Antireflection properties of graphene layers on planar and textured silicon surfaces

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Nanotechnology 24 (2013) 165402 (8pp) doi:10.1088/0957-4484/24/16/165402

Antireflection properties of graphenelayers on planar and textured siliconsurfacesRakesh Kumar1, A K Sharma1, Mehar Bhatnagar1, B R Mehta1 andShyama Rath2

1 Thin Film Laboratory, Department of Physics, Indian Institute of Technology Delhi, Hauz Khas,New Delhi 110016, India2 Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India

E-mail: brmehta@physics.iitd.ernet.in

Received 29 December 2012, in final form 20 February 2013Published 27 March 2013Online at stacks.iop.org/Nano/24/165402

AbstractIn this study, theoretical and experimental investigations have been carried out to explore thesuitability of graphene layers as an antireflection coating. Microwave plasma enhancedchemical vapor deposition and chemically grown graphene layers deposited on polished andtextured silicon surfaces show that graphene deposition results in a large decrease inreflectance in the wavelength range of 300–650 nm, especially in the case of polished silicon.A Si3N4/textured silicon reference antireflection coating and graphene deposited polished andtextured silicon exhibit similar reflectance values, with the graphene/Si surface showing lowerreflectance in the 300–400 nm range. Comparison of experimental results with the finitedifference time domain calculations shows that the graphene along with a SiO2 surface layerresults in a decrease in reflectance in the 300–650 nm range, with a reflectance value of <5%for the case of graphene deposited textured silicon surfaces. The monolayer and inert characteralong with the high transmittance of graphene make it an ideal surface layer. The results of thepresent study show its suitability as an antireflection coating in solar cell and UV detectorapplications.

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

1. Introduction

Graphene with its two-dimensional honeycomb lattice oftightly packed carbon atoms has attracted phenomenalinterest due to its new physics and unique electronic,electrical, mechanical and optical properties. The mobilityof charge carriers in suspended graphene samples goes upto 200 000 cm2 V−1 s−1 for carrier densities below 5 ×109 cm−2 at temperatures near absolute zero [1, 2]. Theexperimentally measured values of thermal conductivity (atroom temperature) and the thermoelectric power of grapheneare 3000–5000 W mK−1 [3] and 50–100 µV K−1 [4, 5],respectively. Recent experiments have established grapheneas the strongest material with second-, third-order elasticstiffness and intrinsic strength for monolayer graphene of

340 ± 50 N m−1,−690 ± 120 N m−1 and 42 ± 4 N m−1,respectively, corresponding to a Young’s modulus of 1.0± 0.1TPa [6]. Startlingly low absorption with high transmittanceof 96–98% in the UV–visible region has been estimatedfor monolayer graphene [7, 8]. High electron mobility andhigh optical transmittance make it inherently attractive asa transparent electrode in optoelectronic devices and ithas been used or proposed in a number of optical andelectronic devices. A graphene–Si Schottky junction [9] hasshown a photovoltaic conversion efficiency of 8.6% [10].Graphene layers have also been used to modify the interfaceproperties of a Ti–CuO–Cu junction where the introductionof multilayer graphene (MLG) in between CuO–Cu leadsto the observation of bipolar resistive switching [11]. Dueto its remarkable optoelectronic properties, a number of

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Nanotechnology 24 (2013) 165402 R Kumar et al

reviews have highlighted that graphene is likely to benefitphotovoltaics devices as a near transparent electrode andantireflection coating [12–17]. This study is a first attemptto examine the suitability of few-layer graphene as anantireflection coating on polished and textured silicon, whichare commonly used in solar cell structures.

An antireflection coating (ARC) is an integral part ofoptoelectronic device fabrication technology. For a fixedwavelength, the phase relationship condition requires theoptical thickness of the layer (the refractive index multipliedby the physical thickness) to be equal to a quarter thewavelength of the incoming wave and the refractive indexto be the geometric mean of the refractive index of thesemiconductor and air. For photovoltaic applications, thereflectance is minimized for a wavelength of 0.6 µm whichis close to the maximum power point of the solar spectrum.By increasing the number of layers of different refractiveindex and thickness, the reflectance can be decreased overa wider spectral range. In silicon solar cell technology,texturing of the silicon surface using chemical etchants andsubsequent coating of silicon nitride (Si3N4) is commonlyused to reduce the reflection losses from 40–58% for polishedSi to 5–15% [18]. The monolayer character of a graphenelayer makes it an ideal surface layer which can adhere wellto a planar, textured or corrugated surface.

