A diamond lattice unit cell represents the real lattice structure of monocrystalline
silicon. Figures 6.1(a) and (b) show the arrangement of the unit cell and the atomic
structure of single crystal silicon, respectively. One can determine from Figure 6.1 (a) that
there are eight Si atoms in the volume of the unit cell. Since the lattice constant of c-Si is
543.07 pm, one can easily calculate that the density of atoms is approximately 5 × 10
22 cm
−3 . Figure 6.1 (a) shows the crystalline Si atomic structure with no foreign atoms. In
practice, a semiconductor sample always contains some impurity atoms. When the
concentration of impurity atoms in a semiconductor is insignificant we refer to such a
semiconductor as an intrinsic semiconductor.
At practical operational conditions, e.g. at room temperature,
1
there are always some
of the covalent bonds broken. The breaking of the bonds results in liberating the valence
electrons from the bonds and making them mobile through the crystal lattice. We refer to
these electrons as free electrons (henceforth simply referred to as electrons). The position
of a missing electron in a bond, which can be regarded as positively charged, is referred to
as a hole. This situation can be easily visualized by using the bonding model illustrated in
Figure 6.2.
In the bonding model the atomic cores (atoms without valence electrons) are
represented by circles and the valence or bonding electrons are represented by lines
interconnecting the circles. In case of c-Si, one Si atom has four valence electrons and four
nearest neighbours. Each of the valence electrons is equally shared with the nearest
neighbour. There are therefore eight lines terminating on each circle. In an ideal Si crystal
at 0 K all valence electrons take part in forming covalent bonds between Si atoms and
therefore no free electrons are present in the lattice. This situation is schematically shown
in Figure 6.2 (a).
At temperatures higher than 0 K the bonds start to break due to the absorption of
thermal energy. This process results in the creation of mobile electrons and holes. Figure
6.2 (b) shows a situation where a covalent bond is broken and one electron departs from
the bond leaving a so-called hole behind. A single line between the atoms in Figure 6.2 (b)
represents the remaining electron of the broken bond. When a bond is broken and a hole
created, a valence electron from a neighbouring bond can “jump” into this empty position
and restore the bond. The consequence of this transfer is that at the same time the jumping
electron creates an empty position in its original bond. The subsequent “jumps” of a
valence electron can be viewed as a motion of the hole – a positive charge representing the
empty position – in the opposite direction to the motion of the valence electron through
the bonds.
Since the breaking of a covalent bond leads to the formation of an electron-hole pair,
silicon. Figures 6.1(a) and (b) show the arrangement of the unit cell and the atomic
structure of single crystal silicon, respectively. One can determine from Figure 6.1 (a) that
there are eight Si atoms in the volume of the unit cell. Since the lattice constant of c-Si is
543.07 pm, one can easily calculate that the density of atoms is approximately 5 × 10
22 cm
−3 . Figure 6.1 (a) shows the crystalline Si atomic structure with no foreign atoms. In
practice, a semiconductor sample always contains some impurity atoms. When the
concentration of impurity atoms in a semiconductor is insignificant we refer to such a
semiconductor as an intrinsic semiconductor.
At practical operational conditions, e.g. at room temperature,
1
there are always some
of the covalent bonds broken. The breaking of the bonds results in liberating the valence
electrons from the bonds and making them mobile through the crystal lattice. We refer to
these electrons as free electrons (henceforth simply referred to as electrons). The position
of a missing electron in a bond, which can be regarded as positively charged, is referred to
as a hole. This situation can be easily visualized by using the bonding model illustrated in
Figure 6.2.
In the bonding model the atomic cores (atoms without valence electrons) are
represented by circles and the valence or bonding electrons are represented by lines
interconnecting the circles. In case of c-Si, one Si atom has four valence electrons and four
nearest neighbours. Each of the valence electrons is equally shared with the nearest
neighbour. There are therefore eight lines terminating on each circle. In an ideal Si crystal
at 0 K all valence electrons take part in forming covalent bonds between Si atoms and
therefore no free electrons are present in the lattice. This situation is schematically shown
in Figure 6.2 (a).
At temperatures higher than 0 K the bonds start to break due to the absorption of
thermal energy. This process results in the creation of mobile electrons and holes. Figure
6.2 (b) shows a situation where a covalent bond is broken and one electron departs from
the bond leaving a so-called hole behind. A single line between the atoms in Figure 6.2 (b)
represents the remaining electron of the broken bond. When a bond is broken and a hole
created, a valence electron from a neighbouring bond can “jump” into this empty position
and restore the bond. The consequence of this transfer is that at the same time the jumping
electron creates an empty position in its original bond. The subsequent “jumps” of a
valence electron can be viewed as a motion of the hole – a positive charge representing the
empty position – in the opposite direction to the motion of the valence electron through
the bonds.
Since the breaking of a covalent bond leads to the formation of an electron-hole pair,