Proximity Gaps Research Articles

Proximity Testing with Logarithmic Randomness

A fundamental result dating to Ligero (Des. Codes Cryptogr. '23) establishes that each fixed linear block code exhibits proximity gaps with respect to the collection of affine subspaces, in the sense that each given subspace either resides entirely close to the code, or else contains only a small portion which resides close to the code. In particular, any given subspace's failure to reside entirely close to the code is necessarily witnessed, with high probability, by a uniformly randomly sampled element of that subspace. We investigate a variant of this phenomenon in which the witness is not sampled uniformly from the subspace, but rather from a much smaller subset of it. We show that a logarithmic number of random field elements (in the dimension of the subspace) suffice to effect an analogous proximity test, with moreover only a logarithmic (multiplicative) loss in the possible prevalence of false witnesses. We discuss applications to recent noninteractive proofs based on linear codes, including Brakedown (CRYPTO '23).

Proximity Gaps for Reed–Solomon Codes

A collection of sets displays a proximity gap with respect to some property if for every set in the collection, either (i) all members are δ-close to the property in relative Hamming distance or (ii) only a tiny fraction of members are δ-close to the property. In particular, no set in the collection has roughly half of its members δ-close to the property and the others δ-far from it. We show that the collection of affine spaces displays a proximity gap with respect to Reed–Solomon (RS) codes, even over small fields, of size polynomial in the dimension of the code, and the gap applies to any δ smaller than the Johnson/Guruswami–Sudan list-decoding bound of the RS code. We also show near-optimal gap results, over fields of (at least) linear size in the RS code dimension, for δ smaller than the unique decoding radius. Concretely, if δ is smaller than half the minimal distance of an RS code V ⊂ 𝔽 q n , then every affine space is either entirely δ-close to the code or, alternatively, at most an ( n/q )-fraction of it is δ-close to the code. Finally, we discuss several applications of our proximity gap results to distributed storage, multi-party cryptographic protocols, and concretely efficient proof systems. We prove the proximity gap results by analyzing the execution of classical algebraic decoding algorithms for Reed–Solomon codes (due to Berlekamp–Welch and Guruswami–Sudan) on a formal element of an affine space. This involves working with Reed–Solomon codes whose base field is an (infinite) rational function field. Our proofs are obtained by developing an extension (to function fields) of a strategy of Arora and Sudan for analyzing low-degree tests.

The Challenges of Translating Ḥāfiẓ into Russian

Abstract Despite the geographical proximity, the cultural and linguistic gaps between the Russian and the Persian languages are too many to enumerate. The Russian translator’s grasp of Islam and Middle Eastern culture at the end of the nineteenth and the beginning of the twentieth century was limited—and frequently Orientalist. While the “exotic nature” of Persian poetry and Ḥāfiẓ’s ghazals in particular evoked great interest among translators and readers, it was presented to the Russian literary circles mostly in the tradition of secular lyrical poetry and was not placed in its mystical or allegorical context. Below, by citing four ghazals and their translation nuances by four Russian poets, this article will examine the means by which Russian translators introduced a nuanced Persian lyrical poetry to their Russian audience.

A Novel Expulsion Control Strategy With Abnormal Condition Adaptability for Resistance Spot Welding

Abstract Welding expulsion is a common problem in the resistance spot welding (RSW) process, which severely impacts weld quality and surrounding facilities. Existing expulsion control strategies are ineffective for complex and changeable welding conditions. This article studied the growth relationship between weld nugget and corona bond under two abnormal conditions: edge proximity (EP) and initial sheet gaps (IG). It is testified that expulsion would occur when the nugget size exceeds the corona bond size under EP and IG conditions. Reducing the welding current before the expulsion time can increase the size difference between the corona bond and the weld nugget, thereby delay and even eliminate the occurrence of expulsion. In this way, a novel online expulsion control strategy, named short-time current regulation (STCR), is proposed through the expulsion moment analysis of historical weld data. The effect of the new control strategy is verified with workpieces ranging from low carbon steel to ultra-high strength steel. Experimental results showed that STCR can effectively reduce the amount of expelled metal, decrease the indentation depth, and increase the nugget diameter. The method not only works well under one specific abnormal condition but also adapts to the transition between different welding conditions. This novel expulsion control strategy can help achieve the expulsion-free RSW process in mass production without frequent manual offline optimization of welding parameters.

