7.5 Shallow Defects
199
7.5.4 Multiple Impurities
If more than one donor species is present, (7.42) can be generalized, e.g. for the case of two donors
D1 and D2 in the presence of compensating acceptors,
n + N A −
N D1
1 + ˆ
g 1 exp(
E F −E D1
kT
)
−
N D2
1 + ˆ
g 2 exp(
E F −E D2
kT
)
= 0 .
(7.51)
This case is treated in [611]. Simple high and low temperature approximations can be found where
the trap with the larger and smaller activation energy, respectively, dominates. The case for multiple
acceptors (and compensating donors) is treated analogously. As detailed in [612], the function dn/dE F
has a maximum at the donor level position; this can be used to visualize the contribution of several
donors (with sufficiently different binding energies) from n(T ) as measured by Hall effect (Fig. 7.20).
7.5.5 Amphoteric Impurities
If an impurity atom can act as a donor and acceptor it is called amphoteric. This can occur if the impurity
has several levels in the band gap (such as Au in Ge or Si). In this case, the nature of the impurity
depends on the position of the Fermi level. Another possibility is the incorporation on different lattice
sites. For example, carbon in GaAs is a donor if incorporated on the Ga-site. On the As-site carbon
acts as an acceptor.
Thus, e.g., crystal growth kinetics can determine the conductivity type. In Fig. 7.21 the conductivity
due to carbon background is shown for GaAs grown using MOVPE under various growth conditions.
At high (low) arsine partial pressure incorporation of carbon on As-sites is less (more) probable, thus
the conductivity is n-type (p-type). Also, growth on different surfaces can evoke different impurity
incorporation, e.g., n-type on (001) GaAs and p-type on (311)A GaAs, since the latter is Ga-stabilized.
The charge density at an impurity nucleus can be investigated via the isomer shift as determined
by Mössbauer spectroscopy [614, 615]. The incorporation of the isotope
119 Sn can be controlled in
III-V compounds to be on cation or anion site as donor or acceptor, respectively. This is accomplished
by introducing
119 In or
119 Sb on group-III and group-V site, respectively, both decaying into
119 Sn
(a)
(b)
Fig. 7.20 a Electron concentration versus temperature as determined from Hall effect for a CdTe sample doped with
indium. b −kT dn/dE F , as determined from the experimental Hall data (symbols). The solid line is theory for three donor
levels (E D1 = E C −0.37 eV, N D1 = 2.5×10 12 cm −3 ; E D2 = E C −0.24 eV, N D2 = 7.0×10 11 cm −3 ; E D3 = E C −0.18 eV,
N D3 = 2.5 × 10 11 cm −3 ) whose energy positions are indicated by dashed lines. Adapted from [612]
199
7.5.4 Multiple Impurities
If more than one donor species is present, (7.42) can be generalized, e.g. for the case of two donors
D1 and D2 in the presence of compensating acceptors,
n + N A −
N D1
1 + ˆ
g 1 exp(
E F −E D1
kT
)
−
N D2
1 + ˆ
g 2 exp(
E F −E D2
kT
)
= 0 .
(7.51)
This case is treated in [611]. Simple high and low temperature approximations can be found where
the trap with the larger and smaller activation energy, respectively, dominates. The case for multiple
acceptors (and compensating donors) is treated analogously. As detailed in [612], the function dn/dE F
has a maximum at the donor level position; this can be used to visualize the contribution of several
donors (with sufficiently different binding energies) from n(T ) as measured by Hall effect (Fig. 7.20).
7.5.5 Amphoteric Impurities
If an impurity atom can act as a donor and acceptor it is called amphoteric. This can occur if the impurity
has several levels in the band gap (such as Au in Ge or Si). In this case, the nature of the impurity
depends on the position of the Fermi level. Another possibility is the incorporation on different lattice
sites. For example, carbon in GaAs is a donor if incorporated on the Ga-site. On the As-site carbon
acts as an acceptor.
Thus, e.g., crystal growth kinetics can determine the conductivity type. In Fig. 7.21 the conductivity
due to carbon background is shown for GaAs grown using MOVPE under various growth conditions.
At high (low) arsine partial pressure incorporation of carbon on As-sites is less (more) probable, thus
the conductivity is n-type (p-type). Also, growth on different surfaces can evoke different impurity
incorporation, e.g., n-type on (001) GaAs and p-type on (311)A GaAs, since the latter is Ga-stabilized.
The charge density at an impurity nucleus can be investigated via the isomer shift as determined
by Mössbauer spectroscopy [614, 615]. The incorporation of the isotope
119 Sn can be controlled in
III-V compounds to be on cation or anion site as donor or acceptor, respectively. This is accomplished
by introducing
119 In or
119 Sb on group-III and group-V site, respectively, both decaying into
119 Sn
(a)
(b)
Fig. 7.20 a Electron concentration versus temperature as determined from Hall effect for a CdTe sample doped with
indium. b −kT dn/dE F , as determined from the experimental Hall data (symbols). The solid line is theory for three donor
levels (E D1 = E C −0.37 eV, N D1 = 2.5×10 12 cm −3 ; E D2 = E C −0.24 eV, N D2 = 7.0×10 11 cm −3 ; E D3 = E C −0.18 eV,
N D3 = 2.5 × 10 11 cm −3 ) whose energy positions are indicated by dashed lines. Adapted from [612]