Theoretical Studies of Plasmonic Effects in Organic Solar Cells - Organic Solar Cells: Materials and Device Physics - page 184

2
4

3
5 ¼

2
4

3
5

2
4

3
5

E 1
E 2
E 3

L 11 L 12 L 13 J 1

J 2
J 3

ð 7 : 18 Þ

L 21 L 22 L 23

L 31 L 32 L 33

where

L ii þ L ii ; i ¼ j
L ij ; i 6¼ j

L ij ¼ ð 7 : 19 Þ

L ii J i ¼ i 0 xl 0 Z
v

g ð r ; r 0 Þ J i ð r 0 Þ dr 0 ð 7 : 20 Þ

Z

g ð r ; r 0 Þ o J j ð r 0 Þ
ou j

L ij J j ¼ i 0
xe 0

o
ou i

dr 0 ð 7 : 21 Þ

v

h i g ð r ; r 0 Þ:
Using the roof-top basis functions to expand the unknown currents, we have

where g ð r ; r 0 Þ is the scalar Green's function, and G ð r ; r 0 Þ¼ I þ rr
k 0

J ð r Þ¼ X u i X

k ; m ; n

3

J i ð k ; m ; n Þ T k ; m ; n ð 7 : 22 Þ

i ¼ 1

where T k ; m ; n , T k ; m ; n , and T k ; m ; n

are the volumetric roof-top functions given by

T k ; m ; n ¼ K k ð u 1 Þ P m ð u 2 Þ P n ð u 3 Þ
T k ; m ; n ¼ P k ð u 1 Þ K m ð u 2 Þ P n ð u 3 Þ
T k ; m ; n ¼ P k ð u 1 Þ P m ð u 2 Þ K n ð u 3 Þ

ð 7 : 23 Þ

The functions K k ð u 1 Þ and P m ð u 2 Þ are defined by

(

K k ð u 1 Þ¼ 1 u 1 kDu 1

j j

; j u 1 kDu 1 j Du 1

Du 1

0 ; else

( ð 7 : 24 Þ

Du 2 \ Du 2

2

u 2 m 2

P m ð u 2 Þ¼ 1 ;

0 ; else

The cuboid cells are employed to discretize the structure to be modeled. Here, Du 1
and Du 2 are the grid sizes of each small cuboid along x and y directions,
respectively. Other functions in ( 7.23 ) can be defined in the same way.
As a result, the discretized form for the operator L ii in ( 7.20 ) can be written as