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

(a) The energy of the photon in
`eV =(12400)/(lamda) =(12400)/(5890) =2.1 eV`
(Wavelength of photon `= 589 nm=5890 A^(0))`
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 `2.1 eV`
(b) At `T=300K,kT=(8.62 xx10^(-5)eV//K)(300 K)`
=`25 xx86 xx 10^(-3) eV` Thus,
`(E)/(kT)=(2.1 eV)/(25.86 xx 10^(-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.