Linear Fresnel Zone Plates Research Articles

Method for a deflection-type refractometer measuring the fringe shift by using linear Fresnelzone plates.

This study describes the design and performance of a deflection-type refractometer based on measuring the fringe shift from the Fresnel diffraction pattern to solve some major limitations of conventional differential refractometers, such as measurement range, resolution, zero balancing, and monitoring analysis. The refractometer apparatus comprises a coherent light source, linear Fresnel zone plate, measuring cell, and image capture device mounted on a movable platform. The distance measurement unit is configured to detect fringe deflection due to the difference in refractive index between the sample and the reference. To achieve this, distance measurements with an accuracy of a few nanometers by using the local frequency method and fringe shift measurement method are quite feasible. The uncertainty in this technique is determined by the smallest change in the longitudinal displacement of the image for which the CCD camera can detect a change in pixel position. The refractive index is obtained with a highly extended measurement range of at least ±0.4R I U and precision of the order of 2×10-4 R I U. A numerical comparison between computer simulation of the diffraction patterns that occur when the linear Fresnel zone plate is illuminated by a plane light traveling parallel to the z axis.

Investigation of Quadrate Fresnel Zone Plates Fabricated by Femtosecond Laser Direct Writing

The circular Fresnel zone plate (FZP) has been extensively used in micro-optics due to its outstanding focusing performance. Despite that, the curved edge of the circular zone has drawbacks limiting its use in terahertz imaging, array generator, and micro/nano-manufacturing. Therefore, a circular structure is not very practical to use. In this paper, Quadrate FZPs were proposed, and diffraction properties of the linear FZP (L-FZP), orthogonal FZP (O-FZP), and square FZP (S-FZP) were studied. Theoretically, the relationship between half side length of S-FZP and the radius of circular FZP is established, and the focal length formula of the S-FZP is derived. The linear and crossline focusing properties of quadrate FZPs were studied experimentally along with simulations. With the addition of blockers and phase shifting, the square and rectangular diffraction patterns were successfully obtained.

Focusing specification of cross-like Fresnel zone plate

Focusing characteristics of cross like Fresnel zone plate is well analyzed. This element is composed of two perpendicular linear Fresnel zone plates. Focusing properties of the element is compared to a classic and square Fresnel zone plate. Analysis clarify that focusing of the elements is well corrected in comparison to square Fresnel zone plate. Resolution is noticeably increased, DC noise and diffraction efficiency are substantially reduced and also secondary maxima have been evidently suppressed. Theoretical results have been completely verified by experiment.

Generation of double line focus and 1D non-diffractive beams using phase shifted linear Fresnel zone plate

Abstract Phase shifted linear Fresnel zone plates are presented for the first time. These diffractive elements are linear Fresnel zone plates in which their phase are laterally shifted. The impact of the phase shifting on their diffractive and focusing properties are studied. It is demonstrated that by shifting the phase, two parallel linear beams can be generated at the focal plane. Furthermore, as they are propagating, a non-diffractive line-shaped beam is generated at a given distance from the focus. Transverse intensity profile of the beam at different distances as well as its cross section of propagation along the optical axis clearly shows that the intensity profile of the beam is really kept unchanged as it is propagated. All results are completely verified by experiments.

Precision alignment of integrated optics in hybrid microsystems.

We achieve submicrometer precision in the integration of micro-optics with surface electrode ion traps. The high-precision alignment is accomplished using off-axis linear Fresnel zone plates (FZPs). Four pairs of FZPs are fabricated on the optics chip that contains the high numerical aperture microlens, a diffractive optical element (DOE). The four pairs of FZPs enable alignment in six translational and rotational degrees of freedom. Four corresponding alignment rulers are etched in the top metal layer of the ion trap, enabling quantification of misalignment. The integration of optics for efficient light delivery and the collection of fluorescence from trapped ions are key to achieving scalability in quantum information processing. An accurate and precise approach to the integration of DOEs advances the scalability of surface electrode ion traps and many other hybrid microsystems.

Kinoform diffractive lenses for efficient nano-focusing of hard X-rays.

A nano-focusing module based on two linear Fresnel zone plates is presented. The zone plates are designed to generate a kinoform phase profile in tilted geometry, thus overcoming the efficiency limitations of binary diffractive structures. Adjustment of the tilt angle enables tuning of the setup for optimal efficiency over a wide range of photon energies, ranging from 5 to 20 keV. Diffraction efficiency of more than 50% was measured for the full module at 8 keV photon energy. A diffraction limited spot size of 100 nm was verified by ptychographic reconstruction for a lens module with a large entrance aperture of 440 μm × 400 μm.

Metal-assisted etching of silicon molds for electroforming

Ordered arrays of high-aspect-ratio micro/nanostructures in semiconductors stirred a huge scientific interest due to their unique one-dimensional physical morphology and the associated electrical, mechanical, chemical, optoelectronic, and thermal properties. Metal-assisted chemical etching enables fabrication of such high aspect ratio Si nanostructures with controlled diameter, shape, length, and packing density, but suffers from structure deformation and shape inconsistency due to uncontrolled migration of noble metal structures during etching. Hereby the authors prove that a Ti adhesion layer helps in stabilizing gold structures, preventing their migration on the wafer surface while not impeding the etching. Based on this finding, the authors demonstrate that the method can be used to fabricate linear Fresnel zone plates.

Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory

The x-ray focusing properties of linear Fresnel zone plates have been derived by solving the Helmholtz equation for the field propagating through the zones. We consider the imaging of a point object into the first diffraction order of a volume zone plate having its zones parallel to the optical axis. For plane wave illumination, the focal spot size is limited by the same material-dependent but wavelength-independent value that affects waveguide focusing. In marked contrast, for the one-to-one imaging condition, corresponding to specular reflection of the x rays from the zone boundaries, the image is found to have a minimal spot size approximately equal to the outermost zone width. Unlike x-ray waveguides, zone plates therefore do not appear to possess a fundamental limit to the smallest spot size to which they can focus.

Wet etching of linear Fresnel zone plates for hard X-rays

We describe the fabrication and testing of a novel type of hard X-ray optics. The diffractive elements are generated by electron beam lithography and chemical wet etching of 〈110〉 oriented silicon substrates. Structures with widths down to 100 nm and very high aspect ratios were obtained using this method. To reduce the destructive effects of capillary forces during the drying of the diffracting structures, freeze drying and critical point drying were applied. The diffraction efficiency of our devices was measured using synchrotron radiation with photon energies between 8 and 29 keV. By tilting the lenses with respect to the X-ray beam, the effective path through the diffracting structures can be varied to optimize the diffraction efficiency over a wide range of photon energies. In this way, the effective aspect ratio can be increased to values exceeding 100, which cannot be obtained with untilted optics. The obtained efficiencies exceed values reported previously for this energy range.

Six-degrees-of-freedom alignment of two-dimensional array components by use of off-axis linear Fresnel zone plates

A novel six-degrees-of-freedom (six-DOFs) alignment technique for assembling two-dimensional array components is presented. The technique uses off-axis linear Fresnel zone plates on one component that are combined with alignment targets on the other. The technique is compact and sensitive to all six DOFs; it was used to package an array of microlenses with a 32 x 32 array of GaAs multiple-quantum-well modulators flip-chip bonded to a 9 mm x 9 mm complementary-metal-oxide-semiconductor chip. By use of interference fringes to control the tilt misalignment, the worst-case misalignment of the microlenses relative to the chip is calculated to be as follows: lateral = 3.0 mum, rotational = 0.023 degrees , longitudinal = 13 mum, and tilt = 0.022 degrees . We also propose alternative implementations of the technique, including one that uses on-chip photodetectors to automate this six-DOF alignment technique.

Wavelength tunable diffractive transmission lens for hard x rays

We report on the fabrication and testing of linear transmission Fresnel zone plates for hard x rays. The diffractive elements are generated by electron beam lithography and chemical wet etching of 〈110〉 oriented silicon substrates. By tilting the cylindrical lenses with respect to the x-ray beam, the effective path through the phase shifting zones can be varied. This makes it possible to optimize the diffraction efficiency over a wide range of photon energies, and to obtain effective aspect ratios not accessible with untilted optics. The diffraction efficiency of such a lens was measured as a function of the tilt angles for various energies between 8 and 29 keV. Values close to the theoretical limit were obtained for all energies. Because of the coherence preserving properties of diffractive optics, the method opens up opportunities for experiments using coherent hard x rays.

Wet-etched diffractive lenses for hard X-rays.

A method for the fabrication of linear transmission Fresnel zone plates for X-rays in the 8-15 keV photon energy range is presented. The diffractive elements are generated by electron-beam lithography and chemical wet etching of (110)-oriented silicon membrane substrates. Diffractive structures with aspect ratios of more than 30 for 300 nm-wide structures were obtained. The diffraction efficiency of such a lens was measured for 13.3 keV radiation to be 20%.

Electromagnetic study of a photolithography setup for periodic masks and application to nonperiodic masks

We develop a rigorous electromagnetic analysis to study the field diffracted by a metallic or dielectric grating made of rectangular rods, lying over a stratified media. The analysis generalizes the modal theory of perfectly conducting lamellar gratings combined with the R-matrix propagation algorithm in order to avoid numerical instabilities, thus allowing treatment of layers and gratings of arbitrary thickness. We then study the field map obtained under the conditions stated in a previous patent that described a process for casting on a support the faithful reproduction of a mask pierced with periodically distributed slits. We make a systematic study of the influence of the various parameters (incidence, mark–space ratio, groove spacing, groove depth, polarization, conductivity of the metal) on the field map below the mask. We discover a large tolerance over the parameters, close to the values stated in the patent. The result is that the setup described in the patent valid for periodic maps can be used for duplicating nonperiodic masks (e.g., linear Fresnel zone plates) as well as chirped gratings or gratings with nonrectilinear grooves.

