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GATE 2026 PH – Question 54

Solid State Physics · conductivity, electron and hole statistics in intrinsic and extrinsic semiconductors, mobility and effective mass · 2 marks · Multiple select

The dispersion (E(k)) of the conduction band (CB) and valence band (VB) for a semiconductor are shown schematically in the figure. Considering the possibility of an electron making a transition from the bottom of the CB to the top of the VB, which of the following options is/are correct?

Indirect semiconductor gap Eg, with valence maximum at k = 0 and conduction minimum at k = q.
  1. The transition is forbidden.
  2. A photon can be emitted with an energy exactly equal to Eg.
  3. A photon can be emitted with an energy less than Eg .
  4. A phonon can be created with a crystal momentum ħq.

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Correct answer: (C) A photon can be emitted with an energy less than Eg .; (D) A phonon can be created with a crystal momentum ħq.

Explanation

The indirect transition needs a phonon to conserve crystal momentum. If a phonon is created carrying momentum hbar q, part of the gap energy goes to it, leaving photon energy below Eg.