, as shown in figures 1(c), (d) and (e) by solidcurves. The fitted κeff along with neff for MoS2 flakes aresummarized in table 1 for Le of 2.54 eV, 2.34 eV and2.09 eV. In this case, if we can calculate I2D(Si)/I0(Si) based

on the fitted ñeff for MoS2 flakes and compare them with theexperimental one, N of MoS2 flakes can be determined.Based on the fitted ñeff for MoS2 flakes, we calculated I(E g2

1 )/I0(Si) and I(A g1 )/I0(Si) as a function of N for

Le = 2.34 eV, where adjustable parameters were introducedto take different efficiencies among E ,g2

1 A g1 and Si modesinto account. The results are shown by solid curves infigure 1(b). The theoretical results basically are in agreementwith the experimental ones, but there exists significant dis-crepancy for N 5.<

3.2. ñeff of NL-WS2 and NL-WSe2 flakes

Now we check the possibility of applying this technique toother TMDs, such as WS2 and WSe2. We obtain 1–8L WS2and WSe2 flakes by mechanical exfoliation from bulk crystaland N is determined by the C and LB modes based on themethod described in [18]. The C and LB modes and the E g2

1

and A g1 modes of 1–8L WS2 and WSe2 were measured by2.54 eV laser excitation at room temperature, as depicted infigures 2(a) and (b), respectively. Pos(C) and Pos(LB) of2–8L WS2 and WSe2 are summarized in figures 2(c) and (d),respectively. Besides a fan diagram [8], the N-dependentPos(C) and Pos(LB) can also exhibit a sin diagram [23],which can be written as follows:

j

Nj

N

C 2 C sin2

,

LB 2 LB sin2

,2

N N j

N N j

, 21

, 21

( ) ( )

( ) ( )( )

⎜ ⎟

⎜ ⎟

⎛⎝

⎞⎠

⎛⎝

⎞⎠

w wp

w wp

=

=

-

-

where j is an integer, j = N-1, N-2,K, 2,1. C21( )w andLB21( )w are the frequencies of the C and LB modes in 2L

flakes, respectively. The measured C modes in bulk WS2 andWSe2 are located at 26.3 and 23.9 cm−1, and then themeasured C21( )w ( LB21( )w ) of 2L-WS2 and 2L-WSe2 are18.4 (31.9) and 16.7 (27.8) cm−1, respectively. Each branchin equation (1) always decreases or increases in frequencywith increasing N. As indicated by the solid lines infigures 2(c) and (d), the branches of j = N-1 and j = N-3are observed for the C modes, and the branches of j = 1 andj = 3 are observed for the LB modes.

The E g21 and A g1 modes of 1–8L WS2 and WSe2 are

found to be insensitive to N, as addressed in previousworks [9, 24]. The E g2

1 mode of WSe2 flakes is very weakand it can be clearly revealed under cross (HV) polarizationconfiguration, as shown in figure 2(b). The frequency shiftof both the E g2

1 and A g1 modes for NL-WS2 and NL-WSe2is less than 3 cm−1, which makes it difficult for Ndetermination.

I2D(Si) from Si substrate underneath WS2 and WSe2flakes decreases with increasing N, as shown in figures 2(a)and (b), similar to the case of MoS2 flakes in figure 1(a). Thissuggests that I2D(Si)/I0(Si) can be used for N identificationof WS2 and WSe2 flakes deposited on SiO2/Si substrate.I2D(Si)/I0(Si) for NL-WS2 and NL-WSe2 flakes as a functionof N (N = 1, 2,K, 8) for hSiO2

= 89 nm were measuredfor two excitations: Le = 2.54 eV and 2.34 eV. Indeed,I2D(Si)/I0(Si) monotonously decreases with increasing N for

Table 1. The empirical ñeff(neff-i effk ) of MoS2, WS2 and WSe2 flakesto calculate I2D(Si)/I0(Si) at different .Le

MoS2 WS2 WSe2

Le (eV) 2.54 2.34 2.09 2.54 2.34 2.54 2.34neff 5.29 4.85 4.58 4.40 4.62 4.22 4.64keff 1.85 1.20 1.22 1.10 0.48 1.86 1.40

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Nanotechnology 27 (2016) 145704 X-L Li et al

WS2 and WSe2 flakes excited by the two excitations. Thecorresponding experimental data were depicted in figure 3 bytriangles and circles, respectively. Considering that the2.09 eV excitation is almost resonant with the A exciton of1L-WS2 and B exciton of 1L-WeS2, [25], the 2.09 eV laserexcitation is not used for WS2 and WeS2 flakes.

To understand the N-dependent I2D(Si)/I0(Si) of WS2and WSe2 flakes for their N determination, similar to the caseof MoS2 flakes as discussed above, we assume neff of WS2and WSe2 flakes as n of 1L-WS2 and 1L-WSe2[15], respec-tively. κeff of WS2 and WSe2 flakes have been used as afitting parameter to fit the experimental I2D(Si)/I0(Si). The

Figure 2. Raman spectra of (a) NL-WS2 and (b) NL-WSe2 in the ultra-low frequency range and in the range of the E ,g21 A g1 and Si modes for

Le = 2.54 eV. Pos(C) and Pos(LB) in (c) NL-WS2 and (d) NL-WSe2 as a function of N. j = 1, 3 and j = N-1 and N-3 correspond to theobserved branches of the sin diagram, see text.

