The concept of the multi-source focus correlation method was presented in 2015 [1, 2]. A more accurate understanding of real on-product focus can be obtained by gathering information from different sectors: design, scanner short loop monitoring, scanner leveling, on-product focus and topography.
This work will show that chip topography can be predicted from reticle density and perimeter density data, including experimental proof. Different pixel sizes are used to perform the correlation in-line with the minimum resolution, correlation length of CMP effects and the spot size of the scanner level sensor. Potential applications of the topography determination will be evaluated, including optimizing scanner leveling by ignoring non-critical parts of the field, and without the need for time-consuming offline topography measurements.
With continuing dimension shrinkage using the TWINSCAN NXT:1950i scanner on the 28nm node and beyond, the imaging depth of focus (DOF) becomes more critical. Focus budget breakdown studies [Ref 2, 5] show that even though the intrafield component stays the same, it becomes a larger relative percentage of the overall DOF. Process induced topography along with reduced Process Window can lead to yield limitations and defectivity issues on the wafer. In a previous paper, the feasibility of anticipating the scanner levelling measurements (Level Sensor, Agile and Topography) has been shown [1]. This model, built using a multiple variable analysis (PLS: Partial Least Square regression) and GDS densities at different layers showed prediction capabilities of the scanner topography readings up to 0.78 Q² (the equivalent of R² for expected prediction). Using this model, care areas can be defined as parts of the field that cannot be seen nor corrected by the scanner, which can lead to local DOF shrinkage and printing issues. This paper will investigate the link between the care areas and the intrafield focus that can be seen at the wafer level, using offline topography measurements as a reference. Some improvements made on the model are also presented.
With continuing dimension shrinkage using the TWINSCAN NXT:1950i scanner on the 28nm node and beyond, the imaging depth of focus (DOF) becomes more critical. Focus budget breakdown studies [Ref 1, 5] show that even though the intrafield component stays the same this becomes a larger relative percentage of the overall DOF. Process induced topography along with reduced Process Window can lead to yield limitations and defectivity issues on the wafer. To improve focus margin, a study has been started to determine if some correlations between scanner levelling performance, product layout and topography can be observed. Both topography and levelling intrafield fingerprints show a large systematic component that seems to be product related. In particular, scanner levelling measurement maps present a lot of similarities with the layout of the product. The present paper investigates the possibility to model the level sensor’s measured height as a function of layer design densities or perimeter data of the product. As one component of the systematics from the level sensor measurements is process induced topography due to previous deposition, etching and CMP, several layer density parameters were extracted from the GDS’s. These were combined through a multiple variable analysis (PLS: Partial Least Square regression) to determine the weighting of each layer and each parameter. Current work shows very promising results using this methodology, with description quality up to 0.8 R2 and expected prediction quality up to 0.78 Q2. Since product layout drives some intrafield focus component it is also important to be able to assess intrafield focus uniformity from post processing. This has been done through a hyper dense focus map experiment which is presented in this paper.
Reflection by wafer topography and underlying layers during optical lithography can cause unwanted
overexposure in the resist [1]. In most cases, the use of bottom anti reflective coating limits this effect. However, this
solution is not always suitable because of process complexity, cost and cycle time penalty, as for ionic implantation
lithography process in 28nm bulk technology. As a consequence, computational lithography solutions are currently under
development to simulate and correct wafer topographical effects [2], [3]. For ionic implantation source drain (SD)
photolithography step, wafer topography influences resulting in implant pattern variation are various: active silicon
areas, Poly patterns, Shallow Trench Isolation (STI) and topographical transitions between these areas. In 28nm bulk SD
process step, the large number of wafer stack variations involved in implant pattern modulation implies a complex
modeling of optical proximity effects. Furthermore, those topography effects are expected to increase with wafer stack
complexity through technology node downscaling evolution. In this context, rigorous simulation can bring significant
value for wafer topography modeling evolution in R and D process development environment. Unfortunately, classical
rigorous simulation engines are rapidly run time and memory limited with pattern complexity for multiple under layer
wafer topography simulation.
A presentation of a fast rigorous Maxwell’s equation solving algorithm integrated into a photolithography
proximity effects simulation flow is detailed in this paper. Accuracy, run time and memory consumption of this fast
rigorous modeling engine is presented through the simulation of wafer topography effects during ionic implantation SD
lithography step in 28nm bulk technology. Also, run time and memory consumption comparison is shown between
presented fast rigorous modeling and classical rigorous RCWA method through simulation of design of interest. Finally,
integration opportunity of such fast rigorous modeling method into OPC flow is discussed in this paper.
