8.6 Impurity Band Transport
243
Fig. 8.21 Zero
temperature conductivity of
Si:P for various (donor)
doping concentrations.
Experimental data
(symbols) and guide to the
eye (dashed line). Adapted
from [781]
10
3
10
2
10
1
10
0
10
-1
10
-2
(T=0) (S/cm)
0
2
4
6
8
N (10 cm )
D
18
-3
Si:P
insulator
metal
8.6 Impurity Band Transport
In Sect. 7.5.7, the formation of an impurity band in the presence of high doping and overlap of impurity wave functions was discussed. The hopping (tunneling) transport of carriers from impurity to
impurity leads to an additional transport channel termed ’impurity band conduction’[775–777]. The
phenomenon has been found for many doped semiconductors, among them more recently GaAs:Mn
[778] or Ga 2 O 3 :Sn [779] where at low temperatures a constant carrier concentration is attributed to
the impurity band conduction effect.
The random distribution of dopants essentially makes a doped semiconductor a disordered system.
The physics of electronic states in disordered systems has been reviewed in [780]. A metal–insulator
transition is observed at a certain value of doping (N P = 3.8 × 10
18 cm
−3 ), as shown in Fig. 8.21 for
Si:P [781]. For a certain value of disorder all states become localized (Anderson localization [782,
783], cmp. Sect. 8.9).
8.7 Polarons
In an ionic lattice, the electron polarizes the ions and causes a change of their equilibrium position.
Depending on the severity of this effect, the lattice polarization leads to a modification of carrier
(electron or hole) mass during band transport (Sect. 8.7.1) (large polarons) or the lattice deformation is
so strong that it leads to carrier localization on the length scale of the lattice constant. Such self-trapped
carriers are termed small polarons and discusssed in Sect. 8.7.1. Reviews are given in [784, 785].
8.7.1 Large Polarons
When the electron moves through the ionic crystal and must drag an ion displacement with it, the
effective electron mass changes to the ‘polaron mass’ m p ,
4
4 For the calculation, many-particle theory and techniques are needed; the best solution is still given by Feynman’s path
integral calculation [786–788].
243
Fig. 8.21 Zero
temperature conductivity of
Si:P for various (donor)
doping concentrations.
Experimental data
(symbols) and guide to the
eye (dashed line). Adapted
from [781]
10
3
10
2
10
1
10
0
10
-1
10
-2
(T=0) (S/cm)
0
2
4
6
8
N (10 cm )
D
18
-3
Si:P
insulator
metal
8.6 Impurity Band Transport
In Sect. 7.5.7, the formation of an impurity band in the presence of high doping and overlap of impurity wave functions was discussed. The hopping (tunneling) transport of carriers from impurity to
impurity leads to an additional transport channel termed ’impurity band conduction’[775–777]. The
phenomenon has been found for many doped semiconductors, among them more recently GaAs:Mn
[778] or Ga 2 O 3 :Sn [779] where at low temperatures a constant carrier concentration is attributed to
the impurity band conduction effect.
The random distribution of dopants essentially makes a doped semiconductor a disordered system.
The physics of electronic states in disordered systems has been reviewed in [780]. A metal–insulator
transition is observed at a certain value of doping (N P = 3.8 × 10
18 cm
−3 ), as shown in Fig. 8.21 for
Si:P [781]. For a certain value of disorder all states become localized (Anderson localization [782,
783], cmp. Sect. 8.9).
8.7 Polarons
In an ionic lattice, the electron polarizes the ions and causes a change of their equilibrium position.
Depending on the severity of this effect, the lattice polarization leads to a modification of carrier
(electron or hole) mass during band transport (Sect. 8.7.1) (large polarons) or the lattice deformation is
so strong that it leads to carrier localization on the length scale of the lattice constant. Such self-trapped
carriers are termed small polarons and discusssed in Sect. 8.7.1. Reviews are given in [784, 785].
8.7.1 Large Polarons
When the electron moves through the ionic crystal and must drag an ion displacement with it, the
effective electron mass changes to the ‘polaron mass’ m p ,
4
4 For the calculation, many-particle theory and techniques are needed; the best solution is still given by Feynman’s path
integral calculation [786–788].