Spatial Dynamics of Intercity Technology Transfer Networks in China’s Three Urban Agglomerations: A Patent Transaction Perspective

Technology transfer has become a vital pipeline for acquiring external knowledge. The purpose of this paper is to portray the spatial dynamics of intercity technology transfer networks in China’s three urban agglomerations based on patent right transaction data from 2008 to 2015. The integration of social networks and spatial visualization is used to explore spatial networks and influencing variables of the networks. The results demonstrate that Beijing, Shanghai, and Shenzhen are emerging as hubs in the three urban agglomerations. The spatial distributions of degree and weighted degree are significantly heterogeneous and hierarchical. The larger cities play the role of a knowledge and technology incubator, highly related to their economic scale, research and development (R&D) input, and innovation output. The evolution of intercity technology linkages is driven by the networking mechanisms of preferential attachment, hierarchical and contagious diffusion, path dependence, and path breaking. Moreover, we found that the geographical proximity and technology gaps are determinants of the strength of intercity technology linkages. As a result, it has been discovered that the network in the Beijing–Tianjin–Hebei agglomeration is organized in a tree network, while the Yangtze River Delta features a polycentric network and the Pearl River Delta has multi-star characteristics.

Unconventional order parameter induced by helical chiral molecules adsorbed on a metal proximity coupled to a superconductor

Following our previous results, which provide evidence for the emergence of a chiral p-wave triplet-pairing component in superconducting Nb upon the adsorption of chiral molecules, we turned to investigate whether such an effect can take place in a proximal superconductor consisting of metal on superconductor bilayer. Note that in such proximity systems, correlated electron-hole (Andreev) pairs exist in the normal metal rather than genuine Cooper pairs. To that end, we used scanning tunneling spectroscopy (STS) on thin Au films grown in-situ on NbN (a conventional s-wave superconductor) before and after adsorbing helical chiral, alpha-helix polyalanine molecules. The tunneling spectra measured on the pristine Au surface showed conventional (s-wave like) proximity gaps. However, upon molecules adsorption the spectra significantly changed, all exhibiting a zero-bias conductance peak embedded inside a gap, indicating unconventional superconductivity. The peak reduced with magnetic field but did not split, consistent with equal-spin triplet-pairing p-wave symmetry. In contrast, adsorption of non-helical chiral cysteine molecules did not yield any apparent change in the order parameter, and the tunneling spectra exhibited only gaps free of in-gap structure.

Enhanced vortex pinning in Nb using proximity effect through organic molecules

While the superconductor proximity effect is well understood in layered superconductor/normal-metal junctions, its understanding is quite limited in systems involving nanoparticles (NPs) and molecules. In recent studies, a unique inverse proximity effect phenomenon was found in which the critical temperatures of Nb films surprisingly increased upon the chemical attachment of gold NPs. Concomitantly, the tunneling density of states on and around the gold NPs was significantly modified, showing either zero-bias peaks or the development of proximity gaps in the NPs. These results seem to be related to the molecule-mediated coupling strength. Here, we study the strong molecular coupling regime of such an architecture, for which proximity gaps are induced in Au NPs. We show that significant pinning is induced in a periodic array of Au NPs coupled to a superconducting surface via organic molecules. The pinning potential in this case is stronger than the potential achieved through the direct proximity of Au or Ni islands to the superconducting surface. A matching field magnetoresistance signal can only be identified using the hybrid Au/organic-linker/Nb system. In this case, the matching vortex lattice density is higher than the saturation number. These results suggest that the NP-Nb electrical coupling through the molecules induces a resonance behavior, which modifies the local pairing amplitude.

