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Optik 125 (2014) 789– 794

Contents lists available at ScienceDirect

Optik

jou rn al homepage: www.elsev ier .de / i j leo

ptimization of Si solar cells with full band optical absorptionncreased in all polarizations using plasmonic backcontact grating

inxing Shia,∗, Zhen Zhoua, Bingshu Tangb

School of Science, Huaihai Institute of Technology, Lianyungang 222005, ChinaDepartment of Physics, Lianyungang Teacher’s College, Lianyungang 222006, China

r t i c l e i n f o

rticle history:eceived 13 March 2013ccepted 10 July 2013

eywords:olar energy

a b s t r a c t

We present a numerical study on the optimization of plasmonic thin-film solar cells with full bandoptical absorption increased in all polarization using plasmonic backcontact gratings. Particle swarmoptimization (PSO) and the finite-difference time domain (FDTD) are combined to achieve the maximumabsorption enhancement. Through optimization, we obtained approximately a 288% average absorp-tion enhancement, 304% and 273% absorption enhancement for TE- and TM-polarized illuminationas compared to a bare cell. The corresponding optimal design parameters of plasmonic solar cell are

urface plasmonshotovoltaiclasmonicsratings

P = 442 nm, h4 = 283 nm, h5 = 191 nm and w = 238 nm. The full band absorption enhancement arises fromthe waveguide-plasmon-polariton, Fabry–Pérot (FP) cavity mode and multiresonant guided modes. Theaverage absorption enhancement under an unpolarized illumination is almost immune to the incidentangle ranging from −40◦ to 40◦. If the thickness of the light absorbing layer is increased, the absorp-tion enhancement could be reduced significantly. And the average absorption enhancement is maximum(2.88) when the thickness of Si layer is 100 nm.

© 2013 Elsevier GmbH. All rights reserved.

. Introduction

Reducing the cost and increasing the conversion efficiency is aajor objective of research and development on solar cells. The thin

lm silicon cells need much less silicon materials, and thereforeffer a possible solution for low-cost solar energy conversion. How-ver, thin film silicon solar cells suffer from a low light absorptionecause of the weak-absorbing nature of silicon. There has beenn increased interest, in recent years, in wavelength-scale lightrapping techniques for application to ultra thin film solar cells. Themproved absorption of light in a silicon thin film solar cell by utiliz-ng plasmonic effects has received a lot of attention in recent years1–4]. As a consequence the absorption of the solar cell is increased,hich results in an increased short circuit current and conversion

fficiency. Single layer of metallic nanogratings or nanoparticleslaced at the top [5–8], bottom [9–11] or within [12–14] the active

ayer have been extensively studied for improving the performancef thin film solar cells. Despite the broadband absorption enhance-ent could be realized through placing one-dimensional periodic

etallic nanostructures on the top of the thin film solar cell [15],

ut that will of course block a fairly large amount of total inci-ent solar power because of the excitation of surface plasmon

∗ Corresponding author.E-mail address: slxopt@hotmail.com (L. Shi).

030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved.ttp://dx.doi.org/10.1016/j.ijleo.2013.07.079

polaritons is normally polarization sensitive [16]. From Pala’s stud-ies [7], they found that putting metallic particles in direct contactwith an absorbing semiconductor material induces an undesired,strong damping of the surface plasmon resonance that is responsi-ble for the enhanced light absorption.

Ferry et al. [17] demonstrated a hydrogenated amorphous Si(with 160 nm and 340 nm a-Si:H thickness) solar cell with plas-monic light trapping structures built into the metallic back contact.The nanopatterns allow ultrathin a-Si:H cells with short circuitcurrent densities exceeding that of similar cells with randomly tex-tured back contacts due to near-field coupling to guided modessupported by the multi-layer solar cell structure. Xiao et al. [16]devised an ultra-thin-film silicon solar cell configuration assistedby plasmonic nanostructures. By placing a one-dimensional plas-monic nanograting on the bottom of the solar cell, the generatedphotocurrent for a fixed 200 nm-thickness crystalline silicon solarcell can be enhanced by 90% in the considered wavelengthrange.

