Electrical Conductivity

Semiconductors are materials in which the conductivity is much lower than for metals, and widely variable through control of their composition. These substances are now known to be poor insulators rather than poor conductors, in terms of their atomic structure. Though some semiconducting substances had been identified and studied by the latter half of the nineteenth century, their properties could not be explained on the basis of classical physics. It was not until the mid-twentieth century, when modern quantum-mechanical principles were applied to the analysis of both metals and semiconductors, that theoretical calculations of conductivity values agreed with the results of experimental measurements.

In a good insulator, electrons cannot move because nearly all allowed orbital states are occupied. Energy must then be supplied to remove an electron from an outermost bound position to a higher allowed state. This leaves a vacancy into which another bound electron can hop under the influence of an electric field. Thus, both the energized electron and its vacancy become mobile. The vacancy acts like a positive charge, called a hole, and drifts in the direction opposite to electrons. Electrons and holes are more generally termed charge carriers.

In good insulators the activation energy of charge carriers is high, and their availability requires a correspondingly high temperature. In poor insulators, that is, semiconductors, activation occurs at temperatures moderately above 80.6°F (27°C). Each substance has a characteristic value.

There are many more compounds than elements that can be classed as semiconductors. The elements are a few of those in column IV of the periodic table, which have covalent bonds: carbon (C), germanium (Ge), and silicon (Si). For carbon, only the graphite form is semiconducting; diamond is an excellent insulator. The next element down in this column, tin (Sn), undergoes a transition from semiconductor to metal at 59°F (15°C), below room temperature, indicative of an unusefully low activation energy. Other elements that exhibit semiconductor behavior are found in the lower portion of column VI, specifically selenium (Se) and tellurium (Te).

There are two principal groups of compounds with semiconducting properties, named for the periodic table columns of their constituents: III-V, including gallium arsenide (GaAs) and indium antimonide (InSb), among others; and II-VI, including zinc sulfide (ZnS), selenides, tellurides, and some oxides. In many respects these compounds mimic the behavior of column IV elements. Their chemical bonds are mixed covalent and ionic. There are also some organic semiconducting compounds, but their analysis is beyond the scope of this article.

A semiconductor is called intrinsic if its conductivity is the result of equal contributions from its own electrons and holes. The equation must then be expanded:

In an intrinsic semiconductor, n_e = n_h, and e has the same numerical value for an electron (-) and the hole left behind (+). The mobilities are usually different. These terms add because the opposite charges move in opposite directions, resulting in a pair of like signs in each product.

For application in devices, semiconductors are rarely used in their pure or intrinsic composition. Under carefully controlled conditions, impurities are introduced which contribute either an excess or a deficit of electrons. Excess electrons neutralize holes so that only electrons are available for conduction. The resulting material is called n-type, n for negative carrier. An example of n-type material is Si with Sb, a column IV element with a column V impurity known as a donor. In n-type material, donor atoms remain fixed and positively ionized. When a column III impurity is infused into a column IV element, electrons are bound and holes made available. That material is called p-type, p for positive carrier. Column III impurities are known as acceptors; in the material acceptor atoms remain fixed and negatively ionized. An example of p-type material is Si with Ga. Both n-type and p-type semiconductors are referred to as extrinsic.

Thermal kinetic energy is not the only mechanism for the release of charge carriers in semiconductors. Photons with energy equal to the activation energy can be absorbed by a bound electron which, in an intrinsic semiconductor, adds both itself and a hole as mobile carriers. These photons may be in the visible range or in the near infrared, depending on E_G. In extrinsic semiconductors, photons of much lower energies can contribute to the pool of the prevailing carrier type, provided the material is cooled to cryogenic temperatures in order to reduce the population of thermally activated carriers. This behavior is known as photoconductivity.

Each separate variety of semiconductor is ohmic, with the conductivity constant at constant temperature. However, as the temperature is increased, the conductivity increases very rapidly. The concentration of available carriers varies in accordance with an exponential function:

where E_G is the gap or activation energy, k is Boltzmann's constant (1.38 × 10²³ joules/kelvin), T is absolute (kelvin) temperature, and the product kT is the thermal energy corresponding to temperature T. The increase in available charge carriers overrides any decrease in mobility, and this leads to a negative value for a. Indeed, a decrease in resistance with increasing temperature is a reliable indication that a substance is a semiconductor, not a metal. Graphite is an example of a conductor that appears metallic in many ways except for a negative ALPHA. The converse, a positive ALPHA, is not as distinct a test for metallic conductivity.

The Fermi level, E_F, can be shown differently for intrinsic, n-type, and p-type semiconductors. However, for materials physically connected, E_F must be the same for thermal equilibrium. This is a consequence of the laws of thermodynamics and energy conservation. Thus, the behavior of various junctions, in which the interior energy levels shift to accommodate the alignment of the Fermi level, is extremely important for the semiconductor devices.