556
21 Diodes
Fig. 21.41 pn junction
(abrupt approximation) in
thermal equilibrium (zero
bias) for Si at room
temperature and
N A = N D = 10 18 cm −3 . a
Schematic representation
of p-doped and n-doped
region with depletion layer
(grey area) and fixed space
charges, b diffusion
potential, c band diagram
with Fermi level (dashed
line), d electric field, e
free-carrier concentrations
n and p and f total
free-carrier density n + p
n p 0 = n n 0 exp (−βV bi )
(21.102a)
p n 0 = p p 0 exp (−βV bi ) .
(21.102b)
Microscopically, the equilibration of the Fermi levels on the n- and p-side occurs via the diffusion
of electrons and holes to the p- and n-side, respectively. The electrons and holes recombine in the
depletion layer. Therefore, on the n-side the ionized donors and on the p-side the ionized acceptors
remain (Fig. 21.41a). These charges build up an electric field (Fig. 21.41d) that works against the
diffusion current. At thermal equilibrium the diffusion and drift currents cancel and the Fermi level is
constant.
Values for the built-in potential are depicted in Fig. 21.42 for Si and GaAs diodes. The spatial
dependence of the potential in the depletion layer is determined by the Poisson equation.
We assume here the complete ionization of the donors and acceptors. Also, we neglect at first majority
carriers in the depletion layers on the n- and p-sides.
22 With these approximations, the Poisson equation
in the depletion layers on the n- and p-side reads
22 An abrupt decrease of the majority carrier density at the border of the space-charge region corresponds to zero
temperature.
21 Diodes
Fig. 21.41 pn junction
(abrupt approximation) in
thermal equilibrium (zero
bias) for Si at room
temperature and
N A = N D = 10 18 cm −3 . a
Schematic representation
of p-doped and n-doped
region with depletion layer
(grey area) and fixed space
charges, b diffusion
potential, c band diagram
with Fermi level (dashed
line), d electric field, e
free-carrier concentrations
n and p and f total
free-carrier density n + p
n p 0 = n n 0 exp (−βV bi )
(21.102a)
p n 0 = p p 0 exp (−βV bi ) .
(21.102b)
Microscopically, the equilibration of the Fermi levels on the n- and p-side occurs via the diffusion
of electrons and holes to the p- and n-side, respectively. The electrons and holes recombine in the
depletion layer. Therefore, on the n-side the ionized donors and on the p-side the ionized acceptors
remain (Fig. 21.41a). These charges build up an electric field (Fig. 21.41d) that works against the
diffusion current. At thermal equilibrium the diffusion and drift currents cancel and the Fermi level is
constant.
Values for the built-in potential are depicted in Fig. 21.42 for Si and GaAs diodes. The spatial
dependence of the potential in the depletion layer is determined by the Poisson equation.
We assume here the complete ionization of the donors and acceptors. Also, we neglect at first majority
carriers in the depletion layers on the n- and p-sides.
22 With these approximations, the Poisson equation
in the depletion layers on the n- and p-side reads
22 An abrupt decrease of the majority carrier density at the border of the space-charge region corresponds to zero
temperature.