Conductors, insulators, semiconductors
Atoms:
Electrons of a single atom occupy a discrete set of energy levels. When measuring the energies of electrons in an isolated atom, we do not find a continuous distribution of energies, but a set of quantized energies.
The plot above shows the potential energy of an electron and three possible values for the total energy. This model of discrete energy levels can also be extended to simple compound molecules, and experimental evidence can easily be found in the emission and absorption spectra of gases.
 | Electron energies are are quantized |
| Only two electrons are allowed to occupy an energy level characterized by the quantum numbers n, l, and m. |
| One of these electron will have spin up and the other will have spin down. |
| Electrons that are more tightly bound are more likely to be found closer to the nucleus |
| We build atoms by filling energy levels from the most negative to the least negative |
Solids:
When atoms form a solid, the potential energy of each electron changes, and its possible energy values change. The energy of the more tightly bound electrons changes very little, and these electrons remain localized about a single atom. The less tightly bound electrons do not remain localized, and their possible energy values now fall into bands of allowed values.
The plot above shows the potential energy of an electron, one possible energy for a localized electron, and two energy bands for delocalized electrons.
Consider a single atom of a particular species. This atom has a discrete set of energy levels. When another atom of the same species is brought close to the first atom, each of the energy levels becomes degenerate. But the interaction between the atoms breaks the degeneracy and the level splits into two separate energy levels. If this procedure is repeated >1020 times, each energy level will have split into >1020 level, effectively forming a continuous band of energy states.
Although there may be an infinite number of bands in the band structure of a given material, there are two bands that are of particular significance in determining the electronic and optical properties of a material. These are the conduction band and the valence band. Note that these terms may refer to the same band in materials that are conductors.
One of the most useful aspects of the band structure is the feature known as the band gap. In semiconductor and insulator materials, this is the gap between the valence band and the conduction band. The band gap and defect states created in the band gap by doping can be used to create devices such as solar cells, laser diodes, transistors, and a range of other electronic devices.
| Crystalline solids are collections of atoms arranged in a repetitive three-dimensional structure. | ||||||
| The energy levels in solids become grouped into "bands" which are separated by "gaps". | ||||||
| Electrons cannot have energies that would fall into the gaps.
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| The highest lying band containing filled states (as T --> 0) is called the valence band. | ||||||
| The lowest lying band band containing empty states (as T --> 0) is called the conduction band. | ||||||
| There are three types of solids:
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The properties of conductors, semiconductors and insulators are determined by the number of electrons that occupy the two highest lying energy bands that can hold electrons under normal circumstances. We therefore often only show these two bands in an energy level diagram. Each of the two bands can only accept a fixed number of electrons because it only contains a fixed number of states.
If all the states in a band are occupied, no net movement of electrons can occur and the band cannot contribute to the conduction of current. (All the wave functions of all the electrons interfere in such a way to only form standing waves with zero average value for the momentum.) An unoccupied band also does not contribute to the conduction of current.
In a conductor, the valance band is totally occupied, but the conduction band is only partially occupied. Electrons can be accelerated by an electric field and current can flow.
In an insulator, the valance band is totally occupied, but the conduction band is empty. The amount of energy electrons can gain from thermal agitation is not enough to lift them from the valence band into the conduction band. The energy gap is too large. No current can flow.
In a semiconductor the energy gap between the valence and the conduction band is small, and at higher temperatures some electrons can gain enough energy from thermal agitation to lift them from the valence band to the conduction band. The valence band now contains holes, i.e. some states in that band are empty, and the conduction band is no longer totally empty, but contains some electrons. Both bands can contribute to the conduction of current, but the conductivity is low, because the number of unoccupied states in the valence band and the number of occupied state in the conduction band is small.
Doping:
The addition of impurities in a p-type semiconductor creates some holes in the valence band. The addition of impurities in a n-type semiconductor puts some electrons in the conduction band. (The addition of impurities also changes the band structure slightly, but we ignore this in this simple model.) The holes in the valence band of the p-type material and the electrons in the conduction band of the n-type material can have net movement through the material and we call them free carriers. The doped material can conduct current.
How does a voltage affect the energy levels?
Assume you established an electric field between the two semiconductors. Assume they are not in contact and no current flows.
If the field points from the n-type to the p-type semiconductor, then the potential is higher in the n-type semiconductor, and the potential energy of the electrons is higher in the p-type semiconductor. (Electrons are negatively charged and their potential energy has the opposite sign as the potential.)
A PN junction photodiode
The simple model presented here mixes a quantum mechanical with a classical description. Assume you bring a n-type and a p-type semiconductor in contact with each other.
Electrons in the n-type semiconductor fill some of the holes in the p-type semiconductor because these holes are available lower-energy states. This leaves positively charged cores in the n-type and extra negatively charged electrons in the p-type semiconductor material. The n-type semiconductor becomes positively charged and the p-type semiconductor becomes negatively charged. The charge on each doped semiconductor repels the free carriers in the other doped semiconductor. The free carriers move away from the junction. A depletion layer free of mobile electrons and holes forms. An electric field points from the n-type to the p-type semiconductor in this depletion layer. This is equivalent to an applied voltage as in the previous figure. The energy bands in the p-type semiconductor move up and the energy bands in the n-type semiconductor move down. When the energy of the states in the conduction band of the n-type semiconductor is equal to the energy of the states in the valence band of the p-type semiconductor, lower lying energy states are no longer available for the electrons in the conduction band of the n-type semiconductor, and the filling of the holes stops.
Exposing the junction to light
If a photon strikes the PN junction and creates an free electron-hole pair in the depletion layer, then the electron will be accelerated towards the n-type and the hole towards the p-type side. If many photons create electron-hole pairs, a pico-ammeter connected across the junction will register the flow of a small current. This current crosses the junction from the n-type to the p-type material.
Reverse biasing the junction, i.e. connecting the positive terminal of an external power supply to the n-type side and the negative terminal to the p-type side will increase the size of the depletion layer. The external field will pull free electrons in the n-type material and holes in the p-type material away from the junction.
An ordinary diode
An ordinary diode is forward biased. Connecting the positive terminal of an external power supply to the p-type side and the negative terminal to the n-type side prevents a shift of the energy levels due to the the buildup of negative charge on the p-type side and positive charge on the n-type side. The external field cancels the internal field. Recombination of electrons and holes can continue and a current will flow across the junction from the p-type to the n-type material.
During the recombination energy is released. It can be released in the form of heat, or in the form of light, as in LED's and Laser diodes.
