Temperature Dependence Of Conductivity
As a block of pure semiconductor is gradually warmed from room temperature, its measured electrical resistance is observed to fall steadily. Which statement best explains this behaviour of the semiconductor?
Select the correct option:
Solution
Heating breaks more covalent bonds, increasing carrier density faster than mobility falls
Unlike metals, semiconductors have a negative temperature coefficient of resistance, meaning their resistance decreases as temperature rises. The dominant reason is that thermal energy breaks additional covalent bonds, exponentially increasing the number of free electrons and holes available to carry current. Although increased lattice vibrations at higher temperature do scatter carriers more and slightly reduce mobility, this effect is far weaker than the rapid exponential growth in carrier concentration. The net result is that conductivity rises and resistance falls. Mathematically the carrier concentration depends on temperature through an exponential factor of the form (e^{-E_g/2kT}), so even a modest rise in temperature can multiply the carrier population substantially, whereas mobility only declines as a gentle power of temperature. The option claiming fewer carriers is wrong, as that describes metals where added scattering raises resistance. The option that the band gap widens is incorrect; the gap actually narrows slightly with temperature, further aiding conduction. The option crediting mobility is wrong because mobility in fact decreases with heating. As a sanity check, this strong carrier-generation effect is precisely why semiconductor devices like thermistors are used as temperature sensors and why semiconductor resistance behaviour is opposite to that of ordinary metallic conductors.
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About This Question
- Subject
- physics
- Chapter
- semiconductor electronics
- Topic
- temperature dependence of conductivity
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
Heating breaks more covalent bonds, increasing carrier density faster than mobility falls
Unlike metals, semiconductors have a negative temperature coefficient of resistance, meaning their resistance decreases as temperature rises. The dominant reason is that thermal energy breaks additional covalent bonds, exponentially increasing the number of free electrons and holes available to carry current. Although increased lattice vibrations at higher temperature do scatter carriers more and slightly reduce mobility, this effect is far weaker than the rapid exponential growth in carrier concentration. The net result is that conductivity rises and resistance falls. Mathematically the carrier concentration depends on temperature through an exponential factor of the form (e^{-E_g/2kT}), so even a modest rise in temperature can multiply the carrier population substantially, whereas mobility only declines as a gentle power of temperature. The option claiming fewer carriers is wrong, as that describes metals where added scattering raises resistance. The option that the band gap widens is incorrect; the gap actually narrows slightly with temperature, further aiding conduction. The option crediting mobility is wrong because mobility in fact decreases with heating. As a sanity check, this strong carrier-generation effect is precisely why semiconductor devices like thermistors are used as temperature sensors and why semiconductor resistance behaviour is opposite to that of ordinary metallic conductors.
This medium difficulty physics question is from the chapter semiconductor electronics, covering the topic of temperature dependence of conductivity. It appeared in the 2025 exam.
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