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Absorption Depth

Absorption Depth Definition

The absorption depth is defined as the inverse of the absorption coefficient. And it describes how deeply light can penetrate into a semiconductor material before being fully absorbed. Light of higher energy is of a shorter wavelength and has a shorter absorption depth than light of lower energy, which is not absorbed as readily, and also has a larger absorption depth. Different features of solar cell design -such as the semiconductor material thickness- are affected by the absorption depth.

When an electromagnetic radiation strikes the surface of a material, it can be reflected from off that surface and a field of the energy that will be transmitted into the material is created. The created electromagnetic field interacts with the electrons and atoms within the material. Based on the type of the material, the electromagnetic field can move far into the material, or can expire quickly. For any specific material, absorption or penetration depth will usually be a function of wavelength.

The absorption coefficient and wavelength relationship make the different wavelengths penetrate variable distances into a semiconductor material before the majority of the light is fully absorbed.  Absorption depth is defined as the inverse of the absorption coefficient, or α. The absorption depth is a valuable factor which defines the distance from the surface into the material at which the light falls to around 36% of the original intensity, or alternatively to fall by a factor equal to 1/e.

Since light of high energy (shorter wavelength), as an example blue light, has a greater absorption coefficient, so it is absorbed in a shorter distance (for silicon based solar cells in less than a few microns) from the surface, light of lower energy (longer wavelength), as an example red light is less strongly absorbed .Not all of the red light is fully absorbed in silicon even after a few hundred microns.

 

Beer-Lambert law

As per Beer-Lambert law, the electromagnetic wave intensity inside a material drops down exponentially from the surface as

I(Z) = I0 e αz

δp = 1/ α

Where

δp: the penetration depth which describes electromagnetic waves decay inside of a material.

The above equation defines the depth at which the power or intensity of the field falls down to 1/e of the surface value.  The power of the wave in a certain medium is directly proportional to the square of the field quantity. One may describe the penetration depth at which the amount of the electric field has dropped down to 1/e of the surface value.  Also at which point the wave power has consequently dropped down to 1/e2  or nearly 13% of the surface value.

 

 

 

 

 

References:

https://www.pveducation.org/pvcdrom/pn-junctions/absorption-depth

 

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