Advanced nanoimprint lithography (NIL) is promising for inorganic semiconductor patterning because it enables high-resolution replication with a relatively simple process flow; however, yield loss increasingly originates from spatially distributed, subcritical distortions accumulated across coating, exposure, etching, and imprinting. In this study, we propose an integrated physics-based and data-driven framework for pre-manufacturing defect-risk prediction in NIL. The framework combines an NDA-safe layout database, a physics-based process twin, and a stochastic risk prediction model using a physics-augmented convolutional neural network with conformal uncertainty calibration. Starting from binary design layouts, the process twin sequentially captures resist thickness variations during spin coating, proximity-induced dose redistribution and development-induced pattern deformation during electron-beam lithography (EBL), density-sensitive pattern transfer during reactive ion etching (RIE), and three-dimensional resist filling during imprinting, thereby generating physically consistent parameter maps for downstream learning. The results demonstrate an end-to-end virtual inspection flow that converts layouts into spatially resolved risk maps before fabrication. In addition, patterns with similar contour extent but different local density exhibit distinctly different risk distributions, indicating that manufacturability is governed not only by nominal geometry but also by local pattern environment. These findings support pre-manufacturing virtual inspection as a physically interpretable route for early yield-risk screening in advanced NIL.

We conducted a theoretical analysis on the diffusiophoretic motion of a dielectric droplet in a cylindrical pore in the presence of an induced diffusion potential, such as that in a NaCl electrolyte solution. The fundamental electrokinetic governing equations are solved using a patched pseudo-spectral method based on Chebyshev polynomials, coupled with a geometric mapping scheme to handle the irregular solution domain. The impact of the boundary confinement effect on droplet mobility is examined in detail. Interesting electrokinetic phenomena are found in this work, such as mobility reversal in narrow cylindrical pores with the droplet moving against the direction expected based on the classical Coulomb electrostatic law due to the strong boundary confinement effect. Moreover, “solidification phenomenon” is also found at some specific pore radius where the droplets move as rigid particles with no interior recirculating vortex flows regardless of the droplet viscosities. Corresponding critical points of Rw*, the ratio of droplet radius to the cylindrical radius are found where the spinning orientation on the droplet surface changes each time as it passes them. The profound boundary confinement effect, both electrostatically and hydrodynamically, is responsible for these peculiar phenomena. The results presented here have direct applications in microfluidic and nanofluidic operations as well as drug delivery applications.

Diffusiophoresis of a liquid metal droplet (LMD) in a cylindrical pore is investigated theoretically in this study. A patched pseudo-spectral method based on Chebyshev polynomials combined with a geometric mapping technique is adopted to solve the resulting governing electrokinetic equations in irregular geometries. Several interesting phenomena are found which provide useful guidelines in practical applications involving liquid metal droplets (LMDs) such as drug delivery. In particular, the severe boundary confinement effect brings about unique features of droplet motion, leading to mobility reversal and a “stagnation phenomenon” where droplets cease to move regardless of their surface charge densities in a narrow cylindrical pore. An overwhelming exterior vortex flow nearly enclosing the entire droplet is found to be responsible for this. This finds various practical applications in droplet microfluidics and drug delivery. For instance, a cylindrical pore or blood vessel may be clogged by a droplet much smaller than its radius. In addition, the “solidification phenomenon”, where all droplets move with identical speed regardless of their viscosities like rigid particles with no interior recirculating vortex flows, is also discovered. The electrokinetic mechanism behind it and its potential applications are discussed. Overall, the geometric configuration considered here is a classic one, with many other possible applications yet to be found by experimental researchers and engineers in the field of colloid industry and operations.

Diffusiophoresis of a weakly charged dielectric droplet in a cylindrical pore is investigated theoretically in this study. The governing fundamental electrokinetic equations are solved with a patched pseudo-spectral method based on Chebyshev polynomials, coupled with a geometric mapping scheme to take care of the irregular solution domain. The impact of the boundary confinement effect upon the droplet motion is explored in detail, which is most profound in narrow channels. We found, among other things, that the droplet moving direction may reverse with varying channel widths. Enhanced motion-inducing double-layer polarization due to the presence of a nearby channel wall is found to be responsible for it. In particular, an interesting and seemingly peculiar phenomenon referred to as the “solidification phenomenon” is observed here at some specific critical droplet sizes or electrolyte strengths in narrow channels, under which all the droplets move at identical speeds regardless of their viscosities. They move like a rigid particle without the surface spinning motions and the induced interior recirculating vortex flows. As the corresponding shear rate is zero at this point, the droplet is resilient to undesirable exterior shear stresses tending to damage the droplet in motion. This provides a helpful guideline in the fabrication of liposomes in drug delivery in terms of the optimal liposome size, as well as in the microfluidic and nanofluidic manipulations of cells, among other potential practical applications. The effects of other parameters of electrokinetic interest are also examined.

