Effect of embedding silica nanoparticles and voids in the performance of c-Si solar cellsSonali Das, Avra Kundu, Hiranmay Saha, and Swapan K. Datta Citation: J. Renewable Sustainable Energy 5, 031603 (2013); doi: 10.1063/1.4807618 View online: http://dx.doi.org/10.1063/1.4807618 View Table of Contents: http://jrse.aip.org/resource/1/JRSEBH/v5/i3 Published by the American Institute of Physics. Additional information on J. Renewable Sustainable EnergyJournal Homepage: http://jrse.aip.org/ Journal Information: http://jrse.aip.org/about/about_the_journal Top downloads: http://jrse.aip.org/features/most_downloaded Information for Authors: http://jrse.aip.org/authors

Effect of embedding silica nanoparticles and voidsin the performance of c-Si solar cells

Sonali Das, Avra Kundu, Hiranmay Saha, and Swapan K. Dattaa)

Centre of Excellence for Green Energy and Sensor Systems, Bengal Engineeringand Science University, Shibpur, Howrah 711103, West Bengal, India

(Received 31 December 2012; accepted 25 April 2013; published online 24 May 2013)

The effect of embedding nanoentities (silica and voids) on the optical and electrical

performance of Si solar cells has been investigated in an attempt to decouple the

Anti-Reflection (AR) properties of the standard nitride coated Solar Cells (SCs)

and the scattering properties of the nanoentities. The decoupling will ensure the use

of the scattering properties of the nanoentities without disturbing the optimized

reflection characteristics of a standard SC. LumericalVR

Finite Difference Time

Domain Solutions software has been used to simulate the optical performance of

solar cells after embedding nanoentities in the emitter region. Simulation results

indicate that total decoupling of the AR properties and the scattering properties of

the nanoentities is not obtained. Electrical performance evaluation of the system

reveals a substantial relative improvement (1.7%) in the efficiency of thick

(200 lm) SCs which further increases for thin (2 lm) film cells (23%) when

100 nm radius nanovoids having 30% area coverage are embedded at a depth of

200 nm from the silicon surface. The relative improvement is compromised if the

changes in the material parameters due to embedding nanoentities are taken in to

account. VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4807618]

I. INTRODUCTION

Nanoparticles (NPs) of noble metals placed on the front surface of silicon Solar Cells

(SCs) have been vastly investigated for their role in the performance enhancement of SCs due

to the high polarizability of the NPs leading to a plasmonic scattering of the incident electro-

magnetic spectrum.1,2 Due to the plasmonics scattering, an enhanced optical coupling with large

angular spread into the substrate is obtained. The enhanced optical coupling ensures a reduction

in the reflection losses whereas the large angular spread results in increased absorption due to

path length enhancement inside the active region of the SC. However, the improvement in the

performance of SCs by the application of metal NPs on the front surface is limited due to the

ohmic losses in the metal NPs.3,4 The reduction in reflection losses is therefore not mapped

completely into an equal amount of injection into the silicon substrate as a portion of the inci-

dent power is lost due to ohmic dissipation by Joule heating in the particle itself. One may note

here that the origin of ohmic dissipation in NPs is due to the presence of imaginary part of the

refractive index/dielectric constant of the material of the NP. The imaginary part indicates the

amount of absorption loss by joule heating when the electromagnetic wave propagates through

the NP material.3 For bare silicon SCs (avg. reflectance �30%), an improvement in the per-

formance of the cell is obtained as the application of metal NPs reduces the reflection losses as

compared to the bare surface in spite of the ohmic dissipation in the NPs. But the application

of metal NPs on the top of an antireflection (AR) coated cell often degrades the photon trans-

mission into the SC.4 In such cases, the joule heating in metal NPs becomes critical and the

injection of photons into the AR coated SC may not be improved further as the reflection losses

a)Author to whom correspondence should be addressed. Electronic mail: swapansumana@gmail.com

1941-7012/2013/5(3)/031603/11/$30.00 VC 2013 AIP Publishing LLC5, 031603-1

JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 5, 031603 (2013)

from a high efficiency conventional silicon nitride (75 nm thick) coated SC are quite low (avg.

