The energy of a photon of sodium light `(lambda=589 nm)`equal the band gap of a semiconducting material.(a)Find the minimum energy E requried to create a hole-electron pair.(b)Find the value of `E//kT`at a temperature of 300K.

Explanation

The energy of the photon in `eV=(12400)/(lambda)`
Wavelength of photon `=589nm=5890Å`
`=(12400)/(5890)=2.1eV`
Thus the band gap is 2.1 eV . This is also the minimum energy E required to push an electron from the valence band into the conduction band . Hence , the minimum energy required to create a hole - electron pair is 2.1eV .
(b) At `T=300K, kT=(8.62xx10^(-5)eV//K)/(300K)`
`=25.86xx10^(-3)eV`.
Thus, `(E)/(kT)=(2.1eV)/(25.86xx10^(-3)eV)=81`
The available thermal energy is nearly 81 times less than that of the required energy to create electron hole pair . So it is difficult for the thermal energy to create the hole - electron pair but a photon of light can do it easily .