Page 491 - Physics Coursebook 2015 (A level)

Chapter 30: Quantum physics
metal
insulator
it is similar to an insulator. Its valence band is full and its conduction band is empty. However, the gap between the two is very small. At room temperature, a few electrons have enough energy to jump across the gap into the conduction band. These electrons are ‘free’ and can form a current.
As we saw in Chapter 9 when discussing the drift velocity of electrons, a metal typically has one free
electron per atom. A semiconductor has perhaps one free electron per million atoms at room temperature, and so its electrical conductivity will be of the order of one-millionth of that of a metal.
If a piece of semiconductor is heated, more electrons will gain the energy needed to jump up into the conduction band and the material will conduct better –
its resistance decreases because of the increased number density of electrons in the conduction band. This is the opposite of a metal, whose resistance increases when it is heated. There is no increase in the number density of free electrons when a metal is heated. Instead, its atoms vibrate more, and the electrons collide more frequently with the vibrating atoms.
Silicon and germanium are examples of semiconductor materials like this. They are described as intrinsic semiconductors because their conductivity is a property of the pure material itself. Diodes, transistors and computer chips use semiconductors which have small amounts of other elements added to them to increase their conductivity.
There is another way to give electrons in a semiconductor the energy needed to jump across the forbidden gap. In a light-dependent resistor (LDR), photons of light are absorbed by electrons in the valence band so that they jump the gap and enter the conduction band. This is why an LDR has high resistance in the dark but its resistance decreases as the light level increases.
QUESTIONS
17 What materials are being described here?
a Valence band full, conduction band empty,
wide forbidden gap
b Valence band full, conduction band partially filled
c Number density of conduction electrons increases rapidly with increasing temperature.
18 Use band theory to explain why the resistivity of an intrinsic semiconductor increases as the temperature decreases.
electron energy
conduction band
forbidden gap
valence band
Figure 30.20 How the energy bands are filled in a metal and in an insulator.
How does this explain the difference between metals and insulators? When a piece of metal is connected to a cell, the electrons in the metal gain energy. For this to happen, there must be empty energy levels higher in the band into which these electrons can move. When they have moved upwards they are free to move through the metal, and so there is a current.
In an insulator, there is a large energy gap between the top of the valence band and the bottom of the conduction band. The voltage of a cell is insufficient to lift even the most energetic electrons across the gap and into the conduction band. This means that electrons are not free to move through the material – it is an insulator.
(In some metals, the top of the valence band overlaps with the bottom of the conduction band, so there are plenty of free electrons in the conduction band to carry a current.)
A semiconductor is a material which conducts electric current, but only very slightly. As shown in Figure 30.21,
semiconductor
electron
energy valence band
Figure 30.21 Electron energy bands in a semiconductor.
conduction band
narrow gap
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