Optical properties of Ag nanoparticle layers deposited on silicon substrates

This article has been downloaded from IOPscience. Please scroll down to see the full text article.

2013 J. Opt. 15 035005

(http://iopscience.iop.org/2040-8986/15/3/035005)

Download details:

IP Address: 144.32.128.51

The article was downloaded on 05/03/2013 at 04:35

Please note that terms and conditions apply.

View the table of contents for this issue, or go to the journal homepage for more

Home Search Collections Journals About Contact us My IOPscience

IOP PUBLISHING JOURNAL OF OPTICS

J. Opt. 15 (2013) 035005 (7pp) doi:10.1088/2040-8978/15/3/035005

Optical properties of Ag nanoparticlelayers deposited on silicon substrates

Eshwar Thouti, Nikhil Chander, Viresh Dutta and Vamsi K Komarala

Photovoltaic Laboratory, Centre for Energy Studies, Indian Institute of Technology Delhi,New Delhi-110016, India

E-mail: vamsi@ces.iitd.ac.in

Received 10 January 2013, accepted for publication 31 January 2013Published 27 February 2013Online at stacks.iop.org/JOpt/15/035005

AbstractSilver nanoparticles of various sizes, shapes and modified distances between them wereprepared on silicon substrates using thermally evaporated metal thin films of varyingthicknesses followed by annealing. The ∼4 nm silver thin film annealed around ∼300 ◦Cshowed considerable reflectance reduction from the silicon substrate in the entirepolychromatic spectrum. The effects of dipolar and quadrupolar resonances of silvernanoparticles on the reflectance reduction from the silicon substrate are discussed. Thequadrupolar resonances of silver nanoparticles lead to reduced reflectance from the siliconsubstrate in the near UV–visible region (∼350–600 nm) due to the enhanced forwardscattering. The reflectance reduction in the Vis and NIR regions (∼600–1300 nm range) isexplained by the interaction of the surface plasmons of the metal nanoparticles, which is verysensitive to the size and shape of the particles, and the distances between them. Some of thewaveguide modes existing at the interface between the silicon and the metal nanoparticles alsocouple the excited surface plasmons, which helps in trapping the light near the NIR region.With proper tuning of the metal particle sizes, shapes and distances between the particles inthe layers, one can reduce the total reflectance from the silicon substrate in the entirepolychromatic solar spectrum.

Keywords: localized surface plasmons, dipole resonances, quadrupole resonances, silvernanoparticles

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

1. Introduction

Silicon based solar cells are promising candidates forharnessing solar energy in order to address the issue ofincreasing global energy demand. A considerable amountof research has been focused on enhancing silicon cellefficiency by understanding optical losses like reflection andtransmission. Conventionally, the reflectance of a silicon solarcell can be reduced by texturing on the front side of the celland/or using appropriate antireflection (AR) coatings [1–3].However, there are some solar cell configurations (e.g. thinfilm a-Si:H and also thin crystalline silicon solar cells)where one cannot texture the front side of the cell, andantireflection coatings also reduce the reflection losses overa relatively narrow bandwidth of the solar spectrum [4].

The surface texturization may also increase the surfacerecombination process due to increase in the surface area. Thetunability of antireflection from the silicon is also an issuewith conventional antireflection coatings. These limitationsindicate that one should still look for alternative and efficientmethods to reduce reflection losses by effectively trappingthe entire polychromatic solar spectrum in silicon based solarcells to address some of the above mentioned issues.

A recent light trapping approach to enhance siliconsolar cell efficiency is to exploit the surface plasmons ofthe metal nanoparticles’ absorption (near-field enhancement)or scattering (far-field enhancement) [4–7, 19]. Scatteringphenomena appear to be advantageous for silicon baseddevices, while absorption is beneficial for organic andpolymer devices. Light trapping in any active material can

12040-8978/13/035005+07$33.00 c© 2013 IOP Publishing Ltd Printed in the UK & the USA

