the fifth valence electron of the P atom does not take part in forming a bond, is rather
weakly bound to the atom and is easily liberated from the P atom. The energy of the
liberated electron lies in the CB. The energy levels, which we denote E D , of the weaklybound valence electrons of the donor atoms have to be positioned close to the CB, as
shown in Fig. 6.7 b). This means that an electron, which occupies the E D level, is localized
in the vicinity of the donor atom. Similarly, the acceptor atoms introduce allowed energy
levels E A close to the VB, as in Fig. 6.7 c).
Doping also influences the position of the Fermi energy. When we increase the
electron concentration by increasing the donor concentration the Fermi energy will
increase, which is represented by bringing the Fermi energy closer to the CB in the band
diagram. In the p-type material the Fermi energy is moved closer to the VB. These
changes in the Fermi energy positions are illustrated in Figure 6.7.
Figure 6.7: A shift of the position of the Fermi energy in the band diagram and the introduction of the allowed energy
level into the bandgap due to the doping.
The position of the Fermi level in an n-type semiconductor can be calculated with
Eqs. (6.6a); in a p-type semiconductor Eqs. (6.6b) and (6.20) can be used:
Example
This example demonstrates how much the concentration of electrons and holes can be manipulated by doping. A
c-Si wafer is uniformly doped with 1 × 10 17 cm −3 P atoms. P atoms act as donors and therefore at room
temperature the concentration of electrons is almost equal to the concentration of donor atoms:
n = ≈ N D = 10
17
cm
−3
.
The concentration of holes in the n-type material is calculated from Eq. (6.17),
We notice that there is a difference of 14 orders of magnitude between n (10 17 cm −3 ) and p (2.25 × 10 3 cm −3 ). It
is now obvious why electrons in n-type materials are called the majority carriers and holes the minority carriers.
We can calculate the change in the Fermi energy due to the doping. Let us assume that the reference energy level
weakly bound to the atom and is easily liberated from the P atom. The energy of the
liberated electron lies in the CB. The energy levels, which we denote E D , of the weaklybound valence electrons of the donor atoms have to be positioned close to the CB, as
shown in Fig. 6.7 b). This means that an electron, which occupies the E D level, is localized
in the vicinity of the donor atom. Similarly, the acceptor atoms introduce allowed energy
levels E A close to the VB, as in Fig. 6.7 c).
Doping also influences the position of the Fermi energy. When we increase the
electron concentration by increasing the donor concentration the Fermi energy will
increase, which is represented by bringing the Fermi energy closer to the CB in the band
diagram. In the p-type material the Fermi energy is moved closer to the VB. These
changes in the Fermi energy positions are illustrated in Figure 6.7.
Figure 6.7: A shift of the position of the Fermi energy in the band diagram and the introduction of the allowed energy
level into the bandgap due to the doping.
The position of the Fermi level in an n-type semiconductor can be calculated with
Eqs. (6.6a); in a p-type semiconductor Eqs. (6.6b) and (6.20) can be used:
Example
This example demonstrates how much the concentration of electrons and holes can be manipulated by doping. A
c-Si wafer is uniformly doped with 1 × 10 17 cm −3 P atoms. P atoms act as donors and therefore at room
temperature the concentration of electrons is almost equal to the concentration of donor atoms:
n = ≈ N D = 10
17
cm
−3
.
The concentration of holes in the n-type material is calculated from Eq. (6.17),
We notice that there is a difference of 14 orders of magnitude between n (10 17 cm −3 ) and p (2.25 × 10 3 cm −3 ). It
is now obvious why electrons in n-type materials are called the majority carriers and holes the minority carriers.
We can calculate the change in the Fermi energy due to the doping. Let us assume that the reference energy level