7.7 Deep Levels
217
Fig. 7.40 a Model
calculation of the
wave-vector dependence of
the probability density of
an electron bound to a
10 meV deep isoelectronic
trap (N) and to a 100 meV
deep shallow donor (S) in
GaP. Adapted from [690].
b Wavefunction (isosurface
at 20% of maximum) of
isolated nitrogen (N) and
neighboring N–N pair
(NN 1 ) in GaP. Adapted
from [544]
(a)
(b)
Fig. 7.41 Energy levels of nitrogen impurity states in GaP (left) and GaAs (right). The energy scale is relative to the
bulk GaP valence band maximum, the conduction band minima (CBM) are thus shown relative to the vacuum level.
The conduction band is shown in grey. For both materials, (a) denotes the isolated N impurity level calculated without
lattice relaxation (dashed line), and (b) with lattice relaxation. (c) denotes the position of N–N pair levels, m denoting
the neighbor. (d) shows selected experimental data. NN 1 denotes the direct neighbor NN-pair. The other NN n follow the
usual nomenclature as in [694]. Data taken from [544]
than at a shallow donor such as sulfur [690]. This way a large oscillator strength for optical transitions
occurs (Sects. 9.7.9, 10.3.2). The wavefunction of an isolated single N impurity and a neighboring N–N
pair (NN 1 ) in GaP are shown in Fig. 7.40b.
Isolated nitrogen impurities in (unstrained) GaAs introduce states only within the conduction band
(Fig. 7.41). The reason is that the GaAs conduction band edge is further from the vacuum level than
that of GaP (see Fig. 12.21). Only the NN 1 and NN 4 pair levels are theoretically expected to be
within the GaAs band gap. The index denotes the nth neighbor position. The NN 1 level has been
experimentally observed [691, 692]. The isolated nitrogen impurity level is forced into the GaAs band
gap upon hydrostatic pressure [692, 693] (Fig. 7.42). Further levels deeper within the band gap are due
to clusters containing more than two nitrogen atoms.
7.7.10 Surface States
The investigation of (semiconductor) surfaces is a large field with sophisticated methods that allow
real-space imaging with atomic resolution by scanning probe microscopy and highly depth resolved
electronic studies. The surface represents first of all a break in the periodic crystal potential and thus
a defect of the bulk crystal. The unsatisfied bonds partly rearrange, e.g. by building dimers, forming
a surface reconstruction or remain as dangling bonds. The surface exhibits a surface density of states.
217
Fig. 7.40 a Model
calculation of the
wave-vector dependence of
the probability density of
an electron bound to a
10 meV deep isoelectronic
trap (N) and to a 100 meV
deep shallow donor (S) in
GaP. Adapted from [690].
b Wavefunction (isosurface
at 20% of maximum) of
isolated nitrogen (N) and
neighboring N–N pair
(NN 1 ) in GaP. Adapted
from [544]
(a)
(b)
Fig. 7.41 Energy levels of nitrogen impurity states in GaP (left) and GaAs (right). The energy scale is relative to the
bulk GaP valence band maximum, the conduction band minima (CBM) are thus shown relative to the vacuum level.
The conduction band is shown in grey. For both materials, (a) denotes the isolated N impurity level calculated without
lattice relaxation (dashed line), and (b) with lattice relaxation. (c) denotes the position of N–N pair levels, m denoting
the neighbor. (d) shows selected experimental data. NN 1 denotes the direct neighbor NN-pair. The other NN n follow the
usual nomenclature as in [694]. Data taken from [544]
than at a shallow donor such as sulfur [690]. This way a large oscillator strength for optical transitions
occurs (Sects. 9.7.9, 10.3.2). The wavefunction of an isolated single N impurity and a neighboring N–N
pair (NN 1 ) in GaP are shown in Fig. 7.40b.
Isolated nitrogen impurities in (unstrained) GaAs introduce states only within the conduction band
(Fig. 7.41). The reason is that the GaAs conduction band edge is further from the vacuum level than
that of GaP (see Fig. 12.21). Only the NN 1 and NN 4 pair levels are theoretically expected to be
within the GaAs band gap. The index denotes the nth neighbor position. The NN 1 level has been
experimentally observed [691, 692]. The isolated nitrogen impurity level is forced into the GaAs band
gap upon hydrostatic pressure [692, 693] (Fig. 7.42). Further levels deeper within the band gap are due
to clusters containing more than two nitrogen atoms.
7.7.10 Surface States
The investigation of (semiconductor) surfaces is a large field with sophisticated methods that allow
real-space imaging with atomic resolution by scanning probe microscopy and highly depth resolved
electronic studies. The surface represents first of all a break in the periodic crystal potential and thus
a defect of the bulk crystal. The unsatisfied bonds partly rearrange, e.g. by building dimers, forming
a surface reconstruction or remain as dangling bonds. The surface exhibits a surface density of states.