This study delves into the convergence challenges of Inverse Lithography Technology (ILT) in advancing Optical Proximity Correction (OPC). While ILT shows promise, it faces runtime hurdles and intricate stitching issues caused by data inconsistencies at tile boundaries, particularly in complex corrections. Here, we perform a comprehensive and comparative analysis of the run time and data consistency at tile boundaries for four gradient descent-based algorithms: Steepest Descent (SD), Momentum, Adaptive gradient, and Adaptive Moment Estimation (Adam). Our findings reveal that stitching problems arise from insufficient ambient range and convergence issues during ILT optimization. We recommend using an ambient size equal to or larger than the kernel size. Furthermore, we show that robust convergence can mitigate data inconsistency challenges, even with a limited ambient range. Notably, Adam emerges as a powerful solution, offering substantial runtime acceleration, often ten to hundreds of times faster than SD. Renowned for its prowess in optimizing complex models and GPU-accelerated parallel processing, Adam is a key strategy for expediting computational lithography in semiconductor manufacturing, paving the way for future advancements in ILT.
KEYWORDS: Education and training, Data modeling, Performance modeling, Denoising, Signal to noise ratio, Scanning electron microscopy, Manufacturing, Critical dimension metrology
Semiconductor manufacturing relies on Critical Dimension Scanning Electron Microscopy (CD-SEM) for precision in resist pattern measurements. High-resolution CD-SEM images, while desirable, can damage the resist due to increased electron beam exposure with higher frame numbers. To address this, Noise2Noise, a deep-learning noise reduction method, is introduced. Noise2Noise employs multiple noise images for unsupervised noise reduction. However, it struggles with unknown samples and limited training data. This research enhances the Noise2Noise model by introducing Attention and Residual-Recurrent structures to extract high-precision images from low-resolution inputs (1 frame). The Attention-boosted Noise2Noise model in particular exhibits superior accuracy with improved Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) for unseen patterns. Overall, the modeling error characterized by (ΔCD/CD) has been reduced compared to the conventional Noise2Noise method, promising improved CD-SEM accuracy for advanced CMOS manufacturing.
This work presents a disordered metadiffuser that can achieve a uniform angular scattering distribution with a numerical aperture (NA) of 0.85 at a working wavelength of λ=532 nm, as demonstrated through simulations using the Gerchberg- Saxton algorithm. Additionally, we demonstrate the capability of the metadiffuser to achieve near diffraction-limit high NA focusing (NA>0.8) through the use of a spatial light modulator and the optical phase conjugation method for wavefront shaping. Finally, we propose a deep ultraviolet (DUV) model-based optical proximity correction (OPC) system that uses optical and photoresist simulations via Hopkins’s partially coherent image formation and fully convolutional networks (FCN). This system enables larger-area device fabrication with DUV lithography while maintaining precise critical dimension (CD) of meta atoms. The proposed OPC system achieves a lithography accuracy with an average ΔCD/CD of 0.235%. These results offer promising implications for the practical application of metadiffusers and the DUV lithography technique in the field of optical devices.
Dielectric metalenses realized by economic photolithography technology are vital to their mass deployment in optoelectronic applications. However, pattern fidelity has become a serious issue that degrades the device performance due to optical proximity effects. Here, we demonstrate an intelligent reticle modification system which modifies the sizes and shapes of designed patterns based on a neural-network U-net lithographic model to produce nanostructures with desired dimensions. We demonstrate 2 mm-diameter visible metalenses with diffraction-limited focusing using DUV KrF 248 nm photolithography. This work bridges between the semiconductor process and lens-making industries to realize high-volume manufacturing of versatile metalens and metasurface products.
