The band gap of indium gallium arsenide varies based on the concentration of gallium in the material. A sample of InGaAs absorbs light with a wavelength less than 1.37 microns. What is the band gap of the InGaA sample in eV
To determine the band gap of InGaAs in electron volts (eV), we need to know the relationship between the band gap energy and the wavelength of light absorbed by the material. The equation that relates the band gap energy (Eg) and the wavelength (λ) is given by:
Eg = hc / λ
where:
- Eg is the band gap energy in joules (J)
- h is Planck's constant (approximately 6.63 x 10^-34 J.s)
- c is the speed of light in a vacuum (approximately 3 x 10^8 m/s)
- λ is the wavelength of light in meters (m)
First, we need to convert the given wavelength of 1.37 microns (μm) into meters by dividing it by a conversion factor (1 μm = 1 x 10^-6 m):
λ = 1.37 x 10^-6 m
Next, we can substitute the values of h, c, and λ into the equation:
Eg = (6.63 x 10^-34 J.s) * (3 x 10^8 m/s) / (1.37 x 10^-6 m)
After performing the calculation, we can convert the band gap energy from joules to electron volts using the conversion factor (1 eV = 1.6 x 10^-19 J):
Eg (eV) = Eg (J) / (1.6 x 10^-19 J/eV)
This will give us the band gap energy of InGaAs in electron volts.