Figure 3. The experimental (Exp., triangles and circles) and theoretical (Theo., solid lines) data of I2D(Si)/I0(Si) for the excitation energies ofLe = 2.54 eV and 2.34 eV as a function of N. (a) NL-WS2, (b) NL-WSe2. hSiO2

= 89 nm.

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Nanotechnology 27 (2016) 145704 X-L Li et al

ñeff of WS2 and WSe2 flakes for Le = 2.54 and 2.34 eV aresummarized in table 1. The calculated I2D(Si)/I0(Si) based onthe fitted ñeff are shown by solid lines in figure 3, which agreewell with the experimental values.

3.3. Identifying layer number of MoS2 flakes deposited on302 nm SiO2/Si substrate

As discussed above, the empirical ñeff of MoS2, WS2and WSe2 flakes are obtained by fitting the theoreticalI2D(Si)/I0(Si) to the experimental data excited by differentexcitation energies. Once ñeff for TMD flakes at specific Le isavailable, one can compare the theoretical I2D(Si)/I0(Si) withthe corresponding experimental data excited by the same Le todetermine N of the TMD flakes. As an example, we apply thistechnique to MoS2 flakes on Si substrate covered by 302 nmSiO2 film, where N is precisely determined by the C and LBmodes of MoS2 flakes [8] and N = 1, 3, 4, 6, 7. Based on thefitted ñeff for MoS2 flakes, the theoretical I2D(Si)/I0(Si)were calculated as a function of N for Le = 2.09, 2.34and 2.54 eV, as shown by crosses and solid lines infigures 4(a), (b) and (c), respectively. They agree well withthe experimental data, as depicted by squares in figure 4. TheN-dependent I2D(Si)/I0(Si) of TMD flakes is found to besensitive to ,Le as demonstrated in figures 1 and 3. Thus, thedetermined N of TMD flakes by an excitation energy can beconfirmed from further measurement by another excitationenergy, which leads to an accurate N determination of ultra-thin TMD flakes by the Raman intensity from substrate.

4. Conclusions

In conclusion, a technique to determine the N of TMD flakessuch as MoS2, WS2 and WSe2 deposited on SiO2/Si substratehas been proposed by measuring I2D(Si)/I0(Si), i.e. the

intensity ratio of the Si peak from SiO2/Si substrates under-neath the 2D flakes of TMDs to that from bare SiO2/Sisubstrates. The real part (neff) of the empirical ñeff of TMDflakes is assumed as that of 1L TMD. The imaginary part( effk ) of the empirical ñeff is a fitting parameter to theexperimental intensity ratio between the Si peak from SiO2/Sisubstrates underneath TMD flakes and that from bare SiO2/Sisubstrates. The empirical ñeff of MoS2, WS2 and WSe2 flakesfor Le of 2.54, 2.34 or 2.09 eV is obtained. The resulting ñeffof MoS2 flakes has been used to identify N of MoS2 flakesdeposited on 302 nm SiO2/Si substrate. This opens the pos-sibility of identifying the N of ultrathin 2D flakes with aN-dependent complex refractive index by measuring Ramanintensity from the substrate. For application purposes of Nidentification of TMD and MLG flakes for the researchcommunity, I2D(Si)/I0(Si) of TMD flakes deposited on SiO2/Si substrate is provided in the supplementary data for com-monly used excitation energies (2.34 eV and 2.54 eV) andSiO2 thicknesses (80–110 nm and 280–310 nm), along withthe corresponding data for MLG.

Acknowledgments

We acknowledge support from the National Natural ScienceFoundation of China, grants 11225421, 11434010, 11474277and 11504077.

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Figure 4. The experimental (Exp., squares) and theoretical (Theo., solid lines and crosses) data of I2D(Si)/I0(Si) related with NL-MoS2 flakesas a function of N for the excitation energies of (a) 2.09 eV, (b) 2.34 eV and (c) 2.54 eV. The solid lines are calculated based on the fittedñeff from figure 2. hSiO2

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Nanotechnology 27 (2016) 145704 X-L Li et al

Supplementary Data

Determining layer number of two dimensional flakes of

multilayer graphenes and transition-metal

dichalcogenides by the Raman intensity from substrateXiao-Li Li1, Xiao-Fen Qiao1, Wen-Peng Han1, Xin Zhang1, Qing-Hai Tan1, Tao Chen1, and

Ping-Heng Tan1

1.State Key Laboratory for Superlattices andMicrostructures, Institute of Semiconductors, Chinese Academy of

Sciences, Beijing 100083, China E-mail: phtan@semi.ac.cn

Content

1. Calculating the Si mode intensity from SiO2/Si substrates underneath TMD flakes (I2D(Si))

and that (I0(Si)) from bare SiO2/Si substrates.

