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GATE 2021 EC – Question 16

Electronic Devices · Energy Bands and Carrier Concentration · 1 mark · Multiple choice

A bar of silicon is doped with boron concentration of $10^{16}\ \text{cm}^{-3}$ and assumed to be fully ionized. It is exposed to light such that electron-hole pairs are generated throughout the volume of the bar at the rate of $10^{20}\ \text{cm}^{-3}\text{s}^{-1}$. If the recombination lifetime is $100\ \mu\text{s}$, intrinsic carrier concentration of silicon is $10^{10}\ \text{cm}^{-3}$ and assuming 100% ionization of boron, then the approximate product of steady-state electron and hole concentrations due to this light exposure is

  1. $10^{20}\ \text{cm}^{-6}$
  2. $2\times10^{20}\ \text{cm}^{-6}$
  3. $10^{32}\ \text{cm}^{-6}$
  4. $2\times10^{32}\ \text{cm}^{-6}$

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Correct answer: (D) $2\times10^{32}\ \text{cm}^{-6}$

Explanation

The excess carrier density is $\Delta n=\Delta p=G\tau=10^{20}\times100\times10^{-6}=10^{16}\ \text{cm}^{-3}$. The equilibrium values are $p_0=10^{16}$ and $n_0=n_i^2/p_0=10^4$, so $n\approx10^{16}$ and $p=10^{16}+10^{16}=2\times10^{16}$. The product is $np\approx2\times10^{32}\ \text{cm}^{-6}$.