A new approach for the realization of highly dispersive dielectric transmission gratings is presented. By covering
conventional transmission gratings with a plane substrate a complete suppression of any reflection losses and, thus,
100% diffraction efficiency can be achieved. Theoretical design considerations, a physical investigation of the
diffraction as well as very promising experimental results are shown.
Laser polarization control is revisited at the light of the possibilities offered by resonant gratings associated with the multilayer mirror of the laser. As compared with classical Brewster elements, resonant grating mirrors have a richer functionality in that they can achieve transverse mode control. Furthermore, they are fully planar monolithic elements which can be fabricated by batch technologies and lead to the utmost miniaturization of the laser module. A number of designs and experimental demonstrations are presented.
A sinusoidally weakly undulated continuous thin gold film embedded between a polymer substrate and a thin cover of the same polymer, the metal film thickness, the period and the wavelength being such that a normally incident wave excites the long range plasmon mode of the metal film, is shown to exhibit strong resonant transmission for the local TM polarization and strong reflection of the TE polarization. Such structure represents a very simple, average performance polarization beam splitter for white light processing.
The formalism of the True Modal Method up to now written for diffraction gratings with a rectangular profile is extended to 1D-periodic structures with parallelogramic grooves. An appropriate coordinate transformation is proposed in order to express analytically in a simple form the modes propagating in the grating region. Numerical examples of calculation of the propagation constants of the eigenmodes of the grating and of the total diffraction efficiency of lamellar parallelogramic structures are given and results are compared with those obtained by other methods.
For gaining a deeper understanding of the diffraction processes that take place in deep dielectric transmission gratings, a phenomenological explanation has been developed on the basis of a modal field, which propagates vertically through the grating region. The excitation of these modes by the incident wave, their propagation constants and how they couple to the diffraction orders determines the diffraction efficiency of the transmitted orders. The explicit modal analysis discloses the description of the highly efficient diffraction for polarized or unpolarized light by a very simple interference mechanism, which will be the subject of this paper.
The synthesis of a narrow band, wide angular aperture 1D grating filter exhibiting close to 100% reflection of a focused beam is developed analytically on the basis of a phenomenological coupled wave representation.
Narrow band resonant reflection of a polarized focused beam from a single-crystal silicon grid is demonstrated at terahertz frequencies with an efficiency close to 100 %. A spectral width of less than 7 μm at a resonance wavelength of 570 μm is achieved with a 4 mm-waist beam which overlaps with only ~10 grid periods. This compact reflection filter is a scale model of what can be expected at optical frequencies, but also represents a new type of compact terahertz device.
An ultra-high resolution measurement technique makes the assessment of the period uniformity in a long grating used as a phase mask for Fibre Bragg Gratings (FBG). It comprizes a pair of two identical displacement sensors placed close to each other at a strictly constant spacing flying over the grating under test at an essentially constant velocity. The phase difference between the two sensors is a simple function of the local spatial frequency of the grating. A proper solution of an inverse problem provides the period variation along the grating. The technique is used here to characterize phase masks fabricated by means of a MEBES 4500 electron beam pattern generator. The period does not deviate by more than 3 pm from the prescribed period over a length by more than 100 mm.
An analytical derivation is provided giving the normalized waveguide thickness at which a corrugation grating defined at the surface of a graded index slab waveguide has a maximum radiation coefficient for TE and TM modes. This condition is also that for a maximum sensing sensitivity for biochemical species placed on top of the slab waveguide.
The presented interference detector comprises a standard pn junction in a silicon substrate and a corrugation grating engraved at its surface. Two beams with unknown phase difference impinge onto the detector under the Littrow condition for some diffraction order of the grating. The detected power exhibits a non-zero AC component as the relative phase between the incident beams changes. The present paper describes the operation principle and brings the evidence of non-zero interference contrast in the application case of a displacement sensor.