2. I2D(Si)/I0(Si) for NL-TMDs deposited on SiO2/Si substrate.

3. I2D(Si)/I0(Si) for N Layer graphenes deposited on SiO2/Si substrate.

1. Calculating the Si mode intensity from SiO2/Si substrates un-

derneath TMD flakes (I2D(Si)) and that (I0(Si)) from bare SiO2/Si

substrates

Raman intensity in multilayer structure is determined by multiple reflection at the interfaces and

optical interference within the medium. We adopt the multiple reflection interference method [1–4,8]

to calculate the Raman mode intensity of a medium in the multilayer structure. When N layer (NL)

transition-metal dichalcogenide (TMD) flakes (NL-MX2) are deposited on SiO2/Si substrate, the four-

layer structure can be established, containing air(n0), NL(n1, d1), SiO2(n2, d2), Si(n3, d3), where ni

and di (i=0,1,2,3) are the complex refractive index and the thickness of each medium, respectively, as

demonstrated in Fig. S1.

In the following text, we will discuss how to calculate the Si mode intensity from SiO2/Si sub-

strates underneath TMD flakes (I2D(Si)) and that (I0(Si)) from bare SiO2/Si substrates.

1

air

NL-MX2

SiO2

Si

d1

d2

θ0 θ0

Laser I+(Si)

n~3

n~2

n~0

n~1

d3

z3

⊗S

P

.I-(Si)

Figure 1 Schematic diagrams of multiple reflection and optical interference in the multilayer structures

containing air, NL-MX2, SiO2, and Si for the incident laser and out-going Raman signals of the Si peak from

Si substrate. n0, n1 (d1), n2(d2), and n3(d3) are the complex refractive indices (thickness) of air, NL-MX2,

SiO2 and Si layers, respectively.

Similar to previous works [1–4,8], to calculate the intensity of Raman signal from the multilayer

structures, one must treat the laser excitation and Raman scattering processes separately. Raman sig-

nals from the depth z3 in the Si layer will be excited by the laser excitation power at the corresponding

depth. The multiple reflection and optical interference are also taken into account in the transition pro-

cess of Raman signal from Si layer to air. We defined FL and FR as respective enhancement factors for

laser excitation and Raman signal, similar to the notation of Yoon et al. [2,4,8]. The Raman intensity of

Si mode can be expressed by integrating over its thickness, dSi, as the following equation:

I ∝∫ dSi

0|FL(z3)FR(z3)|2dz3. (1)

The transfer matrix formalism can be used to calculate FL and FR in the multilayer structures, which

has been widely used to calculate the Raman signal and optical contrast of NL flakes on SiO2/Si sub-

strate. [3,5,6,8] Because the penetration depth of laser excitation into Si layer is far less than the actual

thickness of Si substrate (d3), the value of dSi is taken as the penetration depth of laser excitation into

Si layer in the numerical integration. In order to take the numerical aperture (N.A.) of the objective

into account, we calculate contributions from each portion of the laser beam by integrating the inci-

dent angle θ from 0 to arcsin(N.A.). The s-polarization (transverse electric field, E, perpendicular

to the c-axis) and p-polarization (transverse magnetic field, H, associated with the electric field by

2

H = nE) field components [5] are also treated for the transfer matrices. Thus, the total Raman inten-

sity of the Si mode is given by integrating over the solid angles (θ ,φ for the laser beam and θ ′,φ ′ for

the Raman signal) of the microscope objective and the depth z3 in the Si layer:

I ∝∫ dSi

0

∫ arcsin(N.A.)

0

∫ 2π

0

∫ arcsin(N.A.)

0

∫ 2π

0

∑i=s,p⊥,p∥

∑j=s′,p′⊥,p

′∥

∣∣∣F iL(z3,θ ,φ)F j

R(z3,θ ′,φ ′)∣∣∣2

sinθ cosθdθdφ sinθ ′ cosθ ′dθ ′dφ ′dz3,

(2)

We use the transfer matrix formalism calculate FL and FR in Eq. (2). The transmission and reflec-

tion of total electric and magnetic fields in the four-layer structure can be described by characteristic

matrices Ai j and B(z j), where Ai j describes the propagation across the interface from i to j layer

applying the boundary conditions, and B(z j) denotes the propagation through the j layer at depth z j.

The s-polarization and p-polarization field components are treated separately in analyzing the

characteristic matrices. As(p)i j can be expressed as follows:

As(p)i j =

1

ts(p)i j

1 rs(p)i j

rs(p)i j 1

(3)

where ts(p)i j and rs(p)

i j are transmission and reflection coefficients from i to j layer for s-polarization

and p-polarization, which depend on the complex refractive index ni, n j and the refractive angle θi,θ j.

The complex refractive index in the dielectric layer i is denoted by ni(λ ) = ni(λ )− iki(λ ), which is

dependent on λ . Similar to previous works, [8] we consider only the in-plane complex refractive

index of NL-MX2 flakes, and thus the s- and p-components of laser excitation can share the same

expression. The refracted angle θi in the dielectric layer i is calculated with the Snell law as follows:

tsi j =

2ni cosθini cosθi+n j cosθ j

, rsi j =

ni cosθi−n j cosθ jni cosθi+n j cosθ j

, t pi j =

2ni cosθin j cosθi+ni cosθ j

, rpi j =

n j cosθi−ni cosθ jn j cosθi+ni cosθ j

.

