GATE EC 2021 Set 1 — Question 17
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Electronic Devices → Semiconductor Physics → Energy Bands
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Question
The energy band diagram of a p-type semiconductor bar of length under equilibrium condition (i.e., the Fermi energy level is constant) is shown in the figure. The valence band is sloped since doping is non-uniform along the bar. The difference between the energy levels of the valence band at the two edges of the bar is .
If the charge of an electron is , then the magnitude of the electric field developed inside this semiconductor bar is
Correct answer
(A) (Δ)/(qL)
Solution
In a semiconductor under equilibrium, the Fermi level is constant. However, if the doping is non-uniform, the intrinsic level , conduction band , and valence band will vary with position, creating an internal electric field. The relationship between the electric field and the gradient of the energy bands is given by:From the provided energy band diagram, the valence band varies linearly over the length of the semiconductor bar. The total change in energy is over the distance . Therefore, the magnitude of the slope of the valence band is:Substituting this into the expression for the electric field magnitude:Thus, the magnitude of the electric field developed inside the semiconductor bar is .
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