Tuning Plasmon Resonances for Light Coupling into Silicon:a “Rule of Thumb” for Experimental Design

Christian Uhrenfeldt & Thorbjørn Falk Villesen &

Britta Johansen & Thomas Garm Pedersen &

Arne Nylandsted Larsen

Received: 14 May 2012 /Accepted: 6 August 2012 /Published online: 17 August 2012# Springer Science+Business Media, LLC 2012

Abstract For Si thin-film solar cells to become efficient,schemes to increase the optical absorption in the films arenecessary. Scattering of light using plasmonic resonances inmetal nanoparticles has been suggested as a feasible route.When placed on a dielectric layer on the front of a solar cell,such metal nanoparticles can scatter a large fraction of theincident light into the solar cell at the resonance wavelength,and hence increase the light collection. However, manyrelated effects may lead to a reduction in photocurrent.Thus, nanoparticle plasmon resonances must be optimizedin order to improve the overall light collection. From anexperimentalist’s point of view, simple and fast experimen-tal design tools should be explored. In this work, we inves-tigate the plasmon-related photocurrent enhancements for Sitest-solar cells with a number of different metal nanoparticleshapes and materials placed on top of a dielectric layer. Thespectral position of the photocurrent-enhancement onset iscompared to plasmon resonance calculations based on afairly simple model. Despite the fact that the optical inter-actions in nanoparticle solar cell configurations can be quitecomplex, the photocurrent enhancement in the investigatedtest-solar cells can be predicted qualitatively well for

particles with a plasmon resonance in the visible spectrum.This simple and fast model can be used as a rule of thumb indesigning nanoparticle arrays for a specific photocurrentenhancement profile.

Keywords Localized surface plasmon resonance . Thin-filmsolar cells . Nanoparticles . Modified long wavelengthapproximation

Introduction

In addition to reflection losses at the front, the weak absorp-tion coefficient of silicon at red to infrared wavelengths is achallenge for thin-film Si-solar cells. The use of resonantscattering of light from a localized surface plasmon reso-nance in metal nanoparticles placed on the front of the solarcell is being intensively investigated presently [1]. In thin-film cells, this scattering effect can lead to a large relativeincrease in the light collection probability at long wave-lengths, due to an increase in the optical path length withinthe cells [2].

Moreover, Ag nanoparticles placed in arrays on dielectriclayers have been shown to increase the light coupling intosilicon, which can be interpreted in terms of optical imped-ance matching or an antireflective effect [3]. The introduc-tion of a dielectric spacer layer between the particles and theSi surface serves to increase the resonance-driving field [4],due to interference in the dielectric layer, and also allows atuning control of the plasmon-resonance wavelength [5].

An important feature of the impedance matching is that,although a photocurrent enhancement is observed at wave-lengths larger than the plasmon-resonance wavelength, aphotocurrent reduction is observed at shorter wavelengths.This leads to a Fano-like profile of the photocurrent-

C. Uhrenfeldt (*) : B. Johansen :A. Nylandsted LarsenDepartment of Physics and Astronomy, Aarhus University,Ny Munkegade 120,8000 Aarhus, Denmarke-mail: chru@phys.au.dk

T. F. Villesen :A. Nylandsted LarsenInterdisciplinary Nanoscience Center, Aarhus University,Ny Munkegade 120,8000 Aarhus, Denmark

T. G. PedersenDepartment of Physics and Nanotechnology, Aalborg University,Skjernvej 4a,9220 Aalborg, Denmark

Plasmonics (2013) 8:79–84DOI 10.1007/s11468-012-9424-7

enhancement spectrum [3], and the effect was explained byLim et al. [6] to be caused by destructive interferencebetween the incident field and the field scattered by theplasmonic particle into the Si, which is out of phase atwavelengths below the resonance wavelength. The spectralposition of the cross-over point, 1cross, is crucial to theoverall improvement of thin Si-solar cells, since any largerelative improvement in the weak red response of a thin Si-solar cell with plasmonic scatterers may easily be counter-acted by a reduction in the blue-visible spectrum where thin-film cells have the highest absorption ability.