B(z j) can be expressed as follows:

B(z j) =

eiδ (z j) 0

0 e−iδ (z j)

(4)

where δ (z j) = 2π n jz j cosθ j/λ is phase factor, which is determined by the propagation distance z j of

laser or Raman scattering lights in j layer. The differences between the wavelengths of the laser and Si

Raman peak should be considered in ts(p)i j , rs(p)

i j and δ (z j) due to the λ -dependent complex refractive

index for each layer. Finally, the complete transfer matrix for the whole multilayer structures can be

obtained by multiplication of above simple matrices.

3

In the calculation of I2D(Si), the laser approaches at the Si layer and is absorbed finally, and thus

there is no laser components transmitting toward the surface at any depths in the Si layer, as illustrated

in Fig. S1. The transfer equation for the laser beam transmitting from air to the depth z3 in the Si

layer is expressed as follows:

Es(p),+L0

Es(p),−L0

= As(p)01 B(d1)A

s(p)12 B(d2)A

s(p)23 B(z3)

Es(p),+LS (z3)

0

(5)

where the symbols +,− denote light propagating directions from air to the dielectric layers and the

opposite direction. Es(p),+L0 is the electric field component of laser source in air, which is assumed

as 1. Es(p),+LS (z3) is the electric field component at the depth z3 in Si layer. The laser excitation en-

hancement factors in this process can be calculated by FsL(z3) = Es,+

LS (z3), F p⊥L (z3) = E p,+

LS (z3)cosθ3

and F p∥L (z3) = E p,+

LS (z3)sinθ3. Es(p),+LS (z3) can be calculated with the transfer equation Eq. (5) and

Fs(p⊥,p∥)L (z3) can be obtained.

For the Raman scattering process of the Si mode, only one pathway for the emission of Raman

signal toward (up,U) the NL-MX2 surface is considered, and that away from (down,D) the NL-MX2

surface is absorbed by the Si layer, as illustrated in Fig. S1. The transfer equation for the Raman

signal excited by the laser at the depth z3 in the Si layer is expressed as follows:

0

Es′(p′),−RU0

= As′(p′)01 B(d1)A

s′(p′)12 B(d2)A

s′(p′)23 B(z3)

Es′(p′),+RUS

(z3)

Es′(p′),−RUS

(z3)

(6)

where Es′(p′),−RUS

(z3) is the electric field component of Raman signal source related with ’U’ pathway

at the depth z3 in the Si layer and is assumed as 1.

The Raman scattering enhancement factors in this process can be calculated by Fs′R (z3) = Es′,−

RU0,

Fp′⊥

R (z3) = E p′,−RU0

cosθ ′3 and F

p′∥R (z3) = E p′,−

RU0sinθ ′

3. Es′(p′),−RU0

can be calculated by the transfer equation

Eq. (6) and Fs′(p′⊥,p

′∥)

R (z3) can be obtained.

The total Raman intensity of I2D(Si) from SiO2/Si substrates underneath TMD flakes can be

calculated by the formula of Eq. (2).

I0(Si) from bare SiO2/Si substrates can be calculated directly based on the above model once the

thickness of NL flakes is set to zero.

4

2. I2D(Si)/I0(Si) for NL-TMDs deposited on SiO2/Si substrate

As demonstrated in the main text, the calculated I2D(Si)/I0(Si) of NL-TMDs based on the ne f f

for different εL can be used for N determination of NL-TMDs flakes deposited on SiO2/Si substrates.

I2D(Si)/I0(Si) is expected to be sensitive to N, N.A., εL and hSiO2 . [8] It is evident that a variation

of 10 nm for hSiO2 can introduce a change on the N-dependent I2D(Si)/I0(Si), therefore, a precise

determination of hSiO2 is very important for N identification of NL-TMDs flakes on SiO2/Si substrates

by I2D(Si)/I0(Si).

It is found that an effective N.A. must be used for optical contrast calculation of multilayer

graphene deposited on SiO2/Si substrates once the 100× objective with N.A. of ∼ 0.9 is used for

optical microscope. [5,6] If one uses an objective with N.A. less than 0.5 for the measurement of Ra-

man spectra and optical contrast, the actual N.A. can be used for the theoretical calculation of Raman

intensity and optical contrast for N identification of two-dimensional flakes. [6,8] For the sake of N

identification of TMD flakes for research community, I2D(Si)/I0(Si) of NL-MoS2, NL-WS2 and NL-

WeS2 excited by commonly-used 2.54-eV and 2.34-eV excitations for 80nm< hSiO2 <110nm and

280nm< hSiO2 <310nm are calculated for the objective N.A. of 0.35 (Olympus SLMPLN 50× ob-

jective with a long-working distance of 18mm) or of 0.50 (Olympus LMPLFLN 50× objective with

a long-working distance of 10.6mm). The results are summarized in Table 1-6.

For an approximation, I2D(Si)/I0(Si) for any hSiO2 in the range of 80-110nm or 280-310nm can be

obtained by the interpolation between the two values corresponding to two nearest hSiO2.