The optical proximity correction using machine learning has been a promising alternative to physical three-dimensional Maxwell solvers in recent years. The benefits are mainly reduced CPU runtime and the incorporation of the resist and etching phenomena that lack proper physical models. The network architecture has been a key to the accuracy of the machine learning model. The appropriate architecture should grasp the physics and essential features in mask-resist mapping so that the test set prediction is improved. In addition, the architecture also affects the training process where the fine mask feature should be fitted and reflected in the corresponding resist patterns. In this work, we use a modified Unet with attention (Ozan Oktay et al. MIDL 2018) to construct a machine-learning model for OPC. The modification is on the attention layers inserted to the place where the up-sampling and cropped skip connection are combined. Instead of solely using concatenation to combine the up-sampled and skip-connected data flow, self-attention mechanism is shown to be effective in increasing the prediction accuracy. The mask-to-resist pattern, the image-to-image dataset, is from the Canon FPA
Reticle modification involving model-based optical proximity correction (MB-OPC) has driven generations of advanced CMOS nodes for more than two decades and may soon be carried over by inverse lithography technology (ILT). However, the demand for computational resources for ILT reticles cannot be addressed easily but only through massive parallel computation to this date. The development of quantum computing, in particular, quantum annealing algorism (QAA) is aimed to solve optimization problems in the real world, provided that the tasks can be framed into a binary quadratic model (BQM). Moreover, QAA is potentially capable of finding the global minimum solution of an optimization problem, instead of the local minimum provided by many gradient-based approaches. As the current ILT reticles have been largely generated using gradient-based algorithms, it is of great interest to investigate the applicability of QAA for reticle optimizations. We recast the mask optimization problem into a quadratic unconstrained binary optimization (QUBO) problem by defining the Hamiltonian as the difference between the target absolute amplitude image to that of an optimized mask. The approximation is valid due to the dominated first kernel in the sum of the coherent system (SOCS) approach for the aerial image calculation. The simulations are carried out in D-wave Advantage 6 system accessed through Amazon Bracket. Due to the limited number of qubits, we restrict the reticle optimization problems to N= 25, 36, 49, and 64 variables which map to a maximal 5760 physical qubits thru Pegasus embedding. In QAA, we investigate the effects of annealing time and inter-sample correlation, as well as the pausing strategies in the annealing schedule on the probability of finding the best solution to the target mask. We also compare the problem solved by QAA followed by the classical steepest descent (SD) algorithm versus the SD algorithm only. The hybrid QAA/SD approach produces the highest probability of finding the target mask with approximately two-thirds run time reduction from the SD solver only, suggesting that QAA indeed has the potential in finding the global-minimal solution.
In this study, we propose a deep-learning approach to establish the lithographic model for i-line photolithography and develop an optical proximity correction (OPC) algorithm to increase the resolution limit. The applications of RETs are not only on CMOS semiconductor, but also on some metasurface which used to patterning by electron beam lithography. With the OPC algorithm, we are able to manufacture a near-infrared metalens patterning by i-line photolithography in a more efficient and less expensive way.
In detailed balance model, the efficiency of single-junction solar cells can be potentially as high as 33.5% under AM 1.5G illumination. However the best state-of-the-art devices are still far lower than those figures, even the electronic quality is nearly perfect. Therefore the efficiency gap should stem from the light management inside solar cells. Recently, external radiation efficiency (ηext) derived from detailed balance model is emphasized to evaluate light management and photon recycling, which aggregates the loss of backward emission into substrate and non-radiative recombination. This factor can be highly relevant to the cell’s performance, especially open-circuit voltage (Voc), and maximizing Voc is generally considered as the last mile to approach ultra-high efficiency limit. In this work, we try to quantify the Voc enhancement in GaAs solar cells by enhancing light extraction. The simulation tools are RCWA simulation and photon recycling model NREL developed recently. The top structures we simulate here are TiO2 cones arranged in three PC/QPC lattices. After our calculation, the QPC 12-folds symmetry can make the biggest Voc enhancement 11.21meV compared with bare one, and the structure also possess extraordinary omni-directional anti-reflection ability for maintaining high Jsc. Our results also show that using this way to enhance Voc is especially suitable for cells with ordinary material quality. Therefore, the requests of ideal top structures for solar cells’ use are not only near-perfect anti-reflection, but the ability to maximize light extraction if no feature of angular filter exists.
