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Design Method for Light Absorption Enhancement

in Ultra-Thin Film Organic Solar Cells

with the Metallic Nanoparticles

Chen Sun & Hongtao Gao & Ruiying Shi & Chuanhao Li &

Chunlei Du

Received: 13 January 2012 /Accepted: 6 September 2012# Springer Science+Business Media, LLC 2012

Abstract In this paper, a method is presented for designing

the parameters of metallic nanoparticles introduced into

ultra-thin film organic solar cells (OSCs) to improve thelight absorption. On the basis of Mie theory, a relationship

is setup between the scattering efficiency of localized sur-

face plasmon resonance and the size parameter of metallic

nanoparticles, by which metallic nanoparticles with optimal

size can be designed to realize the highest ratio of resonant

scattering to resonant absorption, thus light absorption en-

hancement of OSCs is maximized. By taking spherical Ag

nanoparticles into an OSC system with an active layer of

poly(3-hexylthiophene) and [6, 6]-phenyl-C61-butyric acid

methyl ester as subject, light absorption increase of 26 % at an

average wavelength of incident light is demonstrated. This

design method is also applicable to other types of OSCs.

Keywords OSC . LSPR .NPs . Light absorption

Introduction

In the promising field of solar cells, organic solar cells (OSCs)

are advantageous in its light weight, low cost, low temperature

fabrication, and mechanical flexibility. Although the power

conversion efficiency of OSCs has been increased to over 6 %

[1], significant improvement in the efficiency of the cells is

still required to make them competitive with grid power. Themain reason is poor light absorption. Due to low carriers

mobility, active layers of OSCs must be thin (less than

hundreds of nanometers) in order to meet the short diffusion

length of carriers [2], which lead to insufficient light absorp-

tion. Therefore, the key to optimizing the performance of

OSCs is the combination of shortening the carrier transport

paths as much as possible by reducing the thickness of films

and enhancing light absorption.

One possible way to enhance light absorption of OSCs is

to utilize the field enhancement of localized surface plasmon

resonance (LSPR) excited by metallic nanoparticles (NPs)

array [3

6]. When LSPR is excited, energy scattered andabsorbed by metallic NPs occurs simultaneously, and they

are highly sensitive to the size and distribution of NPs, and

the surrounded medium. In fact, only energy scattered by

NPs is useful for OSC while absorption of NPs undermines

OSCs performance due to a loss of incident light and

thermal effect. However, most records of the utilization of

metallic NPs provide only experiential parameters instead of

optimal ones from systematic design [711], thus a method

for designing the parameters of metallic NPs to explore the

highest scattering efficiency that enhances light absorption

is needed immediately.

In this paper, a universal design method is presented forlight absorption enhancement in ultra-thin film OSCs with the

introduction of metallic NPs. Based on Mie theory, a mecha-

nism of energy scattered and absorbed by NPs under LSPR is

analyzed systematically. Then the relationship between scat-

tering efficiency and the size parameter of metallic NPs is set

up. With the method, the optimal size of metallic NPs can be

obtained by means of the relationship. Simulation results of

OSC device with poly(3-hexylthiophene) and [6, 6]-phenyl-

C61-butyric acid methyl ester (P3HT:PCBM) demonstrate

C. Sun : H. Gao : C. Li : C. Du (*)Chongqing Institute of green and intelligent technology, Chinese

Academy of Sciences,

Chongqing 401122, China

e-mail: [email protected]

C. Sun : R. Shi : C. LiPhysics Department, Sichuan University,

Chengdu 610064, Peoples Republic of China

Plasmonics

DOI 10.1007/s11468-012-9450-5


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that the light absorption in the active layer increases 26 % at

the optimized condition.

Design Method

The schematic of OSC investigated is shown in Fig. 1,

which is constituted by four layers from top to bottom:indium tin oxide glass, a buffer layer with PEDOT:PSS,

an active layer with P3HT:PCBM and Al electrode.

Spherical Ag NPs array is immersed in the buffer layer

(the thickness of 100 nm was selected). The thickness

of active layer is set to be 35 nm to ensure large

exciton collection. When the OSC is lighted, LSPR

can be excited by Ag NPs, and energy scattering and

absorption of Ag NPs occur simultaneously. In order to

realize the maximized light absorption enhancement of

OSC, the parameters of Ag NPs, mainly the size of

diameter and the period, should be optimized.

