# Electron Theory of Metals

The electron theory of metals explains the following concepts viz.,

i. Structural, electrical and thermal properties of materials.

ii. Elasticity, cohesive force and binding force in metals.

iii. Behavior of conductors, semiconductors, insulators etc.

So far three electron theories have been proposed.

### ► Classical Free Electron Theory

This theory was proposed by

**Paul Drude**in 1900 and later it was extend by

**Lorentz**. Therefore this theory is also known as

**Drude-Lorentz theory**. It is a microscopic theory. It obeys the laws of classical mechanics. The most important characteristic of a metal is its high electrical conductivity.

Around 1900, shortly after J. J. Thompson's discovery of the electron, people became interested in understanding more about the mechanism of metallic conduction. The ¯rst work by E. Riecke in 1898 was quickly superseded by that of Drude in 1900. Drude1 proposed an exceedingly simple model that explained a well-known empirical law, the Wiedermann{Franz law (1853). This law stated that at a given temperature the ratio of the thermal conductivity to the electrical conductivity was the same for all metals. The assumptions of the Drude model are:

(i) a metal contains free electrons which form an electron gas.

(ii) the electrons have some average thermal energy [½mv_{T}^{2}], , but they pursue

random motions through the metal so that [v_{T}] = 0 even though v_{T}^{2}≠ 0. The random motions result from collisions with the ions.

(iii) because the ions have a very large mass, they are essentially immovable.

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### ► Quantum Free Electron Theory

This theory was developed by

**Sommerfeld**in 1928. It is a microscopic theory. According to this theory, electron moves in a constant potential and obeys the quantum law.

i. Particles of micro dimension like the electrons are studied under

quantum physics

ii. moving electrons inside a solid material can be associated with

waves with a wave function Ïˆ(x) in one dimension (Ïˆ(r) in 3D)

iii. Hence its behaviors can be studied with the SchrÃ¶dinger's

equation (1D)

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### ► Zone Theory or Band Theory

This theory was formulated by**Felix Bloch**in 1928. According to this theory, electron moves in a periodic potential provided by the lattice. This theory is also known as

**'Band theory of solids'**.

A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands. Crucial to the conduction process is whether or not there are electrons in the conduction band. In insulators the electrons in the valence band are separated by a large gap from the conduction band, in conductors like metals the valence band overlaps the conduction band, and in semiconductors there is a small enough gap between the valence and conduction bands that thermal or other excitations can bridge the gap. With such a small gap, the presence of a small percentage of a doping material can increase conductivity dramatically.

An important parameter in the band theory is the Fermi level, the top of the available electron energy levels at low temperatures. The position of the Fermi level with the relation to the conduction band is a crucial factor in determining electrical properties.

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