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Even though the EUV pellicle has less than 0.04% EUV reflectivity, it could be locally increased at wrinkles on the pellicle and the intensified light could cause a local CD variation. we confirmed that the reflectivity was increased by more than 4 times due to the pellicle wrinkle and it caused the mask CD variation. Therefore, although the pellicle satisfies the EUV reflectivity requirement, we also need to qualify the wrinkle of the pellicle for the CD variation issue during the exposure process.

In semiconductor industry, CD-SEMs (critical dimension scanning electron microscopes) are key enablers for metrology and process control. Additional applications that exploit the potential of CD-SEM equipment have being developed – such as contour extraction algorithms, in order to continue to address the increasing metrology requirements of the semiconductor industry. An important example of the utilization of image information is the industry’s use of full contour extraction for various applications, such as MPC (mask process correction) modeling, OPC (optical proximity correction) modeling, and advanced measurement solutions, especially for newer technologies such as ILT (Inverse Lithography Technology), where the characteristics of the 2D curvilinear patterns are such that standard measurement solutions are no longer an option. As mask errors become more and more critical, providing good measurements is critical for calibrating MPC models, estimating etch bias over complex features, providing CD uniformity analysis, among other. More complex patterns also lead to less robust measurements in traditional CD-SEMs requiring more refined algorithms and statistics control to achieve a good level of certainty. Tool drift can lead to a lack of focus during the image acquisition and induce a blur problem in the image, affecting the quality of the signal to be analyzed, and consequently misleading the measurements. These measurements can induce false statistics and lead to bad decisions in a fab environment. Another important factor for considering over SEM images is the quality of the signal on the pattern edges. This characteristic may have a significant impact over the measurement results, also leading to errors in the production flow. For example, using wrong measurements for addressing etching recipes or for generating MPC models may induce errors in the mask fabrication process, reducing its overall quality. Therefore, being capable of identifying blur on SEM images as well as edge quality variation is an important tool for mask manufacturers to prevent from using erroneous measurements for the decisions required during the entire fabrication flow. In this work, the impact of blur on CD-SEM measurements is evaluated. Also, the impact of the blur over the detection of pattern’s edges is demonstrated over experimental data, coming from three different mask production flows, with different etch signatures and acquisition conditions. The proposed approach enables removing untrustworthy measurements from a calibration or a verification set.

RESUMEN Este ensayo propone analizar la correspondencia entre Damaris Masham y G. W. Leibniz (1704-1705) a través de tres dimensiones de discusión: ontológica, epistemológica y crítica. Dicho análisis puede ser útil para entender los fundamentos epistemológicos del racionalismo moral y pedagógico de la filósofa inglesa. En ese sentido, se ofrece una integración de elementos que permiten entender no sólo la coincidencia de tradiciones tan aparentemente antitéticas como el platonismo y el empirismo en la filosofía de Masham, también permiten apreciar su independencia intelectual. ABSTRACT This essay aims to analyse the correspondence between Damaris Masham and G. W. Leibniz (1703-1705) through three discussion dimensions: ontological, epistemological and critical. This analysis could be useful in order to understand the epistemological grounds of the moral and pedagogical rationalism of the English philosopher. In this sense, it offers an integration of elements that make us able to understand the coincidence of apparently antithetical traditions as platonism and empirism in Masham´s philosophy, moreover let us appreciate her intellectual independence.

To this day there is no established practical method available to identify the “optimal” base dose in e-Beam lithography for mask making. Methods range from choosing the “zero-bias” exposure dose that yields CDmeasured = CDtarget to real isofocal calibrations that require to print the structures at different blurs/focus settings. While the latter yields an optimal base dose, it requires a significant experimental procedure, whereas the former uses a pretty simple experiment but will likely yield a non-optimal base dose due to process effects (e.g., lateral resist development). Here we present a novel method to find the optimum base dose for e-Beam mask exposures that requires only a simple experiment. Surprisingly, the exposure doses required to print features with different densities at the same CD does depend on the process point, adding an error term to the proximity effect correction in case the correction is not aligned to this. This is due to the fact that for a given stack and acceleration voltage, a PEC method will deliver one fixed dose range, whereas the experimentally required dose range depends on the process point chosen. This observation can be used to calibrate the base dose such that it matches the dose range obtained from PEC. Moreover, it can be used to add a new criterion to proximity effect correction – the iso-focal condition - to not only correct for line width (also called critical dimension, CD) linearity and density dependent effect, but to also add immunity to process variations such as focus and blur variations.

This paper demonstrates a series of high-order mode waveguide bends with an ultra-compact footprint and high performance. Gradient-based inverse design with level set method is utilized endow the device excellent critical dimension control.

