Which of the following graph correctly represents the variation of resistivity 's' with temperature 'T' for a semiconductor material ?

Explanation:

The relationship between resistivity and temperature for a semiconductor material is given by the following equation:

s = 

where s₀ is the resistivity at absolute zero temperature, Eg is the bandgap energy of the semiconductor material, k is Boltzmann's constant, and T is the temperature in Kelvin.

• This equation is known as the Arrhenius equation and describes the temperature dependence of the resistivity of semiconductors.
• As the temperature increases, the resistivity of a semiconductor decreases exponentially due to the increasing number of thermally excited charge carriers (electrons and holes).
• Since, the decay is exponential, the resistivity decreases as the temperature increases.
• So, the graph representing resistivity vs temperature would be exponential decay and represented by,

The correct answer is option (3)