Page 45 - Advances in Renewable Energies and Power Technologies

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

D p p no
0I pi ¼ qA e V a =V T 1 (1.16)
L p
Similarly, we get I ni

D n n po
I ni ¼ qA e V a =V T 1 (1.17)
L n
where A is the diode area. Summing up Eqs. (1.16) and (1.17) we obtain the final
expression for I in terms of the voltage V a , i.e.,
2
D p n i D n n 2
i
I ¼ qA þ e V a =V T 1 (1.18)
L p N D L n N A
The current I could be written in the following form:

I ¼ I s e V a =V T 1 (1.19)
with I s ¼ the pre-exponential factor of Eq. (1.19), which is termed the reverse satu-
ration current. It is the current which flows in the ideal diode with a reverse bias
greater than 3V T . In the solar cell mode of the diode, it will be forced to forward
bias, which causes energy loss because the current passing through it. This current$
is a loss current. Therefore, for proper operation in the solar cell mode, the forward
diode current must be minimized. This can be achieved according to Eq. (1.18) by
increasing the doping concentrations N A and N D and the diffusion lengths L n and L p
and decreasing n i by selecting a material with higher energy gap. This is in agree-
ment with the requirement for higher 4.

3.3 REAL DARK DIODE CHARACTERISTICS

The solar cell diode contains an Ohmic resistance dropping a part of the applied
forward voltage, especially apparent at high diode currents as shown in Fig. 1.15.
The leakage current of the diode is much larger than I s . These nonideal effects are
normally modeled by an equivalent circuit consisting of two resistances R s and R sh
along with an ideal diode as will be discussed later, where R s is the series resistance
of the diode and R sh is the shunting resistance of the diode.
In deriving the diode current, the recombination current I scr in the space charge
region is neglected as its width is much smaller than the diffusion lengths. In diodes
with appreciable space charge width which is compared to the widths of the neutral
regions, this recombination current in the space charge region cannot be neglected.
I scr can be expressed by [13].

W scr V j =2V T
I scr ¼ qAn i e (1.20)
T scr
where W scr is the width of the space charge region and T scr is the lifetime of car-
riers in the space charge region. In heterojunctions with high interface state