MPC has been a technology enabler since 32nm technology node, and the number of mask layers receiving MPC increases as technology node advances. Model-based Mask Process Correction (MB-MPC) has evolved from correction based on short-range Gaussian to full Machine Learning (ML) based model and correction. Model-based MPC has demonstrated efficacy in reducing mask error on advanced nodes, but often requires extensive computing resource to achieve the stringent mask fidelity and Critical Dimension (CD) requirements. On the other hand, rule-based Mask Process Correction (RB-MPC) has the advantage of fast turn-around time. This paper presents an approach to rule-based MPC that seeks to extract the maximum benefits of model-based MPC. The rules cover critical geometrical ‘building blocks’ such as lines, contacts, line-ends, notches. Derivation of the rules is guided by a mask process model. The goal of RB-MPC is to mitigate the long runtime of MB-MPC while minimizing loss in patterning fidelity. We will describe the methodology of rule derivation, implementation, and verification of RB-MPC. The RB-MPC approach meets accuracy requirements for 32-22nm technology nodes. For more advanced technology nodes, a hybrid RB-MB-MPC recipe is proposed to achieve both high accuracy and fast runtime.

ArF lithography is still applied to the majority of critical layers, even with increasing of extreme ultraviolet lithography in leading-edge production. As wafer design shrinks, conventional 6% phase shift mask (PSM) becomes hard to meet the ArF lithography requirements especially for array dot on mask (hole on wafer). Therefore, transmission dependency was evaluated by mask 3D simulation, and it was found that 30% transmission has the best lithographic performances for array dot. Based on these results, mask blank and mask making process for new 30% PSM were developed. Wafer printability test using negative tone development demonstrated that new 30% PSM has better process window and mask error enhancement factor (MEEF) than conventional 6% PSM for array dot (hole on wafer). To investigate further application of new 30% PSM, lithography performances of various patterns were evaluated by mask 3D simulation and aerial image measurement system (AIMSTM). The results indicated that new 30% PSM has larger lithography margin than 6% PSM for iso dot, iso line and logic pattern. Additionally, wafer printability test demonstrated that new 30% PSM has better process window than 6% PSM for iso dot. Defect control is also an important factor in high volume manufacturing. Therefore, it is necessary to evaluate the repairability and printability of the defects on new 30% PSM. We repaired various types of defects by electron-beam repair tool and confirmed the repairability by AIMS. And the defect printability of new 30% PSM and 6% PSM to critical dimension (CD) on wafer was evaluated by program defect mask that has pin dot, extrusion and intrusion defects.

Mask process correction (MPC) played a key part improving yield in 14 nm technology node and below using deep ultraviolet lithography (DUVL). Extreme ultraviolet lithography (EUVL) is entering an industry production phase for 7 nm logic and is under development for next node logic and memory applications. A key benefit of EUVL for logic interconnect lithography comes from the ability to pattern layers at aggressive pitch using a single exposure. Mask critical dimension targeting was found to be a critical factor for yielding wafer process, MPC will be necessary to correct for mask process errors. This paper will focus on building MPC models for EUV mask processes exposed on a variable shape beam lithography tool.

Nanoimprint lithography (NIL) is a promising technology on next generation lithography for the fabrication of semiconductor devices. NIL is a one-to-one lithographic technology with a contact transfer methodology using templates. Therefore, critical dimension (CD) error and defect performance of templates has direct impact on wafer performance. The previous paper reported that the self-aligned double patterning (SADP) process on master template had better performance on resolution and defect performance [2]. In proceeding with development of SADP template process technology, we found that CD errors occurred in the area with a pattern density change. CD control over any pattern density is one of the critical issues. In this report, we have investigated the impact of the proximity effect correction (PEC) and fogging effect correction (FEC) parameters for electron beam writing on gap space and core space. It was found that the optimal PEC parameter for resist CD is not the best for the core space and the gap space. The resist CD is uniform, but there is a difference in resist shape on the local pattern density variation. It was also found that the core space had dependency on global pattern density even if the optimal FEC parameter for resist CD was applied. FEC can correct resist CD, but it cannot adjust resist shape. By using the optimal PEC and FEC parameters for SADP process, the gap space range of 0.6 nm and the core space range of 0.5 nm were successfully obtained.

As technology progress with scaling to meet the market requirements, the patterning characterization of dense features suffers a significant challenge for current optic tools, and measurement accuracy will be an important index and great challenge as well. Patterning can mostly be characterized with index of overlay (OVL) and CDU (critical dimension uniformity) measurement. When you break down the budget of the overlay error, one of the challenges is a gap of measurement results between scribe and device, where provides improper information to be used in overlay correction and causes process anomaly (excursion) detection, resulting in a low yield at the end of the production process. An eBeam tool, using high electron landing energies while utilizing the ElluminatorTM technology[1] for improvement backscattered electrons (BSE) imaging efficiency, can be utilized to directly capture OVL performance of device unit in-die, including local and global level, due to BSE function of eBeam tool[2]. In this paper, we demonstrate overlay measurement of M0 to Poly line in device for advanced logic node (only OVL X measurement), obtaining Overlay gap between in-die and scribe line to capture the actual behavior of device unit in-die. Massive OVL data is measured using eBeam tool with fast speed and high resolution, and local OVL results have been analyzed in detail. We’ve quantified what is the impact of overlay correction by different measurement ways whether it depends on optical tool or eBeam tool and benefits yield improvement.

