The concentration profile of charge carriers in a p-n junction is schematically
presented in Fig. 8.5. In the quasi-neutral regions the concentration of electrons and holes
is the same as in the isolated doped semiconductors. In the space-charge region the
concentrations of majority charge carriers decrease very rapidly. This fact allows us to use
the assumption that the space-charge region is depleted of mobile charge carriers. This
assumption means that the charge of the mobile carriers represents a negligible
contribution to the total space charge in the depletion region. The space charge in this
region is fully determined by the ionized dopant atoms fixed in the lattice.
The presence of the internal electric field inside the p-n junction means that there is
an electrostatic potential difference, V bi , across the space-charge region. We shall
determine a profile of the internal electric field and electrostatic potential in the p-n
junction. First we introduce an approximation, which simplifies the calculation of the
electric field and electrostatic-potential. This approximation (the depletion approximation)
assumes that the space-charge density, ρ, is zero in the quasi-neutral regions and it is fully
determined by the concentration of ionized dopants in the depletion region. In the
depletion region of the n-type semiconductor it is the concentration of positively charged
donor atoms, N D , which determines the space charge in this region. In the p-type
semiconductor, the concentration of negatively charged acceptor atoms, N A , determines the
space charge in the depletion region. This is illustrated in Fig. 8.6. Further, we assume that
the p-n junction is a step junction; it means that there is an abrupt change in doping at the
metallurgical junction and the doping concentration is uniform both in the p-type and the
n-type semiconductors.
In Fig. 8.6, the position of the metallurgical junction is placed at zero, the width of
the space-charge region in the n-type material is denoted as ℓ n and the width of the
spacecharge region in the p-type material is denoted as ℓ p . The space-charge density is
described by
presented in Fig. 8.5. In the quasi-neutral regions the concentration of electrons and holes
is the same as in the isolated doped semiconductors. In the space-charge region the
concentrations of majority charge carriers decrease very rapidly. This fact allows us to use
the assumption that the space-charge region is depleted of mobile charge carriers. This
assumption means that the charge of the mobile carriers represents a negligible
contribution to the total space charge in the depletion region. The space charge in this
region is fully determined by the ionized dopant atoms fixed in the lattice.
The presence of the internal electric field inside the p-n junction means that there is
an electrostatic potential difference, V bi , across the space-charge region. We shall
determine a profile of the internal electric field and electrostatic potential in the p-n
junction. First we introduce an approximation, which simplifies the calculation of the
electric field and electrostatic-potential. This approximation (the depletion approximation)
assumes that the space-charge density, ρ, is zero in the quasi-neutral regions and it is fully
determined by the concentration of ionized dopants in the depletion region. In the
depletion region of the n-type semiconductor it is the concentration of positively charged
donor atoms, N D , which determines the space charge in this region. In the p-type
semiconductor, the concentration of negatively charged acceptor atoms, N A , determines the
space charge in the depletion region. This is illustrated in Fig. 8.6. Further, we assume that
the p-n junction is a step junction; it means that there is an abrupt change in doping at the
metallurgical junction and the doping concentration is uniform both in the p-type and the
n-type semiconductors.
In Fig. 8.6, the position of the metallurgical junction is placed at zero, the width of
the space-charge region in the n-type material is denoted as ℓ n and the width of the
spacecharge region in the p-type material is denoted as ℓ p . The space-charge density is
described by