reflectance �3%–4%). This indicates that plasmonic metal NPs are more effective on a bare sil-

icon SC rather than conventional silicon nitride coated SC. However, dielectric NPs having no

ohmic losses due to joule heating (negligible imaginary part of refractive index/dielectric con-

stant) in the wavelength region of 300–1100 nm may be an alternate solution to improve the

performance of conventional silicon nitride coated SC. Dielectric NPs placed on the top of con-

ventional silicon nitride coated SC helps in grading the refractive index mismatch between the

single antireflection layer coated silicon and air to maximize the photon injection. However, it

is seen that dielectric NPs do not produce large angular scattering which is necessary for light

trapping.3,4 It is found that smaller sized (about 50 nm–70 nm radius) dielectric NP array with

optimized surface coverage placed on the top of bare or standard AR coated SC as a combined

optical system substantially improves the photon transmission but does not produce large angu-

lar scattering which is necessary for light trapping. On the other hand, larger sized dielectric

NPs on the front surface do produce large scattering due to the excitation of higher order

modes, but coupling to the underlying silicon substrate is low degrading the injection of inci-

dent photons into the SC.

To incorporate large angular scattering inside the SC, without significantly effecting the

photon injection into the SC, a suitable dielectric NP array may be embedded in the active

layer of silicon SCs.4 This may also be beneficial as the AR properties of the already present

dielectric (silicon nitride in this case) layer are decoupled from the light trapping properties of

the embedded NPs. The key requirements for choosing the material for the NPs for embedment

are that (1) the embedded particles should possess maximum refractive index mismatch with

silicon leading to high scattering efficiency and (2) the particles should have minimum ohmic

dissipation. Embedding silica NPs in c-Si SCs with an AR coating has been reported by Nagel

et al. and it is seen that total integrated absorption of incident photon flux across the visible

AM-1.5 spectrum is 5%–10% greater with dielectric scatterers.4 However, the role of the path

length enhancement due to large angular scattering by the dielectric scatterers in the efficiency

enhancement of the SCs has not been reported.

In this paper, we investigate the light trapping properties of the NPs embedded inside the

active Si-layer in an attempt to decouple the effect of the AR coating and NPs by using the

Finite Difference Time Domain (FDTD) method. Silica NPs (n¼ 1.46) and voids (n¼ 1) have

been considered separately for getting the maximum mismatch in the refractive index inside the

SC which will lead to an enhanced scattering leading to light trapping due to obliqueness of the

light path inside the SC. Nanoentities (NEs) of different sizes, various coverage and embedded

at different depths in the active Si layer have been considered in the optical simulations. The

results of the optical simulations in a single pass of SC without back reflector have been used

to find out the absorption in multiple passes using standard SC device physics having a back

reflector. Finally SC parameters like short circuit current, open circuit voltage, fill factor (FF),

and efficiency have been calculated from the optical results. Further, it is seen that the SC pa-

rameters are modified if the change in material parameters of the silicon is considered due to

embedment.

II. DEVICE STRUCTURE AND SIMULATION MODEL

Figure 1 shows the simulation model used in Lumerical FDTD Solution software5 and re-

fractive index from sampled data from Palik.6 We have separately considered silica (n¼ 1.46)

and voids (n¼ 1) of different radii (a) for different area coverage to be uniformly embedded at

different depths (z). The fractional surface coverage area is given as

CA ¼ ndpa2; (1)

where “a” is the NPs radius and nd is the particle density per unit surface area and the centre to

centre distance (dc) is 1ffiffiffiffindp .

031603-2 Das et al. J. Renewable Sustainable Energy 5, 031603 (2013)

A Si block coated with 75 nm thick silicon nitride on the front surface has been considered

for baseline optical simulation. The optical simulations are repeated after embedding the NEs

of various sizes, coverage at different depths in the baseline model to find out the effect of

embedment. A planar source is used to simulate the AM 1.5G spectrum and an air block is

used to fill up the simulation region not containing the cell structure [Figure 1]. The simulation

region is bounded by Perfectly Matched Layer (PML) in the z direction resulting in a semi-

infinite substrate.7–9 Periodic boundary has been applied along the x and y directions in order

to simulate the periodicity of the structure.