3. I2D(Si)/I0(Si) for N Layer graphenes deposited on SiO2/Si sub-

strate

I2D(Si)/I0(Si) has been used to identify N of intrinsic and defective multilayer graphenes up to

N =100. [8] For a purpose of practise application, the calculation values of I2D(Si)/I0(Si) are provided

here for several typical hSiO2 (80-110nm or 280-310nm), commonly-used εL (2.34 and 1.96 eV) and

the objective N.A. (0.35 and 0.50), as summarized in Table 7 and Table 8.

For an approximation, I2D(Si)/I0(Si) for any hSiO2 in the range of 80-110nm or 280-310nm can be

obtained by the interpolation between the two values corresponding to two nearest hSiO2.

5

Table1

I2D (Si)/I0 (Si)ofNL

-MoS

2flakes

depositedon

SiO2 /Sisubstrate

asa

functionofN

forhSiO

2 =80nm,90nm

,100nm,110nm

,and280nm

,290nm,

300nm,310nm

.εL =2.54

eVand

N.A

.=0.35and

0.50.nofN

L-M

oS2 ,SiO

2and

Siare5.29-1.85i,1.462,4.360-0.086i.

hSiO

280nm

90nm100nm

110nm280nm

290nm300nm

310nm

NA

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

1L0.686

0.6930.644

0.6490.624

0.6260.627

0.6250.627

0.6270.645

0.6360.679

0.6610.723

0.699

2L0.466

0.4740.420

0.4250.402

0.4040.409

0.4070.408

0.4070.433

0.4210.477

0.4540.537

0.505

3L0.318

0.3250.281

0.2850.268

0.2690.277

0.2750.276

0.2730.301

0.2890.346

0.3230.409

0.375

4L0.220

0.2260.192

0.1950.185

0.1850.194

0.1920.193

0.1900.216

0.2050.257

0.2360.318

0.285

5L0.156

0.1600.135

0.1370.131

0.1310.140

0.1380.139

0.1350.160

0.1490.196

0.1770.252

0.222

6L0.112

0.1160.097

0.0990.095

0.0950.104

0.1020.103

0.0990.121

0.1120.153

0.1360.203

0.175

7L0.083

0.0850.072

0.0730.071

0.0710.079

0.0770.078

0.0750.093

0.0850.121

0.1060.166

0.141

8L0.062

0.0640.054

0.0550.054

0.0540.061

0.0600.060

0.0570.073

0.0670.098

0.0850.137

0.116

9L0.048

0.0490.042

0.0430.042

0.0420.048

0.0470.047

0.0450.059

0.0530.080

0.0690.115

0.096

10L0.037

0.0380.033

0.0330.033

0.0330.039

0.0380.038

0.0360.048

0.0430.066

0.0570.098

0.081

6

Tabl

e2

I 2D

(Si)

/I0(

Si)o

fNL

-MoS

2fla

kes

depo

site

don

SiO

2/Si

subs

trat

eas

afu

nctio

nof

Nfo

rhSi

O2=

80nm

,90n

m,1

00nm

,110

nm,a

nd28

0nm

,290

nm,

300n

m,3

10nm

.εL=2

.34

eVan

dN

.A.=

0.35

and

0.50

.nof

NL

-MoS

2,Si

O2

and

Siar

e4.

85-1

.20i

,1.4

60,4

.143

-0.0

54i.

h SiO

280

nm90

nm10

0nm

110n

m28

0nm

290n

m30

0nm

310n

m

NA

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

1L0.

855

0.86

20.

806

0.81

30.

770

0.77

50.

748

0.75

10.

796

0.81

70.

764

0.77

90.

746

0.75

50.

745

0.74

6

2L0.

708

0.71

90.

637

0.64

60.

587

0.59

30.

561

0.56

40.

622

0.65

20.

580

0.60

00.

560

0.57

00.

561

0.56

0

3L0.

574

0.58

70.

497

0.50

70.

447

0.45

30.

423

0.42

60.

482

0.51

40.

440

0.46

10.

423

0.43

20.

428

0.42

6

4L0.

459

0.47

20.

386

0.39

50.

342

0.34

80.

323

0.32

50.

373

0.40

30.

337

0.35

40.

324

0.33

00.

331

0.32

7

5L0.

365

0.37

70.

300

0.30

80.

263

0.26

80.

249

0.25

10.

290

0.31

50.

260

0.27

40.

250

0.25

50.

259

0.25

5

6L0.

290

0.30

00.

235

0.24

10.

205

0.20

90.

194

0.19

60.

226

0.24

80.

202

0.21

40.

196

0.20

00.

206

0.20

1

7L0.

230

0.23

90.

185

0.19

00.

161

0.16

40.

154

0.15

50.

178

0.19

60.

159

0.16

80.

156

0.15

80.

165

0.16

1

8L0.

184

0.19

10.

147

0.15

10.

128

0.13

00.

123

0.12

40.

141

0.15

60.

127

0.13

40.

125

0.12

60.

134

0.13

0

9L0.

148

0.15

40.

117

0.12

10.

103

0.10

50.

100

0.10

00.

113

0.12

50.

102

0.10

80.

102

0.10

20.

111

0.10

6

10L

0.12

00.

125

0.09

50.

098

0.08

30.

085

0.08

20.

082

0.09

20.

101

0.08

30.

088

0.08

30.

084

0.09

20.

