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GATE 2017 EC – Question 20

Electronic Devices · P-N Junction and Semiconductor Devices · 1 mark · Multiple choice

An $n^+$-$n$ Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of $N_{D1} = 1 \times 10^{18}$ cm$^{-3}$ and $N_{D2} = 1 \times 10^{15}$ cm$^{-3}$ corresponding to the $n^+$ and $n$ regions respectively. At the operational temperature $T$, assume complete impurity ionization, $kT/q = 25$ mV, and intrinsic carrier concentration to be $n_i = 1 \times 10^{10}$ cm$^{-3}$. What is the magnitude of the built-in potential of this device?

  1. 0.748 V
  2. 0.460 V
  3. 0.288 V
  4. 0.173 V

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Correct answer: (D) 0.173 V

Explanation

Both regions are $n$-type, so the built-in potential comes from the difference in electron concentrations, $V_{bi} = \frac{kT}{q}\ln\frac{N_{D1}}{N_{D2}} = 0.025 \times \ln(1000) = 0.025 \times 6.908 = 0.173$ V.