J. Opt. 15 (2013) 035005 E Thouti et al

also be tuned by maximizing the absorption or scatteringprocess in the Vis–NIR regions using metal nanoparticles,which is a major advantage. Noble metal nanoparticles likesilver (Ag) and gold (Au) support localized surface plasmons,where light can be resonantly absorbed or scattered dependingon the metal nanoparticles’ size, shape and the distancesbetween them, and the surrounding environment. Plasmonicnanoparticles on top of the silicon based solar cells takeadvantage of light scattering. Increased angular distributionof the scattered light by nanoparticles predominantly intothe high refractive index medium leads to enhanced effectiveoptical path length and thus multiple extinctions in siliconsolar cells [6]. Pillai et al observed a seven-fold enhancementin the photocurrent from wafer based silicon solar cells near1200 nm and a 16-fold enhancement in the photocurrent from1.25 µm silicon on insulator cells (SOI) near 1050 nm, whichis attributed to the light trapping by the Ag nanoparticles [4].Spinelli et al reported reduced reflection losses and enhancedabsorption in the near infrared solar spectrum (λ > 800 nm)compared to the standard antireflection coating, with theoptimized Ag nanoparticle array placed on a dielectric spacerlayer coated silicon substrate [7]. The surface plasmons ofmetal nanoparticles work efficiently not only for silicon basedsolar cells but can also be exploited for applications likesilicon based photo-detectors and light emitting diodes [4,8–10]. For plasmonic based solar cells, researchers havemainly employed Au and Ag metal nanoparticles becausetheir surface plasmonic resonances can be tuned in theVis–NIR region. These two metals have their own advantagesand disadvantages, e.g., Au nanoparticles do not oxidizeeasily under ambient conditions, while Ag nanoparticles havehigher scattering efficiency than Au [8]. Due to the lowerwavelength interband transition threshold for Ag metal, frontside integration of Ag nanoparticles in a plasmonic solarcell would be a better choice. In this paper, we present theoptical properties of Ag island films prepared on silicon andglass substrates using a thermal evaporation technique, in thewavelength region from 200 nm to 1300 nm.

2. Experimental procedure

Ag films with mass thicknesses of nearly 1, 2, 4, 6, 8,10 and 12 nm were deposited on chemically treated baresilicon (200 µm thick, n-type, (100) oriented), and also onglass substrates simultaneously using a thermal evaporationtechnique. Prior to the Ag film deposition on the glasssubstrates, the substrates were cleaned with soapy waterand then sequentially ultra-sonicated for 10 min each indeionized water, acetone and isopropyl alcohol. The silverwas thermally evaporated at a chamber pressure of ∼10−5

mbar. The silver film thickness was measured using a quartzcrystal oscillator attached inside the chamber. A quartz crystaloscillator cannot give an exact film thickness, but it cangive relative thickness variation. It is difficult to measure thethicknesses of Ag films using a surface profiler as the filmsget scratched by the profiler tip. Therefore, the thicknessesstated above were purely given by a quartz crystal oscillator.The deposited Ag films were subsequently annealed at 200,

300 and 400 ◦C for 1 h in N2 environment to modify thesurface morphology. In the annealing process the ultra-thinfilm breaks into island structures due to the Ostwald ripeningand coalescence process. During the deposition, maintaininga lower deposition rate (∼0.01–0.03 nm s−1) is an importantstep for forming nanoparticles after the annealing step.

Silver island films were also deposited on glass substratesin order to study the extinction properties. Here, we mustemphasize that simultaneous depositions on silicon andglass substrates would not give the same results (particlesizes) because of their different thermal conductivitiesand interfacial properties. Optical characterization (totaltransmission and total reflectance) of the samples wasperformed using a Perkin Elmer Lambda 1050 double beamUV–Vis–NIR spectrophotometer with a 150 mm integratingsphere. A Carl Zeiss scanning electron microscope was usedto study the morphology of the Ag island films.

3. Results and discussion

As-deposited Ag film forms either an ultra-thin or adiscontinuous film depending upon the initial mass thickness.Discontinuous Ag films contain irregular shape, size andelongated particles with large surface coverage. After anannealing step is performed at ∼200 ◦C, an ultra-thin filmbreaks into island structures due to the coalescence process,and a discontinuous film transforms into regular shaped andsized particles with reduced surface coverage. The annealingtemperature is well below the melting point of Ag metal(∼960 ◦C), so during the annealing process no material is lostfrom the substrate. Figure 1 shows SEM micrographs of Agfilms with mass thicknesses of nearly 2, 4 and 6 nm depositedon glass substrates followed by annealing at ∼200 ◦C for 1 hin nitrogen environment. For the ∼2 nm mass thickness Agfilm, the surface coverage and average particle size (the sizeof a nanoparticle is taken as the diameter of a circle with equalarea) are found to be∼48% and∼102 nm, respectively; whichare calculated using ImageJ Toolbar [11]. As the Ag massthickness increases, the island shape becomes more irregular,elongated and larger in size.

