Question

Consider an intrinsic semiconductor crystal at room temperature, where kBT is 0.025 eV. The probability of a state close to the valence-band edge being occupied by a hole is 1.0 x 10-5. Calculate the band gap.

Answer 1

$k_BT=0.025 \space eV$

$f(E_c)=1\times10^{-5}$

$f(E_c)=e^{-E_g/2k_BT}$

Taking natural log both sides

$\ln(f(E_c))=\dfrac{-E_g}{2k_BT}$

$E_g=-2k_BT\ln(f(E_c))$

$E_g=0.575\space eV$

Bandgap = 0.575 eV