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GATE 2014 EC (EC1) – Question 45

Electronic Devices · Energy Bands and Carrier Concentration · 2 marks · Multiple choice

A silicon diode has p-side doping $10^{16}$ cm⁻³ and n-side doping $10^{17}$ cm⁻³. Forward bias is 0.3 V. At 300 K, $n_i=1.5\times10^{10}$ cm⁻³ and $kT/q=26$ mV. Find electron concentration at the p-side depletion edge.

  1. $2.3\times10^9$ cm⁻³
  2. $10^{16}$ cm⁻³
  3. $10^{17}$ cm⁻³
  4. $2.25\times10^6$ cm⁻³

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Correct answer: (A) $2.3\times10^9$ cm⁻³

Explanation

The equilibrium minority-electron concentration is np0=ni²/NA=(1.5×10¹⁰)²/10¹⁶=2.25×10⁴cm⁻³. Forward bias multiplies it by exp(V/VT)=exp(0.3/0.026). Thus np≈2.305×10⁹cm⁻³, matching **2.3×10⁹cm⁻³,A**. Use the p-side acceptor density, not the n-side donor density.