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GATE 2020 EC – Question 41

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

A one-sided abrupt $pn$ junction diode has a depletion capacitance $C_D$ of 50 pF at a reverse bias of 0.2 V. The plot of $1/C_D^2$ versus the applied voltage $V$ for this diode is a straight line as shown in the figure below. The slope of the plot is ________ $\times10^{20}\ \text{F}^{-2}\text{V}^{-1}$.

Diagram for GATE 2020 EC question 41
  1. $-5.7$
  2. $-3.8$
  3. $-1.2$
  4. $-0.4$

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Show answer and explanation

Correct answer: (A) $-5.7$

Explanation

For an abrupt one-sided junction, $\frac{1}{C_D^2}=\frac{2(\phi_{bi}-V)}{q\varepsilon N A^2}$, so the slope is $-\frac{1}{C_D^2(\phi_{bi}+V_R)}$ at any reverse bias $V_R$. At $V_R=0.2$ V, $\frac{1}{C_D^2}=\frac{1}{(50\text{ pF})^2}=4\times10^{20}$, and with $\phi_{bi}\approx0.5$ V the slope is $-\frac{4\times10^{20}}{0.7}\approx-5.7\times10^{20}\ \text{F}^{-2}\text{V}^{-1}$.