Nanoimprint lithography (NIL) has emerged as a promising sub-10 nm patterning at low cost; yet, robust process control remains difficult because of time-consuming physics-based simulators and labeled SEM data scarcity. We propose a data-efficient, two-stage deep-learning framework here that directly reconstructs post-imprint SEM images from binary design layouts and delivers calibrated pixel-by-pixel uncertainty simultaneously. First, a shallow U-Net is trained on conformalized quantile regression (CQR) to output 90% prediction intervals with statistically guaranteed coverage. Moreover, per-level errors on a small calibration dataset are designed to drive an outlier-weighted and encoder-frozen transfer fine-tuning phase that refines only the decoder, with its capacity explicitly focused on regions of spatial uncertainty. On independent test layouts, our proposed fine-tuned model significantly reduces the mean absolute error (MAE) from 0.0365 to 0.0255 and raises the coverage from 0.904 to 0.926, while cutting the labeled data and GPU time by 80% and 72%, respectively. The resultant uncertainty maps highlight spatial regions associated with error hotspots and support defect-aware optical proximity correction (OPC) with fewer guard-band iterations. Extending the current perspective beyond OPC, the innovatively model-agnostic and modular design of the pipeline here allows flexible integration into other critical stages of the semiconductor manufacturing workflow, such as imprinting, etching, and inspection. In these stages, such predictions are critical for achieving higher precision, efficiency, and overall process robustness in semiconductor manufacturing, which is the ultimate motivation of this study.

Nanoimprint lithography (NIL) master fidelity is governed by coupled variations beginning with resist spin-coating, proceeding through electron beam exposure, and culminating in anisotropic etch transfer. We present an integrated, physics-based simulation chain. First, it includes a spin-coating thickness model that combines Emslie–Meyerhofer scaling with a Bornside edge correction. The simulated wafer-scale map at 4000 rpm exhibits the canonical center-rise and edge-bead profile with a 0.190–0.206 μm thickness range, while the locally selected 600 nm × 600 nm tile shows <0.1 nm variation, confirming an effectively uniform region for downstream analysis. Second, it couples an e-beam lithography (EBL) module in which column electrostatics and trajectory-derived spot size feed a hybrid Gaussian–Lorentzian proximity kernel; under typical operating conditions (σtraj ≈ 2–5 nm), the model yields low CD bias (ΔCD = 2.38/2.73 nm), controlled LER (2.18/4.90 nm), and stable NMSE (1.02/1.05) for isolated versus dense patterns. Finally, the exposure result is passed to a level set reactive ion etching (RIE) model with angular anisotropy and aspect ratio-dependent etching (ARDE), which reproduces density-dependent CD shrinkage trends (4.42% versus 7.03%) consistent with transport-limited profiles in narrow features. Collectively, the simulation chain accounts for stage-to-stage propagation—from spin-coating thickness variation and EBL proximity to ARDE-driven etch behavior—while reporting OPC-aligned metrics such as NMSE, ΔCD, and LER. In practice, mask process correction (MPC) is necessary rather than optional: the simulator provides the predictive model, metrology supplies updates, and constrained optimization sets dose, focus, and etch set-points under CD/LER requirements.

Electrophoresis of a weakly charged dielectric droplet with constant surface charge density in a chargeless cylindrical pore is investigated theoretically in this study, focusing on the boundary confinement effect of the double layer, which in turn determines the ultimate motion of the droplet. A patched pseudo-spectral method based on the Chebyshev polynomial is adopted to solve the resulting governing fundamental electrokinetic equations. Mobility reversal, among other interesting phenomena, is observed when the droplet is in a narrow cylindrical pore. No such observation was made in the corresponding motion of a rigid particle. The droplet with a thick double layer may even move against the prediction based on the Coulomb electrostatic law, for instance, a positively charged droplet may move against the electric field. The significant enhancement of the motion-deterring double layer polarization due to the severe steric boundary confinement within a narrow cylindrical pore is found to be responsible for this seemingly peculiar phenomenon. Moreover, smaller droplets may move in the opposite direction of the larger ones. The results are useful in capillary electrophoresis involving droplets in particular and migration of droplets through narrow channels in general.