Figures 2(a) and (b) show extinction spectra of Agnanoparticles on glass substrates, and total reflectance spectraof Ag nanoparticles on silicon substrates, respectively. Theextinction spectrum is calculated simply from 100−T , whereT is the measured diffusive and normal transmission (in theabsence of reflection). The observed extinction maximumis due to the absorption as well as the scattering by themetal nanoparticles. With an increase in film thickness,the extinction spectra of the Ag nanoparticles were notonly red shifted but also broadened. For the case of the∼6 nm thin film, one can clearly see the deformation fromthe nearly spherical shape (figure 1), which resulted inthe increased extinction broadness. Two resonance peaksare observed in the extinction spectra of some samples;the shorter wavelength maximum at ∼364 nm correspondsto quadrupolar resonances and the variable maximum atlonger wavelengths correspond to dipolar resonances of Agnanoparticles [12]. The dipolar resonance peaks are red

2

J. Opt. 15 (2013) 035005 E Thouti et al

Figure 1. SEM images of Ag with mass thicknesses correspondingto (a) 2 nm, (b) 4 nm and (c) 6 nm on glass substrates annealed at200 ◦C.

shifted with an increase in the Ag mass thickness of thefilm; this is because of the increase in average particlesize (figure 1). However, the quadrupolar resonance peaks(∼364 nm) remain constant for all mass thicknesses. Theunchanged quadrupolar resonance peak position is due tothe near lying interband transition edge [12]. The effectof interband transitions on the quadrupolar resonance peakbecomes less pronounced when Ag nanoparticle layers aredeposited on high refractive index silicon. From figure 2(b),it is evident that the quadrupolar resonance valleys and dipoleresonance peaks are red shifted with an increase in Ag massthickness on silicon. Up to ∼10 nm mass thickness films, onecan distinguish two resonance peaks, but they vanish withparticle size increment, i.e. for the case of the ∼12 nm thinfilm, due to the overlap of dipolar and quadrupolar resonancemodes. The individual identities of these peaks are lost dueto the large distribution of nanoparticles and high surfacecoverage.

Figure 2. (a) Extinction spectra of various mass thick Agnanoparticle layers deposited on glass substrates. (b) Totalreflectance spectra of various mass thick Ag nanoparticle layersdeposited on bare silicon substrates. All samples were annealed at200 ◦C.

The large reflectance reduction (figure 2(b)) in thewavelength range of ∼350–600 nm (except for the ∼1 nmthin film) is because of excitation of quadrupolar resonances,and their high radiative scattering efficiency, which canpredominantly scatter in the forward direction [18]. The∼10 nm Ag nanoparticle film showed the minimumreflectance due to the quadrupolar resonances, which is alsoclearly reflected in the extinction spectra with the largerquadrupolar peak intensity. For the case of the ∼12 nmAg film, the observed increase of forward scattering upto ∼700 nm can be interpreted as due to the overlap ofquadrupolar and dipolar resonances. In the wavelength regionfrom 200 to 310 nm, all the Ag nanoparticle films (except the1 nm thin Ag film) act as antireflection coatings. The presenceof the Ag nanoparticle layer leads to drastic reflectancereduction from the silicon substrate below ∼310 nm due tothe combined effects of interband transitions [12] and reduced

3

J. Opt. 15 (2013) 035005 E Thouti et al

Figure 3. (a) The extinction and (b) the total reflectance spectrum of the 2 nm Ag film on glass and silicon substrates annealed at 200 ◦C,300 ◦C and 400 ◦C. SEM images of the 2 nm Ag film on silicon annealed at (c) 200 ◦C, (d) 300 ◦C and (e) 400 ◦C. (f) The nanoparticle sizedistribution of the 2 nm Ag film on a silicon substrate annealed at 400 ◦C.

refractive index mismatch; this reflectance reduction has alsobeen observed for a continuous Ag film.

With the increase of metal nanoparticle size, higherorder mode excitation will take place, which can eitherenhance or decrease the light trapping efficiency intothe substrate depending on the excited mode. All theexcited modes in the metal nanoparticles have the forwardscattering feature, but alternating modes have backwardscattering like dipolar and octupolar mode resonances,etc, i.e. backward scattering is absent in the quadrupolarresonances [13, 14]. As the nanoparticle size increases,the forward scattering efficiency of the particle increasesbecause of the excitation of quadrupolar resonances. Dipolarresonances have equal probabilities of forward and backward

scattering. The scattering efficiency also further increaseswhen these plasmonic nanoparticles are deposited on highrefractive index silicon substrates [15].

