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GATE 2017 EC – Question 48

Electronic Devices · P-N Junction and Semiconductor Devices · 2 marks · Numerical answer

As shown, two Silicon (Si) abrupt $p$-$n$ junction diodes are fabricated with uniform donor doping concentrations of $N_{D1} = 10^{14}$ cm$^{-3}$ and $N_{D2} = 10^{16}$ cm$^{-3}$ in the $n$-regions of the diodes, and uniform acceptor doping concentrations of $N_{A1} = 10^{14}$ cm$^{-3}$ and $N_{A2} = 10^{16}$ cm$^{-3}$ in the $p$-regions of the diodes, respectively. Assuming that the reverse bias voltage is $\gg$ built-in potentials of the diodes, the ratio $C_2/C_1$ of their reverse bias capacitances for the same applied reverse bias, is ________.

Diode 1 has $10^{14}$ cm$^{-3}$ on both the p-side and the n-side. Diode 2 has $10^{16}$ cm$^{-3}$ on both sides.

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Correct answer: 10

Explanation

For a large reverse bias the junction capacitance per unit area goes as $\sqrt{\frac{N_A N_D}{N_A + N_D}}$. For diode 1 this is $\sqrt{5 \times 10^{13}}$ and for diode 2 it is $\sqrt{5 \times 10^{15}}$. The ratio is $\sqrt{100} = 10$.