7.7 Deep Levels
209
(a)
(b)
Fig. 7.30 a Population of states of a double donor (neutral: black, single ionized: red, double ionized: blue) according to
(7.64a–c) as a function of the Fermi level. The ionization energies have been chosen as E 1 = −0.2 eV and E 2 = −0.4 eV
and are indicated by dashed lines (kT = 25 meV); these energies are similar to Si:Te (cmp. Table 7.8). The conduction
band edge is taken as zero energy. b depicts the according number of electrons ˜
n ionized from the donor
-3
Si:Te
10
18
10
17
10
15
10
16
2 10
17
10
17
8 10
16
6 10
16
4 10
16
0
1000 500
300
200
1000/T (1000/K)
1
2
3
4
5
6
1.0
1.5
2.0
2.5
3.0
1000/T (1000/K)
500
400
900 700 600
(a)
(b)
Si:Te
Fig. 7.31 Temperature dependent electron concentration (from Hall data) for Si:Te. a Experimental data and fit with
double donor model using N Te = 5 × 10 16 cm −3 , E 1 = 200 meV and E 2 = 440 meV (solid line). Single donor models
would fail (N Te = 5 × 10 16 cm −3 and N Te = 2 × 10 17 cm −3 , dashed lines). b Second ionization step in more detail with
fits using different values for E 2 ; the solid line is for E 2 = 440 meV, the other dashed lines for E 2 = 420 and 460 meV.
Adapted from [657]
play no role). From the fit E 1 = 200 ± 2.7 meV is determined [657]. Single donor models would fail.
The second ionization step is somewhat masked by the onset of intrinsic conduction. According to
(7.15), the slope of n i is E g /2 ≈ 500 meV which is similar to E 2 ≈ 440 meV.
7.7.3 Double Acceptors
In analogy to double donor defects, double acceptors can introduce up to two holes into the valence
band. A typical example is Zn in silicon [658], exhibiting its ‘normal’ acceptor level (Zn
0 /Zn
− ) at
E V + 0.31 eV. In moderately n-doped silicon another level (Zn
− /Zn
2− ) is observed at E C − 0.55 eV,
209
(a)
(b)
Fig. 7.30 a Population of states of a double donor (neutral: black, single ionized: red, double ionized: blue) according to
(7.64a–c) as a function of the Fermi level. The ionization energies have been chosen as E 1 = −0.2 eV and E 2 = −0.4 eV
and are indicated by dashed lines (kT = 25 meV); these energies are similar to Si:Te (cmp. Table 7.8). The conduction
band edge is taken as zero energy. b depicts the according number of electrons ˜
n ionized from the donor
-3
Si:Te
10
18
10
17
10
15
10
16
2 10
17
10
17
8 10
16
6 10
16
4 10
16
0
1000 500
300
200
1000/T (1000/K)
1
2
3
4
5
6
1.0
1.5
2.0
2.5
3.0
1000/T (1000/K)
500
400
900 700 600
(a)
(b)
Si:Te
Fig. 7.31 Temperature dependent electron concentration (from Hall data) for Si:Te. a Experimental data and fit with
double donor model using N Te = 5 × 10 16 cm −3 , E 1 = 200 meV and E 2 = 440 meV (solid line). Single donor models
would fail (N Te = 5 × 10 16 cm −3 and N Te = 2 × 10 17 cm −3 , dashed lines). b Second ionization step in more detail with
fits using different values for E 2 ; the solid line is for E 2 = 440 meV, the other dashed lines for E 2 = 420 and 460 meV.
Adapted from [657]
play no role). From the fit E 1 = 200 ± 2.7 meV is determined [657]. Single donor models would fail.
The second ionization step is somewhat masked by the onset of intrinsic conduction. According to
(7.15), the slope of n i is E g /2 ≈ 500 meV which is similar to E 2 ≈ 440 meV.
7.7.3 Double Acceptors
In analogy to double donor defects, double acceptors can introduce up to two holes into the valence
band. A typical example is Zn in silicon [658], exhibiting its ‘normal’ acceptor level (Zn
0 /Zn
− ) at
E V + 0.31 eV. In moderately n-doped silicon another level (Zn
− /Zn
2− ) is observed at E C − 0.55 eV,