In this paper, we present a numerical study on the optimiza-tion of conformal thin film solar cell with or without metallic backcontact layer. The finite-difference time domain (FDTD) method isused here to analyze the integrated quantum efficiency of the cell,

and particle swarm optimization (PSO) technique is used to opti-mize the cell structure. We systematically study the optimizationof plasmonic thin-film solar cells with full band optical absorptionincreased in all polarization using plasmonic backcontact gratings.

790 L. Shi et al. / Optik 125

Fig. 1. Cross-sectional view of the thin film solar cell structure (one period) understudy. The top electrode (ITO) thickness is h1, the active layer (Si) thickness is h2,tac

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he bottom electrode (ZnO:Al) thickness is h3, the height and width of metal gratingre h4 and w, N is filled media with refractive index from 1 to 4, the metallic backontact layer (Ag) thickness is h5, the period is P.

e further study the effects of incident angle of illumination andhe thickness of Si active layer on overall optical absorptivity.

. Model and numerical method

.1. Model

Fig. 1 shows the cross-sectional view of the solar cell structurender study. This structure represents the one-period element of

1D plasmonic backcontact grating solar cell. As shown in Fig. 1,he designed solar cell has an Ag back-reflector of h5 in thicknessn SiO2 substrate. In the calculations, we assume that the thick-ess of substrate is infinity. The structure shown in Fig. 1 has aidth of P, which corresponds to the period of 1D Ag grating. At

he center, there is an Ag grating of w and h4 in width and height,espectively. The insulator N with index refractive nd from 1 to 4nd height h4 were filled between Ag grating. The insulator cane chosen with suitable dielectric materials, which could providen additional ability to fine-tune the dielectric environment of theanowaveguide [18]. We choose the insulator N as ZnO:Al whenhe cell structure was optimized. But at last, the effect of nd on per-ormance of the solar cell will be studied. An transparent 10 nmhick Al doped ZnO (ZnO:Al) film is followed on top of the Ag grat-ng (with insulator filled) layer for providing an cathode layer. Thehin silicon layer acts as the device layer, where the absorption ofhe light is enhanced by plasmonic nanostructures. The thicknessf Si layer is h2, here h2 is equal to 50, 100, 150, 200 and 250 nm tonvestigate the differences in the enhancement performance andifferences in the dimensions of the optimized structures. A trans-arent 10 nm thick ITO (indium-tin-oxide) anode layer is followedn top of the Si layer for providing an electrical contact from theolar cell. The sunlight incident angle is defined as �.

.2. Numerical methods

FDTD was used to analyze and optimize the performance of theltra thin-film solar cell. To model the material dispersion of Ag,

TO, silica and silicon, the multi-coefficient model (MCM) is used19]. The perfectly matched layer (PML) boundary conditions are

sed for upper and lower boundary and periodic boundary con-itions are used for the side boundaries to model the periodicature of the nanoparticles. Symmetric and anti-symmetric bound-ry conditions are used to reduce the required memory size and

(2014) 789– 794

computation time. To model the sunlight, a normally incident planewave with a wavelength range from 400 nm to 1100 nm was used.To calculate the absorption in the Si slab for a normally incidentplane wave as a function of space and frequency, the followingformula is used,

Pabs = −0.5ω|E|2imag(ε) (1)

where ω is the frequency of the incident plane wave, E is the local,simulated electric field, and imag(ε) is the imaginary part of thepermittivity.

