Question:
The probability of electrons to be found in the conduction band of an intrinsic semiconductor at a finite temperature :
The probability of electrons to be found in the conduction band of an intrinsic semiconductor at a finite temperature :
Updated On: Aug 15, 2022
- decreases exponentially with increasing band gap
- increases exponentially with increasing band gap
- decreases with increasing temperature
- is independent of the temperature and the band gap
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The Correct Option is A
Solution and Explanation
The fermi function $f(E)$ gives the probability that a given available electron energy state will be occupied at a given temperature.
The fermi function comes from Fermi-Dirac statistics and has the form
$f(E)=\frac{1}{E^{\left(E-E_{F}\right) / k T}+1}$
The basic nature of this function dictates that at ordinary temperatures, most of the levels up to the fermi level are filled.
At higher temperature, a larger fraction of the electrons can bridge this gap and participate in electrical conduction.
Hence, at finite temperature, the probability decreases exponentially with increasing band gap.
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Concepts Used:
Semiconductors
Semiconductors are a crystalline solid materials, whose electrical conductivity lies between a conductor and an insulator. Semiconductors are mainly used in the manufacturing of electronic devices like capacitors, transistors, diodes, Integrated circuits, etc.
Properties of Semiconductor:
- Semiconductor acts like an insulator at Zero Kelvin. On increasing the temperature, it works as a conductor.
- Due to their exceptional electrical properties, semiconductors can be modified by doping to make semiconductor devices suitable for energy conversion, switches, and amplifiers.
- Lesser power losses.
Uses of Semiconductor:
- Semiconductors are widely used in manufacturing electronics devices like transistors, diodes, sensors, integrated circuits.
- Semiconductors are widely used in all electronic devices, like mobile phones, digital cameras, communication devices, trains, ATMs, etc.