In recent year, InGaN-based alloy was also considered for photovoltaic devices owing to the distinctive material properties which are benefit photovoltaic performance. However, the Indium tin oxide (ITO) layer on top, which plays a role of transparent conductive oxide (TCO), can absorb UV photons without generating photocurrent. Also, the thin absorber layer in the device, which is consequent result after compromising with limited crystal quality, has caused insufficient light absorption. In this report, we propose an approach for solving these problems. A hybrid design of InGaN/GaN multiple quantum wells (MQWs) solar cells combined with colloidal CdS quantum dots (QDs) and back side distributed Bragg reflectors (DBRs) has been demonstrated. CdS QDs provide down-conversion effect at UV regime to avoid absorption of ITO. Moreover, CdS QDs also exhibit anti-reflective feature. DBRs at the back side have effectively reflected the light back into the absorber layer. CdS QDs enhance the external quantum efficiency (EQE) for light with wavelength shorter than 400 nm, while DBRs provide a broad band enhancement in EQE, especially within the region of 400 nm ~ 430 nm in wavelength. CdS QDs effectively achieved a power conversion efficiency enhancement as high as 7.2% compared to the device without assistance of CdS QDs. With the participation of DBRs, the power conversion efficiency enhancement has been further boosted to 14%. We believe that the hybrid design of InGaN/GaN MQWs solar cells with QDs and DBRs can be a method for high efficiency InGaN/GaN MQWs solar cells.
Triple-junction solar cells offer extremely high power conversion efficiency with minimal semiconductor material usage, and hence are promising for large-scale electricity generation. To fully exploit the broad absorption range, antireflective schemes based on biomimetic nanostructures become very appealing due to sub-wavelength scale features that can collectively function as a graded refractive index (GRIN) medium to photons. The structures are generally fabricated with a single-type dielectric material which guarantees both optical design robustness and mechanical durability under concentrated illumination. However, surface recombination and current matching issues arising from patterning still challenge the realization of biomimetic nanostructures on a few micrometer thick epitaxial layers for MJSCs. In this presentation, bio-inspired antireflective structures based on silicon nitride (SiNx) and titanium dioxide (TiO2) materials are demonstrated on monolithically grown Ga0.5In0.5P/In0.01Ga0.99As/Ge triple-junction solar cells. The nano-fabrication employs scalable polystyrene nanosphere lithography, followed by inductively-coupled-plasma reactive-ion-etching (ICP-RIE). We show that the fabricated devices exhibit omni-directional enhancement of photocurrent and power conversion efficiency, offering a viable solution to concentrated illumination with large angles of incidence. Moreover, a comprehensive design scheme is also presented to tailor the reflectance spectrum of sub-wavelength structures for maximum photocurrent output of tandem cells.
We demonstrate the GaAs solar cells which utilize the high-transmittance textured polydimethylsiloxane (PDMS) film can outstanding increase the short circuit current density and power conversion efficiency of solar cells. The transmittance of PDMS film is exceeded 90%, which can pass through almost all the light of GaAs Solar cells can be absorbed. We used a special imprint technology to let the PDMS film possess a highly textured surface. Then we measured the characteristics of textured PDMS film and found out that it has a very excellent Haze performance. The effect of flexible textured PDMS film on the suppression of surface reflection in GaAs solar cells is also investigated. The presented technology provides an inexpensive surface anti-reflection process, which can potentially replace typically complex anti-reflection coating (ARC) layer. The GaAs solar cells with textured PDMS layer can effectively enhance the short-circuit current density from 22.91 to 26.54 mA/cm2 and the power conversion efficiency from 18.28 to 21.43 %, corresponding to a 17 % enhancement compared to the one without textured PDMS. The open-circuit voltage (Voc) and the fill-factor (FF) of GaAs solar cells exhibit negligible change, because the textured PDMS film was pasted up on the surface of GaAs solar cells and did not interfere with the diode operation. At the same time, we observed through the EQE measurement that the textured PDMS film not only proved wonderful light scattering effect but also generated more electron-hole pairs in all absorption spectrum range. Finally, through this simple PDMS process, we believe this technology shall be a great candidate for next generation of highly efficient and low-cost photovoltaic devices.
