Temperature Dependence of Resistivity for Conductors, Semiconductors and Insulators

The temperature dependence of resistivity determines how the electrical resistivity of the material changes with fluctuations in temperature. This relationship plays an important role for understanding the behaviour of materials when put in different thermal environments and their implications in various practical applications. For JEE Main exam and IIT JAM entrance exam aspirants, knowing about this concept is very important.

Mathematically, the temperature dependence of resistivity is expressed as:

${\rho }_t = {\rho }_0 [ 1 + \alpha ( T - T_0 \left) \right]$

Through the above equation, the relation between temperature and resistivity of the material is established.

/Here:

• ${\rho }_0$ indicates the resistivity at standard temperature
• ${\rho }_t$ is the resistivity at  $T_0$ Celsius
• α represents the temperature coefficient of resistivity

Let us understand the temperature dependence of resistivity for conductors, insulators and semiconductors in more detail. NEET exam and CUET exam may ask questions to understand whether the student is aware that resistivity varies with temperature:

CBSE board students must be well aware of how the resistivity varies with temperature:

• For the conductors, the resistivity increases with increasing temperature. Let us understand why this happens. 
• As the temperature rises, the lattice ions vibrate more vigorously because of the increased thermal energy. 
• Once electrons start moving through the lattice, they collide with the vibrating ions. These collisions obstruct the flow of electrons, which in turn, increases resistivity.

Let us understand the temperature dependence of resistivity for insulators:

• By property, insulators are those materials that have very strong resistance against the flow of electric current. These have very high resistivity and low conductivity at the room temperature. 
• Electrons are very tightly bound to their atoms in insulators and they cannot move as freely as they do in conductors. This happens because of the large energy gap called band gap between valence gap and conduction band. 
• As soon as the thermal energy is supplied to electrons in the insulator, some of the electrons gain sufficient energy to jump from the valence band to conduction band. This is a process of thermal excitation. 
• With an increase in temperature, more electrons become excited across the band gap into conduction band. This results in the increase in number of charge carriers that contribute to electrical conduction. 

Now, let us take a look at the dependence of resistivity on temperature for semiconductors:

• When it comes to semiconductor, the energy gap between conduction band and valence band decreases with an increase in temperature. 
• Valence electrons in semiconductors will gain enough energy to break covalent bonds and jump to conduction band at high temperatures. This creates more charge carriers in semiconductors at high temperatures. 
• Higher concentration of charge carriers decreases the resistivity of semiconductors. IISER exam students must know about this.
• With an increase in the temperature, the resistivity of semiconductors decreases and they become conductive.