Question

A pure, defect-free, semiconductor material will absorb the electromagnetic radiation incident on it only if the energy of the individual photons in the incident beam is larger than a threshold value known as the band-gap of the semiconductor. Otherwise, the material will be transparent to the photons. The known room-temperature band-gaps for germanium, silicon, and gallium-arsenide, three widely used semiconductors, are \(0.66 \mathrm{eV}\) \(1.12 \mathrm{eV},\) and \(1.42 \mathrm{eV},\) respectively. a) Determine the room-temperature transparency range of each semiconductor. b) Compare these with the transparency range of \(\mathrm{ZnSe},\) a semiconductor with a band-gap of \(2.67 \mathrm{eV}\), and explain the yellow color observed experimentally for the ZnSe crystals. c) Which of these materials could be used to detect the \(1550-\mathrm{nm}\) optical communications wavelength?

Short answer

Question: Determine the room-temperature transparency range of Ge, Si, GaAs, and ZnSe semiconductors, compare the transparency range of ZnSe with other materials and explain the yellow color observed in ZnSe. Lastly, determine which material is suitable for detecting the 1550-nm optical communications wavelength.

Step-by-step solution

Calculate the wavelength corresponding to the band-gap of each material

First, we'll find out the wavelength corresponding to each semiconductor's band-gap using the formula: E = (hc) / λ Where E is the band-gap energy, h is the Planck's constant (6.63 × 10 ^{-34} Js), c is the speed of light (3 × 10 ^{8} m/s), and λ is the incident wavelength. λ = (hc) / E Calculate λ for Ge, Si, GaAs, and ZnSe using their band-gap values.

Determine the transparency range of each material

Once you've calculated the incident wavelength for each material, determine the transparency range for each semiconductor. The material will be transparent if the incident photon's wavelength is greater than the calculated wavelength (λ). #a) Compare with transparency range of ZnSe and explain the yellow color observed#

Compare the transparency range of ZnSe with other materials

Compare the transparency range of germanium, silicon, gallium-arsenide to ZnSe and analyze the difference.

Explain the observed yellow color in ZnSe

The yellow color observed experimentally for ZnSe crystals is due to the fact that ZnSe absorbs shorter wavelengths of light and lets the longer wavelengths pass through it. This phenomenon is responsible for the observed yellow color in ZnSe crystals. #c) Determine the suitable material for detecting the 1550-nm optical communications wavelength#

Determine which material can detect 1550-nm wavelength

To determine which material is suitable for detecting optical communications, we need to find out which semiconductor has its transparency range higher than the 1550-nm wavelength. Compare the transparency range of each material to 1550-nm to see which material can be used for optical communication detection.