088

7

Table3

I2D (Si)/I0 (Si)ofNL

-WS

2flakes

depositedon

SiO2 /Sisubstrate

asa

functionofN

forhSiO

2 =80nm,90nm

,100nm,110nm

,and280nm

,290nm,

300nm,310nm

.εL =2.54

eVand

N.A

.=0.35and

0.50.nofN

L-W

S2 ,SiO

2and

Siare4.40-1.10i,1.462,4.360-0.086i.

hSiO

280nm

90nm100nm

110nm280nm

290nm300nm

310nm

NA

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

1L0.833

0.8390.791

0.7960.766

0.7690.760

0.7600.762

0.7660.769

0.7650.790

0.7790.820

0.804

2L0.679

0.6890.620

0.6270.589

0.5920.583

0.5830.585

0.5890.598

0.5910.631

0.6140.680

0.654

3L0.547

0.5580.485

0.4920.455

0.4580.453

0.4520.453

0.4560.471

0.4620.511

0.4900.569

0.538

4L0.438

0.4480.380

0.3860.354

0.3570.355

0.3540.355

0.3570.376

0.3660.418

0.3960.480

0.447

5L0.349

0.3590.299

0.3050.278

0.2800.282

0.2800.282

0.2820.303

0.2930.345

0.3240.409

0.375

6L0.279

0.2880.237

0.2420.221

0.2230.227

0.2250.226

0.2250.247

0.2370.288

0.2670.351

0.318

7L0.224

0.2320.189

0.1940.178

0.1790.184

0.1820.183

0.1820.204

0.1940.243

0.2230.304

0.271

8L0.181

0.1880.153

0.1560.144

0.1450.151

0.1490.150

0.1480.170

0.1600.207

0.1880.265

0.234

9L0.148

0.1530.124

0.1270.118

0.1190.125

0.1240.124

0.1220.143

0.1340.178

0.1600.233

0.203

10L0.121

0.1250.102

0.1040.098

0.0980.105

0.1040.104

0.1020.122

0.1130.154

0.1370.206

0.178

8

Tabl

e4

I 2D

(Si)

/I0(

Si)o

fNL

-WS 2

flake

sde

posi

ted

onSi

O2/

Sisu

bstr

ate

asa

func

tion

ofN

forh

SiO

2=80

nm,9

0nm

,100

nm,1

10nm

,and

280n

m,2

90nm

,

300n

m,3

10nm

.εL=2

.34

eVan

dN

.A.=

0.35

and

0.50

.nof

NL

-WS 2

,SiO

2an

dSi

are

4.62

-0.4

8i,1

.460

,4.1

43-0

.054

i.

h SiO

280

nm90

nm10

0nm

110n

m28

0nm

290n

m30

0nm

310n

m

NA

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

1L0.

970

0.97

70.

920

0.92

70.

875

0.88

20.

844

0.84

80.

907

0.93

00.

866

0.88

60.

839

0.85

30.

826

0.83

3

2L0.

908

0.92

20.

819

0.83

10.

747

0.75

70.

701

0.70

70.

798

0.83

70.

734

0.76

50.

695

0.71

50.

679

0.68

8

3L0.

824

0.84

20.

710

0.72

50.

626

0.63

80.

576

0.58

30.

686

0.73

40.

612

0.64

70.

571

0.59

20.

557

0.56

5

4L0.

728

0.74

80.

603

0.61

90.

519

0.53

00.

471

0.47

80.

578

0.62

90.

505

0.54

00.

467

0.48

70.

458

0.46

3

5L0.

629

0.65

00.

505

0.52

10.

426

0.43

70.

385

0.39

10.

482

0.53

20.

415

0.44

70.

382

0.39

90.

377

0.38

0

6L0.

535

0.55

50.

419

0.43

30.

349

0.35

90.

315

0.32

00.

399

0.44

40.

340

0.36

80.

313

0.32

70.

312

0.31

3

7L0.

450

0.46

80.

346

0.35

90.

286

0.29

40.

259

0.26

30.

328

0.36

90.

279

0.30

30.

258

0.26

90.

259

0.25

9

8L0.

376

0.39

20.

285

0.29

60.

235

0.24

20.

213

0.21

70.

271

0.30

60.

229

0.24

90.

214

0.22

20.

217

0.21

6

9L0.

313

0.32

70.

235

0.24

50.

194

0.20

00.

177

0.18

00.

223

0.25

30.

190

0.20

60.

178

0.18

40.

183

0.18

1

10L

0.26

00.

273

0.19

50.

203

0.16

10.

166

0.14

80.

150

0.18

50.

210

0.15

80.

171

0.14

90.

154

0.15

50.

