Greek ladder is a technique for approximating Cn by rational numbers where n is a positive integer and C is a positive real number. For the classical Greek ladder, the value isC. Based on the continued fraction theory and algebraic equation, the classical Greek ladder in a special case can be reduced to the generalized Fibonacci sequence. By means of proper switching and binary, ternary or quaternary phase modulation, here we have successfully designed the various kinds of nano-photonic devices to produce three-dimensional array foci whose focusing properties satisfy the above mathematical characteristics. With this technology, the diffraction-limited array foci are freely designed or distributed under the requirement at the desired multiple focal planes.

Three-dimensional array diffraction-limited foci from Greek ladders to generalized Fibonacci sequences.

The invention relates to a generalized Fibonacci zone plate. The generalized Fibonacci zone plate consists of a transparent medium, a light-tight metal film and an annular wave zone structure and is used for substituting an amplitude-type Fresnel zone plate formed on the basis of odd-even alternation binary sequences. Under the illumination of plane waves, the generalized Fibonacci zone plate can realize the distribution of two focal points in the axial direction, the light intensities at the two focal points are identical, and the ratio of the two focal lengths is adjustable. The generalized Fibonacci zone plate is a series of concentric annular structures, easy to process and duplicate and applicable to the fields such as an optical imaging system, biomedicine and the like.

Generalized Fibonacci zone plates

Organic–inorganic hybrid resists are emerging as an effective way of addressing stringent process requirements for aggressive down-scaling of semiconducting devices. However, hybrid resists generally require complex chemical synthesis while being predominantly negative-tone with high dose requirements. For positive-tone processes and high-aspect-ratio pattern transfers, resist choices are limited to costly, non-hybrid alternatives, whose etch resistance is still inferior compared with hybrid resists. Here, we demonstrate a novel hybrid positive-tone resist platform utilizing simple ex situ vapor-phase inorganic infiltration into standard resist materials. A model system based on poly(methyl methacrylate) (PMMA) thin film hybridized with aluminum oxide has been demonstrated for electron-beam lithography patterning, featuring a fully controllable critical exposure dose, contrast, and etch resistance. The hybrid resist not only achieves contrast as high as ∼30, six-fold enhancement over standard PMMA, but also enables Si nanostructures with resolution down to ∼30 nm and an aspect ratio as high as ∼17, owing to enhancement of the Si etch selectivity to ∼70, with an estimated achievable maximum of ∼300, far exceeding known commercial positive-tone resist systems. The easy implementabilility, combined with versatile ex situ control of resist characteristics, makes this hybrid resist synthesis approach uniquely suited for addressing the resist performance and high throughput required for advanced nanolithography techniques, such as extreme ultraviolet lithography, potentially.

Advancing next generation nanolithography with infiltration synthesis of hybrid nanocomposite resists

We successfully extend the standard Fibonacci zone plates with two on-axis foci to the generalized Fibonacci photon sieves (GFiPS) with multiple on-axis foci. We also propose the direct and inverse design methods based on the characteristic roots of the recursion relation of the generalized Fibonacci sequences. By switching the transparent and opaque zones, according to the generalized Fibonacci sequences, we not only realize adjustable multifocal distances but also fulfill the adjustable compression ratio of focal spots in different directions.

Generalized Fibonacci photon sieves.

We report the fabrication of a phase photon sieve (PS) on the tip of a standard single mode fiber by focused ion beam (FIB) milling. The fiber tip was dip-coated with a conductive polymer (PEDOT:PSS) as an alternative, more advantageous method to the metallization prior to FIB milling. The near field scans of the intensity profile along the optical axis under fiber illumination of a laser at λ = 1.55 μm are presented. We have analyzed the focusing properties and demonstrated the validity of our structure for light coupling into silicon photonics waveguides with improved efficiency and alignment tolerance.

Fabrication of a phase photon sieve on an optical fiber tip by focused ion beam nanomachining for improved fiber to silicon photonics waveguide light coupling.

A novel diffractive optical element, named phase zone photon sieve (PZPS), is presented. There are three kinds of phase plates in PZPSs: PZPS1, PZPS2, and PZPS3. Each of the PZPSs has its own structure and is made on quartz substrate by etching. The three PZPSs have stronger diffraction peak intensity than a photon sieve (PS) when the margin pinhole and zone line width are kept the same. The PZPS3 can produce a smaller central diffractive spot than the ordinary PS with the same number of zones on the Fresnel zone plate. We have given the design method for and the simulation of PZPS and PS. PZPS has potential applications in optical maskless lithography.

http://iopscience.iop.org/article/10.1088/1674-1056/18/1/029/pdf

Phase zone photon sieve

Silicon nanocrystals synthesized by electron beam (e-beam) evaporation of Si and SiO2 mixture are studied. Rutherford backscattering spectrometry of the as-deposited Si-rich silicon dioxide or oxide (SRO) thin film shows that after evaporation, the Si and SiO2 concentration is well kept, indicating that the e-beam evaporation is suitable for evaporating mixtures of Si and SiO2. The SRO thin films are annealed at different temperatures for two hours to synthesize silicon nanocrystals. For the sample annealed at 1050°C, silicon nanocrystals with different sizes and the mean diameter of 4.5 nm are evidently observed by high resolution transmission electron microscopy (HRTEM). Then the Raman scattering and photoluminescence spectra arising from silicon nanocrystals are further confirmed the above results.

https://iopscience.iop.org/article/10.1088/0256-307X/26/4/046801/pdf

Fabrication and Characterization of Si Nanocrystals Synthesized by Electron Beam Evaporation of Si and SiO 2 Mixture

Measurement of diffraction properties of photon sieves applied to spectroscopy for soft X-ray

As a kind of inorganic negative-tone resist in electron beam lithography, hydrogen silsesquioxane(HSQ) has a high pattern resolution of about 5 nm, but the poor sensitivity limits its extensive application in the field of micro-fabrication. It's very difficult to fabricate the high aspect-ratio dense resist pattern for HSQ because of backscattering electrons and proximity effect. The methods by optimizing process condition are proposed to improve the contrast of graphic structure of HSQ resist and restrain electron beam proximity effect at the same time. On 450nm thick resist layer, HSQ resist pillar array pattern with 5 aspect-ratio under 50kv voltage and HSQ resist mesh pattern structure with 9 aspect-ratio under 100kv voltage can been achieved with optimization of process condition.

Study of process of HSQ in electron beam lithography

Fine silica-like lines with 11 nm width are successfully fabricated using x-ray Fresnel diffraction exposure. X-rays pass a mask of 175-nm-wide lines and 125-nm-wide spaces and form sharp peaks on a wafer coated with a layer of hydrogen silsesquioxane resist (HSQ). By precisely controlling the mask-wafer gap at 10 μm using the laser interferogram method, the fine structures are defined on HSQ. Experimental images are reproduced by a simulation using the one-dimensional beam propagation method. This lithographic technique presents a novel and convenient way to fabricate fine silica-like structures and devices in nano-optical and nanoelectronic applications.

http://iopscience.iop.org/article/10.1088/0256-307X/26/8/086803/pdf

Xie Changqing

Papers

Phase zone photon sieve

Fabrication and Characterization of Si Nanocrystals Synthesized by Electron Beam Evaporation of Si and SiO 2 Mixture

Measurement of diffraction properties of photon sieves applied to spectroscopy for soft X-ray

Study of process of HSQ in electron beam lithography

Fabrication of 11-nm-Wide Silica-Like Lines Using X-Ray Diffraction Exposure