Source optimization (SO) becomes increasingly important to resolution enhancement in sub-32 nm lithography
nodes because the dense pattern configurations significantly limit the capability of mask correction. A key step in SO is
the image formation by Abbe's method, which is a linear operation of integrating all source points' images incoherently
to form aerial images. However, the aerial images are usually converted to resist images through the nonlinear sigmoid
function. Such operation loses the merit of linearity in optimization and leads to slow convergence and time-consuming
calculation. In this paper we propose a threshold-based linear resist model to replace the sigmoid model in SO. The
effectiveness of our proposed model can be clearly seen from mathematical analysis. We also compare results based on
linear and sigmoid models. Highly similar optimal sources are obtained, but the linear model has a significant advantage
over the sigmoid in terms of convergence rate and simulation time. Furthermore, the process variations characterized by
exposure-defocus (E-D) windows are still in similar trends for optimal sources based on two different resist models.
Improvement of efficiency for crystalline silicon (c-Si) with nanopillar arrays (NPAs) solar cell was demonstrated by
deployment of CdS quantum dots (QDs). The NPAs was fabricated by colloidal lithography of self-assembled
polystyrene (PS) nanospheres with a 600 nm in size and reactive-ion etching techniques, and then a colloidal CdS QDs
with a concentration of 5 mg/mL was spun on the surface of c-Si with NPAs solar cell. Under a simulated one-sun
condition, the device with CdS QDs shows a 33% improvement of power conversion efficiency, compared with the one
without QDs. Additionally, we also found that the device with CdS QDs shows a 32% reduction in electrical resistance,
compared with the one without QDs solar cell, under an ultraviolet (UV) light of 355nm illumination. This reduced
electrical resistance can directly contribute to our fill-factor (FF) enhancement. For further investigation, the excitation
spectrum of photoluminescence (PL), absorbance spectrum, current-voltage (I-V) characteristics, reflectance and
external quantum efficiency (EQE) of the device were measured and analyzed. Based on the spectral response and
optical measurement, we believe that CdS QDs not only have the capability for photon down-conversion in ultraviolet
region, but also provide extra antireflection capability.
KEYWORDS: Scattering, Air contamination, Mie scattering, Light scattering, Thin film solar cells, Thin films, Solar cells, Absorption, Particles, Glasses
Light trapping techniques such as textured interfaces and highly reflective back contacts are important to thin-film solar
cells. Scattering at rough interfaces inside a solar cell leads to enhanced absorption due to an increased optical path
length in the active layers, which is generally characterized by a haze ratio. In this work, we demonstrate the measured
haze characteristics of indium tin oxide nano-whiskers deposited on an ITO-coated glass substrate. A theoretical model
based on a modified Mie theory is also employed to analyze the scattering effects of nano-whiskers. Instead of spherical
model, a cylindrical condition is imposed to better fit the shapes of the whiskers. The calculated haze-ratio of an ITO
whisker layer matches the measurement closely.
The generation of subresolution assist features (SRAFs) using inverse-lithography techniques demands extensive computational resources which limits its deployment in advanced CMOS nodes. In this paper, we propose a wavefront-based pixel inversion algorithm to quickly obtain inverse masks with a high aerial image quality. Further assisted by a flexible pattern simplification technique, we present effective SRAF generation and placement based on the calculated inverse mask. The proposed approach can be easily inserted prior to a conventional mask correction flow for subsequent concurrent optimizations of both drawn patterns and SRAFs. The innovative pixel inversion and pattern simplification techniques allow quality mask corrections as produced by inverse lithography while maintaining the convenience of standardized/validated process flows currently used in the industry.
