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

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CUET Physics 18th Aug 2022 Official Paper
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  1. F1 Madhuri UG Entrance 19.04.2023 D17
  2. F1 Madhuri UG Entrance 19.04.2023 D18
  3. F1 Madhuri UG Entrance 19.04.2023 D19
  4. F1 Madhuri UG Entrance 19.04.2023 D20

Answer (Detailed Solution Below)

Option 3 : F1 Madhuri UG Entrance 19.04.2023 D19
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Explanation:

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

s = \(s_0e^{\frac{E_g}{2KT}} \)

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,

 

F1 Madhuri UG Entrance 19.04.2023 D19

The correct answer is option (3)

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