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Electrical conductivity Electrical conductivity is the ability of a material to conduct electricity. Or The degree to which a specified material conducts electricity, calculated as the ratio of the current density in the material to the electric field which causes the flow of current.

K = J/E Or Electrical conductivity or specific conductance is the reciprocal of electrical resistivity, and measures a material's ability to conduct an electric current.

K = 1/ρ Symbol: K Units: Siemens per metre (S/m)

Explanation: Consider a circuit having   

Cell Bulb Switch

Which are connected by wires. When switch is on, current will be flow through the circuit and bulb will be flow.

Most of solids show some amount of resistance to the flow of current through them.

Resistance: Resistance is the opposition that a substance offers to the flow of electric current. Symbol: It is represented by the uppercase letter R Units: The standard unit of resistance is the ohm Ω

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When an electric current of one ampere passes through a component across which a potential difference (voltage) of one volt exists, then the resistance of that component is one ohm.

Mathematical Derivation of electrical conductivity: Factors which affect electrical resistance are 1. Length of conductor Resistance of conductor depends upon length L of conductor R α L……………. (a)

2.

Area of cross section of conductor:

Resistance of a conductor is inversely proportional to area of cross section of conductor. R α 1 / A………………. (b) Combining (a) and (b)

R α L/A Or

R = ρL/A Here ρ is resistivity. Resistivity:

Resistivity is an electrical property of material. The resistance of a material or conductor of 1 cubic meter volume. Or It is the resistance of a conductor of unit length and unit area. Or Resistivity of a conductor is the resistance of 1 meter long conductor whose area of cross section is 1 meter square. Units: Ohm-m

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Different materials have different values of resistivity. A very high value of resistivity indicates high electrical resistance. Reciprocal of resistivity is electrical conductivity

K = 1/ρ The electrical resistivity, ρ, is also defined as The ratio of the electric field to the density of the current it creates

ρ = E/J Here ρ is the resistivity of the conductor material (measured in ohm-metres, Ωm), E is the magnitude of the electric field (in volts per metre, V⋅m−1), J is the magnitude of the current density (in amperes per square metre, A⋅m−2), As

K = 1/ρ Hence

K = J/E

Example:  

Rubber is a material with large ρ and small K because even a very large electric field in rubber makes almost no current flow through it. Copper is a material with small ρ and large K because even a small electric field pulls a lot of current through it.

Difference between conductors, insulators and semiconductors

Conductors Qualitatively: Those materials through which charges can flow easily and having free electrons are called conductors. The positive ionic cores are considered fixed within conductors.

Insulators Qualitatively: The materials through which charges cannot flow are called insulators and electrons are tightly bond in such materials.

Quantitatively:

Quantitatively:

semiconductors Qualitatively: The intermediate stage between conductor and insulators is called semiconductors. The materials through which charges cannot flow at room temperature but charges begin to flow at high temperature. Quantitatively:

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In a typical conductors each atom may contribute one conduction electron. On average 1023 conduction electrons/cm3 In term of resistivity: The materials having resistivity of order of 10-8 Ωm are good conductors. Example: Resistivity of cu is 1.77x10-8 Ωm

For insulators only one conduction electron/cm3

a typical semiconductor has 1012 conduction electron/cm3

In term of resistivity: The materials having resistivity of the order of 1011-1016 Ωm are good insulators. Example: Resistivity of glass is 2x1011 Ωm In term of band theory: The energy gap between conduction band and valance band in insulator is very high, the electrons cannot jump from valance band to conduction band

In term of resistivity: The material having resistivity between conductors and insulators are semiconductors Example: Resistivity of Germanium is 0.5 Ωm

In term of electrical conductivity:

In term of electrical conductivity:

In term of electrical conductivity:

Conductors are materials with high conductivities:

Insulators are materials having an electrical conductivity

semiconductors have a conductivity

In term of band theory: The conduction band and valance band overlap in conductors

Example: For silver: 106S/cm.)

Type of bonding: covalent Examples:  Copper  Iron  Aluminium

Example: For Diamond: 10-14S/cm)

Type of bonding: Ionic and covalent Examples:  Glass  Plastic  Rubber etc.

In term of band theory: The band gap in semiconductors is similar to insulators but energy gap is much less.

Example: (for silicon it can range from 10-5S/cm to 103S/cm)

Type of bonding: metallic Examples:  Silicon  Germanium

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EFFECT OF TEMPERATURE ON CONDUCTIVITY Semiconductors: With increase in temperature, the conductivity of the semi-conductor material increases. As with increase in temperature, outermost electrons acquire energy and hence by acquiring energy, the outermost electrons leave the shell of the atom. Hence with increase in temperature, number of carriers in the semiconductor material increases and which leads to increase in conductivity of the material. So we call the semi-conductor material have negative temperature coefficient i.e. with increase in temperature, resistance decreases.