We report the antireflection properties of graphene filmson polished surface (PS) and chemically textured surface(TS) commonly used in Si solar cell technology. Graphenelayers formed by microwave plasma enhanced chemical vapordeposition (MPCVD) and chemical methods (chemicallyprepared graphene, RGO) are dispersed on silicon surfacesand reflectance was measured in the wavelength range300–650 nm. The experimental results are compared withthose for a standard Si3N4 ARC used in silicon solar celltechnology. The optical properties of graphene layers havingdifferent configurations on silicon surfaces were studied usingthe finite difference time domain (FDTD) simulation [19]. Themeasured reflectance for both types of graphene depositedsubstrates was compared with simulated results.

2. Experimental details

Two types of graphene layers (i) prepared using the MPCVDtechnique (designated as ‘G1’) and (ii) prepared using achemical route (RGO) procured from ACS Materials USA(designated as ‘G2’) were used in this study.

The graphene films were grown on 25 µm thick Cu foil(99.98%, Sigma Aldrich, item no. 349208) using the MPCVDtechnique with CH4, H2 and Ar as the precursor forminggases. Before deposition, Cu foil was cleaned in acetic acidfollowed by de-ionized water and isopropyl alcohol to removethe copper oxide present at the surface. Keeping the copperfoil substrate at a temperature of about 750 ◦C, a plasma wascreated by using H2 (400 sccm) and Ar (30 sccm) at a gaspressure of 30 Torr with a microwave (2.45 GHz) power of1.5 kW. After annealing the Cu foil for about 20 min, CH4(10 sccm) was introduced and a graphene layer was depositedfor 5 min. The substrate was allowed to cool down naturally.

Flow of all the gases was stopped as the temperature reachedclose to room temperature.

To study the deposition and optical properties of graphenedeposition of Si, the graphene from the Cu foil was transferredonto a Si substrate. The transfer process involved severalsteps [20]. In the first step, polymethylmethacrylate (PMMA)(Sigma Aldrich, average MW ∼ 996 000, item no. 182265,6 wt% in anisole) was spin coated on one side of the Cufoil. The other side of the Cu foil was exposed to O2 plasmato remove graphene from that side since graphene growth isknown to take place on both sides of Cu foil. In a secondstep, Cu foil was etched out using FeCl3 (10%, wt/vol.) for3–4 h and subsequently PMMA/graphene film was cleanedseveral times in a bath of de-ionized water and carefullytransferred to a quartz and silicon substrate. Thereafter, thesample was allowed to dry for 12 h and then PMMA wasremoved using acetone for 5 h at a temperature of 50 ◦C. Thesample was further treated for 5 h in a H2 (200 sccm) and Ar(30 sccm) environment at a temperature of 450 ◦C to removethe remaining traces of PMMA [20, 21].

Chemically prepared graphene films (containing ∼92%carbon, <8% oxygen) produced via thermal exfoliationreduction and hydrogen reduction of single-layer grapheneoxide was obtained from ACS Material USA and wasalso used for studying the deposition and optical propertiesof graphene deposition on Si substrate. The 2 mg ofas-obtained graphene powder was dispersed in 5 ml ofN,N-dimethylformamide (DMF) organic solvent, whichexhibited long-term dispersion stability, using ultra-sonicationand further spin coated on the desired substrate [22].

Raman spectroscopic measurements were carried outin backscattering geometry using the 514.5 nm line of theAr+ laser for excitation. The scattered light was analyzedwith a Renishaw spectrometer and a charged couple devicewas employed for detection. A Quanta 3D FEI fieldemission scanning electron microscope (FESEM) was usedto ascertain the morphology of the graphene films. Atomicforce microscopy (AFM) was done in contact mode using aNanoscope IIIa instrument from Digital Instruments, USA.All the optical spectra were recorded on a Perkin–ElmerLambda 35 UV/Vis spectrophotometer.