KEYWORDS: Picosecond phenomena, Diffraction gratings, Diffraction, Global system for mobile communications, Matrices, Free space, Waveguides, Electromagnetism, Radio propagation, Free space optics
The complete analytical solution of the diffraction problem of an arbitrary incident wave by a 2D grating of arbitrary k-vectors is provided under the Rayleigh hypothesis. It is furthermore shown by deriving an analytical solution from the exact Generalized Source Method (GSM) in the limit of small grating amplitude that the Rayleigh and the exact methods lead to the same analytical results. This proves that the results given by the Rayleigh method in the limit of shallow grooves are exact whatever the groove profile.
The coupling of a 2D focused beam under normal incidence into a grating waveguide was solved by means of a coupled wave formalism where the phenomenological parameters are given by a simple plane wave diffraction analysis [1]. It is shown that the guided modes which must be considered in the situation of normal incidence are waves exhibiting a standing wave as well as a propagating character. The plane wave diffraction analysis of the poles corresponding to these modes reveals their interesting properties and helps establish the suitable phenomenological representation of the coupling event. The aim of this approach was to find out the conditions for maximum light confinement in a grating waveguide in the perspective of the high efficiency excitation of a high density pixellated array of biosensor sites.
A Fabry-Perot comprising a multilayer mirror and a mirror operating according to the resonant reflection of a grating slab waveguide exhibits the remarkable property of possibly being single order. The analysis of this new type of resonator is made and applied to the understanding of the operation of a known filtering laser mirror.
KEYWORDS: Waveguides, Global system for mobile communications, Wave propagation, Waveguide modes, Free space, Spatial frequencies, Electromagnetism, Cladding, Maxwell's equations, Lead
A general method is presented for the exact numerical resolution of Maxwell’s equations for monochromatic wave propagation in a two-dimensional waveguiding structure. The Generalized Source Method using the Green tensor of free space leads to an exact solution of a wide variety of guiding as well as leaky mode structures without setting boundary conditions and without resorting to PMLs.
The present work relates to the design, the fabrication and the spectroscopic characterisation of an efficient grating polarising structure which uses a quasi extra-cavity resonant grating in association with a multilayer to dictate the polarisation emitted by a semiconductor pumped solid-state Nd:YAG laser at 1.064 μm wavelength.
KEYWORDS: Electromagnetism, Diffraction, Global system for mobile communications, Diffraction gratings, Binary data, Modulation, Physics, Free space, Interfaces, Matrices
The generalized source method is shown to give the exact solution to an unsolved electromagnetic problem from the complete solution to another solved problem even when the solution to the known problem is approximate. This is illustrated with the example of a binary grating where an exact solution exists.
A sub-micron grating can be the key miniaturized planar element in Micro-opto-electromechanical systems where it performs a number of optical functions such as light routing, beam splitting, spectral-analysis, polarization filtering, beam recombination, spatial resonance excitation, in the domains of displacement measurement, biochemical sensors, environment monitoring, laser emission control, WDM communications, to quote a few current applications. This paper will describe the main stream technology of sub-micron gratings and illustrate its application potential.
A new, high efficiency diffraction grating configuration for use in the situation of grazing incidence is proposed and analyzed. The structure consists of a flat mirror plane, a thin dielectric film with a grating at the air-film interface. It can advantageously replace corrugation metal gratings in all applications, particularly in high power laser applications using the Littman-Metcalf mounting.
The blazing effect of parallelogramic grooves is analyzed theoretically and demonstrated experimentally in the case of TE and TM modes in large guidance waveguides. A novel fabrication method is proposed, modellized and demonstrated.
A system of two radiationally coupled corrugated waveguides is proposed for remote coupling. Coupling is achieved owing to diffraction of the waveguide mode on the corrugated waveguide surface. Using Rayleigh-Fourier-Kiselev method, we calculated the dispersion curves of the system and the coupling length on their basis. Coupling length changes periodically when waveguide separation increases, this fact makes the remote coupling possible. Optimum distances between the waveguides are also determined. It is shown that the coupling length is related to the radiation loss coefficient of the single waveguide.
A system of two radiationally coupled waveguides is proposed for remote coupling implementation. Radiation loss coefficient and coupling length are determined for two different designs of radiationally coupled waveguides: corrugated and leaky. Remote coupling over a 95 micrometers distance in a pair of radiationally coupled waveguides is demonstrated experimentally for the first time.
The analysis of a corrugated waveguide excitation by normally incident light beam is carried out and the conditions for optimum waveguide mode excitation are determined in the case of a finite size grating region.
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