Frequency domain power monitors (red planes in Figure 1) have been placed at the inter-

face of silicon and silicon nitride layer and at a depth of 500 nm in the silicon surface.4,7

Frequency-domain power monitors collect high-accuracy power flow information in the fre-

quency domain from simulation results across some spatial region within the simulation.5

Power monitors are used as it is most important to get the accurate power measurements at the

mentioned positions. The monitor just below the interface estimates the injected light into sili-

con whereas the difference in the power injected at the interface and the power leaving the sili-

con after a depth of 500 nm gives us the absorbed power within the silicon. It is important to

point out here that power monitor at the silicon/silicon nitride interface is actually placed 1 nm

(which corresponds to the minimum mesh size used in the simulation) below the interface

inside the silicon layer to ensure validity of the monitored data. One may note that the exact

position where the data are to be recorded will change whenever the mesh changes.

The main parameter obtained from the optical simulations is the fraction of incident power

absorbed in presence of NE with respect to baseline model given by

AbsincðkÞ ¼

PabsðkÞPincðkÞ

� �with nano

PabsðkÞPincðkÞ

� �without nano

; (2)

where the numerator is the fraction of incident power absorbed in presence of NE and the de-

nominator is that in absence of NE. One may note that Absinc(k) reflects a combined effect of

injection into the silicon as well as absorption due to path length enhancement. So, this parame-

ter is actually a product of the fraction of incident power which is injected into silicon and frac-

tion of injected power absorbed in presence of NE with respect to baseline model. These two

parameters are defined subsequently as follows:

FIG. 1. Simulation model of the device.

031603-3 Das et al. J. Renewable Sustainable Energy 5, 031603 (2013)

(a) Fraction of incident power which is injected in presence of NE with respect to baseline

model given by

InjincðkÞ ¼

PinjðkÞPincðkÞ

� �with nano

PinjðkÞPincðkÞ

� �without nano

; (3)

where the numerator is the fraction of incident power injected in presence of NE and the de-

nominator is that in absence of NE.

(b) Fraction of injected power absorbed in presence of NE with respect to baseline model given

by

AbsinjðkÞ ¼

PabsðkÞPinjðkÞ

� �with nano

PabsðkÞPinjðkÞ

� �without nano

; (4)

where the numerator is the fraction of injected power that is absorbed in silicon in presence

of NE and the denominator is that in absence of NE. Enhancement in Absinj(k) is only due to

the increased path length owing to the obliqueness of light as a result of scattering thereby

decoupling it from the reflection characteristic of the SC.

III. EFFECT OF EMBEDDING NANOENTITIES ON THE OPTICAL

PERFORMANCE OF Si SOLAR CELL

The effect of embedding nanoentities on the optical performance of Si SCs has been stud-

ied with respect to the parameters described in Sec. II. Simulations have been performed for

different materials, sizes, and coverage of NEs embedded at different depths in the active Si

layer.

For different embedded nanoentities (silica and voids) at the edge (z¼ radius of NE) hav-

ing coverage of 30%, it is seen that there is a loss in the injected fraction of photons with

respect to the base line model for most wavelengths [Figure 2(a)]. The value of 1 in the figure

is indicative of the performance of the baseline model. Further, it is also seen that the loss in

injection is less in case of voids. Figure 2(b) shows that the fraction of injected power absorbed

in presence of NE with respect to baseline model is more for nanovoids as they provide a better

mismatch in refractive index with silicon. This maximized mismatch is responsible for large

FIG. 2. (a) Plot of Injinc(k) for 100 nm radius silica NP and void having 30% coverage embedded at z¼ radius of nanoenti-

ties. (b) Plot of Absinj(k) for 100 nm radius silica NP and void having 30% coverage embedded at z¼ radius of nanoentities.

031603-4 Das et al. J. Renewable Sustainable Energy 5, 031603 (2013)

angular scattering leading to light trapping and finally more absorption. One may therefore con-

clude that the effect of embedding voids in enhancing the optical performance of Si SCs would

be more pronounced than silica.

