Electrical Properties of Solids: From Atoms to Circuits
Imagine a single atom. Its electrons live in well-defined shells, each at a specific energy. Now bring two atoms close together. Their electron clouds overlap, and the sharp energy levels split into two slightly different energies — one for the bonding combination, one for the antibonding. Bring a billion atoms together in a solid, and those two levels split into a billion closely spaced levels, forming a continuous band of allowed energies.
That is the core idea: in a solid, discrete atomic energy levels broaden into energy bands, separated by gaps where no electron can exist. The highest occupied band at absolute zero is the valence band; the next empty band above it is the conduction band. The gap between them is the band gap (Eg).
The electrical conductivity of a solid is determined entirely by how easily electrons can move from the valence band into the conduction band. That ease is controlled by the size of the band gap.
Conductors, Insulators, and Semiconductors
Conductors (metals) have either no band gap — the valence and conduction bands overlap — or a partially filled conduction band. Electrons have a vast number of empty states right next to them in energy, so a tiny electric field sets them drifting. That is why copper and aluminium conduct so well.
Insulators have a large band gap, typically >3 eV. At room temperature, almost no electrons have enough thermal energy to jump the gap. The valence band is full, the conduction band is empty, and no current flows. Diamond (Eg≈5.5 eV) is a classic example.
Semiconductors sit in between. Their band gap is small — about 1.1 eV for silicon, 0.67 eV for germanium. At absolute zero they behave like insulators, but at room temperature enough electrons are thermally excited across the gap to give a small but useful conductivity. This conductivity rises sharply with temperature, opposite to metals.
σ=neμe+peμh
Conductivity depends on the number (n, p) and mobility (μe, μh) of electrons and holes.
The Hole: A Missing Electron
When an electron jumps from the valence band to the conduction band, it leaves behind a vacancy — a missing negative charge. That vacancy behaves as a positive charge carrier called a hole. Under an electric field, a neighbouring electron can move into the hole, leaving a new hole behind. The hole effectively moves in the opposite direction to the electrons, carrying positive charge.
In a pure (intrinsic) semiconductor, every electron excited leaves one hole behind, so n=p. This is called intrinsic conduction.
Doping: Engineering Conductivity
Pure silicon is not very useful. Its conductivity is too low and too sensitive to temperature. The real power comes from doping — deliberately adding impurity atoms to control the number of charge carriers.
n-type doping: Add a group-15 element (phosphorus, arsenic) to silicon. Silicon is group 14, so the impurity has five valence electrons. Four form bonds with neighbouring silicon atoms; the fifth is loosely bound and easily donated to the conduction band. The impurity is called a donor. Now n>p — electrons are the majority carriers. …