Electrical conductivity

Electrical conductivity or specific conductance is a measure of a material's ability to conduct an electric current. When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current. The conductivity σ is defined as the ratio of the current density J to the electric field strength E:

It is also possible to have materials in which the conductivity is anisotropic, in which case σ is a 3×3 matrix (or more technically a rank-2 tensor), which is generally symmetric.

Conductivity is the reciprocal (inverse) of electrical resistivity, ρ, and has the SI units of siemens per metre (S·m^-1) and CGSE units of inverse second (s^–1):

Electrical conductivity is commonly represented by the Greek letter σ, but κ (esp. in electrical engineering science) or γ are also occasionally used.

An EC meter is normally used to measure conductivity in a solution.

Classification of materials by conductivity

• A conductor such as a metal has high conductivity and a low resistivity.
• An insulator like glass has low conductivity and a high resistivity.
• The conductivity of a semiconductor is generally intermediate, but varies widely under different conditions, such as exposure of the material to electric fields or specific frequencies of light, and, most important, with temperature and composition of the semiconductor material.

The degree of doping in solid state semiconductors makes a large difference in conductivity. More doping leads to higher conductivity. The conductivity of a solution of water is highly dependent on its concentration of dissolved salts, and sometimes other chemical species that ionize in the solution. Electrical conductivity of water samples is used as an indicator of how salt-free, ion-free, or impurity-free the sample is; the purer the water, the lower the conductivity (the higher the resistivity). Conductivity measurements in water are often reported as specific conductance, which is the conductivity of the water at 25 C.

Some electrical conductivities

Material	Electrical Conductivity (S·m-1)	Notes
Silver	63.0 × 106	Best electrical conductor of any known metal
Copper	59.6 × 106	Commonly used in electrical wire applications due to very good conductivity and price compared to silver.
AnnealedCopper	58.0 × 106	Referred to as 100% IACS or International Annealed Copper Standard. The unit for expressing the conductivity of nonmagnetic materials by testing using the eddy-current method. Generally used for temper and alloy verification of Aluminium.
Gold	45.2 × 106	Gold is commonly used in electrical contacts because it does not easily corrode.
Aluminium	37.8 × 106	Commonly used for High Voltage Mains electricity distribution cables[citation needed]
Sea water	4.8	Corresponds to an average salinity of 35 g/kg at 20 °C.[1]
Drinking water	0.0005 to 0.05	This value range is typical of high quality drinking water and not an indicator of water quality
Deionized water	5.5 × 10-6	Conductivity is lowest with monoatomic gases present; changes to 1.2 × 10-4 upon complete de-gassing, or to 7.5 × 10-5 upon equilibration to the atmosphere due to dissolved CO2 [2]
Jet A-1 Kerosene	50 to 450 × 10-12	[3]
n-hexane	100 × 10-12
Air	0.3 to 0.8 × 10-14	[4]

Complex conductivity

To analyse the conductivity of materials exposed to alternating electric fields, it is necessary to treat conductivity as a complex number (or as a matrix of complex numbers, in the case of anisotropic materials mentioned above) called the admittivity. This method is used in applications such as electrical impedance tomography, a type of industrial and medical imaging. Admittivity is the sum of a real component called the conductivity and an imaginary component called the susceptivity.

An alternative description of the response to alternating currents uses a real (but frequency-dependent) conductivity, along with a real permittivity. The larger the conductivity is, the more quickly the alternating-current signal is absorbed by the material (i.e., the more opaque the material is). For details, see Mathematical descriptions of opacity.

Temperature dependence

Electrical conductivity is strongly dependent on temperature. In metals, electrical conductivity decreases with increasing temperature, whereas in semiconductors, electrical conductivity increases with increasing temperature. Over a limited temperature range, the electrical conductivity can be approximated as being directly proportional to temperature. To compare electrical conductivity measurements at different temperatures, they must be standardized to a common temperature. This dependence is often expressed as a slope in the conductivity-vs-temperature graph, which can be written as:

where

σ_T′ is the electrical conductivity at a common temperature, T′

σ_T is the electrical conductivity at a measured temperature, T

α is the temperature compensation slope of the material,

T is the measured absolute temperature,

T′ is the common temperature.

