GATE EC 2014 Set 4 — Question 46
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Electronic Devices → Semiconductor Physics → Energy Bands
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Question
An N-type semiconductor having uniform doping is biased as shown in the figure.
If is the lowest energy level of the conduction band, is the highest energy level of the valence band and is the Fermi level, which one of the following represents the energy band diagram for the biased N-type semiconductor?
If is the lowest energy level of the conduction band, is the highest energy level of the valence band and is the Fermi level, which one of the following represents the energy band diagram for the biased N-type semiconductor?
Correct answer
(D) [figure]
Solution
Reading the figure. In the battery symbol the long plate (positive terminal) is on the right, so the right end of the N-type bar is at the higher electrostatic potential and the left end at the lower one.Band bending. Electron energy is . The potential increases linearly from left to right (uniform doping, uniform field), so all electron energies decrease linearly from left to right: and are straight lines sloping downward to the right, parallel to each other (the band gap is constant).Fermi level. A current flows through the biased bar, so the sample is not in equilibrium and is not flat; in a uniformly doped sample is the same everywhere, so is constant and runs parallel to , staying close to (N-type).Options.
- (A) flat bands: zero-bias equilibrium, wrong.
- (B) flat , with tilted : impossible for uniform doping.
- (C) bands slope upward to the right: corresponds to the opposite polarity.
- (D) , , all slope downward to the right, near : correct.
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