Page 44 - Advances in Renewable Energies and Power Technologies

3. The Dark pen Junction Diode 17

FIGURE 1.14
Distribution of excess electrons and holes in a forward-biased diode.

DpðxÞ¼ Dpð0Þe x=L p and (1.11)
DnðxÞ¼ Dnð0Þe x=L n (1.12)
where Dp(0) and Dn(0) are the injected hole and electron concentration.
p
p ffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffi
L p ¼ D p s p and L n ¼ D n s n (1.13)
L p and L n are the diffusion lengths of holes in the n-side and electrons in the p-side.
By definition, s n is the lifetime of electrons in the p-side and s p is that of holes in the
n-side. The applied voltage V a is related to Dp(0) and Dn(0) by the law of the junc-
tion expressed as [11].

Dpð0Þ¼ p no e V a =V T 1 and (1.14)

Dnð0Þ¼ n po e V a =V T 1 (1.15)

where p no ¼ n 2 ¼ the minority carrier concentration in the n-side at no bias, and
i N D
n po ¼ n 2 ¼ the minority electron concentration in the p-side. Then we can get I pi
i N A
because it is the diffusion current at x ¼ 0, i.e.,

vp
I pi ¼ qAD p
vx
x¼0