Semiconductors

Semiconductors are those compounds with small band gaps between fully filled and fully unoccupied bands.

Let us consider the elements of Group 14. These all adopt the structure of diamond, in which the atoms are all tetrahedrally coordinated by other atoms.

Band Structure in Body Centered Cubic crystal		Band Structure in tetrahedral diamond crystal

If the Group 14 elements adopted a typical metal structure, such as the body centered cubic structure, the ns- and np-orbitals would overlap to give an extended band of s/p character with 4N levels. Each atom provides 4 electrons, and so the bottom 2N levels are occupied, and the the band is half-filled. However, the levels near the middle of the band are largely non-bonding in character (the band ranges from fully bonded at the bottom, to fully bonded at the top, with non-bonded in the middle), and so do not contribute to stabilization by bonding.

When the elements adopt the tetrahedral structure, the symmetry does not allow non-bonding orbitals, and now the ns- and np-orbitals still overlap, but now produce a lower band of combined s/p-character, corresponding to bonding behaviour, and an upper band of combined s/p-character, corresponding to antibonding behaviour.

In this geometry, the lower band is completely filled and the upper band is completely empty. The lower band contains the ns²np² valence electrons from each atom, and is known as the valence band. The upper band is known as the conduction band.

As the group is descended, the band gap between the valence and conduction bands decreases because the separation between the basis atomic s- and p-orbitals increases and so the overlap decreases. At tin, the band gap becomes zero, and so there is the trend: C (insulator), Si/Ge (semiconductors), Sn (semimetal), Pb (metal).

For silicon and germanium, at temperatures greater than 0, or when excited by light, some electrons may be promoted from the lower valence band to the higher conduction band, resulting in two partially occupied bands, and hence some metallic character.

Thermal or photoelectric excitation of the compound leads to promotion of valence electrons to the conduction band resulting in two partially filled bands.

The number of electrons promoted to the conduction band at a given temperature increases as the band gap decreases. Therefore, germanium has a higher conductivity than silicon. The number of promoted electrons is given by:

The electrical conductivity, σ, is determined by the number of species which can carry charge, and their ability to move throughout the system. Each promoted electron leaves behind a positive hole in the valence band. These holes can move in addition to the promoted electrons, and so can also act as charge carriers. The conductivity can be given by the expression below, where n_x is the number of charge carriers, x, and μ_x is the mobility of the charge carrier x.

In compounds like Si and Ge, the conduction increases with temperature, as the number of promoted electrons increases. However, their ability to conduct is linked only to the separation of the bands, and not on any outside property, and so these are known as intrinsic semiconductors.

Extrinsic Semiconductors

In intrinsic semiconductors, the conductivity is proportional to the number of charge carriers present. When the materials in the atom are replaced by other atoms with a different number of valence electrons, the number of charge carriers will increase, and so the conductivity will increase.

The process of substituting atoms of a different valency for the atoms of the parent material is known as doping, and the resulting semiconductors are known as extrinsic semiconductors. A dopant level of only 1 in 10⁹ is needed to significantly increase the conductivity.

The nature of the dopant species determines the dominant type of charge carrying species in the resulting extrinsic semiconductor.

n-type semiconductivity: When a P atom replaces an Si atom in the Si crystal, there will be one extra electron for each P atom. At low dopant concentrations, the extra electrons occupy orbitals with a small degree of overlap, and so form a very narrow dopant band situated between the valence and conduction bands. The thermal excitation of electrons from this so called donor band, which lies close in energy to the conduction band, is much easier than promotion from the valence band, so there are more electrons in the conduction band than in pure Si and the conductivity is higher. The extra charge carrying species are these extra electrons, which are negatively charged, and so this type of semiconductor is known as a n-type.

p-type semiconductivity: When a Ga atom replaces an Si atom in the Si crystal, there are now too few electrons to fill the valence band, as each Ga atom has one fewer electrons. This dopant species therefore introduces a narrow band of largely localized positively charged holes into region just above the valence band. Thermal excitation means that electrons leave the valence band to enter this acceptor band, leaving behind positively charged holes in the valence band, and these holes can carry charge. The extra charge carrying species are these extra holes, which are positively charged, and so this type of semiconductor is known as a p-type.

intrinsic semiconductor		n-type extrinsic semiconductor		p-type extrinsic semiconductor
Thermal excitation means there are low levels of electrons in the conduction band		The extra electrons have been excited from the donor band into the conduction band.		The electrons have been promoted from the valence band to fill the holes in the acceptor band, leaving holes in the valence band.