The index of refraction n of a transparent substance is related to its electric polarizability and is given by n2 = 1 + χe/ε0 . As discussed earlier, χe is the electric susceptibility of a medium, and the equation P = χeE relates the polarization of the medium to the applied electric field. For most matter, χe is not a constant independent of the value of the electric field, but rather depends to a small degree on the value of the field. Thus, the index of refraction can be changed by applying an external electric field to a medium. In liquids, glasses, and crystals that have a centre of symmetry, the change is usually very small. Called the Kerr effect (for its discoverer, the Scottish physicist John Kerr), it is proportional to the square of the applied electric field. In noncentrosymmetric crystals, the change in the index of refraction n is generally much greater; it depends linearly on the applied electric field and is known as the Pockels effect (after the German physicist F. R. Pockels).
A varying electric field applied to a medium will modulate its index of refraction. This change in the index of refraction can be used to modulate light and make it carry information. A crystal widely used for its Pockels effect is potassium dihydrogen phosphate, which has good optical properties and low dielectric losses even at microwave frequencies.
An unusually large Kerr effect is found in nitrobenzene, a liquid with highly “acentric” molecules that have large electric dipole moments. Applying an external electric field partially aligns the otherwise randomly oriented dipole moments and greatly enhances the influence of the field on the index of refraction. The length of the path of light through nitrobenzene can be adjusted easily because it is a liquid.
When two metals are placed in electric contact, electrons flow out of the one in which the electrons are less bound and into the other. The binding is measured by the location of the so-called Fermi level of electrons in the metal; the higher the level, the lower is the binding. The Fermi level represents the demarcation in energy within the conduction band of a metal between the energy levels occupied by electrons and those that are unoccupied. The energy of an electron at the Fermi level is −W relative to a free electron outside the metal. The flow of electrons between the two conductors in contact continues until the change in electrostatic potential brings the Fermi levels of the two metals (W1 and W2) to the same value. This electrostatic potential is called the contact potential ϕ12 and is given by eϕ12 = W1 − W2, where eis 1.6 × 10−19 coulomb.
If a closed circuit is made of two different metals, there will be no net electromotive force in the circuit because the two contact potentials oppose each other and no current will flow. There will be a current if the temperature of one of the junctions is raised with respect to that of the second. There is a net electromotive force generated in the circuit, as it is unlikely that the two metals will have Fermi levels with identical temperature dependence. To maintain the temperature difference, heat must enter the hot junction and leave the cold junction; this is consistent with the fact that the current can be used to do mechanical work. The generation of a thermal electromotive force at a junction is called the Seebeck effect (after the Estonian-born German physicist Thomas Johann Seebeck). The electromotive force is approximately linear with the temperature difference between two junctions of dissimilar metals, which are called a thermocouple. For a thermocouple made of iron and constantan (an alloy of 60 percent copper and 40 percent nickel), the electromotive force is about five millivolts when the cold junction is at 0° C and the hot junction at 100° C. One of the principal applications of the Seebeck effect is the measurement of temperature. The chemical properties of the medium, the temperature of which is measured, and the sensitivity required dictate the choice of components of a thermocouple.
The absorption or release of heat at a junction in which there is an electric current is called the Peltier effect (after the French physicist Jean-Charles Peltier). Both the Seebeck and Peltier effects also occur at the junction between a metal and a semiconductor and at the junction between two semiconductors. The development of semiconductor thermocouples (e.g., those consisting of n-type and p-type bismuth telluride) has made the use of the Peltier effect practical for refrigeration. Sets of such thermocouples are connected electrically in series and thermally in parallel. When an electric current is made to flow, a temperature difference, which depends on the current, develops between the two junctions. If the temperature of the hotter junction is kept low by removing heat, the second junction can be tens of degrees colder and act as a refrigerator. Peltier refrigerators are used to cool small bodies; they are compact, have no moving mechanical parts, and can be regulated to maintain precise and stable temperatures. They are employed in numerous applications, as, for example, to keep the temperature of a sample constant while it is on a microscope stage.
Conduction electrons moving in a solid under the influence of an electric field usually lose kinetic energy in low-energy collisions as fast as they acquire it from the field. Under certain circumstances in semiconductors, however, they can acquire enough energy between collisions to excite atoms in the next collision and produce radiation as the atoms de-excite. A voltage applied across a thin layer of zinc sulfide powder causes just such an electroluminescent effect. Electroluminescent panels are of more interest as signal indicators and display devices than as a source of general illumination.
A somewhat similar effect occurs at the junction in a reverse-biased semiconductor p–n junction diode—i.e., a p–n junction diode in which the applied potential is in the direction of small current flow. Electrons in the intense field at the depleted junction easily acquire enough energy to excite atoms. Little of this energy finally emerges as light, though the effect is readily visible under a microscope.
When a junction between a heavily doped n-type material and a less doped p-type material is forward-biased so that a current will flow easily, the current consists mainly of electrons injected from the n-type material into the conduction band of the p-type material. These electrons ultimately drop into holes in the valence band and release energy equal to the energy gap of the material. In most cases, this energy Eg is dissipated as heat, but in gallium phosphide and especially in gallium arsenide, an appreciable fraction appears as radiation, the frequency ν of which satisfies the relation hν = Eg. In gallium arsenide, though up to 30 percent of the input electric energy is available as radiation, the characteristic wavelength of 900 nanometres is in the infrared. Gallium phosphide gives off visible green light but is inefficient; other related III-V compound semiconductors emit light of different colours. Electroluminescent injection diodes of such materials, commonly known as light-emitting diodes (LEDs), are employed mainly as indicator lamps and numeric displays. Semiconductor lasers built with layers of indium phosphide and of gallium indium arsenide phosphide have proved more useful. Unlike gas or optically pumped lasers, these semiconductor lasers can be modulated directly at high frequencies. They are used not only in devices such as compact disc players but also as light sources for long-distance optical fibre communications systems.