COMPENSACIÓN INDUCTIVA DE LÍNEAS SIMPLE CIRCUITO

T he principle application o f tin(II) sulfide is as a sem iconductor. It is also of interest as a heat m irror coating on windows. W ith these applications in m ind, it is useful to have a brief overview of the term s used in discussing sem iconductors, photovoltaics and heat m irrors.

1.3.1

General description o f semiconductors

F rom the aspect o f conductivity, there are five recognised classes o f material. These are, in order of decreasing conductivity, superconductors, m etals, semimetals, sem iconductors and insulators. M etals, and superconductors above their Tc, exhibit m etallic conductivity. This means that the resistance increases w ith tem perature due to lattice vibrations im peding the m otion of electrons. This effect is observed throughout all m aterials. Sem im etals, sem iconductors and insulators have decreasing resistivity w ith tem perature. This is because o f the band structure o f the m aterials.

1.3.1.1 Band theory

In a single atom, there are discreet energy levels. W hen tw o or m ore atoms are brought together, there is a slight perturbation in the energy levels w ith respect to those in the isolated atom. They are still very sim ilar in energy. If a large num ber o f atoms are brought together, then the energy levels form a continuous band.

Each atom ic energy level w ithin an atom m ay contain only tw o electrons - one with spin up and the other with spin down. This is the Pauli exclusion principle, which states that no tw o electrons m ay have identical sets of quantum num bers associated with them.

This means that if n atoms are brought together in a solid, then the band associated with each level will be capable of containing 2n electrons. Figure 1.5 shows how bands may be filled or empty. Energy is plotted along the x-axis and frequency of states with this energy up the y-axis. The figure depicts which states are filled or empty at absolute zero, however temperature affects occupancy according to the Boltzman distribution. In a material, there will be an energy which has exactly half its states occupied at any temperature. This is called the Fermi-level and is denoted B/.

Sem im etal

M etal S em ico n d u cto r

Ef

Insulator

E

Figure 1.5 Density o f states diagram for m etals, sem im etals, sem iconductors and insulators.

In a metal such as sodium, the 3s orbital contains only one electron, and the 3s band of a solid will contain n electrons. Since the band may hold up to 2n electrons it is half full. This is depicted in Figure 1.5. Metallic conduction occurs when a band is partially filled. A metal such as magnesium has two electrons in its 3s orbital, so it would appear that this has a full 3s band and the next band up (3p) would be empty. However, the 3s and 3p bands overlap, allowing electrons to move freely into the 3p orbital. In these cases, the Fermi levels fall within a region of non-zero density of states. This is the strict definition of metallic conduction.

Superconductors behave in an identical manner to metals. The difference is in the resistance at low temperatures. As previously mentioned, atomic vibrations impede electrons flowing through the material. At lower temperatures atoms vibrate less, and conductivity increases. Superconductors are materials whose low-temperature resistance is zero.

Band theory for materials with covalent bonding, such as silicon, needs to be modified according to molecular orbital theory. In silicon, the 3s and 3p orbitals are hybridised to form four sp^ hybrids. These can be shown by symmetry to point toward the comers of a tetrahedron with the atom in the centre. This explains the tetrahedral bonding in

m aterials such as silicon and diamond.

In m olecular orbital theory, when two atoms are brought together, atomic orbitals with the sam e sym m etry, sim ilar energy and sim ilar size can com bine. Tw o atomic orbitals will be transform ed into two m olecular orbitals - bonding and anti-bonding. In the case of silicon, there are four atomic orbitals on each atom, and two atoms will therefore com bine to give four bonding and four anti-bonding orbitals. C onsequently, n atoms will provide 2n bonding and 2n anti-bonding orbitals. Each atom provides four electrons, so there are 4n electrons in total. This is sufficient to fill 2n orbitals. In sum m ary from the m olecular orbital viewpoint, there w ill be tw o bands - bonding and anti-bonding - one o f which is filled, and the other, em pty. In term s of band theory, these are called the conduction (bonding) and valence (anti-bonding) bands.

It is seen from this, that there is no energy level w hich has h alf o f its states occupied and half em pty. In this case, the Ferm i level is found w ithin the region o f zero density of states.

The difference in energy between the valence band and conduction band is called the band gap. It is denoted Eg. Sem im etals differ from sem iconductors and insulators in that their band gap is zero. This m eans that the tw o bands, although they are separate, touch. The Ferm i level is still found in a zero density o f states, although the band gap is zero.

The difference betw een sem iconductors and insulators is som ew hat m ore difficult to define. In some cases charge carrier density is used, how ever this is tem perature dependent, allow ing insulators to becom e sem iconductors at high tem peratures and sem iconductors to becom e insulators at low tem peratures. A m ore universal m ethod is to say that the difference betw een the tw o is the energy of the band gap. Sem iconductors have 0 < Eg < 4 eV, while insulators have Eg > 4 eV.

1.3.1.2 Intrinsic and extrinsic semiconductors

Pure silicon is an elem ental sem iconductor. Each atom has four electrons and shares one from each of the four atoms to w hich it is bound. This creates the noble gas configuration of eight valence electrons. W hen energy is provided and one o f these

electrons is prom oted to the conduction band, a hole is left behind. M any things can occur as a result of this, one of which is recom bination, i.e. the electron dropping back into the hole and releasing energy in the form of electrom agnetic radiation or lattice vibrations (phonons). M ore interesting, how ever is that the electron and hole may m igrate through the silicon.

M ovem ent of the electron is easy to com prehend, and is identical to the m echanism in a m etal w here the electron m ay be anyw here in the delocalised band over the whole sample. Focussing on the hole created, a valence electron from a neighbouring atom m ay m ove to fill this hole. This can be repeated, with the effect that the hole migrates across the sample. If the silicon is placed in an applied field, the electron in the conduction band will m igrate in the opposite direction to the field, and current flows. Any electrons m oving into the hole will also be affected by the applied field and move in the direction opposite to it. The effect of this is that the hole is m oving in the direction o f the field.

In the case o f pure silicon, the num ber o f electrons will always be equal to the num ber of holes. This is called intrinsic conduction. The Ferm i level lies in the centre of the band gap in intrinsic semiconductors.

Im purity atoms can lead to there being a large excess o f one type o f charge carrier over the other, and conduction of this type is said to be extrinsic. If a silicon atom is replaced w ith an atom o f a group V elem ent such as phosphorus, this will have five electrons in its outer shell, and will receive four from neighbouring silicon atoms to w hich it is bound. This creates a total o f nine electrons, w hich is in excess of the noble gas configuration. The extra electron will readily be accepted into the conduction band. It is called a donor electron and the energy level diagram o f this is shown in Figure 1.6. In this case, the m ajority charge carriers are negatively charged electrons, and the sem iconductor is said to be n-type.

A t T = 0 K, the donor levels are all filled, and the Ferm i level is situated between the donor states and the conduction band. This is shown in Figure 1.6. Increasing the tem perature causes electrons to m ove into the conduction band, leaving em pty states in the donor levels, so the Ferm i level m oves down. A t high tem peratures intrinsic conduction takes over, and the Ferm i level w ill be found approxim ately in the centre of