Electromagnetic theory of Bragg–Fresnel linear zone plates

An electromagnetic analysis of diffraction by Fresnel linear zone plates ruled into a homogeneous or a stratified media is developed. It takes advantage of the new possibilities brought by the introduction of the R-matrix propagation algorithm into the theory of lamellar gratings, namely, the large increase of the stability domain of the numerical results. Thus a linear Fresnel zone plate can be delt with as a period of such a grating, and the diffracted field can be computed for both TE and TM polarizations. Numerical examples show the convergence of the method and study the focusing properties of positive and negative zone plates. The influence of different parameters such as incidence or number of lines is pointed out.

Linear-Fresnel-Zone-Plate-Based Two-State Alignment Method for Sub-0.25 µm X-Ray Lithography System

In this paper, we present a linear-fresnel-zone-plate-based two-state alignment method developed at the Center for X-ray Lithography. The alignment system uses a linear Fresnel zone plate (LFZP) as a mask alignment mark and an array of dots as a wafer alignment mark. The alignment error signal extraction is based on a two-state modulation of the incident light. The optical system is arranged outside of the exposure X-ray path and alignment can be performed during X-ray exposures. In the experiment, we obtained an alignment signal depth of focus larger than 4 µm and the gap change between the mask and wafer did not affect the alignment position. The X-ray double-exposure experiment on the system demonstrated an alignment accuracy better than 0.035 µm (3σ) on both Al and silicon nitride marks.

Application of e-beam lithography and reactive ion etching to the fabrication of masks for projection x-ray lithography

Mo/Si multilayer mirrors deposited on silicon wafers by triode sputtering were patterned by electron‐beam lithography and etched by reactive ion etching in a fluorinated plasma with an intermediate metallic mask made by the lift‐off process. The etch rate and etch profile were investigated as a function of the gas mixture, pressure, and plasma rf power. The groove depth was monitored by following the reflectivity of the structure with a helium‐neon laser during etching and comparing it with an optical model. Large structures consisting of gratings and Fresnel zone plates with potential applications to high‐resolution alignment for projection x‐ray lithography were fabricated in Mo/Si. The fabrication feasibility of finer structures such as gratings with 0.3–0.5 μm pitch and linewidths smaller than 100 nm as well as linear and circular Fresnel zone plates with a 0.4‐μm‐wide outer zones were investigated in the similar Mo/C multilayer system.

Fabrication of high-resolution multilayer reflection zone plate microlense for the soft x-ray range

The fabrication of linear, circular, and elliptical reflective zone plate lenses by a multistep process using microfabrication technologies is reported. The diffractive elements were generated by electron-beam lithography on a Mo/C multilayer mirror obtained by means of the triode sputtering technique. The patterns were transferred anisotropically into the multilayer mirror by reactive ion etching in a fluorinated plasma. An intermediate metallic mask made by the lift-off process was used for the transfer process. The groove depth could be monitored by following the reflectivity ofthe structure with a helium-neon laser during etching. Linear, circular (with 0.4-μm outer zones), and elliptical Fresnel zone plates (with 0.8-μ.m outer zones) were produced. Test patterns with a 50-nm top and 90-nm bottom resolution were produced. The groove profile and dimensional control were also investigated.

The effect of process coatings on the alignment signal in a proximity lithography system

The achievement of a high accuracy mask-to-wafer alignment system is one of the key steps in the development of submicron x-ray lithography technology. In this paper, we examine the effects of the depth of the wafer mark and of different process coatings (including photoresist) on the alignment signal in an alignment system that uses linear Fresnel zone plates. A mathematical model based on scalar diffraction theory has been developed to simulate the effect of various coatings on the diffracted signal. An experiment is also carried out to verify the model. From the prediction of the theoretical model and the experimental results, we discuss how the process coating may affect the alignment signals in our two state alignment system. In the light of these results, we deduce the optimal design of the wafer alignment marks in our alignment system.

An alignment system for X-ray lithography

Abstract A new alignment technique for x-ray lithography, projection linear Fresnel zone plate (LFZP) method, has been developed and applied to an x-ray stepper for synchrotron radiation lithography. A wafer alignment mark is magnified and projected using an LFZP on a mask. The wafer mark image position is measured very precisely by a scanning optical system. The alignment error between a mask and a wafer is detected with less than 0.01 μm resolution. Up to date, 0.1 μm (3σ) overlay accuracy has been achieved.

Use of synchrotron radiation for X-ray lithography and semiconductor materials characterization

Synchrotron radiation (SR) has now become one of the important light sources for X-ray lithography and material characterization. An atmospheric environment SR lithography apparatus consisting of an oscillating mirror, a He chamber to extract the SR beam, a vertical stepper with a linear Fresnel zone plate alignment system, and also reliable X-ray masks was developed to make critical problems as clear as possible for the future X-ray lithography using a compact storage ring. At another branch beamline, a few types of characterization experiment were carried out using a high-precision triple-crystal diffractometer applicable to both X-ray topography of the semiconductor substrates and grazing incidence diffraction to study superstructures located between the metal or the insulator layer and the semiconductor substrate.