Search Results (26)

The semiconductor industry has long relied on Statistical Process Control (SPC) for yield and reliability management. In early technology nodes, classic univariate tools such as Shewhart charts, cumulative sums (CUSUM), exponentially weighted moving averages (EWMA), and the Cp/Cpk exponent could effectively monitor a finite set of key variables. However, sub-5nm and emerging 3 nm technologies have fundamentally changed the statistical environment. Advanced patterning, high-aspect-ratio etching, atomic layer deposition (ALD), chemical-mechanical polishing (CMP), and novel materials have drastically narrowed the process window. At these scales, nanometer-level deviations in critical dimensions (CD), overlay, or surface roughness can significantly impact yield. Simultaneously, modern wafer fabs generate massive amounts of high-frequency sensor data and high-dimensional metrology data. Traditional SPC assumptions—such as independence, normality, low dimensionality, and stationarity—often do not hold. Semiconductor data exhibits: (i) extremely high-dimensionality and strong intervariate correlations; (ii) a hierarchical structure encompassing fab → tooling → chamber → recipe → batch → wafer → field; and (iii) metrological delays and sampling limitations leading to incomplete and asynchronous observations. To address these challenges, this paper reviews advanced statistical methods applicable to wafer fabrication. These methods include multivariate statistical process control (MSPC) approaches such as Hotelling T² statistics, PCA/PLS combining T² and Q statistics, contribution diagnostics, time-series drift and change point detection, and Bayesian hierarchical modeling for uncertainty-aware monitoring in data-limited scenarios. Furthermore, we discuss how to integrate these methods with fault detection and classification (FDC), line-to-line monitoring (R2R), advanced process control (APC), and manufacturing execution systems (MES). This paper focuses on scalable, interpretable, and maintainable implementations that transform statistical analysis from a passive monitoring tool into an active component of data-driven fab control. Full article

This study investigates the deposition of silicon nitride (SiN) thin films for advanced semiconductor applications, with a specific focus on overcoming thermal challenges in plasma-enhanced atomic layer deposition (PE-ALD) at an elevated temperature of 550 °C. At such high temperatures, a critical obstacle is wafer warpage induced by thermal and mechanical stress, which increases localized thermal contact resistance and degrades film uniformity. To address this, a wafer chucking function was integrated into a monopolar electrostatic chuck (ESC) heater. The ESC secures the wafer to the heater surface, effectively mitigating warpage and ensuring a uniform temperature distribution. Chucking performance was verified by monitoring lift-up motor torque variations and plasma parameters, such as self-bias voltage (Vdc) and peak-to-peak voltage (Vpp), confirming the formation of stable electrostatic coupling. A comparative analysis was conducted between SiN films deposited with and without a chucking voltage of +1000 V. Statistical evaluation across repeated experimental runs (n = 3) confirmed that ESC chucking significantly enhanced spatial uniformity without altering the fundamental PE-ALD growth mechanism. Notably, the application of ESC chucking suppressed the localized temperature drop at the wafer periphery, reducing the in-wafer temperature gradient from 7~8 °C to 2~3 °C. This thermal stability resulted in improved thickness uniformity (variation < 1 Å) and an increase in film density from 2.83 to 2.94 g/cm³. Furthermore, the physical contact between the wafer and the heater effectively eliminated backside deposition to near-zero levels. Pattern evaluation revealed an exceptional step coverage of 99% in high-aspect-ratio (20:1) structures. These results suggest that ESC-assisted PE-ALD provides a robust and reproducible method for high-quality SiN deposition by minimizing thermally induced film variations. Full article

Observations of photoelectric conversion in Fe- and Mn-rich semiconductor mineral coatings highlight their potential role in the origin of life and the evolution of environmental conditions. However, natural silicate minerals, which make up most of the Earth’s crust, are generally considered wide-bandgap insulators and are not expected to exhibit a photoelectric effect. In this study, we experimentally confirm measurable impurity-like photoelectron activity in natural silicate minerals and explore possible regulatory mechanisms. We show that electron-active elements (e.g., structural Fe and Ti) and lattice defects in minerals such as pyroxene and mica can reduce the optical gap (E_opt) to below ~4.13 eV, producing small photocurrents ranging from 0.010 to 0.114 μA/cm² on ITO substrates (background signal excluded). The structural types of these minerals—chain, island, layer, and framework—may influence their photoelectric responses by affecting electron transport pathways. Notably, light wavelength strongly controls both the photoelectric relative activity (PRA = 3–10 for silicates) and the decay kinetics (0.002–0.021 s⁻¹) of minerals. Visible light (400–800 nm) markedly enhances photocurrent densities in low-bandgap minerals such as limonite (E_opt = 2.11 eV). In contrast, ultraviolet light (UVB, 300 nm) enhances photoelectric responses in high-bandgap minerals, including feldspar and quartz (E_opt = 4.31 and 6.08 eV, respectively). Multivariate statistical analysis further indicates that elemental composition governs spectroscopic features that influence photoelectric behavior. Among these, Fe, Al, Si, and Ti are identified as key regulatory elements. These results provide new insights into the role of natural silicates in photoelectron-driven environmental and geological processes and highlight the potential of silicate-based materials for solar energy conversion applications. Full article