153

9

Table5

I2D (Si)/I0 (Si)ofNL

-WeS

2flakes

depositedon

SiO2 /Sisubstrate

asa

functionofN

forhSiO

2 =80nm,90nm

,100nm,110nm

,and280nm

,290nm,

300nm,310nm

.εL =2.54

eVand

N.A

.=0.35and

0.50.nofN

L-W

eS2 ,SiO

2and

Siare4.22-1.86i,1.462,4.360-0.086i.

hSiO

280nm

90nm100nm

110nm280nm

290nm300nm

310nm

NA

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

1L0.728

0.7330.700

0.7030.690

0.6900.698

0.6950.697

0.6940.717

0.7070.748

0.7320.786

0.766

2L0.533

0.5390.498

0.5020.489

0.4890.501

0.4980.499

0.4950.528

0.5130.572

0.5490.628

0.598

3L0.394

0.4000.362

0.3650.354

0.3550.369

0.3650.367

0.3620.398

0.3820.446

0.4210.510

0.476

4L0.295

0.3000.268

0.2710.263

0.2630.278

0.2750.276

0.2700.306

0.2910.354

0.3290.419

0.384

5L0.223

0.2280.202

0.2040.199

0.1990.214

0.2100.211

0.2060.240

0.2260.285

0.2620.349

0.315

6L0.172

0.1760.155

0.1570.154

0.1530.167

0.1640.165

0.1600.191

0.1780.233

0.2110.294

0.261

7L0.134

0.1370.120

0.1220.121

0.1200.133

0.1300.131

0.1260.154

0.1430.193

0.1730.250

0.219

8L0.106

0.1090.095

0.0960.096

0.0960.107

0.1050.105

0.1010.126

0.1160.162

0.1430.215

0.186

9L0.085

0.0870.076

0.0770.078

0.0770.088

0.0860.086

0.0820.105

0.0960.137

0.1200.186

0.159

10L0.068

0.0700.062

0.0630.063

0.0630.073

0.0710.071

0.0680.088

0.0800.117

0.1020.162

0.138

10

Tabl

e6

I 2D

(Si)

/I0(

Si)o

fNL

-WeS

2fla

kes

depo

site

don

SiO

2/Si

subs

trat

eas

afu

nctio

nof

Nfo

rhSi

O2=

80nm

,90n

m,1

00nm

,110

nm,a

nd28

0nm

,290

nm,

300n

m,3

10nm

.εL=2

.34

eVan

dN

.A.=

0.35

and

0.50

.nof

NL

-WeS

2,Si

O2

and

Siar

e4.

64-1

.40i

,1.4

60,4

.143

-0.0

54i.

h SiO

280

nm90

nm10

0nm

110n

m28

0nm

290n

m30

0nm

310n

m

NA

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

1L0.

822

0.82

90.

778

0.78

40.

746

0.75

00.

729

0.73

00.

769

0.78

80.

741

0.75

40.

728

0.73

50.

731

0.72

9

2L0.

660

0.67

00.

598

0.60

60.

556

0.56

10.

536

0.53

80.

586

0.61

20.

550

0.56

70.

537

0.54

40.

543

0.54

0

3L0.

523

0.53

40.

457

0.46

60.

417

0.42

20.

400

0.40

10.

446

0.47

20.

412

0.42

80.

401

0.40

70.

410

0.40

6

4L0.

412

0.42

20.

351

0.35

80.

315

0.32

00.

302

0.30

40.

341

0.36

50.

312

0.32

60.

304

0.30

80.

315

0.31

0

5L0.

323

0.33

30.

270

0.27

70.

241

0.24

50.

232

0.23

30.

262

0.28

30.

239

0.25

00.

234

0.23

70.

246

0.24

0

6L0.

255

0.26

30.

210

0.21

60.

187

0.19

00.

181

0.18

10.

204

0.22

10.

185

0.19

40.

183

0.18

50.

195

0.18

9

7L0.

202

0.20

90.

165

0.17

00.

147

0.14

90.

143

0.14

30.

160

0.17

40.

146

0.15

30.

145

0.14

60.

156

0.15

1

8L0.

161

0.16

70.

131

0.13

50.

116

0.11

80.

114

0.11

40.

127

0.13

90.

116

0.12

20.

116

0.11

70.

127

0.12

2

9L0.

129

0.13

40.

105

0.10

80.

094

0.09

50.

092

0.09

20.

102

0.11

10.

093

0.09

80.

095

0.09

40.

105

0.10

0

10L

0.10

50.

109

0.08

50.

088

0.07

60.

077

0.07

60.

076

0.08

20.

090

0.07

60.

080

0.07

80.

077

0.08

70.

082

11

Table7

I2D (Si)/I0 (Si)ofNL

Gflakes

depositedon

SiO2 /Sisubstrate

asa

functionofN

forhSiO

2 =80nm,90nm

,100nm,110nm

,and280nm

,290nm,300nm

,

310nm.ε

L =2.34eV

andN

.A.=0.35

and0.50.n

ofNL

G,SiO

2and

Siare2.725-1.366i,1.460,4.143-0.054i.

