Gallium arsenide (GaAs) is an expensive alloy used for high performance multijunction solar cells. A certain GaAs absorber layer is designed to absorb 95% of the incident red light λ=700nm . The complex refractive index of GaAs at this wavelength is given by n~GaAs=3.77+i0.141 . By what fraction can the thickness of the GaAs absorber layer be decreased, if we introduce a lambertian scatterer at the front of the absorber layer and an ideal reflector at the back? Give a percentage [%]
To calculate the fraction by which the thickness of the GaAs absorber layer can be decreased, we need to consider the optical properties of the Lambertian scatterer at the front and the ideal reflector at the back.
Let's start by understanding what a Lambertian scatterer does. A Lambertian scatterer scatters light equally in all directions. It is characterized by its scattering efficiency, denoted by the symbol "s". In this case, we want to maximize the amount of red light absorbed by the GaAs absorber layer, so we need to ensure that the scattered light is redirected into the absorber layer.
Next, let's consider the ideal reflector at the back of the GaAs absorber layer. An ideal reflector reflects all incident light back into the medium, so none of it is lost.
Now, let's calculate the fraction by which the thickness of the GaAs absorber layer can be decreased. We will use the concept of transparency and absorption coefficients.
The transparency coefficient (T) is defined as the fraction of incident light that is transmitted through a material, while the absorption coefficient (α) is the fraction of incident light that is absorbed by the material. These coefficients are related by the equation T = 1 - α.
Given that the GaAs absorber layer is designed to absorb 95% of the incident red light, we can find the absorption coefficient as follows:
α = 1 - T = 1 - 0.95 = 0.05
Now, we want to determine how the introduction of the Lambertian scatterer and the ideal reflector affect the effective thickness of the GaAs absorber layer.
The effective thickness (d') of the absorber layer can be calculated using the following formula:
d' = d / (1 - s)
where d is the original thickness of the absorber layer and s is the scattering efficiency of the Lambertian scatterer.
Since the ideal reflector at the back reflects all light, it does not affect the effective thickness.
In this case, we want to decrease the effective thickness, so we need to find the fraction by which the thickness can be decreased. Let's denote this fraction as f.
f = (d - d') / d = (d - d / (1 - s)) / d = (1 - 1 / (1 - s))
Now, to calculate the fraction f, we need the scattering efficiency of the Lambertian scatterer.
Unfortunately, the scattering efficiency (s) is not given in the question. If you have this information or any other relevant information, please provide it, and I will be happy to continue the calculation.