Band theory of solids
Quantum physics describes the states of
electrons in an atom according to the four-fold scheme of quantum
numbers. The quantum number system describes the allowable states
electrons may assume in an atom. To use the analogy of an amphitheater,
quantum numbers describe how many rows and seats there are. Individual
electrons may be described by the combination of quantum numbers they
possess, like a spectator in an amphitheater assigned to a particular
row and seat.
Like spectators in an amphitheater moving
between seats and/or rows, electrons may change their statuses, given
the presence of available spaces for them to fit, and available energy.
Since shell level is closely related to the amount of energy that an
electron possesses, "leaps" between shell (and even subshell) levels
requires transfers of energy. If an electron is to move into a
higher-order shell, it requires that additional energy be given to the
electron from an external source. Using the amphitheater analogy, it
takes an increase in energy for a person to move into a higher row of
seats, because that person must climb to a greater height against the
force of gravity. Conversely, an electron "leaping" into a lower shell
gives up some of its energy, like a person jumping down into a lower row
of seats, the expended energy manifesting as heat and sound released
upon impact.
Not all "leaps" are equal. Leaps between
different shells requires a substantial exchange of energy, while leaps
between subshells or between orbitals require lesser exchanges.
When atoms combine to form substances,
the outermost shells, subshells, and orbitals merge, providing a greater
number of available energy levels for electrons to assume. When large
numbers of atoms exist in close proximity to each other, these available
energy levels form a nearly continuous band wherein electrons may
transition.
It is the width of these bands and their
proximity to existing electrons that determines how mobile those
electrons will be when exposed to an electric field. In metallic
substances, empty bands overlap with bands containing electrons, meaning
that electrons may move to what would normally be (in the case of a
single atom) a higher-level state with little or no additional energy
imparted. Thus, the outer electrons are said to be "free," and ready to
move at the beckoning of an electric field.
Band overlap will not occur in all
substances, no matter how many atoms are in close proximity to each
other. In some substances, a substantial gap remains between the highest
band containing electrons (the so-called valence band) and the
next band, which is empty (the so-called conduction band). As a
result, valence electrons are "bound" to their constituent atoms and
cannot become mobile within the substance without a significant amount
of imparted energy. These substances are electrical insulators:
Materials that fall within the category
of semiconductors have a narrow gap between the valence and
conduction bands. Thus, the amount of energy required to motivate a
valence electron into the conduction band where it becomes mobile is
quite modest:
At low temperatures, there is little
thermal energy available to push valence electrons across this gap, and
the semiconducting material acts as an insulator. At higher
temperatures, though, the ambient thermal energy becomes sufficient to
force electrons across the gap, and the material will conduct
electricity.
It is difficult to predict the conductive
properties of a substance by examining the electron configurations of
its constituent atoms. While it is true that the best metallic
conductors of electricity (silver, copper, and gold) all have outer s
subshells with a single electron, the relationship between conductivity
and valence electron count is not necessarily consistent:
Likewise, the electron band
configurations produced by compounds of different elements defies easy
association with the electron configurations of its constituent
elements.
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