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2. Properties of Semiconductors for Solar Cells 11

N D is the donor concentration and N A , is the acceptor concentration. The conductiv-
ity increases by increasing the doping of semiconductor according to Eqs. (1.2a)
and (1.2b).

2.3 THE SEMICONDUCTOR CURRENTS

If a voltage V is applied across a semiconductor bar with length L and cross-sectional
area A, a current will flow in the bar because of the drift of electrons and holes under
the influence of the electric field E developed by the voltage V in the bar as shown in
Fig. 1.8.
This current follows the ohm’s law for relatively small electric fields, i.e.,
V

I ¼ qA m n þ m p hAJ d (1.3)
p
n
L
where
V
J d ¼ sE and E ¼
L
J d is the drift current density. The mobility m is the ability of the mobile charges to
acquire drift velocities in the presence of the electric field.
Another type of current exists in a semiconductor when concentration differ-
ences of mobile changes are present. Such current is termed the diffusion current
J dif . This current can be expressed by
vn
J ndif ¼ qD n for electrons; and (1.4a)
vx
vp
J pdif ¼ qD p for holes (1.4b)
vx
where D n and D p are the diffusion coefficients for electrons and holes, respectively,
and vn and vp are the concentration gradients for electrons and holes, respectively.
vx vx
The diffusion coefficient D is related to the mobility by the Einstein equation
k B T
D ¼ m ¼ mV T (1.5)
q

FIGURE 1.8
A drift current I in a semiconductor by applying voltage V.