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GATE 2021 EC – Question 17

Electronic Devices · Energy Bands and Carrier Concentration · 1 mark · Multiple choice

The energy band diagram of a p-type semiconductor bar of length $L$ under equilibrium condition (i.e., the Fermi energy level $E_F$ is constant) is shown in the figure. The valance band $E_V$ is sloped since doping is non-uniform along the bar. The difference between the valance band at the two edges of the bar is $\Delta$.

If the charge of an electron is $q$, then the magnitude of the electric field developed inside this semiconductor bar is

Diagram for GATE 2021 EC question 17
  1. $\frac{\Delta}{qL}$
  2. $\frac{2\Delta}{qL}$
  3. $\frac{\Delta}{2qL}$
  4. $\frac{3\Delta}{2qL}$

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Show answer and explanation

Correct answer: (A) $\frac{\Delta}{qL}$

Explanation

The electric field is the slope of the band edge divided by the electron charge, $E=\frac1q\frac{dE_V}{dx}$. The band edge changes linearly by $\Delta$ over the length $L$, so $|E|=\frac{\Delta}{qL}$.