As already mentioned, polished planar and anisotropi-cally etched textured silicon surface substrates are used inthe present study. A chemically and mechanically polishedp-type Czochralski silicon wafer substrate (〈100〉 oriented,300µm thick, textured Si substrate having a pyramid structureof height 8–12 µm) was used for the study. A polished Sisubstrate as obtained from the supplier was used in the presentstudy without removing native oxide. In textured Si samples,the final step of oxide removal after texturing the Si wasalso not carried out. The textured Si substrate reduces thenet reflection of visible light and thereby increases opticalabsorption in silicon. As silicon nitride (Si3N4) is widely usedin the industrial manufacture of Si solar cells as an ARC wechose a plasma enhanced chemical vapor deposited Si3N4of thickness ∼80 nm coating as a reference to compare theantireflection properties of graphene deposited on planar andtextured silicon surfaces.

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Figure 1. The Raman spectra, AFM micrograph and section profile are shown in (a), (b) and (c) for G1; and (d), (e) and (f) for G2,respectively.

3. Result and discussion

3.1. Elemental and morphological characterization ofgraphene films

Figure 1(a) shows the Raman spectra of graphene depositedon Cu foil using the MPCVD method. As is well known,the three most prominent features of graphene, correspondingto the D peak at ∼1350 cm−1, the G peak at ∼1580 cm−1

and the 2D peak at ∼2680 cm−1, are observed [23]. TheD peak is a defect-induced Raman feature observed due todisorder or defects at the edge of the graphene. The G peakis known to be an indication of the sp2 carbon networks inthe sample. In our sample, the intensity of the D peak is quitesmall which indicates defect-free growth of the graphene film.The 2D peak originates from a second-order Raman processand can be used to determine the thickness of graphene. Theintensity ratio (I2D/IG) higher than 1.9 indicates the formationof single-layer graphene in the presented sample [24]. Thethickness of graphene was further confirmed by using sectionprofile analysis of the AFM image. Figure 1(b) shows theAFM image of the graphene layer on the Si substrate. Somewrinkles may be seen in the graphene film. The thicknessof the graphene film calculated from the section profileanalysis, as shown in figure 1(c), has been observed to be0.352 nm, which indicates the presence of a single layer ofgrapheme [25]. This is in good agreement with the resultsobtained from the intensity ratio of the 2D peak to the G peakin Raman spectra.

Figure 1(d) shows the Raman spectra of chemicallyprepared graphene (RGO). The dominance of the D peak inthe Raman spectra indicates the presence of disorder in theRGO film. This may be due to the presence of folding as well

as the residual oxygen and point defects in the RGO film.Figures 1(e) and (f) show the AFM and section profile imagesof RGO film, respectively. Some wrinkles and folding in theRGO film could be clearly seen. The thickness of the RGOfilm calculated from the section profile analysis, as shownin figure 1(f), has been observed to be 1.21 nm. At somepoints, the thickness seems to be higher due to the presenceof the folding and wrinkles in the RGO film. The presenceof functional groups, structural defects and adsorbed watermolecules is known to result in a greater thickness of the RGOmonolayer compared to monolayer graphene prepared by theMPCVD method [25–27].

Figure 2 shows a FESEM micrograph of graphene layersdeposited on silicon surfaces of polished samples G1–PS(figure 2(a)) and G2–PS (figure 2(c)) and textured samplesG1–TS (figure 2(b)) and G2–TS (figure 2(d)). In sampleG1–PS, graphene with some wrinkles is observed to followmost of the specimen surface. In sample G1–TS, grapheneappears to be well settled on the pyramids. In sample G2–PS,graphene layers are non-uniformly deposited and seem to beagglomerated in comparison to sample G1–PS. In sampleG2–TS, graphene seems to be unattached to the pyramids at anumber of points.

3.2. Optical characterization of graphene films

Figure 3(a) illustrates the transmittance spectra of graphenefilm G1 on quartz glass (sample G1–Q), showing 88–97%transmittance in the 300–650 nm wavelength range. This isconsidered to fulfil the provision of a transparent coatingin solar cell and other optoelectronic devices [28]. Thereflectance spectra show that the graphene overlayer on thepolished Si surface on sample G1–PS results in a drastic

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Figure 2. FESEM micrograph of MPCVD prepared graphene film G1 transferred on (a) polished Si (G1–PS) and (b) textured Si (G1–TS)substrate and chemically prepared graphene film G2 spin coated on (c) polished Si (G2–PS) and (d) textured Si (G2–TS) substrate,respectively.

reduction in the reflectance value from 88–43% to 17–11% inthe 300–650 nm wavelength range. In the case of the graphenelayer on a textured Si surface in sample G1–TS, a reductionin reflectance from 19–15% to 8–14% in the 300–650 nmwavelength range is observed. It may be noted that althoughthe reflectance of sample G1–TS is 8% lower than that ofsample G1–PS (17%), reduction in the reflectance value ongraphene deposition is more in G1–PS than in G1–TS, withrespect to the PS and TS samples without a graphene layer.