Determination for the Size of Metallic NPs

According to the classical Mie theory [12], light scattering

and absorption by a spherical NP embedded in a homoge-

neous non-absorbing medium can be formulated. The rates

at which energy is absorbed and scattered are determined by

the cross-sections of absorption (abs) and scattering (sca).

When LSPR is excited, abs and sca include all kinds of

LSPR mode. Based on the report of Bohren and Huffman

[13], the overall scattering and absorption cross-section can

be expressed as:

sca X1n1

nsca l

2

2p

X1n1

2n 1 anj j2 bnj j

2

1

abs X1n1

nabs

l

2

2p

X1n1

2n 1 Re an bn X1n1

2n 1 anj j2 bnj j

2 ( )

2

Where

an m2jn mx xjnx

01jnx mxjn mx 0

m2jn mx xh1n x

h i01h

1n x mxjn mx

03

bn

1j

nmx xj

nx 0j

nx mxj

nmx 0

1jn mx xh1n x

h i0h

1n x mxjn mx

0 4

Here, an

and bn

are called Mie coefficients that are

determined by the boundary conditions of the field at sphere

surface. They are the key parameters in Mie theory for

computing scattered field. m "11 1 2= " =

1 2=is the

relative refractive index, 1, 1, and , are permittivity,

permeability of particle, and ambient medium, respectively.

The function jn

(z), yn

(z), and h1n z jnz iynz are

spherical Bessel functions of order n. Index n runs from 1

to

, and this infinite series occurring in Mie formulas canbe truncated at a maximum, nmax, this number has been

proposed as:

nmax x 4x1 3= 2 5

x is called size parameter and given by x0kr, r is the sphere

radius, k02/ is the wave number, and is the wavelength

in the ambient medium.

For sufficiently small NP (comparable with the wave-

length of the incident light), it is accurate to determine the

absorption and scattering of NP by retaining only the dipolar

modes [14]. Thus, scattering and absorption cross-section is

given by:

sca 1

6p

2p

l

4aj j2 6

abs 2p

lIm a 7

Here, is the polarizability of the particle for a small

spherical particle, given by:

a 4pr3"0 1

"0

2 8

Here, "0 "1 "= is the relative permittivity of particleand ambient medium. Hence, through taking the polar-

izability into Eqs. 6 and 7, it can be computed that absis much larger than sca. It clearly indicates that absorp-

tion of small NPs dominates in LSPR and such fact

implies that if small NPs are introduced into OSC,

much energy will be absorbed by NPs themselves. In

this condition, enhancement caused by LSPR of NPs

has less contribution to OSC.

Fig. 1 Schematic representation of bulk heterojuction OSC with

spherical Ag NPs array incorporated into buffer layer, D and P denote

the diameter and period of Ag NPs, respectively

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As the size of NPs increases, conduction electrons across

the particle no longer move in phase, polarizability of me-

tallic NPs will be lower and will further lead to multilevel

resonance mode [15], hence the overall cross-section is the

overall contributions from all normal modes, as shown in

Eqs. 1 and 2, which means more energy will be scattered

into the active layer of OSC. Although scattered light can be

harvested in the active layer through high-order modes ofscattering of NPs, the increased absorption of NPs will also

lead to more loss of incident light and worse thermal effect.

To describe the relationship between scattering and ab-

sorption, we define the scattering efficiency (Qsca) as

Qsca sca

sca abs9

In the definition, most of the energy will be scattered into

OSC only when Qsca is maximized, and Qsca can be decided

by computing the cross-section of scattering and absorption.

According to Eqs. 1 and 4, three key parameters govern

the overall scattering and absorption of LSPR in NP: the sizeof the NP, NPs optical property relate to the surrounding

medium and incident wavelength . These parameters are

all included in the size parameter x (because is the wave-

length in the ambient medium) mentioned above. Thus, the

relationship between scattering and absorption of LSPR and

the size parameter x in Eq. 5 is built, and the highest

scattering efficiency will be achieved by modulating the size

parameter x. After x is made sure, we take certain wave-

length into size parameter by x02a/, such wavelength is

picked from the peak range of absorption spectrum of active

layer which is the most propitious absorbed by OSC. Hence,

the size of NPs will be obtained and the maximum enhance-

ment of absorption can also be achieved.

