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.
p-type doping: Add a group-13 element (boron, aluminium) to silicon. It has only three valence electrons. It forms three bonds, leaving one bond incomplete — a hole. The impurity is an acceptor because it readily accepts an electron from the valence band, creating a mobile hole. Now p>n — holes are the majority carriers.
The doped semiconductor as a whole remains electrically neutral. Each impurity atom has the same nuclear charge as its neighbours, so the extra electron or hole is balanced by the fixed ionic core of the impurity.
Why This Matters
A pure silicon crystal has roughly 1010 carriers per cm³ at room temperature. Doping with one phosphorus atom per million silicon atoms raises the electron concentration to about 1016 per cm³ — a million-fold increase. That is the difference between a useless rock and the heart of every modern electronic device.
The p-n junction — a single crystal with p-type on one side and n-type on the other — is the foundation of diodes, transistors, solar cells, and LEDs. The band gap determines the colour of an LED, the efficiency of a solar cell, and the switching speed of a transistor.
To remember the doping types: n-type has negative carriers (electrons) in excess; p-type has positive carriers (holes) in excess. The donor atom gives an electron; the acceptor atom takes one.
Electrical properties of solids, including band theory and doping, are part of the NCERT/CBSE Class 12 Chemistry solid state chapter, and "electrical properties of solids: conductors insulators semiconductors" is a frequently searched revision topic. The n-type and p-type doping distinction it covers is also a common important-question topic in JEE Main and NEET.