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16 CHAPTER 1 Solar Cells and Arrays: Principles, Analysis, and Design

the metallurgical junction. They leave behind them un-neutralized acceptor and
donor ions as shown in Fig. 1.13. The electric field associated with the charges es-
tablishes opposing forces for further migration of holes and electrons, leading to
equilibrium such that no net current of either type exists. The width of this field re-
gion under no bias is of the order of few tenths of a micrometer depending on the
doping concentrations N A and N D . There is a potential difference associated with
this built-in or internal electric field. The name built-in comes from the fact that
this electric field is caused by the material inhomogeneity and not by an external
electric source. This built-in potential difference is termed the contact difference
of potential pointing out that such potential differences are formed if two dissimilar
materials are brought into intimate contact as in a pen junction where it could be
thought that a pen junction is formed by intimately contacting p- and n-type mate-
rials. The contact difference of potential 4 can be expressed by
!
N A N D
4 ¼ V T ln 2
n
i
The contact difference of potential 4 separates the two sides of the pen junction
and therefore constitutes a potential barrier. The electromotive force of the solar cell
as a photoelectric generator is directly related to 4.As 4 increases, the open-circuit
voltage of the cell increases. So, the doping concentrations N A and N D must be as
high as possible. Also, 4 can be increased by selecting a material with higher E g
and consequently with lower n i . The field region is essential for the solar cell oper-
ation. It originates the electromotive force of the cell exactly like the chemical
battery.

3.2 THE IDEAL DARK IeV CHARACTERISTICS OF THE PeN DIODE
Let us now study the current conduction in a forward biased pen diode. To forward
bias the diode, a battery with a voltage V a is connected across the diode with the pos-
itive poles connected to the anode attached to the p-side, whereas the negative pole is
connected to the cathode attached to the n-side as shown in Fig. 1.14.
On forward biasing the diode, the space charge region contracts and the separa-
tion potential decreases. Consequently, holes will be injected from the p-side to the
n-side and electrons will be injected from the n-side to the p-side as illustrated in
Fig. 1.14. The injected holes Dp diffuses away from the space charge region edge
at x ¼ 0 towards the metallic contact where they recombine gradually in the n-
side. The same happens with electrons injected from n-side to the p-side. The rate
of injection of holes across the field region gives a current I pi while that of electrons
gives a current I ni . The total diode current

I ¼ I pi þ I ni (1.10)
As illustrated in Fig. 1.14, the injected charges decay exponentially with distance
measured from the edges of the field region [11].