We focus on detecting defects during hotspot monitoring using scanning electron microscope (SEM) images from the after-development inspection (ADI) phase in semiconductor manufacturing. A primary challenge lies in the significant imbalance between defective and defect-free samples, complicating binary classification. To address this, data augmentation and the synthetic minority over-sampling technique (SMOTE) are applied to generate additional samples for the minority class. A two-stage learning approach is then proposed: first, deep convolutional neural networks are trained on SMOTE-synthesized data to develop a pre-trained defect classification model. Subsequently, this model is fine-tuned with raw, augmented data to enhance its performance on targeted data. Extensive experiments demonstrate that this method improves efficiency, reduces computational costs, and outperforms traditional techniques. The results show that integrating SMOTE-based augmentation with a two-stage learning process mitigates data imbalance and improves defect detection accuracy. This proposed methodology offers a robust solution for automating SEM image inspections during hotspot monitoring, addressing the scalability challenges posed by increasing design complexity and emerging defect types in advanced semiconductor processes.

Electrophoresis of a dielectric fluid droplet with constant surface charge density is investigated theoretically in this study. A pseudo-spectral method based on Chebyshev polynomials is adopted to solve the governing electrokinetic equations. It is found, among other things, that the larger the electrolyte strength in the ambient solution is, the slower the droplet moves in general. This is due to the strong screening effect of the large amount of indifferent counterions in the neighborhood of the droplet, with no reinforcement of potential-determining ions adsorbing to the droplet surface. The droplet comes to a complete halt eventually. Critical points are discovered for highly charged droplets, at which the droplet surface becomes immobile and the interior fluid stops recirculating. The droplet moves like a rigid particle with constant mobility regardless of its viscosity, a situation referred to as the "solidification phenomenon." The deadlock between the spinning motions on the charged droplet surface induced by the electric driving force and the hydrodynamic driving force respectively is responsible for this peculiar phenomenon. This is also observed for a dielectric droplet with constant surface electric potential. We demonstrate here that it occurs in the constant surface charge density situation as well.

Diffusiophoresis of a weakly charged liquid metal droplet (LMD) is investigated theoretically, motivated by its potential application in drug delivery. A general analytical formula valid for weakly charged condition is adopted to explore the droplet phoretic behavior. We determined that a liquid metal droplet, which is a special category of the conducting droplet in general, always moves up along the chemical gradient in sole chemiphoresis, contrary to a dielectric droplet where the droplet tends to move down the chemical gradient most of the time. This suggests a therapeutic nanomedicine such as a gallium LMD is inherently superior to a corresponding dielectric liposome droplet in drug delivery in terms of self-guiding to its desired destination. The droplet moving direction can still be manipulated via the polarity dependence; however, there should be an induced diffusion potential present in the electrolyte solution under consideration, which spontaneously generates an extra electrophoresis component. Moreover, the smaller the conducting liquid metal droplet is, the faster it moves in general, which means a smaller LMD nanomedicine is preferred. These findings demonstrate the superior features of an LMD nanomedicine in drug delivery.

A simple analytical formula is obtained for the diffusiophoresis of a dielectric fluid droplet in symmetric binary electrolyte solutions under Debye-Hückel approximation valid for weakly charged droplets. The chemiphoresis is found to yield negative mobilities most of the time for droplets of constant surface charge density, which implies that the droplets tend to move away from the source releasing ionic chemicals. This is undesirable in some practical applications like drug delivery with liposomes in terms of conveying the drug-carrying liposomes to the desired area in the human body releasing specific ionic chemicals utilizing the self-guiding nature of diffusiophoresis. The further involvement of the electrophoresis component, however, may change the scenario via the oriented electric field generated by the induced diffusion potential. The lesson here is that while the impact of the chemiphoresis component is determined by nature and uncontrollable, the electrophoresis component serves as an artificially adjustable factor via choosing droplets with the surface charge of appropriate sign in practical applications. The results here have potential use in practical applications such as drug delivery. The portable simple analytical formula is a powerful asset to experimental researchers and design engineers in colloid science and technology to facilitate their works.