The temperature compensation slope for most naturally occurring waters is about 2 %/°C, however it can range between (1 to 3) %/°C. This slope is influenced by the geochemistry, and can be easily determined in a laboratory.

At extremely low temperatures (not far from absolute zero), a few materials have been found to exhibit very high electrical conductivity in a phenomenon called superconductivity.

Electrical Conductivity in Semiconductors

Electrical conduction in semiconductors can be visualized by using either a localized bonding model or a model based on band theory.

The Local Bonding Model

Let us first consider a localized bonding model. In such a model, a physical picture is obtained by focusing on the bonds that bind the silicon atoms together. If the temperature is very low, all of the valence electrons are localized in two-electron Si - Si bonds. Since these bonds are relatively strong, the electrons are held fairly tightly, and are not at all mobile. However, if the temperature is increased so that absorption of thermal energy occurs, a few super-energetic electrons are created. Some of these vibrate so vigorously that they are ejected from localized bonds into the surrounding crystal. This process leaves behind a number of one-electron bonds, one of which is indicated in Figure 1 by a dashed line. The most powerful formalism that has been developed to treat electrical conduction in semiconductors is to view the missing electrons in these one-electron bonds as positively charged particles called "holes" (designated in Figure 1 as h⁺).

The electrical conductivity is then determined by both the free electrons ejected from localized bonds, and by the holes created by this process. To see why this is so, consider what happens when a voltage is applied to the semiconductor. The relatively mobile "free electrons" acquire additional energy and migrate toward the positive terminal. At the same time, the holes (or one-electron bonds" migrate toward the negative terminal. The mechanism by which this later process occurs is explained below.

Consider a "normal" two-electron bond situated immediately adjacent to a hole. When an electric field is applied to the crystal, the electrons in this bond are accelerated towards the positive terminal. Occasionally one of them acquires sufficient energy to "jump" into the vacant hole. When this occurs, the original one-electron bond is restored to two-electron status. However, a new one-electron bond (or hole) is created from the original "normal bond". As this process is repeated, the original hole migrates, one bond at a time, toward the negative terminal. It is this migration towards the negative terminal that encourages us to think of the hole as being positively charged.

Both of the processes described above are illustrated in Figure 2. The migration of holes is also depicted in the cartoon shown in Figure 3.

Here, the chairs represent one-electron bonds, and the students represent the additional electrons that "migrate" to complete unsatisfied one-electron bonds.

Band Theory

Now let us consider how the conduction of electric charge can be visualized by using band theory.

At very low temperatures, the valence band is fully occupied, and the conduction band is completely empty. Under these conditions, no current flows and the semiconductor acts as if it were an insulator. However, as the temperature is increased, some thermal energy is acquired, and a few electrons are promoted from the valence band to the conduction band. This process is illustrated in Figure 4, which shows four negatively charged electrons entering the conduction band. In doing this, they leave four vacancies or "holes" in the valence band. Since the conduction band orbitals in the semiconductor are relatively delocalized, charge can be easily transported though the crystal by the small number of electrons promoted to this band. Moreover, the holes can move from one orbital to another in the valence band, also contributing to the overall conductivity.

At room temperature, very little thermal energy is available, and only a few electrons can be promoted to the conduction band of any semiconductor having a band gap greater than about 0.1eV. In fact, in pure silicon (band gap =1.1eV = 105 kJ/mol), only 1 electron in 10¹² occupies an orbital in the conduction band when equilibrium is established at 300 K. This explains why semiconductors are much poorer conductors than are metals. However, as the temperature is raised, the number of electrons promoted to the conduction band increases, as does the conductivity.

Aderlis S. Marquez G
Electronica del Estado Solido
http://en.wikipedia.org/wiki/Electrical_conductivity