From finite-element methods Hägglund et al. [7] calcu-lated the photocurrent enhancement from gold nanoparticleson Si-solar cells and found that the plasmon-resonancewavelength, 1p, was positioned at a wavelength ~50 nmbelow 1cross. On the other hand, Spinelli et al. [3] showedfrom finite-difference time domain calculations on Ag nano-particles on top a Si3N4 spacer layer that 1p coincides with1cross for a number of particle geometries. This indicates thata correlation exists between 1cross and 1p even in the rathercomplex geometries investigated, although differences be-tween the two values may be observed.

Numerical methods are often needed to calculate 1p and1cross in order to accommodate the multitude of opticalinteractions that may be in play, such as interference effectsin the dielectric layer [4], interparticle coupling [8], diffrac-tive effects [9], as well as near-field absorption [7].

Nevertheless, in order to facilitate systematic experimentalinvestigations, without doing numerical calculations, a fastanalytical “rule of thumb” model that can be used for design-ing nanoparticle structures with a given plasmon-resonancewavelength 1p and a given cross-over point is desirable. Apartfrom providing good estimates of which structures to investi-gate, analytical models may also help to discern between thedifferent optical mechanisms that are in play.

In this work, we investigate the correlation between 1crossfrom measured photocurrent-enhancement profiles for anumber of different particle- and spacer-layer geometriesand plasmon-resonance wavelengths 1p calculated usingan electrostatic model combined with the modified longwavelength approximation (MLWA) [10, 11]—an approachwhich has been validated experimentally by Zorić et al. in[12] for a number of different metal nanoparticle geome-tries. Moreover, to further corroborate the applicability ofthe MLWA approach, reflection measurements were madefor selected samples, and were compared to modeled reflec-tion profiles based on the calculated plasmon resonances.

Experimental Methods

Experiments were made on Ag and Al nanoparticles on topof dielectric spacer layers on Si thin-film test-solar cells. Thedetails of the test-solar cells have been described elsewhere

[13]. Dielectric spacer layers of either SiO2 or SiNx weredeposited on the test-solar cells by rf-magnetron sputteringusing a commercial AJA sputtering system, and the thick-ness and refractive index of the layers were determined fromreflection measurements and model fitting. The metal nano-particles were produced in areas of 1–2×1–2 mm2 on top ofthe dielectric spacer layers using electron-beam lithographyfollowed by metal evaporation and lift-off. The nanoparticleswere produced in arrays with a pitch p of 300–400 nm. Theheight of the particles was controlled by the thickness of theevaporated metal layer.

In Fig. 1c, d, scanning electron microscopy (SEM)images of two of the samples are shown. As can be seen,the particles are shaped as slightly asymmetrical disks. Thewidth in the two array directions of the particles as well asthe array pitch were determined by structural analysis ofseveral SEM images, and the structural parameters are sum-marized in Table 1, which provides an overview of thedifferent samples investigated.

The photocurrent in the test-solar cells with and withoutparticles was measured using a set-up equipped with anOriel MS257 monochromator. The external quantum effi-ciencies (EQE) of the test-solar cells were obtained bymeasuring the photon flux in the set-up using a Newport818UV photodiode with calibrated quantum efficiency inthe 300–1,100-nm spectral range.

As a typical example, the measured quantum efficien-cy for the Ag_2 sample and for a reference are shown inFig. 2a. Also shown is the relative photocurrent-enhancement spectrum (Fig. 2b), obtained by normalizing

n2

h

d

pDx,y

a) b)

Ag_2c) Al_2d)

2 mm

Fig. 1 a Structural overview of the sample parameters. b Imageexample of electron beam lithography write-fields on a test-solar cell.c–d SEM images of two of the samples studied (see Table 1)

80 Plasmonics (2013) 8:79–84

the photocurrent response of the samples with Ag nanopar-ticles to the appropriate reference sample.