The quantum efficiency of a solar cell, QE(�), is defined by

QE(�) = Pabs(�)Pin(�)

(2)

where Pin(�) and Pabs(�) is the power of the incident light andabsorbed light within the Si solar cell, respectively, at a wavelength�. Using the quantum efficiency, integrated quantum efficiency,IQE, is defined as

IQE =∫

(�/(hc))QE(�)IAM1.5(�)d�∫(�/(hc))IAM1.5(�)d�

(3)

where h is Plank’s constant, c is the speed of light in the freespace and IAM1.5 is AM1.5 solar spectrum. In Eq. (2), numerator anddenominator means the number of photons absorbed by the solarcell and that falling onto the solar cell.

To see how the efficiency of solar cell with metal nanoparticlesis improved compare with a bare solar cell, we define the followingquantities, absorption enhancement g(�) and G,

g(�) = QEnanoparticle(�)QEbare(�)

(4)

and

G = IQEnanoparticle

IQEbare(5)

The overall absorption enhancement is given by the average ofenhancement under both TE- and TM-polarized illumination, i.e.,GAve = (GTE + GTM)/2.

If we assume that all electron–hole pair contributes to photo-current, the short circuit current density Jsc is given by

Jsc = e

∫�

hcQE(�)IAM1.5(�)d� (6)

where e is the charge on an electron.Optimization of structural parameters is a very important part

of practical solar cell design. The particle swarm optimization (PSO)[20] has been shown to be effective in optimizing difficult multidi-mensional discontinuous problems in a variety of fields. The initialPSO concept was developed in 1995 [21] as a novel evolutionaryoptimization (EO) methodology over a complex solution space. PSOstarts by designating each position in the solution space as potentialdesign. A fitness function is then defined to quantify the perfor-mance of each candidate design. All the encountered positions areevaluated by this fitness function to represent how well the designcriterion is satisfied. Finally, toward the end of the optimization,most particles converge to the global optimum, which expectedlyresults into the best design.

A PSO optimization is initiated by randomly allocating parti-cle positions in the solution space and then searches for optimaby updating generations. Particles profit from the discoveries and

previous experience of other particles during the exploration andsearch for better objective function values. Let i indicate a particle’sindex in the swarm. Each particle flies through the D-dimensionalsearch space with a velocity Vi, which is dynamically adjusted

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L. Shi et al. / Opti

ccording to its own previous best solution pbestiand the previ-

us best solution gbest of the entire swarm. At each iteration thearticles’ velocities are calculated according to

i(j + 1)=w(j)Vi(j)+c1�1(j)[pbesti(j)−Xi(j)]+c2�2(j)[gbest(j)−Xi(j)]

(7)

nd the particles’ positions are updated by

i(j + 1) = Vi(j + 1) + Xi(j) (8)

here each particles’ position Xi (corresponding to a set of solar cellarticles values) represents a possible solution point in the problemearch space. Two random variables, �1 and �2, are both uniformlyistributed within [0,1] to inject the unpredictability in the swarmehavior. c1 and c2 are learning factors, usually about c1 = c2 = 2. And

is an inertial weight, decreases linearly from a maximum wmax

hen the optimization starts to a minimum wmin toward the end.n this investigation, the best trade-off between the particle con-ergence and a fully searched solution space is obtained by usingwmax, wmin) = (0.95, 0.4).

In the PSO/FDTD algorithm, two subroutines are prepared forSO optimization and FDTD simulation. At the beginning of theptimization, the particle positions are initialized the PSO program.hen FDTD subroutine reads each particle’s position, extracts theesired solar cell performance and evaluates the fitness values (that

s the average absorption enhancement GAve for plasmonic solarell). The current iteration ends by transmitting the fitness valuesack to the PSO subroutine to calculate the particle positions in theext iteration.