Order, disorder, and tunable gaps in the spectrum of Andreev bound states in a multiterminal superconducting device

We consider the spectrum of Andreev bound states (ABSs) in an exemplary 4-terminal superconducting structure where 4 chaotic cavities are connected by QPCs to the terminals and to each other forming a ring. Such a tunable device can be realized in 2DEG-superconductor structures. We concentrate on the limit of a short structure and large conductance of the QPCs where a quasi-continuous spectrum is formed. The energies can be tuned by the superconducting phases. We observe the opening and closing of gaps in the spectrum. This concerns the usual proximity gap that separates the levels from zero energy as well as less usual "smile" gaps that split the levels of the spectrum. We demonstrate a remarkable crossover in the overall spectrum that occurs upon changing the ratio of conductance of the inner and outer QPCs. At big values of the ratio, the levels exhibit a generic behavior expected for the spectrum of a disordered system manifesting level repulsion and "Brownian motion" upon changing the phases. At small values of the ratio, the levels are squeezed into narrow bunches separated by wide smile gaps. Each bunch consists of almost degenerate ABSs. We study in detail the properties of the spectrum in the limit of a small ratio, paying special attention to the crossings of bunches. We distinguish two types of crossings: i. with a regular phase dependence of the levels and ii. crossings where the Brownian motion of the levels leads to an apparently irregular phase-dependence. We work out a perturbation theory to explain the observations. The unusual properties of the spectrum originate from unobvious topological effects. Topology of the first kind is related to the winding of the semiclassical Green's function. It is responsible for the proximity gaps. Topology of the second kind comes about the discreteness of the number of modes and is responsible for the smile gaps.

Intensity and phase fields behind phase-shifting masks studied with high-resolution interference microscopy

We try to find out the details of how light fields behind the structures of photomasks develop in order to determine the best conditions and designs for proximity printing. The parameters that we use approach real situations like structure printing at proximity gaps of 20 to 50 μm and structure sizes down to 2 μm. This is the first time that an experimental analysis of light propagation through a mask is presented in detail, which includes information on intensity and phase. We use high-resolution interference microscopy (HRIM) for the measurement. HRIM is a Mach–Zehnder interferometer, which is capable of recording three-dimensional distributions of intensity and phase with diffraction-limited resolution. Our characterization technique allows plotting the evolution of the desired light field, usually called the aerial image, and therefore gives access to the printable structure until the desired proximity gap. Here, we discuss in detail the evolution of intensity and phase fields of elbow or corner structures at different positions behind a phase mask and interpret the main parameters. Of particular interest are tolerances against proximity gap variation and the theoretical explanation of the resolution in printed structures.

Quantum oscillations in the vortex state of underdoped YBa2Cu3O6.5and other multiband superconductors

We argue that the low-frequency quantum oscillations observed recently in the vortex state of underdoped ortho-II YBa${}_{2}$Cu${}_{3}$O${}_{6,5}$ have the same origin as in other strongly correlated electronic systems. Superconductivity driven by strong interactions on several leading Fermi surfaces creates the proximity gaps on the other. The gap that is transferred on a small-sized pocket from larger Fermi surfaces is small. In the case of unconventional pairing symmetry the induced gap is proportional to the ratio of the oscillations' frequencies for small and large Fermi surfaces. The gap is in inverse proportion to the mass enhancement on the latter. We share the view that small pockets in and of themselves exist as a certain band feature among all Fermi surfaces.

Advanced mask aligner lithography: fabrication of periodic patterns using pinhole array mask and Talbot effect

The Talbot effect is utilized for micro-fabrication of periodic microstructures via proximity lithography in a mask aligner. A novel illumination system, referred to as MO Exposure Optics, allows to control the effective source shape and accordingly the angular spectrum of the illumination light. Pinhole array photomasks are employed to generate periodic high-resolution diffraction patterns by means of self-imaging. They create a demagnified image of the effective source geometry in their diffraction pattern which is printed to photoresist. The proposed method comprises high flexibility and sub-micron resolution at large proximity gaps. Various periodic structures have been generated and are presented.

