1174 28 The Structure of Solids, Liquids, and Polymersbe a semiconductor. If the band gap is large compared withkBT, there will be little
chance that electrons can move to the vacant band, and the crystal will be an insulator
at nonzero temperature.
Silicon is the most widely used semiconductor. The structure of the silicon crys-
tal is similar to that of diamond, with each silicon atom covalently bonded to four
other silicon atoms that are arranged tetrahedrally around it. To a first approxima-
tion the bonding orbitals can be approximated as localized bonding LCAOMOs made
from two 3sp^3 hybrid orbitals on adjacent atoms. This can be considered to be a
filled band of orbitals. There is a band of delocalized orbitals that can be represented
as linear combinations of the 3dorbitals, which are vacant in the separated atoms.
Figure 28.13 shows an approximate energy level diagram of silicon. The band gap
between the bonding orbitals and the 3dband is approximately equal to 1.1 eV. At
0 K, no electrons in the silicon crystal would occupy orbitals in the 3dband, and
silicon would be an insulator like diamond. Near room temperature, this band gap
is still much larger thankBT, and very few electrons in silicon occupy orbitals in
this band. Pure silicon conducts only a very small amount of electricity at room
temperature.3 d band1.11 eV band gap
Valence band
(2sp^3 )Figure 28.13 The Electron Bands
of Silicon (Schematic).The band gap,
1.11 eV, is roughly 43 times as large as
kBTat room temperature.
Silicon is frequently “doped” with other substances. If aluminum atoms replace
some silicon atoms, there are “holes” in the bonding orbitals, because aluminum has
13 electrons whereas silicon has 14. This makes the doped silicon into ap-type semi-
conductorthat would conduct some electricity even at 0 K. (The “p” designation refers
to the “positive holes” that can be thought of as moving around.) If arsenic atoms
replace silicon atoms, the doped silicon becomes ann-type semiconductor, because
arsenic atoms have five valence electrons instead of silicon’s four valence electrons,
and the fifth electron would be found in the 3dband. (The “n” designation refers to the
conduction by negative electrons.)Ferromagnetism
Nickel is ferromagnetic (can be permanently magnetized), but copper is not. We present
a few facts about ferromagnetism, and additional information can be found in solid-
state chemistry and physics textbooks.^8 Figure 28.14 shows the 4sand 3dbands for
both nickel and copper. In both elements, the two bands overlap in energy with no
band gap. In copper, which has one 4selectron and ten 3delectrons in the isolated
atom ground state, the Fermi level is at the middle of the 4sband (the higher-energy
band). At 0 K the 3dband is fully occupied and the 4sband is 50% occupied. Nickel
has two 4selectrons and eight 3delectrons. The Fermi level is lower and lies below
the top of the 3dband. The spin-up states of the 3dband have a slightly lower energy
than the spin-down states, due to “exchange interaction,” and at 0 K there is an average
of 0.54 hole per atom in the spin-down states of the 3dband and an average of 2.54
electrons per atom in the 4sband. The spins of the excess spin-up electrons interact
strongly with each other, and tend to form domains in the crystal in which all of the
excess spins are aligned parallel to each other. These domains can be aligned to pro-
duce a permanent macroscopic magnetic moment, a characteristic offerromagnetism.
Above 631 K, theCurie temperaturefor nickel, thermal energy overrides the exchange
interaction, and the ferromagnetism disappears, with an average of 0.27 hole per atom
in each of the 3dspin-up and 3dspin-down states, as shown in the last part of the
figure.(^8) N. B. Hannay,Solid-State Chemistry, Prentice-Hall, Englewood Cliffs, NJ, 1967, p. 38.