R α 1/T Insulators: In insulators, it is basically a semiconductor with a very large bandgap, so ideally it might require a HUGE amount of temperature change to kick them out of the valence band into the conduction band, so in that range of temperature the resistivity should still remain high and constant, once it passes that (usually large) range of temperature, it might lead ]]]]]]to generation of huge amount of electrons as carriers- thus the insulator might breakdown thermally, giving rise to a more huge current. With increase in temperature, the conducting property increases and resistance decrease so we call insulators material have negative temperature coefficient i.e. with increase in temperature, resistance decreases.

R α 1/T Conductors: The outermost shell of conductors is mostly free at room temperature and hence due to the fact that conducting materials leave the outermost electrons, the nucleus of the atom of conducting material is more positive as it is a positive ion. 𝐶𝑢

→

𝐶𝑢⁺ + 𝑒⁻

Hence taking out more electrons from the penultimate shell of the atom is very difficult and when the temperature is increased, the energy supplied is not enough to take out more electrons but due to the energy because of increase in temperature, the nucleus of the atoms start vibrating and hence obstruct the flow of electrons already in the free space. So with increase in temperature, conductivity of the conductors decreases and resistance increases. Hence we say conductors have 5

positive temperature coefficient.

RαT Sensistor: Sensistor is a resistor whose resistance changes with temperature. When there is access doping present in the semiconductor, it is called sensistor. The sensistor also have positive temperature coefficient.

RαT Metallic conductors: 

In metallic conductors the current is transported by the electron. For metallic conductors, the resistance of all pure materials increases linearly with temperature over a limited range of temperature. As the temperature increases, the ions inside the metal acquire energy and starts oscillating about their mean positions. These vibrating ions collide with the moving electrons. Hence resistance increases with increasing temperature.

RαT Electrolytic conductors: For electrolytes and conducting liquids, an increase in temperature of electrolytic solutions will cause a decrease in its viscosity and an increase in the mobility of the ions in solution. An increase in temperature may also cause an increase in the number of ions in solution due to dissociation of molecules. As the conductivity of a solution is dependent on these factors then an increase in the solution’s temperature will lead to an increase in its conductivity.

R α 1/T

Effect of impurities on conductivity of conductors The electrical conductivity of a conductor will decrease with an increase in impurities The relationship is not linear, however, if we consider the resistivity, which is the reciprocal of conductivity, we do get a linear relationship ρ = ρo [1 + β x] 6

Here 

x is the % of impurities



ρo is the resistivity of the material for 0% impurities



β is a constant for a given system

Graphically: The variation of electrical resistivity with composition (impurity additions) for various copper alloys is obtained by plotting a graph between alloy addition on x-axis and resistivity on y-axis. The data is fixed at room temperature (20oC).

Effect of impurities on conductivity of semiconductors When we add impurities to semiconductors we call them dopants and the process is called doping. When small amount of impurity is added to a semiconductor than the impurity contributes either free electrons or holes to the semiconductor. Hence the conducting property of semiconductor changes. The process of changing conductive property of semiconductor by adding impurities is known as doping.

Types of dopant There are two kinds of dopant n type semiconductor (negative charge carriers) p type semiconductor (positive charge carriers)

N-type Semiconductor N-type semiconductors have dopants from the VA group, such as P+5. These donor impurity atoms are in substitutional solid solution. The extra valance electron not needed for the sp3 tetrahedral bonding is only loosely bound to the P atom in a 7

donor energy level, Ed. The energy of this donor energy level is close to the lowest energy level of the conduction band (in Si it is 0.4 eV) and so it is easy to promote an electron from the donor level to the conduction band. These promoted electrons become charge carriers that contribute to the material's conductivity. Since they are negative, the result is called an n-type semiconductor. As temperature increases, more and more of these donor electrons will be promoted into the conduction band. Eventually, a temperature will be reached such that there will be none left. The donor electrons will be "exhausted". During this process the relationship of conductivity to temperature is Sigma = sigma0 e – (Ec-Ed) /kT This is referred to as extrinsic semi conduction. The conductivity depends on the dopants.

After these electrons from the dopants are all promoted to the conductance band, (i.e. are exhausted,) there is a range of temperatures before intrinsic semi-conduction kicks in where the conductivity remains essentially constant. After that, as temperature increases, there will be a promotion of electrons from the valance band into the conduction band (intrinsic behaviour)

The temperatures needed to promote the dopant electrons into the conduction band are lower than the temperatures required to promote the intrinsic electrons into the conduction band.

The slope of the extrinsic range is less steep than the intrinsic range. This reflects the fact that the activation energy to promote a dopant electron into the conduction band is less than the activation energy to promote an intrinsic electron into the conduction band.

P-type Semiconductor P-type semiconductors have dopants from the IIIA group such as B+3. These donor impurity atoms in substitutional solid solution. The lack of an electron needed for sp3 tetrahedral bonding is easily filled by a neighbouring Si atom into an acceptor energy level, Ea. of the dopant atom. The energy of this acceptor level is only slightly above the valance band and so it is easy to promote an electron from the valance band into it. For each promotion of an electron into one of these acceptor levels, a hole is left in the valance band. It is these holes that become the charge carriers and contribute to the conductivity of the semiconductor. Since these holes are positive, the result is called a p-type semiconductor.