Recently, a careful canonical quantisation of the theory of closed bosonic tensionless strings has resulted in the discovery of three separate vacua and hence three different quantum theories that emerge from this single classical tensionless theory. In this note, we perform lightcone quantisation with the aim of determination of the critical dimension of these three inequivalent quantum theories. The satisfying conclusion of a rather long and tedious calculation is that one of vacua does not lead to any constraint on the number of dimensions, while the other two give $D=26$. This implies that all three quantum tensionless theories can be thought of as consistent sub-sectors of quantum tensile bosonic closed string theory., Comment: 21 pages (+ 30 pages in appendices)

Conserved surface roughening represents a special case of interface dynamics where the total height of the interface is conserved. Recently, it was suggested [Caballero et al., Phys. Rev. Lett. 121, 020601 (2018)] that the original continuum model known as the Conserved Kardar-Parisi-Zhang (CKPZ) equation is incomplete, as additional nonlinearity is not forbidden by any symmetry in $dg1$. In this work, we perform detailed field-theoretic renormalization group (RG) analysis of a general stochastic model describing conserved surface roughening. Systematic power counting reveals additional marginal interaction at the upper critical dimension, which appears also in the context of molecular beam epitaxy. Depending on the origin of the surface particle's mobility, the resulting model shows two different scaling regimes. If the particles move mainly due to the gravity, the leading dispersion law is $\ensuremath{\omega}\ensuremath{\sim}{k}^{2}$, and the mean-field approximation describing a flat interface is exact in any spatial dimension. On the other hand, if the particles move mainly due to the surface curvature, the interface becomes rough with the mean-field dispersion law $\ensuremath{\omega}\ensuremath{\sim}{k}^{4}$, and the corrections to scaling exponents must be taken into account. We show that the latter model consist of two subclasses of models that are decoupled in all orders of perturbation theory. Moreover, our RG analysis of the general model reveals that the universal scaling is described by a rougher interface than the CKPZ universality class. The universal exponents are derived within the one-loop approximation in both fixed $d$ and $\ensuremath{\varepsilon}$-expansion schemes, and their relation is discussed. We point out all important details behind these two schemes, which are often overlooked in the literature, and their misinterpretation might lead to inconsistent results.

A microplasma is defined as a plasma (i.e., a mixture of ions and electrons) with one critical dimension (e.g., depth, or length, or radius) in the mm or the sub-mm (m) range. Over the years, we designed and fabricated a variety of microplasmas using technologies ranging from those borrowed from semiconductor fabrication on crystalline-Silicon substrates to 3D printing on polymeric substrates. In this presentation, the determination of excitation temperatures (Texc) is described. Determination of Texc is important because it is affecting detection limits and is described here.

The resolution concept of k1 is introduced along with various methods to reduce the k1 through resolution enhancement techniques. The edge placement error (EPE) of a 5nm node SRAM is analyzed in detail for aligning a via 0 (V0) layer to the metal 0 (M0) layer. These layers are optimized with source mask optimization (SMO), and the EPE is minimized from stochastics, global critical dimension uniformity (CDU), overlay, optical proximity correction (OPC) error, and scanner matching error. The largest source of error in EPE is from stochastic EPE (SEPE) in which 5nm of maximum EPE is produced. Since SEPE is difficult to reduce, more emphasis needs to be placed on reducing the overlay EPE in order to reduce the total EPE.

With reduction in the die sizes it is very critical to control the Critical Dimension (CD) within a very precise window. In this work we present a root cause analysis and solution to a bimodal CD distribution seen from the center of the wafer. The CD bimodality displays a sharp cliff at the center of the wafer, wherein one side of the wafer has the higher CD and the other side has lower CD with respect to the target value. The bimodality was also seen in the center column of the wafer.

In this paper, we discuss two general models of random simplicial complexes which we call the lower and the upper models. We show that these models are dual to each other with respect to combinatorial Alexander duality. The behavior of the Betti numbers in the lower model is characterized by the notion of critical dimension, which was introduced by Costa and Farber in [Large random simplicial complexes III: The critical dimension, J. Knot Theory Ramifications 26 (2017) 1740010]: random simplicial complexes in the lower model are homologically approximated by a wedge of spheres of dimension equal the critical dimension. In this paper, we study the Betti numbers in the upper model and introduce new notions of critical dimension and spread. We prove that (under certain conditions) an upper random simplicial complex is homologically approximated by a wedge of spheres of the critical dimension.