In figure 2(b), for the wavelength region ranging from500 to 1100 nm (above the dipolar resonance wavelength),reduced reflectance for lower mass thickness and increasedreflectance for higher mass thickness films are observed,which can be understood by looking at the morphology ofthe island structures. For the ∼2 and ∼4 nm Ag films onecan observe that the reduced reflectance at longer wavelengthsmight be due to the near-field effects among the Agnanoparticles (the morphology can be seen in figures 3(c) and4(c)). The effects of near fields among the Ag nanoparticleson enhanced light transmission (or reduced reflectance) are

4

J. Opt. 15 (2013) 035005 E Thouti et al

Figure 4. (a) The extinction and (b) the total reflectance spectrum of the 4 nm Ag film on glass and silicon substrates annealed at 200, 300and 400 ◦C. SEM images of the 4 nm Ag film on silicon annealed at (c) 200 ◦C, (d) 300 ◦C and (e) 400 ◦C. (f) The nanoparticle sizedistribution of the 4 nm Ag thin film on a silicon substrate annealed at 400 ◦C.

discussed in detail at a later stage. However, larger filmthickness (above ∼6 nm) with larger nanoparticle size orelongated particle structures increases the reflection due tothe back scattering effect [12]. Here one can see that the∼4 nm Ag film shows a large reduction in reflectanceover the entire spectral region; it seems to be an optimumstructure for light forward scattering over a broad spectralrange. The ∼2 nm and ∼4 nm thin Ag nanostructured layersannealed at 200 ◦C show average reflectance reductions ofaround 6.27% and 7.85% respectively as compared to thebare silicon substrate in the wavelength range from 300 nmto 1100 nm. Larger mass thickness films show reducedwide spectral reflectance in the quadrupolar resonance region,but enhanced reflectance in the longer wavelength region.

Further increase in Ag film thickness (beyond 12 nm) leadsto interconnected aggregates, leading to further enhancementof longer wavelength reflectance, and finally it approachescontinuous Ag film behaviour.

Annealing of the samples was also carried out at highertemperatures to understand further the optical propertiesdue to the cluster fragmentation, shape changes with theinteraction of the substrate, and cluster surface diffusionleading to coalescence. Figure 3 shows the ∼2 nm Ag filmmorphology, extinction and total reflectance after annealingat 200, 300 and 400 ◦C. Increasing the annealing temperaturefrom 200 to 300 ◦C does not show much variation inthe morphology and optical properties of the nanoparticlefilm. Further increase in the annealing temperature from

5

J. Opt. 15 (2013) 035005 E Thouti et al

Table 1. The average reflectance reduction corresponding to the Agnanoparticle films with mass thicknesses of 2 and 4 nm deposited onsilicon substrates.

Annealtemperature (◦C)

Average reflectance reduction (%)(wavelength range 300–1100 nm)

2 nm massthickness Ag film

4 nm massthickness Ag film

200 6.27 7.85300 6.18 9.43400 2.50 1.57

300 ◦C to 400 ◦C led to reduced surface coverage of the Agnanoparticles to∼24% and larger particle sizes, and increasedreflectance in the visible and NIR regions. Figure 4 showsthe morphology, extinction and total reflectance spectra ofthe ∼4 nm Ag film annealed at 200, 300 and 400 ◦C. Thefilm annealed at 300 ◦C showed a considerable reflectancereduction from the silicon substrate in the visible and NIRregions, which was a unique observation when comparedto any other Ag nanoparticle film on the silicon substrate.The enhanced forward scattering due to the quadrupolarresonances is clearly seen in both the reflectance andextinction spectra for the case of 300 ◦C annealed film,compared to film annealed at 200 ◦C. On further increasingthe annealing temperature to 400 ◦C, the reflectance from thesilicon substrate is increased along with shifts in the resonancemodes due to the formation of larger sized Ag particles.

