Theoretical Studies of Plasmonic Effects in Organic Solar Cells - Organic Solar Cells: Materials and Device Physics - page 186

where n c ¼ n r þ i 0 k i is the complex refractive index of the active material, k is the
incident wavelength, and c 0 is the speed of light in free space. It is worth mentioning
that the absorption of metallic nanostructures should be precluded in the volume
integral above. A spectral enhancement factor is the absorption spectrum of the
OSC incorporating metallic nanostructures over that excluding the nanostructures.
Integrating with a standard solar irradiance spectrum (air mass 1.5 global), one
can get the total absorption of OSCs

800 nm

Z

T A ¼ S A ð k Þ C ð k Þ dk ð 7 : 30 Þ

400 nm

where C is the solar irradiance spectrum. Likewise, a total enhancement factor is
the total absorption of the OSC incorporating metallic nanostructures over that
excluding the nanostructures. In addition, a total absorptivity is also an important
physical quantity to evaluate the absorption performance of OSCs, i.e.
A ¼ R 800 nm

400 nm S A ð k Þ C ð k Þ dk
R 800 nm
400 nm C ð k Þ dk

ð 7 : 31 Þ

The exciton generation rate, which determines the short current of OSCs, can be
written as

G ð r Þ¼ Z

800 nm

2p
h

n r ð k Þ k i ð k Þ e 0 j E ð r Þj 2 C ð k Þ dk ð 7 : 32 Þ

400 nm

where h is the Planck constant.
Except for the above physical quantities essential to the performance of OSC,
there are several quantities that can facilitate understanding the physics of plas-
monic effects. The scattering cross-section, which can estimate the scattering
strength of a metallic nanostructure, is defined by [ 79 , 80 ]
r s ¼ R s Re

dS

2 E s conj H ðÞ

1

ð 7 : 33 Þ

j S i j

where ''conj'' denotes the complex conjugation, S is an arbitrary surface enclosing
the metallic nanostructure, S i ¼ 2 E i conj H i is the incident energy flux, and
E s and H s are the scattered electric and magnetic fields, respectively. Considering
the total power absorbed by a metallic nanostructure, the absorption cross-section
is of the form [ 79 , 80 ]
r a ¼ R s Re

dS

¼ R v k 0 e 0 r ð r Þj E ð r Þj 2 dV
j E i j 2

1

2 E conj ðÞ

ð 7 : 34 Þ

j S i j