# Differences

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en:ar [2012/05/09 05:48] deinega |
en:ar [2012/07/20 19:45] (current) valuev |
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- | Textured coatings have antireflective properties for wavelengths much smaller then texture size as well. | + | Textured coatings have antireflective properties for wavelengths much smaller than texture size as well. |

In this case reflection reduction can be illustrated geometrically: rays should be reflected many times until being reverted back. | In this case reflection reduction can be illustrated geometrically: rays should be reflected many times until being reverted back. | ||

At the same time transmitted rays deviate from the incident direction that leads to light trapping effect used in solar cells. | At the same time transmitted rays deviate from the incident direction that leads to light trapping effect used in solar cells. | ||

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- | In the following we specially distinguish two cases: complete tiling case when pyramids bases touch each other along their whole perimeter (this corresponds to the polygon base pyramids in our study) and incomplete tiling case when there are gaps between bases (this corresponds to cones). We consider normal light incidence case. | + | We will specially distinguish two cases: complete tiling case when pyramids bases touch each other along their whole perimeter (this corresponds to the polygon base pyramids in our study) and incomplete tiling case when there are gaps between bases (this corresponds to cones). |

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Textured surface is made from glass (the refractive index <tex>n=1.5</tex>). | Textured surface is made from glass (the refractive index <tex>n=1.5</tex>). | ||

+ | We consider normal light incidence case. | ||

=====Effective medium approximation===== | =====Effective medium approximation===== | ||

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For example, if <tex>f(z)</tex> is polynom of degree <tex>(2k'-1)</tex> with zero derivatives <tex>f^{(i)}(0) = f^{(i)}(d) = 0, 0 < i < k'</tex>, then <tex>R \sim (d/\lambda)^{-2k'}</tex>. | For example, if <tex>f(z)</tex> is polynom of degree <tex>(2k'-1)</tex> with zero derivatives <tex>f^{(i)}(0) = f^{(i)}(d) = 0, 0 < i < k'</tex>, then <tex>R \sim (d/\lambda)^{-2k'}</tex>. | ||

- | In particular, for profiles <tex>f(z)=3z^2-2z^3</tex> and <tex>f(z)=10z^3-15z^4+6z^5</tex> (we assume that <tex>d=1</tex>) have get <tex>R \sim (d/\lambda)^{-4}</tex> and <tex>R \sim (d/\lambda)^{-6}</tex> correspondingly. | + | In particular, for profiles <tex>f(z)=3z^2-2z^3</tex> and <tex>f(z)=10z^3-15z^4+6z^5</tex> (we assume that <tex>d=1</tex>) we have <tex>R \sim (d/\lambda)^{-4}</tex> and <tex>R \sim (d/\lambda)^{-6}</tex> correspondingly. |

Let us find a profile characterized by zero derivatives of all orders at the points <tex>0</tex> and <tex>d</tex>: | Let us find a profile characterized by zero derivatives of all orders at the points <tex>0</tex> and <tex>d</tex>: | ||

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We obtained exponential decrease of the reflection with the growth <tex>d/\Lambda</tex> for the complete tiling case. | We obtained exponential decrease of the reflection with the growth <tex>d/\Lambda</tex> for the complete tiling case. | ||

For the incomplete tiling case the reflection tends to a constant value passing a local minimum while <tex>d/\Lambda</tex> increases. | For the incomplete tiling case the reflection tends to a constant value passing a local minimum while <tex>d/\Lambda</tex> increases. | ||

- | In the following we give our explanation of these results. | + | Below we give our explanation of these results. |

We introduce the following ray classification: | We introduce the following ray classification: | ||

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Only reflected and secondary rays make contribution to the total reflection <tex>R=R_{\rm refl} + R_{\rm sec}</tex>. | Only reflected and secondary rays make contribution to the total reflection <tex>R=R_{\rm refl} + R_{\rm sec}</tex>. | ||

- | It can be shown that (a) number of reflections inside the structure necessary for the propagating rays to obtain the backward direction, growing linearly with the texture height. Since after each reflection ray amplitude is multiplied on reflection coefficient form pyramid surface, <tex>R_{refl}</tex> decreases exponentially with <tex>d/\Lambda</tex>. | + | It can be shown that (a) number of reflections inside the structure, necessary for the propagating rays to obtain the backward direction, grows linearly with the texture height. Since after each reflection ray amplitude is multiplied on reflection coefficient form pyramid surface, <tex>R_{refl}</tex> decreases exponentially with <tex>d/\Lambda</tex>. |