In III–V IC processing, lift-off patterning is universally used. Historically used negative resist has its limitations; hence the image reverse process using positive tone resist has been utilized as the main work horse in lift-off applications. Metal lift-off processes using a specially designed chemically amplified (CAMP) negative tone resist have been evaluated for thin and thick metal layers to have a varying degree of success. Lift-off using CAMP photoresists has made it possible to reduce cycle time (~57% reduction in $1\times$ theoretical cycle time per layer) and reduce cost (due to elimination of steps) as compared to the image reverse process. However, achieving consistent lift-off and critical dimension (CD) control presents challenges, which are discussed in this paper.

The temperature uniformity of heater plates (HPs) should be sustained due to critical dimension uniformity and robust operation in high temperature processing of 300 mm wafers. It is very challenging to maintain the temperature uniformity of the HP despite the dynamic control of power inputs and temperatures. The packaged power terminals (PPTs) of the HPs may considerably affect their thermal reliability. Hence, the sophisticated thermal modellings and designs of the HPs and the PPTs are necessary. In this study, the finite element analysis (FEA) thermal models of the HP and the PPT were generated, experimentally validated, and employed for the analysis and the design. The influences of the heating element width, the heating element gap, and the zone gap on the thermal performance of the HP were investigated. The parametric influences of the substrate thickness on the thermal performance of the PPT were also explored. The results show that the effect of the heating element width on the temperature of the HP is almost negligible. The results have found that a sophisticated design of the heating elements may reduce the radial temperature difference of the HP by 56 % compared with the baseline case. The results suggest that the sophisticated design may enable both the simplified structure and the enhanced temperature uniformity of the HP.

We establish uniform a-priori bounds for solutions of the quasilinear problems$$\begin{array}{} \displaystyle \begin{cases} -{\it\Delta}_Nu=f(u)\quad&\mbox{in }{\it\Omega},\\ u=0\quad&\mbox{on }{\partial{\it\Omega}}, \end{cases} \end{array}$$whereΩ⊂ ℝNis a bounded smooth convex domain andfis positive, superlinear and subcritical in the sense of the Trudinger-Moser inequality. The typical growth offis thus exponential. Finally, a generalisation of the result for nonhomogeneous nonlinearities is given. Using a blow-up approach, this paper completes the results in [1, 2], extending the class of nonlinearities for which the uniform a-priori bound applies.

In-line metrology for measuring 3D features of the high aspect ratio (HAR) holes is becoming more challenging due to the progressing semiconductor technology, particularly in memory devices. Measurements of the bottom critical dimension (CD), taper angles and 3D profiles of the HAR holes require new imaging capabilities. In this work, we explored the characteristics of high-energy backscattered electron (BSE) signals and demonstrated their promising application to 3D metrology. From Monte Carlo simulation results, it is worth noting that BSE signal intensity emitted from an irradiated location in the depth of the hole decreases exponentially with the increase of the depth from the top surface (perpendicular depth) of the hole. Furthermore, the influences of various factors including the electron energy, the depth and the sidewall angle (SWA) of the hole on the attenuation of the BSE signal intensity were investigated. The simulation results show that the attenuation of the BSE signal intensity depends on the electron energy, the depth and the density of the hole but is independent of the SWA and the incident angle of the primary electron beam. Based on the characteristics of the BSE signal intensity, an algorithm was proposed for the 3D metrology of the HAR holes. Finally, the differences in CDs between the measured value and the target value of HAR holes with various geometries were examined. A maximum measurement bias within ±2.0 nm for various holes with different depths, densities and SWA values shows great potential of depth-correlated BSE signals in 3D metrology.

Ultrathin gold nanowires (AuUNWs) and nanorods (AuUNRs) with diameters smaller than the critical dimension for quantization (∼2 nm), are a new class of anisotropic nanostructures. Due to their uniq...