. Results and discussion

As shown in Fig. 1, the thickness h2 of the Si film is 100 nm. Theeometrical parameters to be optimized are the width w and height4 of Ag grating, the period P of 1D Ag grating, the thickness h5 of Agack-reflector. The dimension of the solution space is 4. The geo-etrical parameters are optimized within (unit: nm) w ∈ [20, 300];

4 ∈ [20, 300]; P ∈ [50, 800]; h5 ∈ [10, 400]. Fig. 2 shows the conver-ence properties of the average absorption enhancement, width,eight and period of Ag grating and thickness of Ag back-reflectors a function of iteration of the PSO/FDTD algorithm by using a 20-article swarm for 40 iteration. The global optimum is observedt the thirty-fifth iteration. From Fig. 2, by this optimization, webtained approximately a 288% average absorption enhancement,04% and 273% absorption enhancement for TE- and TM-polarized

llumination as compared to a bare cell, i.e., without metallic struc-

ures. The corresponding optimal design parameters of plasmonicolar cell are P = 442 nm, h4 = 283 nm, h5 = 191 nm and w = 238 nm.

Large scattering cross section and light coupling efficiency of theetallic nanoparticles could improve the absorption in Si active

ig. 2. Convergence results for plasmonic thin film solar cell designs which thehickness of Si active layer is 100 nm.

Fig. 3. Quantum efficiency as a function of the wavelength for plasmonic and baresolar cell.

layer when the metallic nanoparticles were placed at the top of theactive layer. But backside gratings will diffract the incident light tolarge propagation angles beyond the angle of total internal reflec-tion and, thus, significantly increase the interaction length of longwavelength photons [22]. To investigate the reasons for the absorp-tion enhancement of the plasmonic solar cell, the absorption, i.e.,quantum efficiency QE(�) were calculated at optimized parame-ters. Fig. 3 shows the simulated quantum efficiency for TE- andTM-polarized illumination as a function of the wavelength. Data forthe same cell calculated without nanoparticles is included for ref-erence. As shown in Fig. 3, the absorption peak located at 455 nm,labeled 0, of bare solar cell is attributed to the Fabry–Pérot (FP)cavity modes which play a very important role in the absorptionof thin-film solar cell [23]. The absorption is obviously enhancedin the full band range (400–1100 nm) compared to that of baresolar cell. For TM-polarized illumination, there are seven peaks ofenhanced absorption located at 455 nm, 524 nm, 536 nm, 628 nm,647 nm, 713 nm, 965 nm, labeled from 1 to 7, respectively. ForTE-polarized illumination, there are five peaks of enhanced absorp-tion located at 459 nm, 551 nm, 609 nm, 690 nm, 1063 nm, labeledfrom 8 to 12. Incident electromagnetic radiation excites dipolarplasmon resonances on the metal particles, which then reradiateinto the Si waveguide because of the very high refractive indexof silicon. For TM, light could be converted into surface plasmonpolariton (SPPs), which are electromagnetic waves that travel alongthe interface between a metal back contact and the semiconductorabsorber layer. Near the plasmon resonance frequency, the evanes-cent electromagnetic SPP fields are confined near the interface atdimensions much smaller than the wavelength. SPPs excited at themetal/semiconductor interface can efficiently trap and guide lightin the Si active layer. But for TE, SPPs could not be excited. MetalAg nanoparticles act as scatterers, which result from the couplingof incident light to diffracted modes in the structure. The reradi-ation is trapped into the multiresonant guided modes of the Siwaveguide (see Fig. 5). Fig. 4 shows the absorption profiles (also theelectric field profiles, because absorption is proportional to the elec-tric field) upon illuminating a plasmonic solar cell with optimizedparameters by a plane wave (Fig. 4(a)–(g) for TM and Fig. 4(h)–(l)for TE) at the wavelengths corresponding to 12 resonant modes.As shown in Fig. 4(a) and (h), labeled 1 and 8, located at 455 and459 nm, the modes are attributed to the Fabry–Pérot (FP) cavitymodes.

