Question
Download Solution PDFWhich of the following graph correctly represents the variation of resistivity 's' with temperature 'T' for a semiconductor material ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
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,
The correct answer is option (3)
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