Question

Imagine that you are in the lab and you can decide the thickness of the Si layer of your solar cell. You want to optimize the solar cell performance for a wavelength of λ=1000nm, for which the absorption coefficient is α(1000nm)=102cm−1.
Which of the following thicknesses dSi would give a better performance? Take into account that you already know two things:

(1) Beer-Lambert's law.

(2) For silicon, the minority carrier diffusivity is around D=27cm2/s and the minority carrier lifetime is around τ=15μs.

a) 100μm
b) 180μm
c) 300μm

Answer 1

Using Beer-Lambert's law we can calculate the intensity of the light after passing through the silicon layer:

II0=e−α(1000nm)dSi
For dSi=100μm, we have II0=0.37, so 63% of the light is absorbed in the silicon layer.

For dSi=180μm, we have II0=0.17, so 83% of the light is absorbed in the silicon layer.

For dSi=300μm, we have II0=0.05, so 95% of the light is absorbed in the silicon layer.

It would seem that dSi=300μm is the best option. However, we can calculate the diffusion length as

Ld=Dτ−−−√=27∗15∗10−6−−−−−−−−−−−√=0.02cm=200μm
If we choose dSi=300μm, we would have a silicon layer much thicker than the diffusion length, hence an inefficient collection of the charge carriers. Therefore the best option would be dSi=180μm, which achieves a slighlty lower absorption but better collection, since it is smaller than the diffusion length.

Answer 2

180