Electronic Structure of Inorganic Solids

The electronic structure of inorganic solids is described by bands of orbitals formed across the crystal, whose filling and gaps distinguish insulators, semiconductors, and metals.

Definition

The electronic structure of inorganic solids is the description of the energies and occupancy of electronic states in an extended crystal as continuous bands derived from atomic orbitals, which determine optical and electrical properties.

Scope

This topic covers the chemical view of electronic structure in extended solids: the formation of bands from overlapping atomic orbitals, band width and density of states, the band gap and the classification of insulators, semiconductors, and metals, intrinsic and extrinsic (doped) semiconduction, and the limits of the band picture in correlated transition-metal oxides where Mott insulating behaviour appears. It treats the chemical bonding view; the detailed solid-state physics of band theory is covered in condensed-matter physics.

Core questions

• How do atomic orbitals combine into bands in a solid?
• What determines whether a solid is an insulator, semiconductor, or metal?
• How does doping create n-type and p-type semiconductors?
• Why do some transition-metal oxides insulate despite partly filled bands?

Key concepts

• Energy bands and band width
• Density of states
• Band gap
• Insulators, semiconductors, and metals
• Doping and carrier type
• Mott insulators and correlation

Key theories

Band formation from orbital overlap

As atomic orbitals overlap across a periodic solid their discrete levels broaden into bands; the band width reflects the strength of overlap and the density of states describes how electronic levels are distributed in energy.

Band gaps and conductivity classes

A filled valence band separated from an empty conduction band by a large gap gives an insulator, a small gap gives a semiconductor, and a partly filled band gives a metal, classifying solids by their electrical behaviour.

Electron correlation and Mott insulators

In some transition-metal oxides strong electron–electron repulsion localizes electrons and opens a gap even in a nominally half-filled band, producing Mott insulators that the simple band picture cannot explain.

Clinical relevance

Understanding the electronic structure of inorganic solids underpins the design of semiconductors, photovoltaics, transparent conductors, catalysts, and the functional transition-metal oxides used in electronics and energy materials.

History

Band theory grew from Bloch's 1928 treatment of electrons in periodic potentials and was applied to chemistry through the linking of molecular-orbital and solid-state pictures, articulated for chemists by Hoffmann. Mott's work on correlated oxides and Goodenough's studies of transition-metal oxides revealed where the simple band model breaks down.

Key figures

• Felix Bloch
• Nevill Mott
• John Goodenough
• Roald Hoffmann

Seminal works

• hoffmann1987
• west2014
• cox2010

Frequently asked questions

How is a band like a molecular-orbital diagram?

A band is the limit of a molecular-orbital diagram for an enormous number of atoms: as more atoms contribute orbitals, the discrete bonding and antibonding levels crowd together into a near-continuous range of energies, the band.

Why does a small band gap make a semiconductor?

When the gap between the filled valence band and the empty conduction band is small, thermal energy can promote some electrons across it, leaving mobile holes behind; both carriers conduct, so the material conducts modestly and increasingly with temperature.