In order to distinguish these 12 enhanced absorption peaks thatarise from localized or guided modes in the Si active layer, the

map of the absorption versus photon energy and reciprocal lat-tice constance, G = 2�/P, is generated. In such a map, the two keyenhancement process (localized or guided) can conveniently beseparated and studied. Fig. 5 shows such a map of the absorption

792 L. Shi et al. / Optik 125 (2014) 789– 794

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ig. 4. Absorption profiles at the wavelength labeled 1–12, (a)–(g) for TM-polarizedllumination and (h)–(l) for TE-polarized illumination.

or plane wave illuminations (Fig. 5(a) for TM and Fig. 5(b) for TE).ach point in the map represents a full-field simulation result withts corresponding illumination energy and period. For TE illumina-ion, as shown in Fig. 5(b), we observe narrow features exhibitingigh absorption bands. These features correspond to the excitationf the TE waveguide modes of the structure and the absorptionnhancement directly results from an increased interaction lengthf the light with the Si film. The simulated absorption pattern inig. 4(i)–(l) corresponds to point 9–12 on this map. In addition, aroad red feature with high absorption is visible and stretchingver a large range of G-value. This feature shows the mode whichs attributed to the Fabry–Pérot (FP) cavity mode (Fig. 4(h) corre-ponding to point 8 on the map). Unlike the TE case, TM-polarizedight can drive surface plasmon resonances in the metallic nanopar-icles and this causes additional features in the E–G maps of thebsorption (Fig. 5(a)). For this polarization coupling to waveguideodes (labeled 3–6) is possible. The Fabry–Pérot (FP) cavity mode

s also observed (labeled 1). In addition, points 2 and 3 deserve spe-ial attention. The strong coupling between the optical waveguide

odes and the localized grating plasmons resonances results in the

ormation of a waveguide-plasmon-polariton. A clear anti-crossingehavior for the modes is observed and gives rise to a Rabi splitting.

weak localized plasmons resonance exists at point 7.

ig. 5. Map of the absorption vs. the incident photon energy and reciprocal latticeonstant, (a) for TM-polarized illumination and (b) for TE-polarized illumination.

Fig. 6. The refractive index nd of insulator dependence of absorption enhancementfor optimized plasmonic solar cell.

The insulator, as shown in Fig. 1, denoted “N”, can be chosen withsuitable dielectric materials, which can provide an additional abil-ity to fine-tune the dielectric environment of the nanowaveguide.Here, the refractive index of insulator could affect the propertiesof the plasmonic solar cell. Fig. 6 shows the refractive index ndof insulator dependence of absorption enhancement for optimizedplasmonic solar cell. The absorption enhancement is always largeabove 2.3 as nd is between 1 and 4. But we find that the absorptionenhancement is largest 2.88 when nd = 1.4, i.e., the insulator “N” isthe bottom electrode (ZnO:Al).

The performance of a thin film plasmonic solar cell with respectto illumination angle is very important because the solar illumi-nation reaches the surface as a scattered illumination. Fig. 7 plotsthe overall absorption enhancement with respect to the incidentangles. We investigate how much the absorption enhancement isreduced as the angle of incidence is increased from surface nor-mal towards off-axis angles for the backcontact design. As shownin Fig. 7, the absorption enhancement for the TM-polarized is rel-atively sensitive to the incident angle. It is probably because thatthe optical absorption in Si active layer further decreases with theincreasing angle due to depleted localized surface plasmon res-onance (SPRs) around the metallic gratings. When the incidentangle is increased, the light travels a longer way in the Si activelayer until it hits the metallic gratings on the backcontact surface.Thus, this reduces the intensity of the light, which results in weaksurface plasmons and reduce field localizations around the metal-lic surfaces [11]. However, the absorption enhancement for theTE-polarized is high insensitivity to the incident angle. The aver-age absorption enhancement under an unpolarized illumination isalmost immune to the incident angle ranging from −40◦ to 40◦.