For different sized embedded nanovoids (100 nm and 200 nm radius) at the edge (z¼ radius

of NE) having 30% coverage, it is seen that the loss in the injected fraction of photons is higher

for larger sized nanovoids as they hamper the reflection characteristics more than their smaller

counterpart [Figure 3(a)] for wavelengths below 850 nm. However, it is seen from Figure 3(b)

that larger particles offer an enhanced absorption of the injected power due to higher scattering

efficiencies.3

For different coverage of embedded nanovoids (10%, 30%, and 50%) at the edge

(z¼ radius of NE) for 100 nm radius, it is seen that the loss in the injected fraction is maximum

for 50% coverage while it is minimum for 10% coverage [Figure 4(a)]. For high values of cov-

erage, the effective refractive index of the Si itself may be changed significantly disturbing the

phase matching of the whole optical system. However, Figure 4(b) shows that a higher value of

coverage may lead to an increased absorption in certain wavelength regions where the Si ab-

sorbance is low.

For embedded nanovoids of 100 nm radius at different depths (z¼ 100 nm, 150 nm and

200 nm) having 30% coverage, it is seen that voids embedded deeper into the Si cause more

loss in the injected fraction of photons than those embedded at the interface [Figure 5(a)]. NEs

at the interface (z¼ a as per Figure 1) experience a non-homogeneous medium around it

FIG. 3. (a) Plot of Injinc(k) for 100 nm and 200 nm radius void having 30% coverage embedded at z¼ radius of nanoenti-

ties. (b) Plot of Absinj(k) for 100 nm and 200 nm radius void having 30% coverage embedded at z¼ radius of nanoentities.

FIG. 4. (a) Plot of Injinc(k) for 100 nm radius void having different coverage embedded at z¼ radius of nanoentities. (b)

Plot of Absinj(k) for 100 nm radius void having different coverage embedded at z¼ radius of nanoentities.

031603-5 Das et al. J. Renewable Sustainable Energy 5, 031603 (2013)

leading to more coupling of power in the forward direction as compared to the backward direc-

tion as the refractive index of the embedding medium is higher in the forward direction.3

However, voids embedded deeper into the Si (z> a), experience a homogeneous medium

around it resulting in significant back scattering as the refractive index of the embedding uni-

form around it. This back scattering from the voids alters the reflection characteristics of the

SC which is more for voids embedded deeper into the silicon. However, the absorption of

injected photons increases with depth of embedding which is possibly due to photon absorption

by both front and back scattered radiation into the Si [Figure 5(b)].

The enhanced absorption of the injected photons, in all the cases, is attributed to the

increase in path length of light inside the SC. The path length of the scattered light into the SC

may be estimated by a factor of 1/cos(hav) where

cos hav ¼�aW

ln 1� PabsðkÞPinjðkÞ

� �with nano

� � : (5)

Here hav is the angle between the scattered light and the surface normal, a is the absorption

coefficient of Si, and W is the thickness of the Si layer.

Finally, the obtained loss in injection, enhancement in absorption and increased path length

estimated by 1/cos hav in the 500 nm silicon block must be mapped into the model of a real SC

having back reflector for producing multiple light passes in the SC to evaluate the effect of

embedding on the efficiency of the SC.

IV. ELECTRICAL PERFORMANCE OF SILICON SOLAR CELL OF DIFFERENT

THICKNESSES HAVING ALUMINIUM BACK REFLECTOR WITH EMBEDDED

NANOENTITIES

Multiple internal reflections, inside the Si region, of the light scattered by the NPs have

been considered to evaluate the electrical performance of SC with planar front and back surface

embedded with nanoentities. The optical generation rate of the SC under illumination needs to

be evaluated for estimating the electrical performance of the SC. For a SC with front surface

external reflectance of “R,” front surface internal reflectance of “Rfn” and the reflectivity of

“Rbn” from the aluminium back surface, the generation rate of electron hole pairs at a distance

of x is given by10

Gðk; xÞ ¼ N0ðkÞð1� RÞa e�ax þ Rbne�að2W�xÞ

1� RbnRf ne�2ax

� �; (6)

FIG. 5. (a) Plot of Injinc(k) for 100 nm radius void having 30% coverage embedded at different depths (z). (b) Plot of

Absinj(k) for 100 nm radius void having 30% coverage embedded at different depths (z).

