# Light Trapping

The optimum device thickness is not controlled solely by the need to absorb all the light. For example, if the light is not absorbed within a diffusion length of the junction, then the light-generated carriers are lost to recombination. In addition, as discussed in the Voltage Losses Due to Recombination, a thinner solar cell which retains the absorption of the thicker device may have a higher voltage. Consequently, an optimum solar cell structure will typically have "light trapping" in which the optical path length is several times the actual device thickness, where the optical path length of a device refers to the distance that an unabsorbed photon may travel within the device before it escapes out of the device. This is usually defined in terms of device thickness. For example, a solar cell with no light trapping features may have an optical path length of one device thickness, while a solar cell with good light trapping may have an optical path length of 50, indicating that light bounces back and forth within the cell many times.

Light trapping is usually achieved by changing the angle at which light travels in the solar cell by having it be incident on an angled surface. A textured surface will not only reduce reflection as previously described but will also couple light obliquely into the silicon, thus giving a longer optical path length than the physical device thickness. The angle at which light is refracted into the semiconductor material is, according to Snell's Law, as follows:

## Snell's Law

${n}_{1}\mathrm{sin}{\theta }_{1}={n}_{2}\mathrm{sin}{\theta }_{2}$

where θ1 and θ2 are the angles for the light incident on the interface relative to the normal plane of the interface within the mediums with refractive indices n1 and n2 respectively. θ1 and θ2 are shown in the animation below.

Refraction of a ray of light at a dielectric boundary. You can adjust the angle of incidence and see how this affects the angle of the ray transmitted to the second medium by clicking in the right side of the graph and dragging the mouse to change the angle. When n2 has a higher refractive index than n1 the refracted ray is closer to normal than the incident ray.

By rearranging Snell's law above, the angle at which light enters the solar cell (the angle of refracted light) can be calculated:

## Snell's Law (rearranged)

${\theta }_{2}={\mathrm{sin}}^{-1}\left(\frac{{n}_{2}}{{n}_{1}}\mathrm{sin}{\theta }_{1}\right)$

In a textured single crystalline solar cell, the presence of crystallographic planes make the angle θ1 equal to 36° as shown below.

Reflection and transmission of light for a textured silicon solar cell.

The amount of light reflected at an interface is calculated from the fresnel reflection formula. For light polarised in the parrallel to the surface the amount of reflected light is:

## Fresnel Reflection (parrallel)

${R}_{\parallel }=\frac{{\mathrm{tan}}^{2}\left({\theta }_{1}-{\theta }_{2}\right)}{{\mathrm{tan}}^{2}\left({\theta }_{1}+{\theta }_{2}\right)}$

For light polarised perpendicular to the surface the amount reflected is:

## Fresnel Reflection (perpendicular)

${R}_{\perp }=\frac{{\mathrm{sin}}^{2}\left({\theta }_{1}-{\theta }_{2}\right)}{{\mathrm{sin}}^{2}\left({\theta }_{1}+{\theta }_{2}\right)}$

For unpolarised light the reflected amount is the average of the two:

## Fresnel Reflection (plane and perpendicular)

${R}_{T}=\frac{{R}_{\perp }+{R}_{\parallel }}{2}$

Light Trapping Calculator

If light passes from a high refractive index medium to a low refractive index medium, there is the possibility of total internal reflection (TIR). The angle at which this occurs is the critical angle and is found by setting θ2 in Snell's law to 0.

## Snell's Law (Critical Angle)

${\theta }_{1}={\mathrm{sin}}^{-1}\left(\frac{{\eta }_{2}}{{\eta }_{1}}\right)$

Total Internal Reflection Calculator

Using total internal reflection, light can be trapped inside the cell and make multiple passes through the cell, thus allowing even a thin solar cell to maintain a high optical path length.
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