Question

Prove that in semiconductor, radiative recombination produces the emission of wavelength, λ (μm) =1.24/ Eg (eV).

Answer 1

Emission of wavelength

Explanation:

The energy of a photon (E) and the wavelength of the light (λ) are related inversely by the equation:

$E=\frac{hc}{\lambda }$                                 (1)

Where,

h = 6.626 × $10^{-34}$ joule·s  and c = 2.998 × $10^{8}$ m/s

which means hc= 1.99 ×$10^{-25}$  joules-m

in terms of ev

hc= (1.99 × $10^{-25}$  joules-m) × (1ev/1.602 × $10^{-19}$ joules)

hence, hc= 1.24 × $10^{-6}$  eV-m                                                  (2)          

where 1 eV is the energy required to raise an electron through 1 volt and its value is  equal to 1.602 × $10^{-19}$ J.

Also to get the value of hc in micro meters, we will multiply equation (2) by $10^{6}$

hc = 1.24 × $10^{-6}$  eV × ($10^{6}$ µm) = 1.24 eV-µm                           (3)

Now, put equation (3) in (1)

$E=\frac{1.24}{\lambda }$

where energy is in eV and wavelength is in micro meters

or we can rewrite this relation as:

    $\lambda (\mu m)=\frac{1.24}{E(eV)}$