As we know, the metallic gratings on the back surface of a thinphotovoltaic absorber layer can couple sunlight into SPP modes

supported at the metal/semiconductor interface as well as guidedmodes in the semiconductor slab, whereupon the light absorp-tion of the Si active layer is enhanced. But, if the thickness of the

1

2

3

4

60

30

0

−30

−60

−90 90

TMTEAverage

Fig. 7. Incident angle vs. overall absorption enhancement for the optimized plam-onic solar cell.

L. Shi et al. / Optik 125 (2014) 789– 794 793

Table 1The absorption enhancement, peaks, Jsc results and optimized parameters for various thickness of Si active layer under TM-, TE-polarized and unpolarized illumination.

Parameters (nm) Pol Enh Absorption peaks (nm) Jsc (mA/cm2)

h2 P h4 h5 w

50 471 215 192 102 TE 3.13 458, 627, 872, 980, 1081 4.15TM 2.57 448, 472, 537, 690, 784, 1050 3.41Ave 2.85 – 3.78

100 442 283 191 238 TE 3.04 459, 551, 609, 690, 1063 6.75TM 2.73 455, 524, 536, 628, 647, 713, 965 6.07Ave 2.88 – 6.41

150 544 136 394 358 TE 2.56 555, 641, 794, 848, 910 7.82TM 2.55 541, 628, 682, 826, 1045 7.78Ave 2.56 – 7.80

200 611 142 423 273 TE 2.28 560, 668, 730, 980 8.50TM 2.52 675, 775, 909, 1012 9.38Ave 2.44 – 8.94

TE

TM

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ight absorbing layer is increased, the absorption enhancement maye reduced significantly. In order to understand the differences

n the enhancement performance from the metallic gratings andifferences in the dimensions of the optimized structures for thearious Si active layer thickness, the thickness of Si layer is set to0, 100, 150, 200 and 250 nm. The optimized parameters, absorp-ion enhancement, absorption peaks and the short circuit currentensity Jsc results for various thickness of Si layer under TM-, TE-olarized and unpolarized illumination are illustrated in Table 1.rom Table 1, we can see that, Jsc further increases with the increas-ng the thickness of Si layer. The increase in Jsc is mainly due to thencrease of the absorption of Si layer. But the average absorptionnhancement increases to 2.88 when the thickness of Si layer is00 nm. And the enhancement further decreases with the increas-

ng the thickness of Si layer. At the same time, it is worth noting thathe optimized parameters of the metallic grating further increasesith the increasing the thickness of Si layer. In other words, in order

o get the maximum absorption enhancement for thicker Si layer,e shall consume more noble metal, which is somewhat not worth.

. Conclusion

In conclusion, we modeled and simulated the performance oflasmonic architectures under both TE- and TM-polarized illumi-ation and also presented the parametric study results for thisevice structure. The optimal parameters (P = 442 nm, h4 = 283 nm,5 = 191 nm and w = 238 nm) of the plasmonic solar cell with00 nm Si active layer were obtained using FDTD and PSO. Withhese parameters, we can attain approximately a 288% averagebsorption enhancement, 304% and 273% absorption enhance-ent for TE- and TM-polarized illumination as compared to a

are cell. The full band absorption enhancement arises from theaveguide-plasmon-polariton, Fabry–Pérot (FP) cavity mode andultiresonant guided modes. In addition, we also estimate low

ngular dependency, providing very high enhancements for a wideange of incident angles ranging from −40◦ to 40◦. We also com-utationally investigate impacts of the thickness of Si active layer

n overall absorption enhancement performance. If the thicknessf the light absorbing layer is increased, the absorption enhance-ent could be reduced significantly. And the average absorption

nhancement is maximum (2.88) when the thickness of Si layers 100 nm. The design strategy can potentially be extended to 3-imensional metallic structures and different kinds of solar cellrchitectures.

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2.28 598, 775, 847, 1063 9.922.39 615, 675, 756, 795, 884, 909 10.392.33 – 10.16

Acknowledgements

This work is financially supported by Huaihai Institute of Tech-nology (Grant nos. KQ08027 and KX08039) and Qing Lan project.

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