031603-6 Das et al. J. Renewable Sustainable Energy 5, 031603 (2013)

where a is the absorption coefficient of Si (/cm) without NE which is modulated by a factor of

(1/cos hav) in presence of embedded NEs, and N0(k) is the number of incident photons (/m2/s/

nm). Cos hav is calculated from the optical simulation studies using Eq. (5) for some particular

cases including both silica and voids of different sizes having different coverage embedded at

different depths reported in Figure 6. The front surface external reflectance R which is [1 �Injinc(k)] also obtained from the optical simulations. Rfn has been calculated by the transfer ma-

trix method8 for SCs with and without embedded NPs. Rbn of 0.65 has been considered for the

entire wavelength range.10

Considering We, Wsp and Wb as the width of emitter, space charge and base region of the

SC, respectively, the transport equations for different regions have been solved under appropri-

ate boundary conditions and the total photocurrent (Jph(k)) has been found out as

JphðkÞ ¼ JeðkÞ þ JspðkÞ þ JbðkÞ; (7)

where Je, Jsp, and Jb are the current densities in the emitter, space charge and base region of the

SC, respectively.

The short circuit current Isc for the cell with a series resistance Rs has been derived by

solving the following equation using bisection method:

Isc ¼ Iph � I0ðeIscRs

VT � 1Þ: (8)

The open circuit voltage is the evaluated by the equation given by

Voc ¼kT

qlnð1þ Jph=J0Þ: (9)

J0 is the reverse saturation current density.

Finally, the FF and the efficiency (g) of the SC have been found out from the following

equations:

FF ¼ VmIm

VocIsc(10)

and

FIG. 6. Plot of cos (hav) for some optimum cases.

031603-7 Das et al. J. Renewable Sustainable Energy 5, 031603 (2013)

g ¼ FFVocIsc

Pinc; (11)

where Vm and Im are obtained from the plots of I-V curves.

Also, the External Quantum Efficiency (EQE) is calculated by the equation

EQEðkÞ ¼ JphðkÞqN0ðkÞ

; (12)

where q is the electronic charge.

A. Calculation of efficiency ignoring the changes in material parameters

due to embedding

Embedding NEs in the emitter region of the SCs is likely to modify the diffusion length,

lifetime of minority carriers and also the mobility of carriers. However, to examine only the

light trapping effects due to embedding NEs in Si SCs, we first ignore the changes in the mate-

rial parameters due to embedding. Two sets of baseline silicon SC parameters are considered in

the calculation as given in Table I. The material parameters of the second set given in Table I

are inferior to those in the first set. This has been considered because c-Si SCs have been

reported to have the diffusion length in the range of 100–600 lm corresponding to varied influ-

ence of the defect states introduced by carbon, oxygen, and iron impurities in solar grade Si

wafers.11

Figure 7(a) shows the plot of efficiency of the 100 sq. cm SC (having the material parame-

ters: Set I as shown in Table I) for cases considered in Figure 6 for different thicknesses of the

cell (Wb¼ 2� 200 lm, We¼ 0.5 lm, and Wsp¼ 0.3 lm). From Figure 7(a), it can be observed

that the best embedding case is when 100 nm radius void having 30% coverage is embedded

200 nm deep inside silicon and the worst case is when 100 nm radius void having 50% coverage

is embedded 100 nm deep inside silicon. The relative percentage improvement in efficiency for

the best embedding case is 1.7% for 200 lm thick cell and 23% for 2 lm thick cell from a

baseline efficiency of 16.76% and 10.71%, respectively.

