knjiga solarna energija dobra

86 THE PHYSICS OF THE SOLAR CELL
Thus, in 1D, utilizing the Einstein relationship, the electric field can be written as
⃗E = kT q
1 dp o
p o dx
(3.92)
Rewriting equation (3.85) and substituting equation (3.92) yields
V bi =
∫ xP
−x N
∫ xP
Edx ⃗
kT
=
−x N
q
1
p o
dp o
dx dx = kT q
∫ po (x P )
p o (−x N )
dp o
= kT [ ]
p o q ln po (x P )
p o (−x N )
(3.93)
Since we have assumed nondegeneracy, p o (x P ) = N A and p o (−x N ) = n 2 i /N D. Therefore,
V bi = kT [ ]
q ln ND N A
n 2 . (3.94)
i
Figure 3.14 shows the equilibrium energy band diagram, electric field, and charge density
for a simple abrupt pn-junction silicon diode in the vicinity of the depletion region.
The conduction bandedge is given by E C (x) = E 0 − qφ(x) − χ, the valence bandedge
qf(x)
c
E 0
E
E C
(a)
qV bi
E i
E F
E V
E →
(b)
qN D
0
r
(c)
0
−qN A
x = −x N x = 0
x = x P
Figure 3.14 Equilibrium conditions in a solar cell: (a) energy bands; (b) electric field; and
(c) charge density