knjiga solarna energija dobra

68 THE PHYSICS OF THE SOLAR CELL
1.0
0.8
Fermi function
0.6
0.4
0 K
300 K
400 K
0.2
0.0
−0.4 −0.3 −0.2 −0.1 0.0 0.1 0.2 0.3 0.4
E − E F
[eV]
Figure 3.4
The Fermi function at various temperatures
and
( 2πm
∗ )
p kT 3/2
N V = 2
. (3.14)
h 2
When the Fermi energy, E F , is sufficiently far (>3 kT) from either bandedge, the carrier
concentrations can be approximated (to within 2%) as [7]
and
n o = N C e (E F−E C )/kT
p o = N V e (E V−E F )/kT
(3.15)
(3.16)
and the semiconductor is said to be nondegenerate. In nondegenerate semiconductors, the
product of the equilibrium electron and hole concentrations is independent of the location
of the Fermi energy and is just
p o n o = n 2 i = N C N V e (E V−E C )/kT = N C N V e −E G/kT . (3.17)
In an undoped (intrinsic) semiconductor in thermal equilibrium, the number of electrons in
the conduction band and the number of holes in the valence band are equal; n o = p o = n i ,
where n i is the intrinsic carrier concentration. The intrinsic carrier concentration can be
computed from (3.17), giving
n i = √ N C N V e (E V−E C )/2kT = √ N C N V e −E G/2kT . (3.18)