The GATE Grind

GATE 2018 EC – Question 40

Electronic Devices · P-N Junction and Semiconductor Devices · 2 marks · Multiple choice

Red (R), Green (G) and Blue (B) Light Emitting Diodes (LEDs) were fabricated using $p$-$n$ junctions of three different inorganic semiconductors having different band-gaps. The built-in voltages of red, green and blue diodes are $V_R$, $V_G$ and $V_B$, respectively. Assume donor and acceptor doping to be the same ($N_A$ and $N_D$, respectively) in the $p$ and $n$ sides of all the three diodes.

Which one of the following relationships about the built-in voltages is TRUE?

  1. $V_R>V_G>V_B$
  2. $V_R<V_G<V_B$
  3. $V_R=V_G=V_B$
  4. $V_R>V_G<V_B$

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Correct answer: (B) $V_R<V_G<V_B$

Explanation

The built-in voltage $V_{bi}=\frac{kT}{q}\ln\frac{N_AN_D}{n_i^2}$ rises as $n_i$ falls, and $n_i$ is smaller for a wider bandgap. Blue has the largest bandgap and red the smallest, so $V_R<V_G<V_B$.