Reflection measurements1 were carried out using a Shi-madzu UV3600 double-beam spectrometer with an integrat-ing sphere. The combined diffusely and specularly reflectedlight was measured in the 300–1,200-nm spectral rangeusing a BaSO4 white standard as the reflectance reference.

By inspection of Fig. 2b, photocurrent reduction is observedat wavelengths below ~560 nm, whereas a photocurrent en-hancement is observed at larger wavelengths. By inspection ofthe reflectance measurements (not shown here), it is found thatthe enhancement region corresponds to a spectral region wherethe reflectance of the Ag_2 sample is reduced compared to thereference, thus indicating that the enhancement is due to theantireflective characteristics of the plasmonic particles.

As can be seen, the photocurrent reduction occurs in apart of the solar spectrum where the EQE of the referencecell is at its highest. This emphasizes the need for sampleswith plasmonic particles, where the reduction is shifted outof this part of the solar spectrum.

Model for Polarisability and Reflection

The polarisability α0,i along the ith direction (i0x, y) of asmall ellipsoidal particle with dimensions rx, ry, and rx (seeFig. 3a) can be calculated in the electrostatic approximationusing the following expression [14]:

a0;i ¼ 4p3rxryrz

"p � "h

"h þ Li "p � "h� �

!

where i0x, y; εp and "h ¼ nhð Þ2 are the dielectric functionsof the metal nanoparticle and the host material, and Li

are the shape-dependent depolarization factors [14]. Inline with the approach by Zorić et al. [12] the host-dielectric function was determined as an average betweenthe air and the dielectric layer beneath the particles accord-

ing to: "h ¼ 0:5ð1Þ2 þ 0:5 ndielectricð Þ2.For larger particles, the effects of radiative damping and

dynamic depolarisation modifies the polarizability whichcan be calculated from α0,i in the MLWA [10]. This cor-rected polarisability αi can then be obtained from the fol-lowing expression [11]:

ai ¼ a0;i

1� k24pri

a0;i � i k3

6p a0;i

where k ¼ 2pnh l0= . The above formulas for ellipsoids canbe adapted to disk-shaped particles by assigning rx ¼ Dx 2= ,ry ¼ Dy 2= , and rz ¼ h 2= [12].

In order to compare the calculated plasmon resonan-ces with reflectance measurements, the following model

Table 1 Structural properties of the different samples

Sample Metal h Dx

� �Dy

� �p Dielectric d n2 (at 500 nm)

Ag_1 Ag 25 71 (±5) 59 (±4) 400 SiO2 51 1.46

Ag_2 Ag 25 105 (±5) 87 (±5) 400 SiO2 51 1.46

Ag_3 Ag 25 84 (±3) 72 (±6) 400 SiNx 23 2.1

Ag_4 Ag 25 114 (±3) 104 (±6) 300 SiNx 23 2.1

Al_1 Al 100 101 (±11) 98 (±10) 400 SiO2 54 1.46

Al_2 Al 100 152 (±6) 140 (±8) 400 SiO2 53 1.46

The dimensional properties of the particles are given as height (h), average width Dx

� �, average breadth Dy

� �, and array pitch (p). Also shown is the

type of dielectric spacer layer as well as the fitted thickness (d) and refractive index (n2). The standard deviation in the values of Dx and Dy are listedin parenthes as (±) values. All structural dimensions are given in nanometers

1 Due to practical circumstances the reflectance of the Al_1 samplewas measured using a Perkin Elmer Lambda 1050 high-performancespectrometer also with an integrating sphere, using a Spectralon whitestandard as the reflectance reference.

