Electrical conduction in metals and semiconductors

The most obvious electronic conductors are metals, in which the current carriers can be regarded to a first approximation as free electrons. Before discussing electronic conductivity in polymers it is useful to consider briefly the mechanisms for conduction in metals and semiconductors. 

The simplest metals are the alkali metals. Each alkali atom has an electronic structure consisting of a core of filled electronic sub-shells with one outer electron rather loosely bound to the atom. When the atoms come together to form a solid this outer electron comes under the influence of the positively charged cores of all the neighbouring atoms as well as its own core. This results in the outer electrons of all the atoms becoming rather like a gas of electrons, with each electron moving in the relatively smooth potential due to the atomic cores and all the other electrons. To a first approximation the wave function of each electron can be treated as that of a particle moving in a uniform potential, i.e. as if it were in free space. The 

An important question now arises how many electron states are there within each of the regions between energy gaps It is clear from equation (9.37) that X = Id/nl whenever is a whole multiple n of Njl. There are, however, two waves moving in opposite directions for every value of X and, when allowance is made also for the two possible directions of electron spin, it follows that there are IN allowed electron states within each energy band between band gaps. Each alkali-metal atom supplies one electron to 

If there were no mechanism to scatter electrons from states corresponding to travel in one direction to states corresponding to travel in the other direction, the electrons would continue to pick up energy from the electric field and the current would increase continuously. Such scattering mechanisms are always present in the form of phonons (thermal vibrations of the atoms), impurities, dislocations, etc., so that the current settles to a finite value. These scattering mechanisms determine the mobility of the electrons. 

The above discussion shows that the simplest form of electronic conduction can occur in a medium with loosely bound electrons only if there are states above the Fermi level that are thermally populated. The con- 

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Electrical conduction in metals and semiconductors can be explained in terms of molecular orbitals that spread throughout the solid. We have already seen that when N atomic orbitals merge together in a molecule, they form N molecular orbitals. The same is true of a metal but in the case of a metal, N is enormous (around 1023 for 10 g of copper, for... 

FIGURE 21.10 Bands of MO energy levels for (a) a metallic conductor, (b) an electrical insulator, and (c) a semiconductor. A metallic conductor has a partially filled band. An electrical insulator has a completely filled valence band and a completely empty conduction band, which are separated in energy by a large band gap. In a semiconductor, the band gap is smaller. As a result, the conduction band is partially occupied with a few electrons, and the valence band is partially empty. Electrical conductivity in metals and semiconductors results from the presence of partially filled bands. 

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