Neutral particle proximity lithography: Noncontact nanoscale printing without charge-related artifacts

The authors present neutral particle proximity lithography, a high resolution, parallel exposure technique where a broad beam of energetic neutral particles floods a stencil mask and transmitted beamlets transfer the mask pattern to resist on a substrate. It preserves the advantages of nanoscale penumbra, diffraction, and resist scattering of ion beam lithography (IBL) yet is intrinsically immune to charge accumulation on the mask and substrate. In a series of direct comparisons, involving insulating substrates, large proximity gaps, and ultrasmall features, the authors show that the use of neutral particles provides a simple method for completely eliminating the charging artifacts of IBL. They demonstrate the ability to print 8nm mask features with 5nm pattern fidelity. Exposure times are about 200s in poly(methyl methacrylate) resist.

Neutral particle lithography: a simple solution to charge-related artefacts in ion beam proximity printing

Neutral particle lithography (NPL) is a high resolution, proximity exposure technique where a broad beam of energetic neutral atoms floods a stencil mask and transmitted beamlets transfer the mask pattern to resist on a substrate. It preserves the advantages of ion beam lithography, including extremely large depth-of-field, sub-5 nm resist scattering, and the near absence of diffraction, yet is intrinsically immune to charge-related artefacts including line-edge roughness and pattern placement errors due to charge accumulation on the mask and substrate. This paper reviews the principles of NPL, surveys recent advances in the field and discusses applications involving insulating substrates, large proximity gaps or ultra-small features where the approach has particular advantages.

The superconductor proximity effect in Au–YBa2Cu3O7−δ bilayer films: the role of order parameter anisotropy

Scanning tunneling spectroscopy of Au–YBa2Cu3O7−δ bilayers reveals proximity effect features that reflect the anisotropic dx2−y2-wave order parameter in YBa2Cu3O7−δ (YBCO). No proximity effect takes place at the (001)YBCO–Au interface, manifesting the quasi two-dimensional nature of the order parameter. Proximity gaps are induced in the gold primarily via (100)YBCO facets, and their size decays exponentially on a scale of ∼30nm, in good agreement with estimations for the dirty limit. In the nodal (110)YBCO–Au interface, the proximity effect manifests itself by the penetration of Andreev bound states into the gold. The corresponding zero bias conductance peaks are nearly constant in magnitude for Au layers thinner than 7nm, and then decay abruptly with Au thickness, vanishing above 10nm, on the scale of the (ballistic) mean free path.

Patterning Characteristics of Hole Patterns in Synchrotron Radiation Lithography

The patterning characteristics of synchrotron radiation lithography for hole patterns using a low-contrast mask (contrast: 3.5) are investigated. A resolution of 110 nm provides a large exposure dose latitude of more than 10% when the proximity gap is less than 15 µm, and the replicated minimum hole size is 70 nm with a 10-µm gap. Resist pattern sizes from 110 to 360 nm are kept within ±10% with proximity gaps of less than 20 µm. However, the exposure dose margin to guarantee mask linearity decreases to several percent because of the different optimum exposure dose for each pattern. Pattern size correction using mask bias to improve the mask linearity and exposure dose margin is proposed.

Extendibility of synchrotron radiation lithography to the sub-100 nm region

This article discusses the resolution of synchrotron radiation lithography in the sub-100 nm region, taking into consideration the mass production of large-scale integrated circuits, under attainable conditions for the x-ray mask, proximity gap, and resist processes. Resolution and exposure latitude for line-and-space patterns are markedly improved by using a mask with a contrast of only 2.5. Resolutions of 90, 80, 70, and 60 nm can be achieved with proximity gaps of 30, 20, 15, and 10 μm if a high-contrast resist and a low-surface tension developer are used. The latitude will be 10% for pattern sizes as small as 70 nm when the proximity gap is narrower than 15 μm. The effects of mask duty [which is defined to be the ratio of the absorber (line) width to the pattern pitch, i.e., duty cycle] on the optimum exposure dose and mask linearity are also evaluated.