According to the above analysis, calculation is carried

out and the dependency of scattering, absorption, and Qscain Ag NPs on different size parameter x02a/ is repre-

sented, as is shown in Fig. 2. The incident wavelength is

350800 nm, and material properties in the calculation are

provided by the handbook of Palik [16].

Figure 2a shows the curves of both scattering and

absorption of Ag NPs. It is clear that strong scattering

is obtained when the size parameter x is from 0.5 to 0.7,

which is caused by the high-order modes of LSPR. In

this range, size parameter x around 0.635 witnesses the

highest Qsca, which means that relatively strong scattering

and low absorption occur simultaneously so that most of

the energy in LSPR is scattered by Ag NPs. Taking the

absorption spectrum of P3HT:PCBM (Fig. 2b) into con-

sideration, incident light is more propitious to be

absorbed by the active layer at the wavelength of around

500 nm. According to Eq. 5, the size of Ag NPs satisfies

the relationship 2r0x /, and when taking the wave-

length into this formula, the optimal diameter of Ag NPs

is calculated to be 100 nm, which corresponds to the

highest scattering efficiency of Ag NPs.

Period Optimization

After optimal size of metallic NPs for OSCs is designed,

another effect should be taken into consideration. In prac-

tice, metallic NPs in a periodic array are introduced, it will

strongly influence LSPR. In periodic structure, interaction

between metallic NPs will be excited by the interference of

the polarized electric field of particles [17], which is called

electric resonance and shown in the inset of Fig. 3c. Since

different periods lead to different energy densities between

metallic NPs, it is important to clarify the impact of period

on scattering and absorption by metallic NPs. Thus, a sim-

ulation about electric resonance of the periodic square-

arrayed metallic NPs in different array periods is carried

out, and we utilize spherical Ag NPs of 100 nm diameter

as determined above. In this simulation, transmission and

absorption of incident light in Ag NPs array is calculated

which can reflect the influences on LSPR of periodic Ag

Fig. 2 a Mie efficiency of scattering and absorption in Ag NP (lefty-

axis) and scattering efficiency Qsca (right y-axis) in different size

parameter. b Imaginary parts of refractive index k (absorption spec-

trum) of active layer with P3HT:PCBM

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metallic by electric resonance. The simulation is conducted

in a wide range of array periods, the transmission and

absorption spectrum of Ag NPs array in different periods

are shown in Fig. 3a and b, from which the peaks of the

curve imply the excited of LSPR in Ag NPs.

From Fig. 3a and b, the influences on LSPR of

metallic NPs by its periods can be well summarized as:

(1) For the periods less than 500 nm, as metallic NPs aresetting close, the peak of resonance will move to short-

wave direction, the intensity of resonance will also be

strengthened which lead to a stronger scattering than that

excited by single NP, and it will have a contribution to

light absorption in OSCs, however, excessively close an

array which less than 200 nm may greatly block incident

light, and it leads to no transmission in metallic NPs and

prevents light from reaching the active layer when intro-

duced into OSCs; (2) For period more than about

500 nm, too wide an array undermines the interaction

between metallic NPs, which demonstrates a resonance

similar to one excited by a single metallic NP, and theeffect of electric resonance disappear.

According to above simulation, absorption spectrums of

OSC with square-arrayed Ag NPs of different periods are

calculated and a contrast can be made. The diameter of the

Ag NPs is set at an optimized value of 100 nm. The simu-

lation is conducted in a range of periods from 250 to

650 nm, and the absorbing spectrums of OSC are shown

in Fig. 3c with symbol line, spectrum of OSC without Ag

NPs is also presented in the figure with a dash line.

From Fig. 3c, it can be seen that absorption is greatly

enhanced when the period is in the range of 250450 nm,

which means that scattered energy by Ag NPs is trapped by

the active layer of OSC effectively. In this range, electric

resonance between metallic NPs has the positive contribu-

tion to OSC. The average absorption enhancement of OSC

at the wavelength of 350800 nm is further calculated at this

period range. The result is shown in Fig. 3d, the largestabsorption enhancement 26 % is obtained when the period

of the Ag NPs is 328 nm.