Inverse lithography which generates model-based patterns theoretically has superior patterning fidelity comparing to
conventional rule-based technique. Cost functions are the determinant of performance inverse lithography that is also an
optimization problem. However, the design and know-how of cost functions have rarely been discussed. In this paper,
we investigate the impacts of various cost functions and their superposition for inverse lithography patterning exploiting
a steepest descent algorithm. We research the most generally used objective functions, which are the resist and aerial
images, and also deliver a derivation for the aerial image contrast. We then discuss the pattern fidelity and final mask
characteristics for simple layouts with a single isolated contact and two nested contacts. Moreover, the convergences
which are expressed by edge-placement error (EPE) and contrast versus iteration numbers rapidly attain to steady sate in
most hybrid cost functions. All in all, we conclude that a cost function composed of a dominant resist-image component
and a minor aerial-image or image-contrast component can carry out a good mask correction and contour targets when
using inverse lithography patterning.
As lithography still pushing toward to low-k1 region, resolution enhancement techniques (RETs) including source
optimization (SO) and mask optimization (MO) are expected to overcome the fundamentally physics in optics. Recently
inverse lithography (IL) is widely studied for source and mask optimization (SMO) to enhance the resolution for over
diffraction limit integrate circuit (IC) patterns. In this paper, we propose a gradient based SMO algorithm where the SO
and MO are two sequential steps due to their different image formation mechanism. Moreover, we employ three cost
functions including aerial and resist image and the image contrast which is proposed in our previous work. We show that
IL patterns produced by SMO have better pattern fidelity and image contrast than MO only patterns.
In this work, we present a solution that employs combined micro- and nano-scale surface textures to increase light
harvesting in the near infrared for crystalline silicon photovoltaics, and discuss the associated antireflection and
scattering mechanisms. The combined surface textures are achieved by uniformly depositing a layer of indium-tin-oxide
nanowhiskers on passivated, micro-grooved silicon solar cells using electron-beam evaporation. The nanowhiskers
facilitate optical transmission in the near-infrared, which is optically equivalent to a stack of two dielectric thin-films
with step- and graded- refractive index profiles. The ITO nanowhiskers provide broadband anti-reflective properties
(R<5%) in the wavelength range of 350-1100nm. In comparison with conventional Si solar cell, the combined surface
texture solar cell shows higher external quantum efficiency (EQE) in the range of 700-1100nm. Moreover, the ITO nano-whisker
coating Si solar cell shows a high total efficiency increase of 1.1% (from 16.08% to17.18%). Furthermore, the
nano-whiskers also provide strong forward scattering for ultraviolet and visible light, favorable in thin-wafer silicon
photovoltaics to increase the optical absorption path.
In this work, we demonstrate a thorough device design, fabrication, characterization, and analysis of biomimetic
antireflective structures implemented on a Ga0.5In0.5P/GaAs/Ge triple-junction solar cell. The sub-wavelength structures
are fabricated on a silicon nitride passivation layer using polystyrene nanosphere lithography followed by anisotropic
etching. The fabricated structures enhance optical transmission in the ultraviolet wavelength range, compared to a
conventional single-layer antireflective coating (ARC). The transmission improvement contributes to the enhanced
photocurrent, which is also verified by the external quantum efficiency characterization of fabricated solar cells. Under
one-sun illumination, the short-circuit current of a cell with a biomimetic structures is enhanced by 24.1% and 2.2% due
to much improved optical transmission and current matching, compared to cells without an ARC and with a conventional
ARC, respectively. Further optimizations of the biomimetic structures including the periodicity and etching depth are
conducted by performing comprehensive calculations based on a rigorous couple-wave analysis method.
Convergence speed and local minimum issue have been the major issues for inverse lithography. In this paper, we
propose an inverse algorithm that employs an iterative gradient-descent method to improve convergence and reduce the
Edge Placement Error (EPE). The algorithm employs a constrained gradient-based optimization to attain the fast
converging speed, while a cross-weighting technique is introduced to overcome the local minimum trapping.
