# Roughness

How do I describe surface roughness?

Roughness can be taken into account in different ways in optical models for thin films.

The easiest way is to replace the sharp interface between two materials by a thin layer with mixed optical constants. This is a good approach for roughness dimensions clearly below the light wavelength. Mixed optical constants can be computed using an effective medium model. The Bruggeman formula (also known as EMA – effective medium approximation) is a good choice (please read the remarks below). Start with a very thin intermediate layer (e.g. 2 nm) and select its thickness as fit parameter. The volume fraction of the effective medium model should be an adjustable fit parameter as well.
An advanced version of this kind of roughness modeling is to use a concentration gradient layer. This type of layer can describe a smooth transition between adjacent materials. The depth dependence of the volume fraction can be expressed by a user-defined formula with up to 6 parameters that can be fitted.
A warning must be raised using effective medium models to describe roughness effects. All effective medim models in our software are made for two phase composites which are isotropic in three dimensions. They are not valid for surface roughness effects. To apply these concepts anyway can be justified by saying that there is no reasonable alternative and that it is very common to do so …
Describing rough metal surfaces with an effective medium model may be a little tricky. This is especially true for silver. Inhomogeneous metal layers can be efficient absorbers with very special optical properties, and effective medium approaches can be very wrong – please read SCOUT tutorial 2 about this.

The roughness described by effective medium layers does not lead to light scattering but modifies the reflectance and transmittance properties of the interface between the adjacent materials. Light scattering at heavily rough interfaces can be taken into account in a phenomenological way in cases where the detection mechanism of the spectrometer system does not collect all the scattered radiation. You can introduce a layer of type ‘Rough interface’ which scales down the reflection and transmission coefficients for the electric field amplitude of the light wave. The loss function is a user- defined function which may contain 2 parameters C1 and C2 which are fit parameters. In addition, the symbol x in the formula represents the wavenumber.
The expression C1*EXP(-(X/C2)^2), for example, would describe an overall loss by a factor C1 and an additional frequency dependent loss which is large for small wavelengths and small for large wavelengths. This kind of approach has turned out to be satisfying in several cases.

# SPRAY surface textures

SPRAY is a powerful tool to optimize the performance of solar cells. In order to simplify the modeling of crystaline silicon PV modules we have added an easy way to define macroscopic surface texture. This new feature can be used for both the covering glass and the Si wafer surface.

A PV module consists of a silicon wafer with top and backside contacts:

The wafer is embedded in EVA:

The EVA is covered by glass which gives mechanical strength and protection for the next 30 years. In order to maximize the generation of electric power one may introduce an

• anti-reflection (AR) layer between silicon and EVA
• AR layer between glass and air
• surface texture of the silicon wafer
• surface texture of the cover glass
• diffusely reflecting white backside
• low-absorptive cover glass

In order to find out how much the PV output is increased by these improvements one can perform realistic ray-tracing computations with SPRAY. This can save a lot of experimental work and costs. SPRAY performs 3D spectral ray-tracing and records where how much radiation is absorbed. It can, for example, output the spectrum of absorbed light in the wafer

as well as the spatial distribution of absorbed light:

The graph below shows a comparison of the absorbed fraction with and without a simple AR coating (a single SiN layer) between silicon and EVA:

The modeling of macroscopic surface textures is now much easier using the new object type ‘Periodic surface texture’. This is a rectangle with a regular surface pattern in the x- and y-direction. You can set the periodicities in both directions and select a pattern type. Depending on the type of texture you can set additional parameters in the object dialog:

The available textures are the following:

Sine profile

Pyramids
Inverted pyramids
Cones
Inverted cones

Half spheres

Inverted half spheres