The purpose of the work consists in the critical dimension definition of a germ and the finite quantity of a titanium carbide crystalline phase during the realization of a self-propagating high temperature synthesis in aluminum melt. For investigations there were used the following components: A7 technical aluminum (cleanness 99.7%), TPP-7 titanium powder (cleanness 97.9%), P-701 technical carbon (cleanness 99.7%), PMC-1 copper powder (cleanness 99.5%), Mn-95 manganese powder (cleanness 95%), halide salt Na2TiF6 (mass share of basic matter not less than 99.0%). A metallographic analysis was carried out with the aid of Jeol JSM-6390A raster electronic microscope. X-Ray spectrum shooting was carried out with the aid of ARL X’tr A diffractometer and with the use of Cu-radiation during continuous scanning in the range of 20 from 20 to 80 degrees at the rate of 2 degrees per minute. By results of theoretical computations of the microstructures and diffractograms analysis of the obtained samples of the composite alloy of (Al-5%Cu-2%Mn) – 10%TiC system there was revealed that: 1) germ critical dimension of the titanium carbide phase in aluminum melt was about 2 nm; 2) according to the exponential dependence of the rate of titanium carbide crystalline growth upon a temperature, at the melt temperature of 1173 K its dimension must be 50 nm; 3) calculation of particles of the titanium carbide phase according to diffractograms data with use of Sekyakov-Sherrer formula confirms their nano-dimensional level; 4) presence of the titanium carbide phase both in nano-dispersed state, and in nano-structural one results in composite stress-strain characteristics increase.

Al-xMg-0.3Sc (x = 0, 3%, 5%) alloys with different Mg contents were designed to study the effect of Mg on the precipitation characteristics and morphological transitions of Al3Sc precipitates. All the alloys were annealed at 450 °C for 2–1000 h, and Al3Sc precipitates were observed by transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM). The results show that the addition of Mg has various effects on the precipitation behavior of Al3Sc precipitates. Notably, Mg addition increases the critical dimension for the loss of coherency and retards the morphological evolution from spherical to cuboidal. These findings provide a new reference for studies of Al3Sc precipitates and the precipitation behavior of Al3Sc based on changing the matrix composition.

We study a random walk diffusion model under the restricted solid-on-solid (RSOS) condition in d = 3 + 1 and d = 4 + 1 dimensions. A dropped particle is allowed to take a random walk until satisfying the RSOS condition. The surface width W increases as tβ in early time with β = 0.081 ± 0.006 and becomes saturated at Lα with α = 0.29 ± 0.03 in d = 3 + 1. In d = 4 + 1, W (t) grows as 2b ln t at the beginning and becomes saturated at 2a ln L. The dynamic exponent z ≈ 3.79 is obtained from the relation $$z = {a \over b}$$ . This value is slightly less than, but consistent with, the value obtained from the related Langevin equation. Our results imply that the upper critical dimension of the model is d =4+1.

Although the effect of specimen size on strength has been well documented for metal micro-samples significantly larger than ~1 μm, less is known about the deformation induced dislocation structure, especially just above the size at which dislocation starvation happens. Here, uniaxial compression tests were performed on cylindrical [011] oriented copper micropillars with diameters of 1 μm, 3 μm and 5 μm. Dislocation cells formed in a fractal geometry in the 3 μm and 5 μm pillars, while dislocations were not retained in the 1 μm pillars. The effects of strain and strain rate on cell formation were also investigated.

Extensive Monte Carlo simulations are carried out in one, two and three dimensions for dynamic local load-sharing fiber bundle models following a power-law breaking rule with exponent ρ . This exponent controls the degree of disorder of the bundle. The results are obtained using two methods of introducing disorder in the simulations. In the standard, or classical, Monte Carlo method the disorder is quenched; in the second, or radioactive method the disorder is annealed. Both methods give identical mean time-to-failure values for systems of the same size. However, the radioactive method proves to be more efficient due to the smaller standard deviation of the probability distribution function of the time-to-failure. We take advantage of this efficiency to compute the asymptotic mean time-to-failure of large systems as a function of the degree of disorder, as parameterized by ρ . Based on these extensive simulations, conclusions are drawn regarding the upper critical dimension of time-dependent local load-sharing fiber bundle models.

We consider the leading order perturbative renormalization of the multicritical $\phi^{2n}$ models and some generalizations in curved space. We pay particular attention to the nonminimal interaction with the scalar curvature $\frac{1}{2}\xi \phi^2 R$ and discuss the emergence of the conformal value of the coupling $\xi$ as the renormalization group fixed point of its beta function at and below the upper critical dimension as a function of $n$. We also examine our results in relation with Kawai and Ninomiya's formulation of two dimensional gravity., Comment: 13 pages, 3 figures; v3: matches the published version

This paper deals with positive solutions of the fully parabolic system { u t = Δ u − χ ∇ ⋅ ( u ∇ v ) in Ω × ( 0 , ∞ ) , τ 1 v t = Δ v − v + w in Ω × ( 0 , ∞ ) , τ 2 w t = Δ w − w + u in Ω × ( 0 , ∞ ) under mixed boundary conditions (no-flux and Dirichlet conditions) in a smooth bounded convex domain Ω ⊂ R 4 with positive parameters τ 1 , τ 2 , χ > 0 and nonnegative smooth initial data ( u 0 , v 0 , w 0 ) . Global existence and boundedness of solutions were shown if ‖ u 0 ‖ L 1 ( Ω ) ( 8 π ) 2 / χ in Fujie–Senba (2017). In the present paper, it is shown that there exist blowup solutions satisfying ‖ u 0 ‖ L 1 ( Ω ) > ( 8 π ) 2 / χ . This result suggests that the system can be regard as a generalization of the Keller–Segel system, which has 8 π / χ -dichotomy. The key ingredients are a Lyapunov functional and quantization properties of stationary solutions of the system in R 4 .

