153.Semiconductors and the Hall Effect

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Number 153

Semiconductors and the Hall Effect Semiconductors are materials that can be identified by two methods: 1. their current-carrying properties, or 2. their electron energy band structure.

For an insulator, the top occupied band (the valence band) is full. The electrons cannot be excited within the band. And the energy gap up to the next band is so great that normal amounts of thermal or electrical energy cannot excite the electrons up into the conduction band. The electrons remain attached to their atoms, and cannot carry current.

Obviously these are linked, and we shall try to explain properties, such as the effect of temperature on resistivity, through the energy band set-up. • • •

Conductors always carry current (although temperature has an effect) Insulators never carry current Semiconductors act as insulators at very low temperatures, and as partial conductors at higher temperatures.

Conduction band (empty) Energy gap Valence band (full)

Energy bands Electrons bonded to an atom can only occupy certain discrete energy levels, with only a maximum allowed number of electrons in each level.

Very large amounts of thermal or electrical energy (very high temperatures or very high voltages) can lift electrons into the conduction band. The insulator “breaks down” and becomes conducting.

n = ∞ (free electrons) increasing energy

n=3

At first glance, a semiconductor seems similar to an insulator. The valence band is full; the conduction band empty. However the energy gap that must be bridged to excite an electron into the conduction band is much smaller. The dividing line is often taken as 4eV.

n=2 n = 1 (ground state)

The n = infinity level is for free electrons, and the energy is defined as zero. The lower energy levels are for trapped electrons and are defined as having negative energy values.

Conduction band Energy gap