hSiO

280nm

90nm100nm

110nm280nm

290nm300nm

310nm

NA

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

0.350.5

1L0.938

0.9390.929

0.9300.924

0.9240.923

0.9230.927

0.9310.924

0.9260.924

0.9240.928

0.926

2L0.879

0.8820.863

0.8660.854

0.8560.853

0.8530.861

0.8680.854

0.8580.855

0.8550.863

0.859

3L0.824

0.8280.803

0.8060.791

0.7930.790

0.7900.800

0.8090.791

0.7960.792

0.7920.803

0.798

4L0.773

0.7780.748

0.7510.733

0.7350.732

0.7320.744

0.7550.733

0.7390.735

0.7350.749

0.742

5L0.726

0.7310.696

0.7010.681

0.6830.680

0.6790.692

0.7040.680

0.6870.683

0.6820.699

0.691

6L0.681

0.6870.649

0.6540.632

0.6350.632

0.6310.644

0.6580.632

0.6390.636

0.6350.653

0.645

7L0.639

0.6460.606

0.6110.588

0.5910.588

0.5880.601

0.6150.588

0.5950.592

0.5910.611

0.602

8L0.600

0.6070.565

0.5710.548

0.5510.548

0.5480.561

0.5750.548

0.5550.553

0.5510.573

0.563

9L0.564

0.5710.528

0.5340.511

0.5130.511

0.5110.523

0.5390.511

0.5180.516

0.5150.538

0.527

10L0.530

0.5380.494

0.5000.477

0.4790.478

0.4770.489

0.5040.477

0.4840.483

0.4810.505

0.494

11L0.499

0.5060.463

0.4680.445

0.4480.447

0.4460.458

0.4730.446

0.4530.452

0.4500.475

0.464

12L0.469

0.4770.433

0.4390.417

0.4190.418

0.4180.429

0.4440.417

0.4240.424

0.4220.447

0.436

13L0.442

0.4490.406

0.4120.390

0.3930.392

0.3920.402

0.4170.391

0.3970.398

0.3950.421

0.410

14L0.416

0.4230.381

0.3860.366

0.3680.368

0.3680.377

0.3910.367

0.3730.374

0.3710.398

0.386

15L0.392

0.3990.358

0.3630.343

0.3450.346

0.3460.354

0.3680.344

0.3500.352

0.3490.376

0.364

12

Tabl

e8

I 2D

(Si)

/I0(

Si)o

fNL

Gfla

kes

depo

site

don

SiO

2/Si

subs

trat

eas

afu

nctio

nof

Nfo

rhSi

O2=8

0nm

,90n

m,1

00nm

,110

nm,a

nd28

0nm

,290

nm,3

00nm

,

310n

m.ε

L=1

.96

eVan

dN

.A.=

0.35

and

0.50

.nof

NL

G,S

iO2

and

Siar

e2.

819-

1.45

0i,1

.457

,3.8

79-0

.021

i.

h SiO

280

nm90

nm10

0nm

110n

m28

0nm

290n

m30

0nm

310n

m

NA

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

0.35

0.5

1L0.

955

0.95

70.

948

0.94

90.

940

0.94

20.

935

0.93

60.

972

0.97

50.

966

0.96

90.

959

0.96

30.

951

0.95

5

2L0.

913

0.91

50.

898

0.90

00.

885

0.88

70.

874

0.87

60.

945

0.95

00.

933

0.93

90.

919

0.92

60.

904

0.91

2

3L0.

872

0.87

50.

851

0.85

40.

832

0.83

60.

818

0.82

10.

918

0.92

50.

901

0.91

00.

881

0.89

10.

860

0.87

1

4L0.

832

0.83

60.

806

0.81

10.

783

0.78

80.

766

0.77

00.

892

0.90

10.

869

0.88

10.

844

0.85

70.

818

0.83

2

5L0.

794

0.79

90.

764

0.76

90.

738

0.74

20.

718

0.72

20.

866

0.87

70.

838

0.85

20.

808

0.82

40.

777

0.79

4

6L0.

758

0.76

40.

724

0.73

00.

695

0.70

00.

674

0.67

80.

840

0.85

30.

808

0.82

40.

773

0.79

20.

739

0.75

8

7L0.

723

0.73

00.

686

0.69

20.

655

0.66

10.

632

0.63

70.

815

0.83

00.

779

0.79

70.

740

0.76

10.

702

0.72

3

8L0.

690

0.69

70.

650

0.65

70.

617

0.62

30.

594

0.59

80.

790

0.80

70.

751

0.77

10.

709

0.73

10.

668

0.69

0

9L0.

658

0.66

60.

617

0.62

40.

582

0.58

90.

558

0.56

30.

766

0.78

40.

723

0.74

50.

678

0.70

20.

635

0.65

8

10L

0.62

80.

636

0.58

50.

592

0.55

00.

556

0.52

50.

530

0.74

30.

762

0.69

70.

720

0.64

90.

674

0.60

40.

628

11L

0.59

90.

607

0.55

50.

562

0.51

90.

525

0.49

40.

499

0.72

00.

740

0.67

10.

696

0.62

10.

647

0.57

40.

600

12L

0.57

20.

580

0.52

60.

534

0.49

00.

497

0.46

60.

470

0.69

70.

719

0.64

60.

672

0.59

40.

621

0.54

60.

572

13L

0.54

60.

554

0.50

00.

507

0.46

30.

470

0.43

90.

444

0.67

50.

698

0.62

20.

649

0.56

90.

596

0.52

00.

546

14L

0.52

10.

529

0.47

40.

482

0.43

80.

445

0.41

40.

419

0.65

40.

678

0.59

90.

626

0.54

40.

573

0.49

50.

521

15L

0.49

70.

506

0.45

00.

458

0.41

40.

421

0.39

10.

395

0.63

30.

658

0.57

60.

605

0.52

10.

550

0.47

10.

498

13

References

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14