Bonding in molecules and solids - Quantum Theory of Solids - page 37

II III IV V VI

B CNO

Atom size

Al Si P S

Zn Ga Ge As Se

In Sn Sb Te

Electronegativity

Figure 2.15 Selected elements from columns II to VI of the Periodic Table. The number
at the top of each column indicates the number of valence electrons which
the atoms in that column can contribute to bonding. Tetrahedral bonding
can occur in group IV, III-V, and II-VI compounds, as the average number
of valence electrons per atom is four in each of these cases.

the number of valence electrons which the given atom can contribute to
bonding. The electronegativity tends to increase as we move along each
row towards the right-hand end, due to increasingly large atomic orbital
binding energies. The covalent radius (atomic size) is relatively constant
within each row, but increases on going down to lower rows, because of
the extra core electrons in the lower rows. The electronegativities also tend
to be larger at the top of the Periodic Table than in lower rows because,
with the increase in core radius in the lower rows, the electrons are less
tightly bound to the nuclei.
As the magnitude of the covalent interaction, ( U or E h in eq. (2.30))
decreases with increasing atomic separation, we can predict that the band
gap will decrease going down the series of purely covalent group IV semi-
conductors, fromdiamond (C) through Si and Ge to

-tin (Sn). We likewise
expect it to decrease going down the series of polar III-V compounds, alu-
minium phosphide (AlP) through GaAs to indium antimonide (InSb). On
the other hand, if we take a set of tetrahedral semiconductors from the
same row of the Periodic Table (where the covalency is constant), then we
would expect the band gap to increase with increasing ionicity, going for
instance fromGe to GaAs and on to the II-VI semiconductor, zinc selenide
(ZnSe). These general trends are indeed confirmed in fig. 2.16, where we
plot the low temperature band gap (in electron volts) against the bond
length for various group IV, III-V and II-VI compounds.
Tetrahedrally bonded III-V compounds span a very wide range of
energy gaps, from0.17 eV for InSb up to 6.2 eV in aluminiumnitride (AlN).
We note here a very useful relation between the band gap energy, E g ,in
electron volts, and emission wavelength

β

λ in microns, namely

λ E g = 1.24 meV (2.37)

µ