Theoretical Studies of Plasmonic Effects in Organic Solar Cells - Organic Solar Cells: Materials and Device Physics - page 188

7.4.1 Periodic Back Nanostrips

We systematically study the angular response of a thin-film OSC with a periodic
metal back nanostrips. The generalized equation of Lambert's cosine law for
arbitrary periodic structure is formulated. We find that the periodic strip structure
can achieve wide-angle absorption enhancement compared with the (planar)
nonstrip structure for both the TE- and TM-polarized light. The quasi-guided
modes supported by the periodic strip structure contribute to the enhancement for
the TE-polarized light. The SPRs excited by the subwavelength Au nanostrips
contribute to the enhancement for the TM-polarized light.
The energy conservation law in a periodic structure is given by

Z 1
2

dS ¼ Z n r k i xe 0 j E j 2 dV

Re E i conj H i

½ 1 L ð h Þ ð 7 : 39 Þ

where E i and H i are the incident electric and magnetic fields, S is a virtual planar
surface in front of a unit cell of the SC, n c ¼ n r þ i 0 k i are the complex refractive
indices of the active materials, and L ð h Þ is an energy loss fraction. One part of the
energy loss is the scattering loss, which can be characterized by the summation of
the reflectance and transmittance of the periodic structure [ 66 ]. The scattering loss
can be reduced by the light guiding, enhancement, and trapping schemes. Another
part of the energy loss is the metallic absorption loss, which can be reduced by
engineering the metal's size, material, and position. The irradiance of the Sun is
the incident power per unit area of an electromagnetic radiation at the surface, i.e.

2

Re E i conj H i

n ¼ E i

I ¼ 1
2

cos h ð 7 : 40 Þ

2Z 0

where Z 0 ¼ l 0 = e p is the wave impedance of free space and h is the incident

angle of the sunlight with respect to the normal direction of the surface S. For the
Lambertian bulk cells, which have an angle-independent energy loss fraction L, the
absorption of the active layers represented by the right hand of Eq. ( 7.39 ) obeys
Lambert's cosine law that the absorption is a cosine function of the incident angle
h. Eq. ( 7.39 ) is a generalized equation of Lambert's cosine law for any periodi-
cally structured SCs.
Figure 7.2 a illustrates a typical structure of standard OSCs without any opti-
mizations. The heterojunction active layer is composed of copper phthalocyanine
(CuPc) and fullerene ð C 60 Þ as an electron donor and acceptor, respectively.
The bathocuproine (BCP) layer is a spacer layer for extracting electrons. A metallic
back nanopattern is made from an Au strips and Poly(3,4-ethylenedioxythio-
phene):poly(4-styrenesulfonic acid) (PEDOT:PSS; AI4083) that can collect holes.
We use the FDFD method presented in Sect. 7.3.2 to calculate the angular response
of the OSC. For the angular response simulation, a challenging problem lies at
the wide angle ð 0 -90 Þ and broadband (400-800 nm) calculations. We employ the
high-performance parallel computing technique to tackle the problem.