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The temperatures needed to promote the dopant electrons into the conduction band are lower than the temperatures required to promote the intrinsic electrons into the conduction band. As temperature increases, more and more of electrons from the valance band will be promoted into these acceptor energy levels. Eventually, a temperature will be reached such that all the acceptor energy levels will have electrons in them. The donor acceptor levels will be "saturated". During this process the relationship of conductivity to temperature is Sigma = sigma0 e – (Ea-Ev) /kT This is referred to as extrinsic semi conduction. The conductivity depends on the dopants. After the acceptor energy levels have been saturated, there is a range of temperatures before intrinsic semi-conduction kicks in where the conductivity remains essentially constant. After that, as temperature increases, there will be a promotion of electrons from the valance band into the conduction band (intrinsic behaviour). Note that the temperatures needed to promote electrons from the valance band into the acceptor levels (leaving holes in the valance band) are lower than the temperatures required to promote the intrinsic electrons into the conduction band. Also note that the slope of the extrinsic range is less steep than the intrinsic range. This reflects the fact that the activation energy to promote an electron from the valance band into the acceptor level less than the activation energy to promote an intrinsic electron into the conduction band.

Conclusion: It is to be noted that when an n type impurity is added to semiconductor, there will be excess electron is a crystal but it does not mean that there would not be any hole. Due to intrinsic nature of semiconductor at room temperature there are always be some electron-holes pairs in the semiconductor. Due to addition of n - type impurities, the electrons will be added to that electron hole pairs and also the number of holes reduced excess recombination for excess electrons. And hence the total number of negative charge carriers or free electrons will be more than that of holes in n type semiconductor. That is why in n - type semiconductor electrons are called majority charge carriers whereas poles are called minority charge carriers. Similarly in p - type semiconductor, holes are called the majority charge carriers and electrons are called minority charge carriers.

Binding energy The energy required to separate particles which are bound by electromagnetic or nuclear forces (infinitely far apart).

Binding Energy of an atom:

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In the case of the nucleus of an atom, these particles are protons and neutrons held together by the nuclear binding energy. The neutron and proton binding energies are the energies necessary to release a neutron or proton from the nucleus. 

The binding energy of nucleons in the nucleus of an atom amounts for most nuclei (i.e. Z>5) to around 8 MeV per nucleon.  In the case of the heaviest nuclei of an atom, such as uranium, the binding energy per nucleon is slightly less negative than for nuclei with medium mass numbers. Therefore, the fission of an uranium nucleus into two nuclei of medium mass number results in a total more negative binding energy leading to energy being released to the outside.  The binding energy of the light nuclei of the hydrogen isotopes deuterium and tritium is significantly less negative than that of the helium nucleus He-4. Thus, energy is released during the fusion of deuterium and tritium to helium

Electron binding energy: Electron binding energy is the energy required to completely remove an electron from an atom or a molecule.

Binding Energy curve:

This curve indicates how stable atomic nuclei are; the higher the curve the more stable the nucleus. 10

For a conductor: Band gap: For a conductor, conduction bands and valence bands are not separated and there is therefore no energy gap. The conduction band is then partially occupied (even at low temperatures), resulting in a “high” electrical conductivity. Binding energy: The energy required to remove electron from shell of atom is binding energy of conductors. Removal of electrons from outermost shell of atom is easy as valance and conduction bands are overlap. No energy is required to remove electron from shell of atom hence there is no binding energy in conductors. For semiconductor: Band gap: A semiconductor is primarily an insulator at 0K. However, since the energy gap is lower compared to insulators (~1eV), the valence band is slightly thermally populated at room temperature, whereas the conduction band is slightly depopulated. Since electrical conduction is directly connected to the number of electrons in the “almost empty” conduction band and to the number of holes in the “almost fully occupied” valence band, it can be expected that the electrical conductivity of such an intrinsic semiconductor will be very small. Binding energy: The energy required to remove electron from shell of atom is binding energy of semiconductor. With increase in temperature, outermost electrons acquire energy and hence by acquiring energy, the outermost electrons leave the shell of the atom. In semiconductors more energy is required to remove electrons from shall of atom hence binding energy of semiconductors is more than conductors. For insulator: Band gap: When the gap energy exceeds ~9eV, because for such gaps, the thermal energy at 300K (~25 MeV) is clearly insufficient to allow electrons from the valence band to be promoted to the conduction band. In this case the valence band (and all bands of lower energy) is fully occupied, and the conduction band is empty. Binding energy: The energy required to remove electron from shell of atom is binding energy of insulators. As the energy gap between valance and conduction bond is very large more 11

energy is required to remove electrons from shell. Hence binding energy of insulator is more than semiconductors and conductors.

References: Electricity and magnetism by Muhammad Kaleem Akhtar Physical chemistry by Sanaullah Inorganic chemistry by Ghulam Rasool www.electrical4u.com www.wikipedia.com

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