In this paper, we develop an image-gradient-based algorithm to simultaneously optimize various cost
functions for inverse mask design. The algorithm employs an iterative approach which evaluates the gradient
decent of the resist image, aerial image, and the aerial image contrast with a pre-assigned step length. Moreover,
an independent iteration step is inserted among iterations for binary mask conversion. We show that the
proposed algorithm allows fast convergence while achieving high aerial image contrast. The impacts of each
cost function on the pattern fidelity and convergence are also discussed.
We propose an inversion calculation method based on a simple "pixel-flipping" approach. The simple method
features innovative wavefront-expansion and wavefront-based damping techniques in order to obtain accentuated
corrections near the drawn pattern. The method is first employed to be a stand-alone optical proximity correction
solution that directly calculates the corrected masks with acceptable contours and image contrast. In addition, a
model-based pre-OPC flow, where the initial sizing of drawn patterns and surrounding sub-resolution assist features
(SRAF) are simultaneously generated in a single iteration using this inversion calculation is also proposed to minimize
technology-transition risks and costs. A mask simplification technique based on the central moments is introduced in
order to snap the corrections into 45 degree and axis-aligned line segments. This approach allows achieving optimized
corrections while minimizing the impact to the existing and validated correction flow.
The conventional segment-based OPC approach has been applied successfully for many CMOS generations and is
currently favored. However, Inverse lithography technology (ILT) is a promising candidate for next-generation optical
proximity correction (OPC). Still, there are issues that need to be thoroughly addressed and further optimized. In this
work, we propose a model-based pre-OPC flow where the sizing of drawn patterns and placement of surrounding
sub-resolution assist features (SRAF) are simultaneously generated in a single iteration using an ILT method. The
complex patterns can then be simplified for a conventional OPC solution.
A free-standing nanopillar with a diameter of 300 nm, and a height of 2 μm is successfully demonstrated by focused ion
beam milling. The measured micro-photoluminescence (μ-PL) from the embedded InGaN/GaN multiple quantum wells
shows a blue shift of 68 meV in energy with a broadened full-width at half maximum, ~200meV. Calculations based on
the valence force field method suggest that the spatial variation of the strain tensors in the nanopillar results in the
observed energy shift and spectrum broadening. Moreover, the power-dependent µ-PL measurement confirms that the
strain-relaxed emission region of the nanopillar exhibits a higher radiative recombination rate than that of the as-grown
structure, indicating great potential for realizing high-efficiency nano devices in the UV/blue wavelength range.
High efficiency GaN-based light-emitting diodes (LEDs) are demonstrated by a nanoscale epitaxial lateral
overgrowth (NELO) method on a SiO2 nanorod-array patterned sapphire substrate (NAPSS). The SiO2 NAPSS was
fabricated by a self-assembled Ni nano clusters and reactive ion etching. The average diameter and density of the formed
SiO2 nanorod-array was about 100 to 150 nm and 3 x 109 cm-2. The transmission electron microscopy images suggest
that the voids between SiO2 nanorods and the stacking faults introduced during the NELO of GaN can effectively
suppress the threading dislocation density. The output power and external quantum efficiency of the fabricated LED by
NELO method on NAPSS were enhanced by 52% and 56% respectively, compared to those of a conventional LED. The
improvements originated from both the enhanced light extraction assisted by the NAPSS, and the reduced dislocation
densities using the NELO method.
We have made a GaN-based single nanopillar with a diameter of 300nm using the focused ion beam (FIB)
technique. The micro-photoluminescence (μ-PL) from the embedded GaN/InGaN multi-quantum wells reveals
a blue shift of 68.3 meV in energy. In order to explain the spectrum shift, we have developed a valence force
field model to study the strain relaxation mechanism in a single
GaN-based nanopillar structure. The strain
distribution and strain induced polarization effect inside the multiple quantum wells is added to our self-consistent
Poisson, drift-diffusion, and Schrodinger solver to study the spectrum shift of μ-PL.
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