Question

Wavelength of infrared light spans from 700nm to 1mm.

a. Someone tells you that GaAs can emit light in the infrared range. Is that correct? Please explain why or why not, and show calculations if needed.

b. The person also says that Si can emit light in the infrared range. Is that correct? Please explain why or why not, and show calculations if needed.

Answer 1

Given: Wavelength range of infrared = 700 nm to 1 mm

or                                                             7 x 10^-7    to 1 x 10^-3 m.

a.

As the bandgap of GaAs at Temperature 0 K is = 1.52 eV (from Internet)

     The photons emitted will have energy E₁ = hc/L₁ = 1.52 eV

or    L₁ = hc/1.52eV = (6.64 x 10^-34 x 3 x 10⁸ )/(1.52 x 1.6 x 10^-19)  

or    L₁ = 8.19 x 10^-7 m

or    L₁ = 819 nm, which is in the range of infrared radiation.

Let us also calculate this for 300K temperature.

The bandgap of GaAs at Temperature 300 K is = 1.43 eV (from Internet)

     The photons emitted will have energy E₁ = hc/L₁ = 1.43 eV

or    L₁ = hc/1.52eV = (6.64 x 10^-34 x 3 x 10⁸ )/(1.43 x 1.6 x 10^-19)  

or    L₁ = 8.70 x 10^-7 m

or    L₁ = 870 nm, which is in the range of infrared radiation.

Hence, we can say that GaAs can emit light in infrared range as per our calculations.

b.

As the bandgap of Si at Temperature 0 K is = 1.17 eV (from Internet)

     The photons emitted will have energy E₁ = hc/L₁ = 1.17 eV

or    L₁ = hc/1.52eV = (6.64 x 10^-34 x 3 x 10⁸ )/(1.17 x 1.6 x 10^-19)  

or    L₁ = 10.64 x 10^-7 m

or    L₁ = 1064 nm, which is in the range of infrared radiation.

Let us also calculate this for 300K temperature.

The bandgap of Si at Temperature 300 K is = 1.11 eV (from Internet)

     The photons emitted will have energy E₁ = hc/L₁ = 1.11 eV

or    L₁ = hc/1.52eV = (6.64 x 10^-34 x 3 x 10⁸ )/(1.11 x 1.6 x 10^-19)  

or    L₁ = 11.21 x 10^-7 m

or    L₁ = 1121 nm, which is in the range of infrared radiation.

Hence, we can say that Si can emit light in infrared range as per our calculations.