Using Eqs. (6.1) and (6.22), which determine the band gap, and the positions of the
Fermi energy in the n- and p-type semiconductor, respectively,
E G = E C − E V ,
E 1 = E C − E F = k B T ln (N C /N D ),
E 2 = E F − E V = k B T ln (N V /N A ).
We can write
Using the relationship between the intrinsic concentration, n i and the band gap, E G [see Eq.
(6.9)],
we can rewrite Eq. (8.15) and obtain
This equation allows us to determine the built-in potential of a p-n junction from the
standard semiconductor parameters, such as doping concentrations and the intrinsic carrier
concentration.
We can calculate the width of the space charge region of the p-n junction in the
thermal equilibrium starting from Eq. (8.13). Using Eq. (8.8), either ℓ n or ℓ p can be
eliminated from Eq. (8.13), resulting in expressions for ℓ n and ℓ p respectively,
The total space-charge width, W, is the sum of the partial space-charge widths in the nand p-type semiconductors. Using Eq. (8.17) we find
The space-charge region is not uniformly distributed in the n- and p- regions. The
widths of the space-charge region in the n- and p-type semiconductor are determined by