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GATE 2014 EC (EC4) – Question 18

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

At 300 K, GaAs has bandgap 1.42 eV and intrinsic carrier concentration $10^6$ cm⁻³. Which incident-wavelength range is most suitable for generating electron–hole pairs? Given Planck constant $6.62\times10^{-34}$ J·s, speed of light $3\times10^{10}$ cm/s and electron charge $1.6\times10^{-19}$ C.

  1. $0.42<\lambda_C<0.87$ µm
  2. $0.87<\lambda_C<1.42$ µm
  3. $1.42<\lambda_C<1.62$ µm
  4. $1.62<\lambda_C<6.62$ µm

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Correct answer: (A) $0.42<\lambda_C<0.87$ µm

Explanation

A photon must have energy hc/λ≥Eg. Using the supplied constants, the threshold wavelength is(6.62×10⁻³⁴×3×10⁸)/(1.42×1.6×10⁻¹⁹)=0.8741µm. Wavelengths below this threshold can excite carriers, so the suitable listed range is **0.42<λ<0.87µm,A**.