The mechanical properties of cells, which influence the properties of the tissue they belong to, are controlled by various mechanisms. Bi et al. theoretically demonstrated that density-independent rigidity transition occurs in two-dimensional confluent tissues that consist of mechanically uniform cells. They also analyzed the dynamical behavior of tissues near the critical point, which is geometrically controlled by `shape parameter'. To investigate whether the behavior of three-dimensional tissues is similar to that of two-dimensional ones, we extend the model proposed by Bi et al. to a three-dimensional one both dynamically and statically. The model reveals that the two mechanical states exist with a phase transition and has some similarities with those of glassy materials. Scaling analysis is applied to the static model focused in the rearrangement viewpoint. The results suggest that the upper critical dimension is also the same as the jamming transition., Comment: 7 pages, 10 figures

Betten and Riesinger have shown that Clifford parallelism on real projective space is the only topological parallelism that is left invariant by a group of dimension at least 5. We improve the bound to 4. Examples of different parallelisms admitting a group of dimension [math] are known, so 3 is the “critical dimension”.

The trend to produce semiconductor devices having more complex nanostructures results in the increasing importance of exquisite systems measuring multiple Critical Dimensions (CDs) of nanostructures. However, from a practical point of view, it is difficult to apply conventional methodologies to mass production because of cost and complexity issues. In this study, we propose an application of machine learning techniques utilizing optical information to measure nanoscale profiles of channel holes in High-Aspect-Ratio (HAR) structure of vertical NAND flash, which is applicable to mass production. By combining the conventional methodologies, the proposed method yields data pairs for supervised learning which include optical spectra obtained with Rotating Polarizer Ellipsometer (RPE) and images obtained with Scanning Electron Microscopy (SEM). Several preprocessing steps and machine learning techniques are introduced to train a model with sufficient performance to be applicable to mass production. In experiments, we obtained a model with coefficient of determination (R2) of 0.8 and Root Mean Square Error (RMSE) of 1.3 nm when predicting hundreds of nanoscale profiles of the channel holes which are measured with SEM. Furthermore, we confirmed that only 500 samples of data are sufficient to achieve the model performance with R2 greater than 0.7 and RMSE less than 1.5 nm. The proposed method is capable of replacing the conventional methods of profile measurement in the mass production stage by reducing the cost of destructive methods and accurately measuring the profiles of complex nanostructures without theoretical modeling.

In light microscopy, optical aberrations always affect the performance of the employed microscope. They can emerge from imperfect optical components of the microscope, like lenses, or from misalignments of such optical components, which may even change over time. In our contribution, we retrieve the optical aberrations in form of Zernike polynomials from measurements of small point structures by applying the extended Nijboer-Zernike approach. Subsequently, we include the expression for these optical aberrations in rigorous simulations of the microscope’s imaging process. Finally, we will compare the simulations with measurements to demonstrate optical bidirectional measurements on aberrant imaging systems.

Extreme ultraviolet lithography (EUVL) has been adopted into high volume production for advanced logic device manufacturing. Due to the continuous size scaling requirement for interconnect fabrication, EUVL with self-aligned double patterning (SADP) formation has attracted substantial research attention. The current challenge in EUV SADP is the pattern transfer process from lithography to mandrel formation. In this step, the target critical dimension (CD) of the feature needs to shrink by half from the lithography CD during the etch process. The increasing aspect ratio during this etch potentially deteriorates the pattern validity and the line edge roughness (LER). In addition to these challenges, EUVL has a fundamental bottleneck due to stochastic effects, which can lead to device degradation by defect formation and edge placement error (EPE). LER of the line and space pattern is one of the main contributors to EPE. Effective methods of LER reduction in both process and integration are needed in order to reduce pattern variation and boost device performance. In our study, we examine a technique to reduce LER on the EUV SADP line pattern. This technique involves the surface modification on the spin-on carbon (SOC) layer in the patterning stack and tone inversion process. We had found a trend between surface hydrophobicity of the SOC and the EUV SADP LER performance. The condition that increased the hydrophobicity of the SOC resulted in a lower LER performance after tone inversion. The tested conditions include direct current superposition (DCS) function with H2 plasma, fluorocarbon plasma, and the combination of DCS with H2 plasma and trimethylsilane dimethylamine deposition. On 20-nm pitch EUV SADP, this technique shows 26% of LER improvement from lithography to SADP formation. PSD analysis recorded about 6% and 30% of the LER improvement at the correlation length of >200 nm and 200 to 30 nm, respectively. A demonstration of this technique for a further scaling to 15-nm pitch also shows an LER reduction of 30% from lithography to SADP formation.

