Light Trapping II - Anti-Reflection and Trapping Methods

When light reaches an interface between 2 media having different refractive indices, the incident light will usually be partly reflected and partly transmitted.  Consider a light ray arriving from the left as shown in the diagram above.  The light ray's behaviour will be described as follows:

Snell's Law: n₁sinθ_i = n₂sinθ_t

θ_i = θ_r

where n₁, n₂ are the refractive indices of the 2 media, and θ_i, θ_r, θ_t are the angles of incidence, reflection, and transmission of the light ray.

If n₁ < n₂, θ_i > θ_t
If n₁ > n₂, θ_i < θ_t

Light rays are light waves with electric field oscillations as shown in the diagram above.  P-polarised light is light with the electric field oscillating in the plane of incidence.  S-polarised light is light with the electric field oscillating perpendicular to the plane of incidence.  The reflection and transmission coefficients are given by the Fresnel equations below:

When light is incident perpendicularly:
θ_i = θ_t = 0°
R_p = R_s
T_p = T_s

As seen in the diagram above, the Brewster angle is the angle of incidence where R_p = 0.  The grey line represents the average of R_p and R_s, which is randomly polarised light.

When n₁ > n₂, there will be a θ_i where θ_t = 90°.  This θ_i is known as the critical angle.  For all θ_i larger than the critical angle, there will be total internal reflection where no θ_t exists.  This is because the light rays are completely reflected.

The optical losses due to reflection between 2 media such as air and silicon is quite high because silicon has a high refractive index.  Hence, an interlayer (Rayleigh film) with a refractive index between air and silicon should be applied between air and silicon.  The diagram below shows the final outcome.  With more than one interlayer, reflection losses can be reduced further.  This is known as refractive index grading.

Another way to do anti-reflection is by super-imposing light waves.  This will lead to constructive and destructive interference of light.  Consider the diagram below.  The yellow wave is the incident light.  The green and red waves are the reflections back from the first and second interface.  Since the green and red waves appear to be in anti-phase, the total amplitude of the electric field of the final wave leaving the system is smaller.  The total irradiance lost is smaller too.

The maximum destructive interference is given by a thickness of the interlayer that is:

d = λ / 4n₂

where λ is the wavelength, and n₂ is the refractive index of the interlayer.

The last way to do anti-reflection is by using textured interfaces.  The size and scale of textured features is usually larger than the wavelength of light, which helps to couple light into the interlayer (see diagrams below).  The importance of this method cannot be over-emphasised.

Another consideration is that the absorber layer is not thick enough to absorb all light, and some light is transmitted.  Usually, absorption coefficients are higher for blue light compared to red and infrared.  The red light transmitted can be reflected back by the back reflector, or be parasitically absorbed at the back contact/reflector.



Reference:
3.3.5 Light Trapping II - Anti-Reflection and Trapping Methods, Delft University of Technology, https://www.youtube.com/watch?v=gyzzaZw6sC4