GATE 2023 PH – Question 20

Solid State Physics · conductivity, electron and hole statistics in intrinsic and extrinsic semiconductors, mobility and effective mass · 1 mark · Multiple choice

For nonrelativistic electrons in a solid, different energy dispersion relations (with effective masses ma∗, mb ∗, and mc∗) are schematically shown in the plots. Which one of the following options is CORRECT?

Three electronic energy dispersions.

$m_a^*=m_b^*=m_c^*$
$m_b^*>m_c^*>m_a^*$
$m_c^*>m_b^*>m_a^*$
$m_a^*>m_b^*>m_c^*$

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Correct answer: (D) $m_a^*>m_b^*>m_c^*$

Explanation

$m^*=\hbar^2/(d^2E/dk^2)$: the broadest parabola has the largest mass, giving $m_a^*>m_b^*>m_c^*$.