0

0.2

0.4

0.6

0.8a)

EQ

E

400 500 600 700 800 900 1000

0.9

1.0

1.1 b)

Wavelength (nm)

Rel

ativ

e G

ain

Fig. 2 Measured external quantum efficiency (EQE) (a) of the Ag_2sample (solid red curve) compared to the EQE of the reference sample(dashed black curve). The relative photocurrent gain (b) is obtained bynormalizing the photocurrent to that of the reference sample

Plasmonics (2013) 8:79–84 81

of the reflection from the particle surfaces at normalincidence is used. In the model, only the scattering fromthe particles in the directions normal to the surface areconsidered together with interference in the dielectriclayer. Thus effects of diffraction or off-normal scatteringor other more complex concepts are not included. Theeffects of interference in the multilayered structure canbe addressed by a transfer-matrix method [15], providedthat the transfer-matrix of the particle layer on the air–dielectric interface is known. This, in turn, can bedetermined if the reflection coefficients and transmissioncoefficients across the particle and layer interface areknown. To this end, a model for the reflection andtransmission coefficients for an interface with a sheetof particles at the boundary is considered.

The geometry of the model can be seen in Fig. 3b,where the incident field Ei, the reflected field Er, andthe transmitted field Et have been assumed to be polar-ized in the +y-direction. The particles are considered aspoint dipoles placed in a sheet of infinitesimal thicknessδ on the boundary between the dielectric layer and the

air above. The polarization Py�!

of the particles gives

rise to a displacement sheet-current density jy!

in theparticle plane. The displacement sheet-current conduc-

tivity σy is related to the polarization Py�!

and the sheet-

current density jy!

via

d Py�!dt

¼ jy!¼ σy Ei þ Erð Þe�iwt y

Py�! ¼ "0

ay

AunitdEi þ Erð Þe�iwt y:

where Aunit ¼ p2. By requiring continuity of the tangen-tial component of the electric field across the sheet andby including the sheet-current contribution in theboundary conditions for the tangential component ofthe magnetic field, the reflection coefficient r12 fromthe particle interface as well as the transmission coef-ficient t12 across the particle interface can be found tobe:

r12 ¼ n1 � n2 � μ0cdσy

n1 þ n2 þ μ0cdσy¼ n1 � n2 þ ik0ay Aunit=

n1 þ n2 � ik0ay Aunit=

t12 ¼ 2n1n1 þ n2 þ μ0cdσy

¼ 2n1n1 þ n2 � ik0ay Aunit=

The coefficients r21 and t21 follow by permutation of theindices 1 and 2. From the above formula the reflectancefrom the surface was calculated using a matrix-transfermethod [15].

By plotting the differential reflectance RNP � RReffð Þ RReff=

the effect of metal nanoparticles on the surface is more clearlyidentified and thus any discrepancy between the modeledvalues and the measured data is more clearly observed.

In Fig. 4, the calculated values of RNP � RReffð Þ RReff= forthe Ag_1, Ag_3, and Al_1 samples are compared to thevalues obtained from the measured reflectances. Since all ofthe reflectance measurements were made using unpolarizedlight, the reflectance and the plasmon spectra were calculatedas the geometric intensity average between polarization alongthe x- and y-direction for the slightly asymmetric particles.

In all cases, it can be seen that the spectral profile ofthe calculated RNP � RReffð Þ RReff= spectra are in good

ryrx

rz

εh

pε

n1

n2

x

z

y

nsub

a) b) δ

Fig. 3 a Schematic of the structural input parameters for the calcula-tion of the polarisability. b Sample geometry used in the model for thesample reflection

−0.6

−0.4

−0.2

0

0.2

(RN

P−R

ref)/

Rre

f

−0.6

−0.4

−0.2

0

0.2

(RN

P−R

ref)/

Rre

f

300 500 700 900

−0.6

−0.4

−0.2

0

0.2

Wavelength (nm)

(RN

P−R

ref)/

Rre

f

Fig. 4 Calculated values of the differential reflectance (red dashedcurves) are compared to values derived from the measured reflectances(solid black curve) for the (top) Ag_2, (middle) Ag_3, and (bottom)Al_1 samples. Blue dash-dotted curves show exctinction cross-sectionsfor the calculated plasmon resonances normalized to the unit area perparticle

82 Plasmonics (2013) 8:79–84

agreement with the measured data, and that the spectralpositions of the distinct features are in excellent agree-ment with the same features in the experimental curves.It is noted, however, that the amplitudes of the modeldata are not in quantitative agreement with the experi-mental values. This may be due to the relative simplenature of the reflection model used.

