21.4 Bipolar Diodes
561
Fig. 21.45 a Diffusion potential, b band diagram, c electric field, d electron and hole concentrations and e n + p under
forward bias +0.4 V (left panel) and reverse bias (right panel) −0.4 V for a silicon pn diode at room temperature with
N A = N D = 10 18 cm −3 (same as in Fig. 21.41). The dashed lines in (b) are the electron and hole quasi-Fermi levels
F n and F p . The depletion layer is shown as the grey area. The diffusion length in the n- and p-type material is taken as
4 nm. This value is much smaller than the actual diffusion length ( µm-range) and is chosen here only to show the carrier
concentration in the depletion layer and the neutral region in a single graph
is very small and the quasi-Fermi levels φ n,p are practically constant. The electron and hole currents
are shown in Fig. 21.46 together with the carrier densities; a more detailed calculation of currents than
presented here can be found in [1763]. The change of carrier density in the depletion layer is mostly
due to the variation of ψ (or E i ).
Therefore, the voltage drop across the depletion layer is V = φ p − φ n and (21.122) reads
n p = n
2
i exp (βV ) .
(21.125)
The electron density at the boundary of the depletion layer on the p-side (at x = −x p ) is (using
(21.125))
n p =
n
2
i
p p
exp (βV ) = n p 0 exp (βV ) .
(21.126)
Similarly, the hole density on the n-side at x = x n is given by
p n = p n 0 exp (βV ) .
(21.127)
561
Fig. 21.45 a Diffusion potential, b band diagram, c electric field, d electron and hole concentrations and e n + p under
forward bias +0.4 V (left panel) and reverse bias (right panel) −0.4 V for a silicon pn diode at room temperature with
N A = N D = 10 18 cm −3 (same as in Fig. 21.41). The dashed lines in (b) are the electron and hole quasi-Fermi levels
F n and F p . The depletion layer is shown as the grey area. The diffusion length in the n- and p-type material is taken as
4 nm. This value is much smaller than the actual diffusion length ( µm-range) and is chosen here only to show the carrier
concentration in the depletion layer and the neutral region in a single graph
is very small and the quasi-Fermi levels φ n,p are practically constant. The electron and hole currents
are shown in Fig. 21.46 together with the carrier densities; a more detailed calculation of currents than
presented here can be found in [1763]. The change of carrier density in the depletion layer is mostly
due to the variation of ψ (or E i ).
Therefore, the voltage drop across the depletion layer is V = φ p − φ n and (21.122) reads
n p = n
2
i exp (βV ) .
(21.125)
The electron density at the boundary of the depletion layer on the p-side (at x = −x p ) is (using
(21.125))
n p =
n
2
i
p p
exp (βV ) = n p 0 exp (βV ) .
(21.126)
Similarly, the hole density on the n-side at x = x n is given by
p n = p n 0 exp (βV ) .
(21.127)