Patterning Characteristics of 0.1-µm Line-and-Space Pattern in Synchrotron Radiation Lithography

A detailed analysis is performed to investigate the effects of mask contrast, mask-pattern size error and proximity gap on resolution and exposure dose margin for replicating 0.1-µm-region line-and-space (L&S) patterns using synchrotron radiation lithography. The analysis is performed by comparing Fresnel diffraction simulation and pattern replication experiments. When a conventional-contrast (7) mask is used, designing the pattern size of a Ta mask absorber to be slightly narrower than the specified value is a great advantage for faithful pattern replication of 0.1-µm L&S patterns. A large dose margin is obtained for proximity gaps of 15 µm or less. On the other hand, a low-contrast (2.5) mask has an advantage over the conventional mask in that it allows the use of a larger proximity gap for replicating 0.1-µm L&S patterns. A relatively large margin is obtained by limiting the Ta size error to the range of -0.05 µm to +0.03 µm for proximity gaps smaller than 25 µm, and ±0.02 µm for a 30-µm gap.

Printability of x-ray mask defects in sub 0.5 μm mask pattern

This paper aims at a description of x-ray mask defects, in order to specify the requirements on defect inspection and repair of 1:1 x-ray masks.For three types of x-ray mask defects the critical sizes are calculated with XMAS (x-ray lithography modelling and simulation) for different defect positions, critical dimensions, defect shapes and proximity gaps. The critical defect size corresponds to a printed defect size on the wafer of one tenth of the critical dimension. Defects larger than the critical size have to be repaired. A comparison between physical and simulated print of a defect is given.

Application of the simulator “XMAS” on specific problems in sub-half-micron lithography

The program XMAS, which allows the simulation of 3-D resist profiles in X-Ray Lithography has been used to evaluate the ultimate resolution capability and the replication of defects of this lithography method. It has been shown that 0.2 μm structures can be transferred with high process latitude at reasonable proximity gaps (30 μm). Dust particles (silicon, resist) up to 0.5 μm thickness do not seriously deteriorate the pattern transfer.

X-ray lithography

X-ray lithography with wavelengths between 0.2 and 2 nm provides a structural resolution as good as 0.1 μm under optimized conditions even in the case of high proximity gaps of 50 μm which are needed in practical applications. But the high performance of X-ray lithography can only be realized by parallel and highly intensive radiation. The wavelength distribution has to be tuned properly to the absorption properties of a special set of mask substrate, absorber and window material. As there are no suitable optics for X-rays in order to fabricate a condensor for a homogeneous illumination of mask and wafer, the type of X-ray source used is the most decisive parameter with respect to both resolution and wafer throughput. Comparing various X-ray sources, such as X-ray tubes, storage rings, and plasma sources, the conclusion is that at present synchrotron radiation offers most advantages. However, the existence of low cost compact storage rings especially designed for the lithography purposes is a precondition for an industrial application.The second most important problem is a mask technology with high geometrical stability (10−6 is needed for the large step field sizes mentioned) and low defect densities. Silicon, siliconnitride and boronnitride for the membrane and gold or tungsten for the absorber are the most promising materials for X-ray masks. Besides a sufficiently high X-ray transparency, the mask membranes have to show a high transparency in the visible wavelength range too. Highly sophisticated optical pattern recognition seems to be the best way to solve the alignment problems with an alignment accuracy of at least 0.05 μm (3δ).Moreover, synchrotron radiation provides a possibility to use single layer resist techniques even in the case of highest resolutions. New resist materials now appearing seem to provide a sufficiently good compromise between radiation sensitivity and technological stability. It is estimated that on this basis the wafer throughput of an X-ray stepper with optical alignment will be 50–100 wafers (125 mm) per hour at a cost level comparable to the optical wafer stepper but at a significantly higher process performance.