Figure 3(b) shows the transmittance spectra of graphenefilm G2 on quartz glass (sample G2–Q) and shows 82–92%transmittance in the 300–650 nm wavelength range. Thetransmittance value of sample G2–Q is lower than that ofsample G1–Q. This may be due to the difference in thequality and thickness of the RGO monolayer from that ofthe graphene layer prepared by MPCVD [25]. Graphenedeposition on the polished Si surface sample G2–PS reducesthe reflectance value from 88–43% to 77–35%, higher thanthat obtained for sample G1–PS in the 300–650 nm range. Thereason for such a difference in the reflectance values may beattributed to the different morphology of graphene depositedon samples G1–PS and G2–PS, particularly noticeable infigures 2(a) and (c) respectively. This observation indicatesthe decisive role of graphene deposition morphology, andthereby of the deposition scheme, to exploit the antireflectioncharacteristics of graphene. In the case of graphene depositionon the textured Si surface sample G2–TS the percentage

reflectance decreases from 19–15% to 15–7% almost the sameas that obtained for sample G1–TS in the 300–650 nm range.

Figure 3(c) illustrates a comparison of the reflectancespectra of MPCVD prepared graphene on a textured Sisubstrate (sample G1–TS) and chemically prepared grapheneon a textured Si substrate (sample G2–TS) with the referenceantireflection coating of silicon nitride (Si3N4) on a texturedSi substrate (sample SN–TS) in the 300–650 nm wavelengthrange. It is important to note that the reflectance spectrumof sample SN–TS is about 30–9% in the 300–650 nmwavelength range with a peak value of 35% at 330 nm. Thegraphene overlayer on textured Si in sample G1–TS showsreflectance values of 8–13% in the 300–430 nm range, wellbelow the reflectance values of SN–TS substrate in samerange. In the wavelength range 440–650 nm, the reflectancevalue of 14% for the G1–TS sample is ∼4% more than thereflectance values of the SN–TS sample. In sample G2–TS,the reflectance values of 14–7% are better than the reflectancevalues for SN–TS in the 300–650 nm wavelength range.

In summary: (i) G1–TS and G2–TS respond withvery similar reflectance values <15% in the 300–650 nmwavelength range; (ii) the G1–TS and G2–TS samplesmore or less follow the reference ARC sample SN–TSin the 450–650 nm range and are somewhat better in300–400 nm wavelength range. The reflectance response ofgraphene deposited samples in the 300–400 nm UV regionmake them promising candidates for nanoscale ultraviolet

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Figure 3. (a) Measured transmittance and reflectance as a function of wavelength of a MPCVD prepared graphene layer (G1) deposited onquartz glass (G1–Q) and polished Si (G1–PS) textured Si substrate (G1–TS), respectively. (b) Measured transmittance and reflectance as afunction of wavelength of a chemically prepared graphene layer (G2) deposited on quartz glass (G2–Q) and polished Si (G2–PS) textured Sisubstrate (G2–TS), respectively. (c) Measured reflectance as a function of wavelength of reference silicon nitride ARC on textured Si(SN–TS) MPCVD prepared graphene layer (G1) and chemically prepared graphene layer (G2) deposited on textured Si substrate.

photo-detectors and other UV sensitive photo-electronicdevices [29].