An analytical formula is presented here for the electrophoresis of a dielectric or perfectly conducting fluid droplet with arbitrary surface potentials suspended in a very dilute electrolyte solution. In other words, when the Debye length (kappa(-1)) is very large, or kappa aMUCH LESS-THAN$\ll $1, where kappa is the electrolyte strength and a stands for the droplet radius. This formula can be regarded as an extension of the famous Huckel solution valid for weakly charged rigid particles to arbitrarily charged fluid droplets. The formula reduces successfully to the ones obtained by Booth for a dielectric droplet, and Ohshima for a perfectly conducting droplet, both under Debye-Huckel approximation valid for weakly charged droplets. Moreover, the formula is valid for a gas bubble and a rigid solid particle as well. Classic results obtained by Huckel for a rigid particle are reproduced as well. We found that for a dielectric droplet, the more viscous the droplet is, the faster it moves regardless of its surface potential, contrary to the intuition based on the purely hydrodynamic consideration. For a perfectly conducting liquid droplet, on the other hand, the situation is reversed: The less viscous the droplet is, the faster it moves. The presence or absence of the spinning electric driving force tangent to the droplet surface is found to be responsible for it. As a result, an axisymmetric exterior vortex flow surrounding the droplet is always present for a dielectric liquid droplet, and never there for a conducting liquid droplet.

Diffusiophoresis of a dielectric fluid droplet in electrolyte solutions is investigated theoretically, focusing on the electrophoresis component resulting from the induced diffusion potential in the electrolyte solution when the diffusivities of cations and anions there are different. The resultant electrokinetic equations are solved with a pseudo-spectral method based on the Chebyshev polynomials. We found, among other things, that the electrophoresis component dominates at a larger Debye length, whereas the chemiphoresis component at a smaller Debye length for a dielectric droplet of a constant surface charge density. The two components are of comparable magnitudes in the NaCl solution. The dual between the spinning electric driving force tangent to the droplet surface and the hydrodynamic drag force reinforced by the motion-deterring electrokinetic Maxwell traction from the surrounding exterior osmosis flow is crucial in the determination of the ultimate droplet motion. Unlike the chemiphoresis component, which is independent of the sign of charges carried by the droplet, the droplet moving direction as well as its magnitude in the electrophoresis component depends on the sign of charges carried by the droplet as well as the direction of the electric field induced by the diffusion potential. This gives the electrophoresis component excellent maneuverability in practical applications like drug delivery and enhanced oil recovery, where migration of droplets toward regions of higher solute concentrations is often desired.

Diffusiophoresis of a perfectly conducting droplet-like liquid metal in electrolyte solutions is investigated theoretically, focusing on the chemiphoresis component, the very heart of diffusiophoresis, where the droplet motion is induced solely by the chemical gradient. The resulting electrokinetic equations are solved with a pseudo-spectral method based on Chebyshev polynomials. For the isothermal electrokinetic system of a perfectly conducting droplet considered here, there is no Marangoni effect, which is a motion-inducing effect due to the variation of interfacial tension along the droplet surface. No Maxwell traction is present as well. The droplet motion is full of hydrodynamic nature. It is found, among other things, that contrary to a dielectric droplet, a conducting droplet always moves up the chemical gradient toward the region with a higher concentration of ions in chemiphoresis. This implies that a perfectly conducting droplet like a gallium or its alloy droplet is superior to the commonly utilized dielectric droplet like a liposome in drug delivery in terms of self-guarding itself toward the desired destination of injured or infected area in the human body, as specific ionic chemicals are often released there. Optimum droplet size yielding the fastest migration rate is predicted.

