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GATE 2022 EC – Question 16

Electronic Devices · Carrier Transport · 1 mark · Multiple choice

Consider a long rectangular bar of direct bandgap $p$-type semiconductor. The equilibrium hole density is $10^{17}\ \text{cm}^{-3}$ and the intrinsic carrier concentration is $10^{10}\ \text{cm}^{-3}$. Electron and hole diffusion lengths are $2\ \mu\text{m}$ and $1\ \mu\text{m}$, respectively.

The left side of the bar ($x=0$) is uniformly illuminated with a laser having photon energy greater than the bandgap of the semiconductor. Excess electron-hole pairs are generated ONLY at $x=0$ because of the laser. The steady state electron density at $x=0$ is $10^{14}\ \text{cm}^{-3}$ due to laser illumination. Under these conditions and ignoring electric field, the closest approximation (among the given options) of the steady state electron density at $x=2\ \mu\text{m}$, is ________.

  1. $0.37\times10^{14}\ \text{cm}^{-3}$
  2. $0.63\times10^{13}\ \text{cm}^{-3}$
  3. $3.7\times10^{14}\ \text{cm}^{-3}$
  4. $10^{3}\ \text{cm}^{-3}$

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Correct answer: (A) $0.37\times10^{14}\ \text{cm}^{-3}$

Explanation

Electrons are the minority carriers, with $n_0=n_i^2/p_0=10^3\ \text{cm}^{-3}$, negligible against $10^{14}$. Excess electrons decay as $e^{-x/L_n}$ with $L_n=2\ \mu$m, so at $x=2\ \mu$m, $n\approx10^{14}e^{-1}=0.37\times10^{14}\ \text{cm}^{-3}$.