192
7 Electronic Defect States
Fig. 7.11 Position of the Fermi level in Si:P (N D = 10 15 cm −3 , E b
D = 45 meV, no acceptors) as a function of temperature.
The temperature dependence of the band gap (as given in Table 6.4) has been taken into account. Zero energy refers to
the conduction-band edge for all temperatures. The dotted curve shows E g /2. The dashed (dash-dotted) line shows the
low- (high-) temperature limit according to (7.31) and (7.18), respectively. The corresponding electron concentration as
a function of temperature is shown in Fig. 7.9b
Fig. 7.12 Fermi level in
silicon as a function of
temperature for various
doping levels (n-type (blue
lines) and p-type (red
lines)) of
10 12 , 10 13 , . . . , 10 18 cm −3 .
The intrinsic Fermi level is
chosen as zero energy for
all temperatures. The
(temperature-dependent)
conduction and valence
band edges are shown as
dashed lines
regimes can be seen in the experimental data on carrier density of electrons in n-Ge (Fig. 7.10) and of
holes in p-Ge (Fig. 7.15).
A similar plot as in Fig. 7.11 is shown in Fig. 7.12 but for different doping levels. With increasing
temperature, the Fermi level shifts from close to the band edge towards the band center. At higher
doping, this shift begins at higher temperatures.
The electronic states of individual donors can be directly visualized by scanning tunneling
microscopy (STM) as shown in Fig. 7.13 for Si:P. For small negative bias, tunneling occurs through
the charged dopant that is located within the first three monolayers. At high negative bias the large
contribution from the filled valence band masks the effect of the donor. This image, however, shows
that the contrast attributed to the dopant atom is not due to surface defects or absorbates.
7.5.2 Acceptors
A group-III atom in Si has one electron too few for the tetrahedral bond. Thus, it ‘borrows’ an electron
from the electron gas (in the valence band) and thus leaves a missing electron (termed hole) in the
7 Electronic Defect States
Fig. 7.11 Position of the Fermi level in Si:P (N D = 10 15 cm −3 , E b
D = 45 meV, no acceptors) as a function of temperature.
The temperature dependence of the band gap (as given in Table 6.4) has been taken into account. Zero energy refers to
the conduction-band edge for all temperatures. The dotted curve shows E g /2. The dashed (dash-dotted) line shows the
low- (high-) temperature limit according to (7.31) and (7.18), respectively. The corresponding electron concentration as
a function of temperature is shown in Fig. 7.9b
Fig. 7.12 Fermi level in
silicon as a function of
temperature for various
doping levels (n-type (blue
lines) and p-type (red
lines)) of
10 12 , 10 13 , . . . , 10 18 cm −3 .
The intrinsic Fermi level is
chosen as zero energy for
all temperatures. The
(temperature-dependent)
conduction and valence
band edges are shown as
dashed lines
regimes can be seen in the experimental data on carrier density of electrons in n-Ge (Fig. 7.10) and of
holes in p-Ge (Fig. 7.15).
A similar plot as in Fig. 7.11 is shown in Fig. 7.12 but for different doping levels. With increasing
temperature, the Fermi level shifts from close to the band edge towards the band center. At higher
doping, this shift begins at higher temperatures.
The electronic states of individual donors can be directly visualized by scanning tunneling
microscopy (STM) as shown in Fig. 7.13 for Si:P. For small negative bias, tunneling occurs through
the charged dopant that is located within the first three monolayers. At high negative bias the large
contribution from the filled valence band masks the effect of the donor. This image, however, shows
that the contrast attributed to the dopant atom is not due to surface defects or absorbates.
7.5.2 Acceptors
A group-III atom in Si has one electron too few for the tetrahedral bond. Thus, it ‘borrows’ an electron
from the electron gas (in the valence band) and thus leaves a missing electron (termed hole) in the