9.8 Impurity Absorption
289
further increased by illuminating the sample with light having a higher energy than the band gap. The
additional charge carriers neutralize charged impurities and allow higher resolution (Fig. 9.34b).
In Fig. 9.35 absorption spectra of highly doped n-type GaAs are shown. For doping concentrations
larger than the critical concentration of ∼1×10
16 cm
−3 (cf. Table 7.6) significant broadening is observed
due to the formation of an impurity band.
9.8.2 Deep Levels
The absorption of deep levels is typically in the infrared. In Fig. 9.36a the possible optical absorption
processes involving the Fe levels in InP (cf. Sect. 7.7.8) during the charge transfer Fe
3+
→ Fe
2+
are shown. These transitions and their fine structure (Fig. 9.36b) have been observed in calorimetric
absorption spectroscopy (CAS) experiments [682].
In Fig. 9.37 photoproductivity of Si:Mg is shown. The sharp peaks are due to transitions of interstitial,
singly ionized Mg, Mg
+
i [907]. Mg in Si is a double donor [653] (see Sect. 7.7.2). Above the ionization
limit of about 256 meV, the peaks are replicated, shifted by the LO phonon energy of 59.1 meV.
However, now they rather appear as dips. This behavior is typical for a discrete state interacting with
a continuum, also called Fano resonance[908, 909] with its characteristic lineshape, going below the
continuum level.
The absorption spectra due to various deep acceptors in GaAs are compared in Fig. 9.38. The
density of states in the band increases with k (proportional to
√
E − E c ). The carrier on the impurity is
strongly localized and described with a wave packet centered around , its k-components decreasing
with increasing k. Thus the maximum absorption will be at an intermediate k-value and an associated
energy larger than the ionization energy E i (lowest transition to continuum at for k = 0). The lineshapes
in Fig. 9.38 fit to a model with a δ-potential (zero range model, neglecting long range Coulomb terms)
[910] with maximum absorption close to 2 E i ,
α(E) ∝
E
1/2
i
(E − E i )
3/2
E 3
.
(9.68)
(a)
Fe
3+
E V
1.34
Fe
2+
InP:Fe
0.78
1.14
5 T 2
0
5 E
E C
0.25
(b)
0.77 0.78
1.14
1.15
TA
InP:Fe
VB
5 E
V B
2
5
T
Fig. 9.36 a Schematic band diagram of InP with levels of Fe impurities in the 3+ and 2+ charge states at low temperature.
All energies are given in eV. The arrows denote the optical transition of a valence-band electron to the Fe center,
Fe 3+ + → Fe 2+ + h. b Calorimetric absorption spectra (at T = 1.3K) of InP:Fe, [Fe]=5 × 10 16 cm −3 . Part b
Adapted from [682]
289
further increased by illuminating the sample with light having a higher energy than the band gap. The
additional charge carriers neutralize charged impurities and allow higher resolution (Fig. 9.34b).
In Fig. 9.35 absorption spectra of highly doped n-type GaAs are shown. For doping concentrations
larger than the critical concentration of ∼1×10
16 cm
−3 (cf. Table 7.6) significant broadening is observed
due to the formation of an impurity band.
9.8.2 Deep Levels
The absorption of deep levels is typically in the infrared. In Fig. 9.36a the possible optical absorption
processes involving the Fe levels in InP (cf. Sect. 7.7.8) during the charge transfer Fe
3+
→ Fe
2+
are shown. These transitions and their fine structure (Fig. 9.36b) have been observed in calorimetric
absorption spectroscopy (CAS) experiments [682].
In Fig. 9.37 photoproductivity of Si:Mg is shown. The sharp peaks are due to transitions of interstitial,
singly ionized Mg, Mg
+
i [907]. Mg in Si is a double donor [653] (see Sect. 7.7.2). Above the ionization
limit of about 256 meV, the peaks are replicated, shifted by the LO phonon energy of 59.1 meV.
However, now they rather appear as dips. This behavior is typical for a discrete state interacting with
a continuum, also called Fano resonance[908, 909] with its characteristic lineshape, going below the
continuum level.
The absorption spectra due to various deep acceptors in GaAs are compared in Fig. 9.38. The
density of states in the band increases with k (proportional to
√
E − E c ). The carrier on the impurity is
strongly localized and described with a wave packet centered around , its k-components decreasing
with increasing k. Thus the maximum absorption will be at an intermediate k-value and an associated
energy larger than the ionization energy E i (lowest transition to continuum at for k = 0). The lineshapes
in Fig. 9.38 fit to a model with a δ-potential (zero range model, neglecting long range Coulomb terms)
[910] with maximum absorption close to 2 E i ,
α(E) ∝
E
1/2
i
(E − E i )
3/2
E 3
.
(9.68)
(a)
Fe
3+
E V
1.34
Fe
2+
InP:Fe
0.78
1.14
5 T 2
0
5 E
E C
0.25
(b)
0.77 0.78
1.14
1.15
TA
InP:Fe
VB
5 E
V B
2
5
T
Fig. 9.36 a Schematic band diagram of InP with levels of Fe impurities in the 3+ and 2+ charge states at low temperature.
All energies are given in eV. The arrows denote the optical transition of a valence-band electron to the Fe center,
Fe 3+ + → Fe 2+ + h. b Calorimetric absorption spectra (at T = 1.3K) of InP:Fe, [Fe]=5 × 10 16 cm −3 . Part b
Adapted from [682]