The effect of embedding is seen to be more pronounced for thin film cells. The reason may

be explained as follows. In both thick and thin solar cells, most of the photons with higher

energies (lower wavelengths) are absorbed in a single pass through the cell. However, for

higher wavelength photons (>900 nm), the photons are not absorbed in a single pass leading to

multiple passes by back and front surface of the solar cells. In thick solar cells, the photons

have to travel larger lengths before they undergo reflection at the front and back, while for thin

solar cells, the path length between reflections is smaller. This leads to carrier generation due

to higher wavelength photons closer to the junction in thin cells compared to that in thick cells

and consequently improved Internal Quantum Efficiency (IQE) is obtained in thin cells. This

TABLE I. Material parameters of silicon used for electrical analysis of 100 sq. cm solar cell.

Parameters of bulk silicon Set 1 Set 2

Doping density in base (NA) in cm�3 1016 1016

Doping density in emitter (ND) in cm�3 1018 1018

Surface recombination velocity in base (Sn) in cm/s 1000 1000

Surface recombination velocity in emitter (Sp) in cm/s 100 100

Minority carrier diffusion length in base (Ln in lm) 100 606

Minority carrier diffusion length in emitter (Lp in lm) 20 21.5

Minority carrier lifetime in base (sn in ls) 4 123

Minority carrier lifetime in emitter (sp in ls) 0.1 1.3

Series resistance (Rs) in ohm 0.015 0.015

031603-8 Das et al. J. Renewable Sustainable Energy 5, 031603 (2013)

effect becomes much more predominant when light is made to travel in oblique paths due to

large angular scattering by embedded nanoparticles. This leads to the comparatively higher rela-

tive efficiency increase in thinner cells.

B. Calculation of efficiency considering the changes in material parameters

due to embedding

In this section, we consider the changes in material parameters in addition to the light trap-

ping effects caused by the embedded NEs. We have also taken into account the increase of se-

ries resistance due to embedding. The modeling of transport parameters of a silicon block con-

taining embedded nanovoids has been reported by Banerjee et al.12 The changes in the material

parameters due to embedded NEs have been calculated using Eqs. (13)–(17) (given below).12

The number of equivalent recombination centers per unit volume due to embedded NPs in

the emitter region is given by

Nr ¼ð4pa2ÞNt

dc3

; (13)

where Nt is the recombination centre density per unit area at the NE/Si interface which is 6.33

� 1012/cm2 for void/Si interface12 and 9 � 1011/cm2 for silica/Si interface.13

The lifetime, diffusion coefficient, and the diffusion length of the minority carriers in the

emitter region are modified to

smod ¼sp

1þ rrNr

ND

� � ; (14)

Dmod ¼Dp

1þ Nr

ND

� � ; (15)

Lmod ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmodsmod

p; (16)

where sp and Dp are the minority carrier lifetime and minority carrier diffusion length in the

emitter region and rr is the ratio of the capture cross sections at the bulk recombination centers

and recombination centers due to embedded NPs, respectively. The baseline material parameter

values (sp, Dp) have been taken from Table I. The mobility is modified according to the follow-

ing equation:

FIG. 7. (a) Plot of efficiency of the solar cell for embedding cases as per Fig. 6 for different thicknesses of the solar cell.

(b) Plot of efficiency of the solar cell for best and worst embedding cases as per Fig. 7(a) for different thicknesses of the so-

lar cell considering and ignoring the changes in material parameters due to embedding.

031603-9 Das et al. J. Renewable Sustainable Energy 5, 031603 (2013)

lmod ¼lp

1þ Nr

ND

: (17)

The new series resistance is approximately taken to be the old series resistance multiplied

by the ratio of mobility ignoring material changes to the modified mobility considering material

changes. With these modifications, the SC parameters are again calculated and the efficiency of

the best and worst embedding cases for different thicknesses of the cell is shown in Figure

7(b). The relative percentage improvement in efficiency for the best embedding case is modified

from 23% to 21.3% for 2 lm thick cell from baseline efficiency 10.71% due to the change in

material parameters. This result compares well with the experimental data reported by

Nunomura et al. where a 16% enhancement in efficiency from a baseline value was obtained

when 130 nm silica nanoparticles were embedded in a 2 lm thick tandem solar cell.14 Table II

summarizes the efficiencies of the Si solar cell of different thicknesses with best and worst

embedding conditions considering or ignoring the changes in the material parameters due to

embedding. Material parameters as per Table I have been considered in calculating the

efficiencies.

