Review on Temperature Dependence of Resistivity

Resistivity, also known as specific electric resistance, is the efficiency of a material to oppose or resist the flow of charge or current. It depends on the material’s behaviour and the temperature. It doesn’t matter what the shape is and the size of the particular substance. The ohm metre is the SI unit for measuring the resistivity of a specific object.

The resistivity of carbon-based resistors has an inverse relationship with the temperature. As the temperature rises, the resistivity of a material decreases and vice versa. The rho (⍴) symbol denotes resistivity. Resistivity is also reciprocally related to the conductivity of the material. If you know the value of the conductivity of a material, you just need to reciprocate it to find out the correct value of resistivity.

Temperature Dependence of Resistivity

There are three kinds of material: metal or conductors, semiconductors, and insulators. Materials that enable electricity to flow across them are conductors. Semiconductors are a type of material that lies between metals and insulators. They hold conductivity more than insulators and less than conducting materials. Insulators are materials that prevent current from flowing.

Metals or conductors have low resistivities and show a positive temperature coefficient. So when the temperature rises, the resistivity of metal increases. Semiconductors are negative temperature coefficient materials. As temperature increases, the value of the resistivity decreases in semiconductors. Semiconductors behave like conductors at high temperatures or critical temperatures or peaks and give a positive temperature coefficient. Semiconductors’ temperature dependence on resistivity dramatically impacts their use in electronics.

Temperature affects the resistivity of a substance. For conductors, semiconductors, and insulators, the temperature dependency of the resistivity varies with the nature of the substance. Before we go into semiconductors, let’s talk about how resistance changes in conductors and insulators.

How Metals or Conductors Resistivity Depends on Temperature

As you heat the conductor, its temperature rises, and its atoms begin to vibrate violently. This results in random movement of free and other electrons and their collision. Free electrons, responsible for the current flow, lose energy due to these collisions.

Under normal conditions, conductors have low resistivities. The resistivity of conductors, particularly metals, increases when the mobility, or drift velocity, decreases owing to energy depletion. The metal’s resistivity increases as the temperature rises, giving it a positive temperature coefficient of resistance. A conductor’s resistance increases and its conductivity decreases as the temperature rises.

How Insulators’ Resistivity Depends on Temperature

Insulators have no free electrons in common conditions. They have electrons that are tightly packed with the nucleus. As the temperature rises, electrons break these bondings and get free to move, and hence the insulators migrate to the conduction zone.

The increasing temperature reduces the energy difference between the valence band and the conduction band. So, the conductivity of an insulator increases as the resistance of the insulator lowers with temperature. Insulators exhibit a negative temperature coefficient of resistivity. 

How Semiconductors Resistivity Depends on Temperature

The energy gap between the conduction and the valence bands shrinks as the temperature rises in semiconductors. At high temperatures, the valence electrons in the semiconductor material gather enough energy to break the covalent connection and hop to the conduction band.

At high temperatures, this results in more charge carriers in the semiconductor. The semiconductor’s resistivity reduces as the charge carrier concentration rises. As the temperature rises, the semiconductor’s resistivity decreases, making it more conductive. At high temperatures, a semiconductor has excellent conductivity.

Semiconductors have a temperature coefficient of resistance that is negative. This feature is utilised to use semiconductors in electronic applications. The temperature of the semiconductor crystal rises when an external voltage is applied, increasing the density of thermally produced carriers in it. More electron-hole pairs are formed, making current passage across the semiconductor easier.

Doping a semiconductor with donor or acceptor impurities improves its performance. Such semiconductors are termed extrinsic semiconductors. Extrinsic semiconductors have higher resistivity than intrinsic (undoped or pure) semiconductors.

The temperature dependence of semiconductor resistivity is highly advantageous. Today’s semiconductor devices are only conceivable because of the negative temperature coefficient of resistance. 

Conclusion

Resistivity indicates the property of an electric circuit. Low resistivity value conductors such as gold and silver allow an efficient flow of electricity. Insulators such as rubber and glass have high resistance and create a hazard for electricity to pass through. Semiconductors hold properties existing between these two materials.

With increase in temperature, resistivity of conductors increases whereas the resistivity of semiconductors and insulators decreases.