The fan out panel level package (FOPLP) has been getting significant attention due to its merit of high I/O density by utilizing fan out area, higher productivity thereby low cost by large form factor, and high-degree heterogeneous integration capability. FOPLP was first adapted in a wearable device and is trying to extend its area such as application processor for smartphone, interposer, chip-lets, and so on. For the chip-lets and interposer of high-end substrate, fine pitch redistribution layer (RDL) is of primary importance. In this paper, capabilities of fine pitch RDL in chip first platform and chip last platform were investigated and compared in point of unit topology, depth of focus margin during exposure process, and perspective of mass production. Under the same conditions of photoresist and photolithographic equipment, the surface flatness of chip last platform was 25 percent of that of chip first platform, which gives wide depth of focus margin even at exposure device with numerical aperture of 0.1∼0.16. For the chip last process, the yield and critical dimension of RDL after seed metal etching was measured for the checking homogeneity of RDL over an entire panel. The chip last product is more advantageous than the chip first products for demonstrating fine pitch RDL. The chip last platform with low numerical aperture of 0.1 has a wide range of focus margin and as a result, fine pitch RDL of 3/3 microns is expected to have mass-production capability.

The low-n attenuated phase-shift mask can strongly improve extreme ultraviolet imaging performance; it enhances contrast by mask 3D mitigation and a phase-shift effect while simultaneously reducing the required exposure dose. The latter happens because the low-n mask gives optimum contrast at more open mask bias values than its Ta-based counterpart. Here, we experimentally verify the imaging physics of the low-n mask. We show that optimum exposure latitude (EL) with the low-n mask is obtained at more open mask bias values compared to the Ta-based reference mask. This leads to dose reductions exceeding 30% for pitch 38-nm regular contact holes (CHs). Initial local critical dimension uniformity (LCDU) data for hexagonal CHs pitch 38 and 40 nm show 15% LCDU improvement with the low-n mask compared to the Ta-based reference. A 16-nm dense lines show a substantial EL increase and dose reduction with the low-n mask compared to the Ta-based case; this can be even further improved by combining the novel mask absorber with asymmetric illumination. As the low-n masks studied here have absolute reflectivities in the range 8% to 15%, side-lobe printing should be carefully monitored. Initial experimental data for pitch 120-nm CHs and simulations on P32 metal clips, show no signs of side-lobe printing. Careful monitoring of stochastic side-lobe printing for various use cases is recommended.

OCD (Optical Critical Dimension) is a sufficiently accurate and reliable metrology used in semiconductor industry. Understanding how to setup a proper library will not only help to give the measurements that is needed, it will also prevent unnecessary downtime to the wafer fab factory. In this paper, a multiple layer stack, Poly-ONO-Poly, was seen performing according to the usual baseline until there was a downward shift seen on an OCD parameter SWA (Side Wall Angle). We took some readings off the suspected processes, ETCH trim time and tool’s dependency and LITHO’s resist thickness correlation to try to understand more on their effects on SWA. However, there is little correlation seen from them to the effects on SWA. Simulations were then done to show the spectra’s relationship to the changes in the parameters: SWA, CD, HEIGHT. SWA was seen to have the least sensitivity to raw spectra versus CD and HEIGHT. This led to the suspicion that there was some changes in the spectra that caused the change in SWA, and thus leading us off the ETCH and LITHO into diffusion that could have changed the stack during ONO formation. It was thus found that ONO thickness has shifted. Once the thickness was tuned back to its original intent, SWA followed suit to recover to its measured units. This shows us that there’s a need to fully understand the library/spectra involved when using OCD.

When subject to applied strain, fiber networks exhibit nonlinear elastic stiffening. Recent theory and experiments have shown that this phenomenon is controlled by an underlying mechanical phase transition that is critical in nature. Growing simulation evidence points to non-mean-field behavior for this transition and a hyperscaling relation has been proposed to relate the corresponding critical exponents. Here, we report simulations on two distinct network structures in three dimensions. By performing a finite-size scaling analysis, we test hyperscaling and identify various critical exponents. From the apparent validity of hyperscaling, as well as the non-mean-field exponents we observe, our results suggest that the upper critical dimension for the strain-controlled phase transition is above three, in contrast to the jamming transition that represents another athermal, mechanical phase transition.

