Question

Find the maximum wavelength of electromagnetic radiation which can create a hole-electron pair in germanium. The band gap in germanium is 0.65 eV.

(Use Planck constant h = 4.14 × 10^-15 eV-s, Boltzmann constant k = 8·62 × 10^-5 eV/K.)

Answer 1

Given:
Band gap of germanium, E = 0.65 eV
Wavelength of the incident radiation, λ = ?
For the electron‒hole pair creation, the energy of the incident radiation should be at least equal to the band gap of the material.
So,

\[E = \frac{hc}{\lambda}\] 

\[ \Rightarrow \lambda = \frac{hc}{E} = \frac{1242  eV - \text{ nm }}{0 . 65  eV}\] 

\[ \Rightarrow \lambda = 1910 . 7 \times  {10}^{- 9}   \text{m}\] 

\[ \Rightarrow \lambda \approx 1 . 9 \times  {10}^{- 6}   \text{m}\]