3.3. Reflectance spectra of different model configurationsusing FDTD simulation

The effect of graphene deposition on the reflectance ofpolished and textured Si surfaces was also evaluated usingFDTD simulation via the Lumerical package [19]. A planelight wave was launched normally to the substrate. Perfectlymatched layer (PML) conduction was used for the boundaryof the simulation window, which absorbs the energy withoutinducing any reflection. An override mesh of 0.5 nm was usedto resolve the graphene film. In this simulation, graphene ofthickness 1 nm with optical constants taken from [30, 31]was used in the simulation models. The simulation modelsare as follows: I, polished Si (PS); II, polished Si with twographene layers (PS + G + G); III, polished Si with SiO2(PS + SO); IV, polished Si with SiO2 layer and two graphenelayers (PS + SO + G + G); V, textured Si (TS); VI, texturedSi with two graphene layers (TS + G + G); VII, textured Siwith SiO2 (TS + SO); VIII, textured Si with SiO2 layer andtwo graphene layers (TS + SO + G + G). In this simulation,

graphene is assumed to be a normal bulk material with thethickness of each layer being 1 nm, the thickness of SiO240 nm and the pyramid height of the textured Si surface1 µm. As already mentioned in the experimental section, thenative oxide on Si samples (PS and TS) was not etched out.Therefore, the 40 nm thickness of SiO2 assumed in the FDTDsimulation corresponds to the native oxide.

Figure 4(a) shows the reflectance spectra of modelconfiguration (I–IV) in the case of a polished Si (PS) surfacein the 300–650 nm wavelength range. The reflectance of a barepolished Si substrate without graphene or SiO2 overlayersis calculated as 60–34%. On assuming two graphene layerson polished Si the reflectance drops to 47–32% in the300–650 nm wavelength range. The presence of a SiO2overlayer on polished Si significantly affects the reflectancevalue. With a 40 nm thick SiO2 layer the reflectance valuereduced to 38–28% on polished silicon. Subsequently, anaddition of two graphene layers of thickness 1 nm eachreflectance was found to reduce 20–24% in the 300–650 nmwavelength range.

Figure 4(b) shows the reflectance spectra of modelconfigurations (V–VIII) in the case of a textured Si (TS)surface in the 300–650 nm wavelength range. Reflectance of a

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Figure 4. Calculated reflectance as a function of wavelength ofdifferent model configurations: (a) I, polished Si (PS); II, polishedSi with two graphene layers of thickness 1 nm each (PS + G + G);III, polished Si with 40 nm thick SiO2 (PS + SO); IV, polished Siwith 40 nm thick SiO2 and then two graphene layers of thickness1 nm each (PS + SO + G + G); (b) V, textured Si (TS), textured Siwith two graphene layer of 1 nm thickness each (TS + G + G); VI,textured Si with 40 nm thick SiO2 (TS + SO); and VII, textured Siwith 40 nm thick SiO2 and then two graphene layer of thickness1 nm each (TS + SO + G + G).

bare textured Si substrate without graphene or SiO2 overlayersis 37–12%. The difference in the reflectance value fromthe experimentally measured 19–15% in the 300–650 nmwavelength range may be due to difference between pyramidsheight of the experimental textured Si substrate and thetheoretically assumed values. On assuming two graphenelayers on a textured Si surface, no significant change wasobserved in reflectance values. With a SiO2 overlayer ona textured Si surface the reflectance attains 10–8% in the300–650 nm wavelength range. Subsequent addition of twographene layers of thickness 1 nm causes the reflectance todrop to 3–6% in the 300–650 nm wavelength range.

3.4. Electric field intensity distribution of different modelconfigurations using FDTD simulation

In order to see the light trapping effect via the electricfield intensity distribution inside and around the Si materialfor different model configurations of polished Si andtextured Si surfaces at wavelengths of 300 and 600 nm,

two-dimensional FDTD simulation [19] was carried out. Themodel configurations assumed for this are: (i) textured Siwith silicon nitride (TS + SN) as reference antireflectionmodel configuration; (ii) polished Si with SiO2 and then twographene layers (PS+ SO+ G+ G) and (iii) textured Si withSiO2 and then two graphene layers (TS+ SO + G+G). Thesemodel configurations will be referred as M1, M2 and M3,respectively. Here again we assume graphene to be a normalbulk material with the thickness of each layer being 1 nm, thethickness of silicon nitride is 80 nm, the thickness of SiO2 is40 nm and the pyramid height of textured Si surface is 1 µm.