TABLE II. Efficiency of the Si solar cell of different thicknesses with best and worst embedding conditions considering or

ignoring the changes in the material parameters due to embedding (A, ignoring changes in material parameters due to

embedding; B, considering changes in material parameters due to embedding).

Efficiency (%)

Results obtained with material parameters: Set 1 Results obtained with material parameters: Set 2

Thickness

(Wb in lm)

of the cell

Best case Worst case Best case Worst case

Baseline A B A B Baseline A B A B

200 16.7582 17.0396 16.6834 16.4144 15.7051 19.7538 20.1129 19.4409 19.2609 18.4233

150 16.8679 17.1967 16.8346 16.5178 15.8012 19.5076 19.9295 19.2636 19.0336 18.2122

100 17.0372 17.4613 17.0907 16.6807 15.9559 19.1297 19.6489 18.9930 18.6888 17.8935

50 17.1263 17.7615 17.3874 16.8076 16.0913 18.3675 19.0733 18.4399 18.0237 17.2834

30 16.8612 17.6774 17.3155 16.6674 15.9812 17.6522 18.5243 17.9138 17.4638 16.7721

20 16.4078 17.3987 17.0548 16.4039 15.7521 16.9489 17.9883 17.3989 16.9653 16.3170

2 10.7074 13.1641 12.9893 12.8048 12.4567 10.7769 13.2702 12.8283 12.9189 12.5857

FIG. 8. Plot of EQE of 2 lm thick solar cell for best and worst cases considering the changes in the material parameters

due to embedding.

031603-10 Das et al. J. Renewable Sustainable Energy 5, 031603 (2013)

Figure 8 shows the EQE for 2 lm thick silicon SC for the best and worst embedding cases

considering the changes in material parameters due to embedding. The change in EQE may be

ascribed to the combined effect of the changes in the injection of the incident photons and

changes in the absorption of the injected photons over the entire wavelength region.

V. CONCLUSION

A systematic study of embedding NPs of different sizes having different area coverage at

various depths in the active Si layer of standard AR coated SC indicates that embedment pro-

duces large angular scattering and light trapping in silicon but the reflectivity of Si is slightly

increased which is contrary to other reported investigations.4 Therefore, the absorption enhance-

ment due to scattering by the NEs is slightly offset by the increased reflectivity. Electrical sim-

ulation of SC with different thickness incorporating optical simulation results shows enhanced

efficiency due to scattering. The maximum relative efficiency enhancement is obtained for 2 lm

thick cell embedded with 100 nm radius void 30% coverage at 200 nm depth. It is seen that the

improvement in efficiency due to enhanced optical absorption is offset when the changes in the

material parameters of silicon due to embedding are also incorporated.

Although the work presented here mainly deals with modeling and simulation of embed-

ding silica NPs and voids in the performance of c-Si SCs, the authors are keen to pursue the

fabrication of such structures. The fabrication of a quasi mono crystalline porous silicon film

when used as a passive substrate for transferring and holding the active epitaxial layer on which

the SC is fabricated will lead to the realization of nanovoids in the active silicon layer.12 Silica

NPs may also be embedded by a technique reported in a very recent work of Nunomura et al.14

ACKNOWLEDGMENTS

This work was supported by Department of Science and Technology (DST), Government of

India. The authors would like to acknowledge Professor A. K. Barua and Professor R Bhattacharya.

The authors would also like to thank Ms. Saptaparna Dey for her help in electrical device

simulations.

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4J. R. Nagel, “Advanced methods for light trapping in optically thin silicon solar cells,” Ph.D. dissertation (The Universityof Utah, Salt Lake City, 2011).

5E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, San Diego, 1985).6See www.lumerical.com for “Lumerical FDTD Solutions: High performance FDTD-method Maxwell solver for thedesign, analysis and optimization of nanophotonic devices, processes and materials.”

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