[Paper Review] Ultra thin anti-reflective coatings designed using Differential Evolution

Emmanuel Centeno, Amira Farahoui+5 more|arXiv (Cornell University)|Apr 5, 2019

Optical Coatings and GratingsMaterials Science3 citations

TL;DR

This paper proposes ultra-thin anti-reflective (AR) coatings with sub-200 nm thickness using Differential Evolution (DE) optimization to design hybrid refractive index (RI) profiles that combine gradual RI transitions with interferential patterning. The method yields coatings with <4% average reflectivity across the visible spectrum, outperforming thicker conventional AR coatings and enabling fabrication via low-cost reactive sputtering.

ABSTRACT

We use a state-of-the-art optimization algorithm combined with a careful methodology to find optimal anti-reflective coatings. Our results show that ultra thin structures (less than $300 \,nm$ thick) outperform much thicker gradual patterns as well as traditional interferential anti-reflective coatings. These optimal designs actually combine a gradual increase of the refractive index with patterns meant to leverage interferential effects. Contrarily to gradual patterns, they do not require extremely low refractive index materials, so that they can actually be fabricated. Using a cheap and easily deployable vapor deposition technique, we fabricated a 4-layer anti-reflective coating, which proved very efficient over the whole visible spectrum despite a total thickness of only 200 nm.

Motivation & Objective

• To design ultra-thin anti-reflective coatings with sub-200 nm thickness that outperform conventional thick graded or multilayer coatings.
• To overcome the fabrication limitations of continuous graded refractive index (RI) coatings requiring very low RI materials (~1.0) and extreme layer counts.
• To leverage both gradual RI transitions and interferential effects in a single design to enhance broadband and angular performance.
• To demonstrate the feasibility of fabricating optimized nanostructured AR coatings using scalable, low-cost vapor deposition techniques.
• To validate the robustness of the optimized designs against fabrication-induced refractive index disorder.

Proposed method

• Employed Differential Evolution (DE), a stochastic optimization algorithm, to search for optimal refractive index (RI) profiles across a 100–200 nm thickness range.
• Defined a cost function based on average reflectivity across the visible spectrum (400–900 nm) and multiple incident angles (0°, 45°, 60°, 70°).
• Used a 4-layer structure with non-stoichiometric silicon oxynitride (SiₓOᵧN_z) films to achieve a RI range from 1.45 to 3.74 via reactive radiofrequency magnetron sputtering.
• Controlled film composition and RI by modulating oxygen flow via pulsed rectangular signals (T_on, T_off, F_max_O2), enabling precise tuning of refractive index per layer.
• Combined a gradual RI envelope with discrete layer thicknesses to create a hybrid design that leverages both adiabatic transition and destructive interference effects.
• Validated designs against refractive index disorder by simulating ±Δn/n variations across 10-pixel segments to test robustness.

Experimental results

Research questions

• RQ1 Can Differential Evolution optimize ultra-thin AR coatings (≤200 nm) that outperform thicker conventional AR coatings in broadband and angular response?
• RQ2 Does a hybrid design combining gradual RI variation and discrete interferential layering achieve better performance than purely continuous or purely multilayered approaches?
• RQ3 Can such optimized AR coatings be fabricated using scalable, low-cost vapor deposition techniques without requiring ultra-low refractive index materials?
• RQ4 How robust are the optimized designs against fabrication-induced refractive index variations?
• RQ5 To what extent does the experimental reflectivity of the fabricated coating match the simulated performance across normal and oblique incidence?

Key findings

• The optimized 4-layer AR coating achieved an average reflectivity of 3.6% across 400–900 nm under normal incidence, a 92% reduction from the 44% reflectivity of bare silicon.
• At 70° incidence, the average reflectivity was 14%, significantly lower than the 14% average of a conventional 86 nm quarter-wave coating at 650 nm.
• The experimental reflectivity spectrum matched simulations closely, with a minimum of 0.56% and a peak of 7.4% across the visible range.
• The design demonstrated robustness against refractive index disorder, maintaining low reflectivity even with ±Δn/n variations across layers.
• The fabricated coating, only 200 nm thick, outperformed theoretical continuous Gaussian RI profiles and multilayer interferometric coatings over 1 μm thick.
• Reactive sputtering enabled precise control of SiₓOᵧN_z composition, achieving a refractive index range from 1.45 (SiO₂-like) to 3.74 (Si-rich), avoiding the need for ultra-low RI materials.