From the two experiments, we can infer that the optimumannealing temperature is around 300 ◦C for reducing thereflectance from the silicon substrate due to the formation ofparticle sizes with larger polarizabilities, to show sufficientforward scattering for efficient light trapping into the silicon.Due to very high density of Ag nanoparticles, we cannotestimate the exact average particle sizes from the SEMmicrograph using ImageJ Toolbar for the 300 ◦C annealedsample. The surface coverage for the case of the 400 ◦Cannealed film is around 32%, despite it showing weakreflection reduction, which is also clearly reflected in theextinction spectra with the narrow band. The percentages ofreflectance reduction from the silicon substrate due to the∼2 and ∼4 nm as-deposited Ag films annealed at differenttemperatures are also shown in table 1. The ∼4 nm thin Agfilm annealed at 300 ◦C showed the maximum reflectancereduction of 9.43% with 6% reflectance reduction near thesilicon band gap region.

When the surface coverage (lower annealing tem-peratures) is large, the reduced reflectance could bedue to the interaction of the Ag nanoparticles’ sur-face plasmon resonances (near-field interactions). Thedipolar/quadrupolar–dipole/quadrupolar interactions willdominate when the interparticle distances are comparable tothe particle diameters [19]. When the Ag particle distancesare less than the incident wavelength, the particle interactionwill be dominated by the near-field effects, and when theparticle distances are larger than the incident wavelengthonly the far-field effects can play a role. After excitationof localized surface plasmon resonances in the particle

layer, the induced polarization currents should transfer or betrapped inside the silicon substrate, depending on the sizeand shape as well as the contribution from the neighbouringparticles. Our observations support the concept that theseparation between the particles will drastically modify theforward scattering enhancement. In the case of the ∼4 nmAg film annealed at 200 ◦C, the small distances betweennanoparticles lead to interacting surface plasmons; however,the 300 ◦C annealed film with optimum nanoparticle size anddistance between the particles only shows large reflectancereduction in a wide spectral range. When the samplesare annealed at 400 ◦C, further increase in the averageparticle size and the distance between the particles leads tonon-interacting surface plasmons after the scattering process;correspondingly no reflectance reduction in the Vis–NIRwavelength region is observed. This type of observationwas also demonstrated theoretically, using finite-differencetime-domain calculations, by considering a close packed arrayof metal nanoparticles with variable distances [16].

The forward and backward scattering depend not onlyon the separation distance, but also the contact area with thesubstrate (particle size and shape). The forward scatteringof light into the substrate increases when the contactarea between the nanoparticles and the substrate decreases.Centeno et al experimentally demonstrated that metalhemispheres show significant backscattering and reducedforward scattering [17]. In the case of hemisphere likestructures, the upper and lower parts of the nanoparticleoscillate out of phase after the excitation and the reducedcoherence on the particle surface leads to reduced forwardscattering. This also gives a clear understanding of ourresults that after annealing the as-deposited films, the forwardscattering is increased. This can be explained by reshaping ofthe Ag particles, where the average lateral size of the particlesis decreased with an increase of vertical height, leading alsoto reduced surface coverage [18]. These results imply thatan optimum size of spherical like particles is essential forforward scattering of the light into the silicon substrate withgood coherence of the plasmon oscillations.

As Stuart and Hall explained, the excited surfaceplasmons from the metal island films can also interactwith the waveguide modes at the silicon–metal island filminterface, and these waveguides can provide an additionalmechanism for particle interaction [19]. We believe thatthe metal nanoparticles’ surface plasmon coupling with thewaveguide modes only could lead to the reduced reflection ina broad wavelength region. It seems that when the distancebetween the particles is very large, the induced field atone Ag nanoparticle cannot be modified by the waveguideinteraction. When we look at the 400 ◦C annealed films wherethere was no reduction in the reflectance, these results alsoconfirm that the propagation length of the guided modes isalso determined by the neighbouring interacting particles. Ourobservations revealed that the reduced reflectance in the longwavelength region is not due to the light scattering by thedipole resonances of individual metal nanoparticles, but dueto the interacting surface plasmons of the metal nanoparticlesthrough the wave guided modes.

