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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. $kT/g=25mV$, and intrinsic carrier concentration to be $n_{i}=1\times 10^{10}cm^{-3}$ .What is the magnitude of the build-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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