Extreme ultraviolet lithography (EUVL) has been adopted into high volume production for advanced logic device manufacturing. Due to the continuous size scaling requirement for interconnect fabrication, EUVL with self-aligned double patterning (SADP) formation has attracted substantial research attention [1]–[6]. Double patterning techniques in EUVL achieve pitch halving in the final feature by using the spacer defined approach and self-aligned block (SAB) mitigates the block placement error by leveraging etch selectivities and material filling capability. The current challenge in EUV SADP is the pattern transfer process from lithography to mandrel formation. In this step, the target critical dimension (CD) of the feature needs to shrink by half from the lithography CD during the etch process. The increasing aspect ratio during this etch potentially deteriorates the pattern validity and the line edge roughness (LER) [5]. In addition to these challenges, EUVL has a fundamental bottleneck due to stochastic effects which can lead to device degradation by defect formation and edge-placement-error (EPE) [7]–[10]. LER of the line and space pattern is one of the main contributors to EPE. Effective methods of LER reduction in both process and integration are needed in order to reduce pattern variation and boost device performance. In our research, we examine three approaches to reduce LER on the EUV SADP line pattern. This includes photoresist surface smoothing techniques, patterning layer material study, and tone inversion integration. The photoresist surface smoothing techniques involve a specific plasma process on the EUV chemical amplified resist (CAR) to achieve > 15% of improvement on LER from lithography to post etch performance. The patterning layer material study reveals an optimum patterning stack to minimize etch-induced line wiggling and etch selectivity requirements for LER performance. Finally, a first demonstration of EUV SADP tone inversion process integration is presented as a method to provide additional benefits to LER reduction. A detailed analysis of line performance from each processing step will be examined.

A new type of delocalization induced by coherent harmonic perturbations in one-dimensional Anderson-localized disordered systems is investigated. With only a few $M$ frequencies a normal diffusion is realized, but the transition to localized state always occurs as the perturbation strength is weakened below a critical value. The nature of the transition qualitatively follows the Anderson transition (AT) if the number of degrees of freedom $M+1$ is regarded as the spatial dimension $d$, but the critical dimension is not $d=M+1-2$ of the ordinary AT but $d=3$., Comment: 5 pages, 4 figures

We study the connection between the magnetization profiles of models described by a scalar field with marginal interaction term in a bounded domain and the solutions of the so-called Yamabe problem in the same domain, which amounts to finding a metric having constant curvature. Taking the slab as a reference domain, we first study the magnetization profiles at the upper critical dimensions $d=3$, $4$, $6$ for different (scale invariant) boundary conditions. By studying the saddle-point equations for the magnetization, we find general formulas in terms of Weierstrass elliptic functions, extending exact results known in literature and finding new ones for the case of percolation. The zeros and poles of the Weierstrass elliptic solutions can be put in direct connection with the boundary conditions. We then show that, for any dimension $d$, the magnetization profiles are solution of the corresponding integer Yamabe equation at the same $d$ and with the same boundary conditions. The magnetization profiles in the specific case of the $4$-dimensional Ising model with fixed boundary conditions are compared with Monte Carlo simulations, finding good agreement. These results explicitly confirm at the upper critical dimension recent results presented in [1]., Version published in Physical Review E. 12 pages, 9 figures, 2 tables

Spin-transfer torque magnetic random-access memory (STT-MRAM) is considered as the most promising candidate to replace the complementary metal-oxide-semiconductor (CMOS) based memories that are dominating the market in the last few decades. What makes STT-MRAM superior to other memories is the high read and write speeds, non-volatility, good cycling endurance and near-zero leakage. Moreover, with the perpendicular device topology and the single transistor cell configuration, it becomes a very promising candidate for further device scaling which is essential to increase the memory densities. This paper focuses on the experiments performed using different lithography approaches in order to explore the smallest printable pitches for orthogonal array magnetic tunnel junction (MTJ) pillars, which are the main components of the STT-MRAM. Considering the high impact of the MTJ patterning process on the robustness of the memory device, several post-litho performance parameters such as wafer critical dimension uniformity (WCDU), local critical dimension uniformity (LCDU) and pillar circularity have also been measured and compared.

It is still challenging to have both statistical measurements of CD (critical dimension) in ease-of-use and flexibility of measuring various features in short turnaround, in combination with analytical TEM techniques. DigitalMicrograph (DM) is a very common software and is compatible with all kinds of analytical TEM techniques. However, this software does not provide massive CD measurements for statistical analysis. This statistical analysis becomes more and more important while the complexity of structures increases, and sub-nanometer control becomes necessary in the semiconductor devices. In this paper, we developed a technique to fill in the gap by combining analytical TEM techniques and development of DM scripts. The analytical TEM techniques have been optimized to provide measurements at their highest available accuracies by considering their spatial resolutions and contrast mechanisms. The developed scripts provide an automatic metrology process at a high time efficiency and avoid measurement bias, which exists in the measurements with human eyes. Last but not least, this developed technique has also been applied to PFA (Physical Failure Analysis) such as contact failure due to oxidation of CoSi, which causes higher sheet resistance.