9.8 Impurity Absorption
287
9.8 Impurity Absorption
9.8.1 Shallow Levels
For charge carriers bound to shallow impurities long range Coulomb forces are most important and
they exhibit a hydrogen-like term scheme
E n =
m
∗
m 0
1
2
r
1
n 2 × 13.6 eV ,
(9.67)
with the ionization limit E ∞ being the conduction (valence) band edge for donors (acceptors), respectively. They can be excited by light to the nearest band edge. Such absorption is typically in the FIR
region and can be used for photodetectors in this wavelength regime. The optical absorption cross
section of impurity absorption can be related to the carrier capture cross section [588, 589].
The actual transition energies can deviate from (9.67) due to deviation of the potential close to the
impurity from the pure Coulomb potential. Such an effect is known as the chemical shift or central
cell correction (cf. Sect. 7.5.5) and is characteristic of the particular impurity. In GaAs such shifts are
small (∼100 µeV) [902].
The term scheme for P in Si is shown in Fig. 9.33a. The ground state (1s) is split because of a reduction
of the tetrahedral symmetry due to intervalley coupling. The anisotropic mass at the X-valley in Si
(a)
-45.31
0
1s(A )
1
1s(T )
1
1s(E)
2p 0
2p ±
4p 0
3p 0
5p 0
3p ±
4p ±
±
11.62 1.33
44.09
43.25
42.41
42.25
40.07
39.14
34.08
(b)
1s
2p
3p
4p
...
h
h ph
Fig. 9.33 a Term scheme of phosphorus donor in silicon, all energies in meV. After [903]. b Schematic sequence for
photothermal ionization, here absorption of a photon with = E 3p − E 1s and subsequent absorption of a phonon with
energy ph ≥ E ∞ − E 3p
287
9.8 Impurity Absorption
9.8.1 Shallow Levels
For charge carriers bound to shallow impurities long range Coulomb forces are most important and
they exhibit a hydrogen-like term scheme
E n =
m
∗
m 0
1
2
r
1
n 2 × 13.6 eV ,
(9.67)
with the ionization limit E ∞ being the conduction (valence) band edge for donors (acceptors), respectively. They can be excited by light to the nearest band edge. Such absorption is typically in the FIR
region and can be used for photodetectors in this wavelength regime. The optical absorption cross
section of impurity absorption can be related to the carrier capture cross section [588, 589].
The actual transition energies can deviate from (9.67) due to deviation of the potential close to the
impurity from the pure Coulomb potential. Such an effect is known as the chemical shift or central
cell correction (cf. Sect. 7.5.5) and is characteristic of the particular impurity. In GaAs such shifts are
small (∼100 µeV) [902].
The term scheme for P in Si is shown in Fig. 9.33a. The ground state (1s) is split because of a reduction
of the tetrahedral symmetry due to intervalley coupling. The anisotropic mass at the X-valley in Si
(a)
-45.31
0
1s(A )
1
1s(T )
1
1s(E)
2p 0
2p ±
4p 0
3p 0
5p 0
3p ±
4p ±
±
11.62 1.33
44.09
43.25
42.41
42.25
40.07
39.14
34.08
(b)
1s
2p
3p
4p
...
h
h ph
Fig. 9.33 a Term scheme of phosphorus donor in silicon, all energies in meV. After [903]. b Schematic sequence for
photothermal ionization, here absorption of a photon with = E 3p − E 1s and subsequent absorption of a phonon with
energy ph ≥ E ∞ − E 3p