Also shown in Fig. 4 is a plot of the exctinction cross-sectionCext;i ¼ kIm aif g (blue dash-dotted lines) normalized

to the particle unit area Aunit ¼ p2. The plasmon resonancewavelength is by definition identified as the peak wave-length in the exctinction cross-section Cext;i ¼ kIm aif gspectra.

It is noted that in the calculations of the particle polar-isabilities, the only input used for the calculation are theparticle structural properties and the properties of the dielec-tric layers. Thus, the reflection measurements corroboratethat the plasmon-resonance wavelength in the samples canto a large extent be modeled by the MLWA analyticalexpression.

In Fig. 5, the relative photocurrent-enhancement spectrafor all of the samples are shown and in each of the graphs,the positions of 1p calculated from the MLWA are indicatedby vertical dashed lines.

In the case of the Al_2 sample, it was possible to performpolarization-resolved photocurrent measurements along the x-and y-direction, and in this case, the 1cross values are comparedto the calculated plasmon resonance for each of the twopolarization directions. As can be seen from Fig. 5 the pre-dicted 1p values are close to the observed 1cross in all cases.

In order to clarify the apparent trend, the observed 1crossvalues are plotted as a function of the predicted 1p in acorrelation diagram shown in Fig. 6; the hypothetical caseof 1p01cross has been added (dashed line) to guide the eye.A very clear linear correlation between 1cross and 1p isobserved even though the samples differ in structural param-eters as well as in metal type and dielectric material.

This clear correlation between 1cross and 1p combinedwith the good agreement between the experimental andmodeled reflectance data 1cross shows that the plasmonresonances calculated using the MLWA to a large extentreflects the actual spectral positions of the plasmonic reso-nances in the experimental samples, even though the ampli-tudes in the applied reflection model does not always matchthe measured values.

Since the only input in the MLWA are material parame-ters and the structural properties of the nanoparticles, this inturn means that the MLWA approach can be used as a “ruleof thumb” design tool for experiments where a specificcross-over point or plasmon-resonance wavelength isdesired.

In conclusion, it has been shown that a clear correlationexists between plasmon-resonance wavelengths 1p calculat-ed from a simple analytical model and the experimentallyobserved 1cross. Moreover, the good agreement between thespectral position of distinct spectral features in the experi-mental reflection measurements and in the modeled reflec-tion, further supports the applicability of the MLWAanalytical model as a “rule of thumb” for the experimentaldesign of plasmonic-enhanced light coupling into silicon.

0.9

1.0

1.1

Rel

ativ

e G

ain

Ag 1 SiO2

Ag 2 SiO2

0.9

1.0

1.1

Rel

ativ

e G

ain

Ag 3 SiNx

Ag 4 SiNx

400 500 600 700 800

0.9

1.0

1.1

Al 1 SiO2

Al 2 SiO2

Rel

ativ

e G

ain

Wavelength (nm)

Fig. 5 Relative photocurrent gain for the following samples: (Top)Ag_1 (solid line) and Ag_2 (dashed line), (Middle) Ag_3 (solid line)and Ag_4 (dashed line) and (Bottom) the Al_1 (solid line) and Al_2samples (dashed lines). The spectral positions of the calculated λpvalues are shown by vertical lines. In the bottom graph, the two dashedcurves and vertical lines represent the response at the two differentpolarization-dependent measurements for the Al_2 sample

400 600 800

400

600

800

λ cros

s

λp,MLWA

Fig. 6 Correlation plot between the experimentally observed 1cross andthe calculated 1p. The case of 1p01cross is indicated by the dashed line

Plasmonics (2013) 8:79–84 83

Acknowledgments The authors greatly acknowledge the financialsupport from the project “Localized surfcae plasmons and siliconthin-film solar cells-PLATOS” financed by the Villum Foundation.

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