24
2 Bonds
(a)
(b)
2p
2s
valence band
conduction band
6 states
per atom
4 states
per atom
2 states
per atom
4 states
per atom
lattice constant
observed
lattice
constant
Energy
Fig. 2.4 a Energy per atom in silicon for various crystal structures. Adapted from [172]. b Electron energy levels in
(diamond structure) carbon as a function of the distance of the atomic nuclei (schematic). Adapted from [173, 174]
Fig. 2.5 Schematic of the origin of valence and conduction band from the atomic s and p orbitals. The band gap E g and
the position of the Fermi level E F are indicated
Fig. 2.6 Schematic representation of a bonding and b antibinding p orbitals. The signs denote the phase of the wavefunction
the distance from the nuclei. First, the energetically sharp states become a band due to the overlap
and coupling of the atomic wavefunctions (cf. Sect. 6). The mixing of the states leads to the formation
of the filled lower valence band (binding states) and the empty upper conduction band (antibinding
states). This principle is valid for most semiconductors and is shown schematically also in Fig. 2.5. The
configuration of bonding and antibinding p orbitals is depicted schematically in Fig. 2.6. The bonding
and antibinding sp
3 orbitals are depicted in Figs. 2.7a, b and 2.13. We note that the energy of the crystal
does not only depend on the distance from the nuclei but also on their geometric arrangement (crystal
structure).
Per carbon atom there are (in the second shell) four electrons and four unoccupied states, altogether
eight. These are redistributed into four states (filled) per atoms in the valence band and four states
per atom (empty) in the conduction band. Between the top of the valence band and the bottom of the
conduction band there is an energy gap, later called the band gap (cf. Chap. 6).
2 Bonds
(a)
(b)
2p
2s
valence band
conduction band
6 states
per atom
4 states
per atom
2 states
per atom
4 states
per atom
lattice constant
observed
lattice
constant
Energy
Fig. 2.4 a Energy per atom in silicon for various crystal structures. Adapted from [172]. b Electron energy levels in
(diamond structure) carbon as a function of the distance of the atomic nuclei (schematic). Adapted from [173, 174]
Fig. 2.5 Schematic of the origin of valence and conduction band from the atomic s and p orbitals. The band gap E g and
the position of the Fermi level E F are indicated
Fig. 2.6 Schematic representation of a bonding and b antibinding p orbitals. The signs denote the phase of the wavefunction
the distance from the nuclei. First, the energetically sharp states become a band due to the overlap
and coupling of the atomic wavefunctions (cf. Sect. 6). The mixing of the states leads to the formation
of the filled lower valence band (binding states) and the empty upper conduction band (antibinding
states). This principle is valid for most semiconductors and is shown schematically also in Fig. 2.5. The
configuration of bonding and antibinding p orbitals is depicted schematically in Fig. 2.6. The bonding
and antibinding sp
3 orbitals are depicted in Figs. 2.7a, b and 2.13. We note that the energy of the crystal
does not only depend on the distance from the nuclei but also on their geometric arrangement (crystal
structure).
Per carbon atom there are (in the second shell) four electrons and four unoccupied states, altogether
eight. These are redistributed into four states (filled) per atoms in the valence band and four states
per atom (empty) in the conduction band. Between the top of the valence band and the bottom of the
conduction band there is an energy gap, later called the band gap (cf. Chap. 6).