Discussion

Based on the above analysis, the method has been setup and

can be well utilized in the design of OSC presented in Fig. 1.

By using the optimized diameter and period for the spherical

Ag NPs, the absorption spectrum (solid line) of the OSC is

shown in Fig. 4. Comparing to the spectrum (dash line)

without Ag NPs, the enhanced region lies mainly in thewavelength of 400600 nm. The enhancement rate for the

two spectral curves is also calculated as shown in the

symbol-line, in which the maximum enhancement rate of

60 % is demonstrated by the active layer at the wavelength

of 490 and 600 nm. Although these two enhancement peaks

exhibit mismatch with peak value of P3HT:PCBMs absorb-

ing spectrum at 500 nm, such absorption spectrum satisfies

our design and is the optimized one that realizes not only

26 % increase at average but also broadband absorption.

Fig. 3 a Transmission of

incident light in Ag NPs arraywith different periods, b

absorption of incident light in

Ag NPs array with different

periods, c absorption spectrum

of our OSC with Ag NPs in

different periods of 150, 250,

350, 450, 550, 650 nm and the

one without Ag NPs. Inset:

sketch map of electric

resonance effect. d Average

absorption enhancement of

OSC within 350800 nm

incident wavelengths, period of

Ag NPs is in the range of 250

450 nm. The optimal structureof Ag NPs can be obtained with

a diameter of 100 nm and

period of 328 nm

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It is shown in Fig. 4 that four absorption peaks, 448, 491,

533, and 588 nm are located in the enhanced region of

absorption spectrum. We further picked these absorptionpeaks to observe the scattered field and energy distribution

around Ag NPs, which is shown in Fig. 5, the electric field

lines are also presented to exhibit the mode shapes. In Fig. 5a

and b, localized surface plasmon energy mainly distributes on

both sides and circumambience of NP, and transmits along the

surface of Ag NPs into the active layer. In Fig. 5c and d, both

of the energy is concentrated on the top and bottom of Ag

NPs. The energy localized on the top is mainly absorbed by

Ag NPs, which does not contribute to OSC. The energy

localized in the bottom penetrates into the active layer effec-

tively, which leads to absorption enhancement of the active

layer. The figures show that localized energy in the bottom of

Ag NPs at 588 nm is stronger than that at 533 nm. Accord-

ingly, absorption enhancement of the active layer at 588 nm is

much higher as is shown in Fig. 4. Generally, it is clear thateach absorption peak is corresponding to different modes of

LSPR which lead to different energy distribution; these dif-

ferent modes of LSPR are all included in the Mie scattering

that is analyzed above. Energy scattered into the active layer

finally improves the performance of OSC.

The fabrication of OSC system with metallic NPs intro-

duced into buffer layer is possible. To be specific, metallic

NPs of 100 nm can be prepared through chemical methods

[18] and incorporated into buffer layer of PEDOT:PSS, and

then both the active layer and buffer layer with metallic NPs

can be prepared by spin coating.

Conclusion

In conclusion, a universal method is presented for designing

the parameters of metallic NPs, which is introduced into ultra-

thin film OSCs to enhance light absorption of the active layer.

On the basis of Mie theory, size parameter of metallic NPs is

Fig. 5 Distribution of energy

on the surface of spherical Ag

NPs and active layer at the

absorption peaks of a 448, b

490, c 533, and d 588 nm whenLSPR excited by Ag NPs in

100 nm diameter with period of

328 nm. The arrowheads

denote the electric field lines

Fig. 4 Left y-axis, the absorption spectrums of the OSC with the

optimal Ag NPs (solid line) and the one without NPs (dash line); right

y-axis, the enhancement rate for the two absorption spectrums

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calculated firstly to achieve the highest Qsca. Combined with

the absorption spectrum of the active layer, the optimized size

of metallic is designed to realize the highest scattering effi-

ciency in the action wavelength region of the active layer.

Through optimal designing, Ag NPs in such OSC system

realizes an increase of 26 % in light absorption at an average

wavelength and 60 % increase of light absorption around the

peak wavelength of absorption spectrum of the active layer.Further discussion demonstrates that absorption enhancement

is caused by different LSPR modes which are all contained in

the Mie scattering mechanism.

Acknowledgments This work was supported by the Chinese Nature

Science grant nos. 11074251, 61007024, and 11174281.

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