# Double Layer Anti Reflection Coatings

A further reduction in reflectivity is achieved through a double layer anti-reflection coating (DLARC). Popular DLARC coatings are zinc sulfide (ZnS) with magnesium flouride (MgF) or layers of silicon nitride with varying refractive index. However, this is usually too expensive for most commercial solar cells. Double layer anti-reflection film on silicon wafer. The layers are usually deposited on a textured substrate to decrease the reflectivity further.

The equations for multiple anti-reflection coatings are more complicated than that for a single layer 1. First we define a series of parameters: r1, r2, r3, θ1 and θ2. As in the diagram above, the surrounding region has a refractive index of n0, the next layer has a refractive index of n1 and a thickness of t1, the layer immediately above the silicon has a refractive index of n2 and a thickness of t2 and the silicon has a refractive index of n3.

$r 1 = n 0 − n 1 n 0 + n 1$

$r 2 = n 1 − n 2 n 1 + n 2$

$r 3 = n 2 − n 3 n 2 + n 3$

$θ 1 = 2π n 1 t 1 λ$

$θ 2 = 2π n 2 t 2 λ$

The reflectivity is then calculated from the above parameters using the following formula:

$R=| r 2 |= r 1 2 + r 2 2 + r 3 2 + r 1 2 r 2 2 r 3 2 +2 r 1 r 2 ( 1+ r 3 2 )cos2 θ 1 +2 r 2 r 3 ( 1+ r 1 2 )cos2 θ 2 +2 r 1 r 3 cos2( θ 1 + θ 2 )+2 r 1 r 2 2 r 3 cos2( θ 1 − θ 2 ) 1+ r 1 2 r 2 2 + r 1 2 r 3 2 + r 2 2 r 3 2 +2 r 1 r 2 ( 1+ r 3 2 )cos2 θ 1 +2 r 2 r 3 ( 1+ r 1 2 )cos2θ+2 r 1 r 3 cos2( θ 1 + θ 2 )+2 r 1 r 2 2 r 3 cos2( θ 1 − θ 2 )$

The graph below simulates a double layer antireflection coating. By adjusting the refractive index and thickness of the two layers it is possible to produce two minima and a overall reflectance of less than 3%.

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Interactive graph showing the effect of thickness and refractive index of a double layer anti-reflection coating (DLARC). The substrate has a constant refractive index of 3.5 and approximates silicon. Under air, the reflection is minimized by setting the top layer to 105 nm with a refractive index of 1.4 and setting the bottom layer to 55 nm and a reflective index of 2.4. Click on the graph for numerical data.

Further reductions in reflectivity can be achieved with stacks of coatings or by grading the index of the layers. In the optical industry stacks of over 10 layers are used for very low reflection losses in photographic equipment. However, the performance benefits of multiple layers are marginal. In most cases the real challenge is to incorporate the anti-reflection coatings in with the surface passivation layers.

OPAL22 at pvlighthouse.com.au provides a simulator for multilayer stacks. It uses concepts similar to what is presented on these pages but has much more complete mathematical models including the effect of refractive index as a function of wavelength.