According to our calculations secondary rays make small contribution to the reflection <tex>R_{\rm sec} \approx R_{\rm refl}</tex> which can be explained by the following considerations. | According to our calculations secondary rays make small contribution to the reflection <tex>R_{\rm sec} \approx R_{\rm refl}</tex> which can be explained by the following considerations. | ||

- | (b) pyramids deflect secondary rays downward since <tex>n_s>n_i</tex> preventing them to revert back to the incident medium. | + | (b) pyramids deflect secondary rays downward since <tex>n_s>n_i</tex>, preventing them to revert back to the incident medium. |

As a result refracted rays can c) transmit to the substrate directly, d) or move onto the inner pyramid side under the total internal reflection angle. | As a result refracted rays can c) transmit to the substrate directly, d) or move onto the inner pyramid side under the total internal reflection angle. | ||

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In the case of incomplete tiling (cones) the reflectance tends to the constant value with the growth of <tex>d/\Lambda</tex> passing over a local minimum. | In the case of incomplete tiling (cones) the reflectance tends to the constant value with the growth of <tex>d/\Lambda</tex> passing over a local minimum. | ||

It can be explained by the following considerations. | It can be explained by the following considerations. | ||

- | While <tex>d/\Lambda \to \infty</tex> e) normal rays remain almost parallel to the scatterer surface after the first reflection and some of them go to the gap between the bases not reaching the neighbouring scatterer. | + | While <tex>d/\Lambda \to \infty</tex>, e) normal rays remain almost parallel to the scatterer surface after the first reflection and some of them go to the gap between the bases not reaching the neighbouring scatterer. |

Afterwards they are directly reflected back into the incident medium. | Afterwards they are directly reflected back into the incident medium. | ||

For the cones case almost all incident rays behave in this way, therefore while <tex>d/\Lambda \to \infty</tex> the reflectance tends to the substrate reflectance value. | For the cones case almost all incident rays behave in this way, therefore while <tex>d/\Lambda \to \infty</tex> the reflectance tends to the substrate reflectance value. | ||

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Using antireflective coatings is one of the way to increase efficiency of solar cells. | Using antireflective coatings is one of the way to increase efficiency of solar cells. | ||

- | For this purpose one can use multi-layered coatings and coatings with porous silicon, which act like film with gradually changing refractive index due to increasing porosity with the depth. | + | For this purpose multi-layered coatings or coatings with porous silicon can be used. Coatings with porous silicon act like a film with gradually changing refractive index if porosity is increasing with the depth. |

However, as we discussed above, these types of coatings are not so easy to produce. | However, as we discussed above, these types of coatings are not so easy to produce. | ||

- | Alternative way to reduce reflectance is using nanotextured coatings. | + | Nanotextured coatings is alternative way for reflection reduction. |

These coatings can be produced using lithographic technique or etching. | These coatings can be produced using lithographic technique or etching. | ||

- | Their use in solar technology leads reducing reflection from the surface of the solar cell by 1 or 2 orders of magnitude. | + | Their use in solar technology reduces reflection from the surface of the solar cell by 1 or 2 orders of magnitude. |

- | Below we present comparison between experimental data and FDTD results for reflectance from chosen textured surface taken from here | + | Below we present comparison between experimental data and FDTD results for reflectance from chosen textured surface taken from |

[[http://www.opticsinfobase.org/abstract.cfm?URI=josaa-28-5-770|http]] | [[http://www.opticsinfobase.org/abstract.cfm?URI=josaa-28-5-770|http]] | ||

{{:deinega_-_minimizing_light_reflection_from_dielectric_textured_surfaces.pdf|PDF}} | {{:deinega_-_minimizing_light_reflection_from_dielectric_textured_surfaces.pdf|PDF}} | ||

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- | In order to model dispersive dielectric permittivity of Silicon in FDTD, one can use technique described in section [[fitting]]. | + | In order to model dispersive dielectric permittivity of silicon in FDTD, one can use technique described in section [[fitting]]. |