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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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