Diffusiophoresis phenomenon of aoft particles suspended in binary electrolyte solutions is explored theoretically in this study based on the spherical cell model, focusing on the chemiphoresis component in absence of diffusion potential. Both the electrostatic and hydrodynamic aspects of the boundary confinement, or steric effect, due to the presence of neighboring particles are examined extensively under various electrokinetic conditions. Significant local extrema are found in mobility profiles expressed as functions of the Debye length in general, synchronized with the strength of the motion-inducing double layer polarization. Moreover, a seemingly peculiar phenomenon is observed that the soft particles may move faster in more concentrated suspensions. The competition between the simultaneous enhancement of the motion-inducing electric driving force and the motion-retarding hydrodynamic drag force from the boundary confinement effect of the neighboring particles is found to be responsible for it. The above findings are also demonstrated experimentally in a very recent study on the diffusiophoretic motion of soft particles through porous collagen hydrogels. The results presented here are useful in various practical applications of soft particles like drug delivery.

Diffusiophoresis of a dielectric fluid droplet with constant surface charge density in a symmetric binary electrolyte solution is investigated theoretically in this study, focusing on the chemiphoresis component, the very heart of diffusiophoresis. The resultant electrokinetic equations are solved with a pseudo-spectral method based on Chebyshev polynomial in the spirit of a computational fluid dynamic simulation. Reversions of moving directions are found for droplets less viscous than ambient solution when the electrolyte strength is increased due to the buildup of osmosis pressure in front of the moving droplets leading to an osmosis pressure gradient upon the droplet. The upward spouting effect of the spinning droplet surface is also responsible this buildup, which hinders the downward migration of ions and holds them up there. A solid particle may move faster than a gas bubble due to the energy consumption in the formation of an induced exterior vortex flow nearby surrounding the gas bubble. The less viscous the droplet is, the more severe this consumption is. A “solidification” phenomenon is observed where all the droplets move at the same speed with their surfaces and interior fluids motionless like rigid particles. Funnel-shape local extrema of mobility profiles provide solid evidence that the diffusion-induced double layer polarization is the very cause of the droplet motion in chemiphoresis. Excellent agreement with experimental data for a rigid particle is obtained. The study provides insights and guidelines in practical applications like drug delivery and other dead-end-pore types of operations such as EOR.

Diffusiophoresis of a soft particle in electrolyte solutions normal to a conducting solid plane is investigated theoretically in this study, focusing on the highly charged particle in particular. A pseudo-spectral method based on Chebyshev polynomial is adopted to solve the resultant governing electrokinetic equations. It was found, among other things, that the closer the soft particle is to the plane, the faster it moves in general, provided only the chemiphoresis component of the diffusiophoresis is involved, i.e., no diffusion potential is present. The presence of the conducting plane is found to have three effects upon the particle motion nearby: the geometric boundary confinement effect, the electrostatic mirror-image force analog effect, and the hydrodynamic retarding effect. The enhancement of the double layer polarization by the first two effects leads to the seeming intriguing observation mentioned above. The particle always moves away from the plane in chemiphoresis. If a diffusion potential is present, however, then it is possible to drive the particle toward the plane. The results have potential applications in drug delivery.

Diffusiophoresis of a soft particle suspended in an infinite medium of symmetric binary electrolyte solution is investigated theoretically in this study, focusing on the chemiphoresis component when there is no global diffusion potential in the bulk solution. The general governing electrokinetic equations are solved with a pseudo-spectral method based on Chebyshev polynomials, and particle mobility, defined as the particle velocity per unit concentration gradient, is calculated. Parameters of electrokinetic interest are examined, in general, to explore their respective impact upon particle motion, such as the fixed charge density and permeability in the outer porous layer, the surface charge density and size of the inner rigid core, and the electrolyte strength in the solution. Nonlinear phenomena such as the motion-deterring double-layer polarization and the counterion condensation effects are scrutinized, in particular, for highly charged soft particles. Mobility reversal is observed in some range of electrolyte strength for highly charged particles. The generation of an axisymmetric counterclockwise vortex flow across the porous layer is found to be responsible for it. The onset of the mobility reversal is synchronized with the appearance or disappearance of this vortex flow. Mobility reversal may happen more than once, with particle moving toward or away from the region of higher solute concentration. The latter is undesirable in the application of drug delivery and thus should be avoided by delicate control of the electrokinetic environment. A local micro diffusion potential is discovered, which always speeds up the migration of coions and slows down that of counterions to guarantee that there is no net electric current across the double layer. Moreover, multilayer structure of the double-layer polarization is discovered when the electrolyte strength is high. The study presented here provides insight and crucial information for practical applications of soft particles, such as drug delivery.