From figures 5(a)–(c), at 300 nm, the electric fieldintensity distribution for the reference antireflection modelconfiguration M1 shows that the light in not well trappedinside the Si pyramidal structure and the magnitude ofintensity is lower outside Si for model configurations M2and M3. This observation states that the reflectance is lessfor model configurations M2 and M3 in comparison withM1. This is consistent with the experimental results oflower reflectance for sample G1–PS and G1–TS shown infigure 3(a). At 600 nm, the electric field intensity distributionof the reference antireflection model configuration M1 showsweak intensity outside the Si pyramidal structure, alsofollowed by model configurations M2 and M3, consistentwith its antireflection properties at this wavelength valueshown in figure 3(c). The electric field intensity distributionshown in figure 5(c) implies that the model configuration M3has lower reflectance than the reference antireflection modelconfiguration M1 at 300 nm and almost the same reflectanceat 600 nm.

The comparison of experimental and simulated resultsshows that the presence of SiO2 and a graphene layer, onboth PS and TS substrates, results in a significant reductionin reflectance values throughout the UV–visible spectralrange. Both PS and TS substrates used in the experimentalinvestigation are expected to have 20–40 nm of SiO2. Theassumption of a 1 nm thick graphene layer in the calculationwas done keeping in mind the two to three monolayergraphene, especially in case of the chemically preparedsample G2. It is important to note that without the presenceof SiO2 layer, inclusion of two to three graphene layers in themodel configuration did not result in a significant reduction inreflectance. It is worth noting that graphene transferred ontosilicon substrates has some wrinkles and defects. Especiallyin the case of textured Si (as shown in figures 2(b) and (d)),poor adhesion seems to have resulted in locally suspended andloosely adherent graphene. This can significantly affect thetransmittance value.

It is clear that a SiO2 overlayer is essential to realize theantireflection properties of graphene. Similar inferences havebeen drawn in a study on the identification of graphene by thetotal color difference method, which shows that a 72 nm thickAl2O3 film is most suited for this purpose [32]. NormallySiO2 or Si3N4 films are used for graphene identification [33].These results indicate that the dielectric thickness and numberof graphene layers can be the control parameters to reduce thereflectance of the silicon substrate in a particular wavelengthrange. Near field enhancement of plasmonic nanostructures

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Figure 5. FDTD simulated electric field intensity distribution for different model configurations: (a) M1, silicon nitride referenceantireflection coating on textured Si (TS + SN); (b) M2, polished Si with SiO2 and then two graphene layers (PS + SO + G + G); and(c) M3, textured Si with SiO2 and then two graphene layers (TS + SO + G + G). The vertical scale Y (µm) is the silicon to source stackheight and the horizontal scale X (µm) is material width.

has been used to explain the spectral selectivity of graphenelayers [34]. A combination of high Fermi velocity in grapheneand the presence of high electric field at the graphene–siliconinterface has been proposed to explain the high quantumefficiency of graphene-layer-based photovoltaic cells [35]. Anincreased degree of field enhancement and interaction strengthhas been proposed in graphene layers having 2D, 1D and 0Dconfinement [36]. In addition to refractive index matching,the above effects may also influence the reflectance and theantireflection properties of graphene layers deposited on asilicon surface. The inert nature of the graphene layer maybe an additional advantage in antireflection applications. Itmay be interesting to explore the passivation properties ofgraphene on silicon surfaces.

4. Conclusion

We have studied the optical reflectance of few-layer MPCVDand chemically grown graphene deposited on polished andtextured silicon surfaces and compared these results withthe Si3N4/textured silicon reference ARC. The results of thepresent study show that the graphene overlayers result ina large decrease in reflectance in the wavelength range of

300–650 nm, with an enormous decrease in case of polishedsilicon. Si3N4 reference antireflection coating and graphenedeposited polished and textured silicon is observed to havesimilar reflectance values in the 450–650 nm range. In the300–400 nm range, graphene/Si surfaces show significantlylower reflectance values (8–10% in comparison to about 30%in the case of Si3N4). The FDTD calculations show thatthe presence of a SiO2 intermediate layer is an importantrequirement for the observed decrease in reflectance in the300–650 nm range. It is conjectured that thickness of SiO2

and the number of graphene layers can be varied to achievelow reflectance in a desired wavelength range. Depositionof graphene onto large areas seems to be important forexploiting its antireflection properties for photovoltaic andother optoelectronic applications.

Acknowledgments

The authors thank Ms Pratha Jhawar, Mr S Ravi and Mr SajiSalkalachen from the Semiconductor Device and PhotovoltaicDepartment, BHEL, Bangalore, for discussion related to thiswork.

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