Page 52 - Applied Photovoltaics

holes
electrons

p n

V

Figure 2.10. Application of a voltage to a p-n junction.

Once Ê is no longer large enough to stop the flow of electrons and holes, a current is
produced. The built in potential reduces to V bi – V and the current flow increases
exponentially with the applied voltage. This phenomenon results in the Ideal Diode
Law, expressed as
ª § qV · º
I I 0 « exp ¨ ¸ 1 » (2.2)
¬ © kT ¹ ¼
where I is the current, I 0 is the dark saturation current (the diode leakage current
density in the absence of light), V is the applied voltage, q is the charge on an
electron, k is Boltzmann’s constant and T is absolute temperature.
Note that
x I 0 increases as T increases
x I 0 decreases as material quality increases
x at 300 K, kT/q = 25.85 mV, the thermal voltage.
For actual diodes, the Eqn. (2.2) becomes

ª § qV · º
I I exp ¨ ¸ 1 (2.3)
0 « »
¬ © nkT ¹ ¼
where n is the ideality factor, a number between 1 and 2 that typically increases as the
current decreases.
The diode law is illustrated for silicon in Fig. 2.11.

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