6

J. Opt. 15 (2013) 035005 E Thouti et al

4. Conclusions

The optical (reflectance and extinction) properties of Agnanoparticle layers deposited on silicon and glass substrateswere studied in a wide range of Vis and NIR wavelengthregions. The∼4 nm silver thin film annealed at around 300 ◦Cshowed considerable reflectance reduction from the siliconsubstrate in the entire polychromatic spectrum. We found thatquadrupolar resonance excitation in the Ag particle surfacecan be beneficial for solar cells in reducing the reflectionof light from the silicon substrate in the visible region byincreasing the forward scattering to improve the performanceof silicon based solar cells. We attribute the reduced reflectionin the longer wavelength region from 600 to 1300 nm tolight scattering by interacting surface plasmons of the metalnanoparticles with optimum sizes and distances betweenthem. Some of the waveguide modes between the silicon andmetal nanoparticle interface can support the excited surfaceplasmons to trap the light near the NIR region. Silicon is apoor light absorber near the band gap, so a small reductionin reflectance near the band gap is significant. In order toexploit the metal nanoparticles’ surface plasmons to trap theentire polychromatic solar spectrum, one needs to carefullyunderstand the effects of metal nanoparticle size, shape anddistance between them and also the effect of the interface.

Acknowledgments

This research project is sponsored under the Solar EnergyResearch Initiative programme by the Department of Scienceand Technology, Government of India. We would like toacknowledge the Nanoscale Research Facility of IIT Delhi forthe optical characterization of samples.

References

[1] Chiao S-C, Zhou J-L and Macleod H A 1993 Optimizeddesign of an antireflection coating for textured silicon solarcells Appl. Opt. 32 5557–60

[2] Jellison G E Jr and Wood R F 1986 Antireflection coatings forplanar silicon solar cells Sol. Cells 18 93–114

[3] Ein-Eli Y, Gordon N and Starosvetsky D 2006 Reduced lightreflection of textured multicrystalline silicon via NPD for

solar cells applications Sol. Energy Mater. Sol. Cells90 1764–72

[4] Pillai S, Catchpole K R, Trupke T and Green M A 2007Surface plasmon enhanced silicon solar cells J. Appl. Phys.101 093105

[5] Spinelli P and Polman A 2012 Prospects of near-fieldplasmonic absorption enhancement in semiconductormaterials using embedded Ag nanoparticles Opt. Express20 A641–54

[6] Atwater H A and Polman A 2010 Plasmonics for improvedphotovoltaic devices Nature Mater. 9 205–13

[7] Spinelli P, Hebbink M, De Waele R, Black L, Lenzmann F andPolman A 2011 Optical impedence matching using coupledplasmonic nanoparticles arrays Nano Lett. 11 1760–5

[8] Stuart H R and Hall D G 1998 Island size effects innanoparticles-enhanced photodetectors Appl. Phys. Lett.73 3815–7

[9] Kim S K, Chao C H, Kim B H, Choi Y S, Park S J, Lee K andIm S 2009 The effect of localized surface plasmon on thephotocurrent of silicon nanocrystal photodetectors Appl.Phys. Lett. 94 183108

[10] Catchpole K R and Pillai S 2006 Surface plasmons forenhanced silicon light-emitting diodes and solar cellsJ. Lumin. 121 315–8

[11] Schneider C A, Rasband W S and Eliceiri K W 2012 NIHImage to ImageJ: 25 years of image analysis NatureMethods 9 671–5

[12] Kreibig U and Vollmer M 1995 Optical Properties of MetalClusters vol 25 (Berlin: Springer)

[13] Bohren C F and Huffman D R 1983 Absorption and Scatteringof Light by Small Particles (New York: Wiley-Interscience)

[14] Paris A, Vaccari A, Cala Lesina A, Serra E and Calliari L 2012Plasmonic scattering by metal nanoparticles for solar cellPlasmonics 7 525–34

[15] Schmid M, Klenk R, Lux-Steiner M Ch, Topic M andKrc J 2011 Modeling plasmonic scattering combined withthin-film optics Nanotechnology 22 025204

[16] Catchpole K R and Polman A 2008 Design principles forparticle plasmon enhanced solar cells Appl. Phys. Lett.93 191113

[17] Centeno A, Breeze J, Ahmed B, Reehal H and Alford N 2010Scattering of light into silicon by spherical andhemispherical silver nanoparticles Opt. Lett. 35 76–8

[18] Temple T L, Mahanama G D K, Reehal H S andBagnall D M 2009 Influence of localized surface plasmonexcitation in silver nanoparticles on the performance ofsilicon solar cells Sol. Energy Mater. Sol. Cells 93 1978–85

[19] Stuart H R and Hall D G 1998 Enhanced dipole–dipoleinteraction between elementary radiators near a surfacePhys. Rev. Lett. 80 5663–6

7