Semiconductor manufacturing equipment such as vacuum pumps, wafer handling mechanisms, etching machines, and deposition systems operates for a long time under high vacuum, high temperature, strong electromagnetic, and high-precision continuous production environments. Its reliability is directly related to the yield and stability of the production line. During equipment operation, the fault signals are often weak, the noise is strong, and the working conditions are variable, so traditional methods are difficult to achieve high-precision recognition. To solve this problem, this paper proposes a fault diagnosis and health monitoring method for semiconductor manufacturing equipment based on deep learning and subspace transfer. Firstly, considering the cyclostationary characteristics of the operating signals of key equipment, the cyclic spectral analysis technology is used to obtain the cyclic spectral coherence map, which effectively reveals the feature differences under different health states. Then, a deep fault diagnosis model based on the convolutional neural network (CNN) is constructed to extract deep feature representations. Furthermore, the subspace transfer learning technology is introduced, and group normalization and correlation alignment unsupervised adaptation layers are designed to achieve automatic alignment and enhancement of the statistical characteristics of deep features between the source domain and the target domain, which effectively improves the generalization and adaptability of the model. Finally, simulation experiments based on the public bearing dataset verify that the proposed method has strong feature representation ability and high classification accuracy under different working conditions and different loads. Because the key components and experimental scenarios of semiconductor manufacturing equipment have similar signal characteristics, this method can be directly transferred to the early fault diagnosis and health monitoring of semiconductor production line equipment, which has important engineering application value. Full article

Interfaces of rather different natures—as, e.g., bacterial colony or forest fire boundaries, or semiconductor layers grown by different methods (MBE, sputtering, etc.)—are self-affine fractals, and feature scaling with universal exponents (depending on the substrate’s dimensionality d and global topology, as well as on the driving randomness’ spatial and temporal correlations but not on the underlying mechanisms). Adding lateral growth as an essential (non-equilibrium) ingredient to the known equilibrium ones (randomness and interface relaxation), the Kardar–Parisi–Zhang (KPZ) equation succeeded in finding (via the dynamic renormalization group) the correct exponents for flat $d=1$ substrates and (spatially and temporally) uncorrelated randomness. It is this interplay which gives rise to the unique, non-Gaussian scaling properties characteristic of the specific, universal type of non-equilibrium roughening. Later on, the asymptotic statistics of process $h\left(x\right)$ fluctuations in the scaling regime was also analytically found for $d=1$ substrates. For $d>1$ substrates, however, one has to rely on numerical simulations. Here we review a variational approach that allows for analytical progress regardless of substrate dimensionality. After reviewing our previous numerical results in $d=1$, 2, and 3 on the time evolution of one of the functionals—which we call the non-equilibrium potential (NEP)—as well as its scaling behavior with the nonlinearity parameter $\lambda$, we discuss the stochastic thermodynamics of the roughening process and the memory of process $h\left(x\right)$ in KPZ and in the related Golubović–Bruinsma (GB) model, providing numerical evidence for the significant dependence on initial conditions of the NEP’s asymptotic behavior in both models. Finally, we highlight some open questions. Full article

Semiconductor wafer fabrication is one of the most complex and demanding processes in industry. The process involves numerous sequential steps, including photolithography, deposition, etching, and chemical–mechanical polishing (CMP). At advanced process nodes below 5 nanometers, even angstrom-level deviations in parameters such as oxide thickness or critical dimension (CD) can lead to yield degradation or device failure. Traditional single-factor experimental methods are insufficient to capture the inherent multivariate interactions within plasma, thermal, and chemical processes. This review introduces the application of Design of Experiments (DOE) in wafer fabrication and demonstrates that it provides a statistically rigorous framework for addressing these challenges. It enables the simultaneous analysis of multiple variables, quantifying main effects and interactions, and developing predictive models with fewer runs. DOE can accelerate process development, reduce wafer consumption, enhance process robustness, and support applications in processes such as photolithography, CMP, and deposition. Beyond process optimization, DOE, combined with virtual metrology, machine learning, and digital twin technologies, provides a balanced dataset for predictive analytics and real-time control. Its functions encompass proactive monitoring, adaptive formulation optimization, and eco-efficient manufacturing aligned with sustainability goals. As wafer fabs adopt AI-assisted, simulation-driven environments, experimental design remains the foundation for knowledge-intensive, data-driven decision-making. This ensures continuous improvement in yield, manufacturability, and competitiveness in future semiconductor miniaturization processes. Full article

This study proposes a novel theoretical approach to understanding the statistical–mechanical similarities between nuclear fission phenomena and semiconductor physics. Using the Hill–Wheeler formula as a quantum mechanical distribution function and establishing its correspondence with the Fermi–Dirac distribution function, we analyzed nuclear fission processes for nine nuclides (²³²Th, ²³³U, ²³⁵U, ²³⁸U, ²³⁷Np, ²³⁹Pu, ²⁴⁰Pu, ²⁴²Pu, ²⁴¹Am) using JENDL-5.0 data. Full article

Planar microwave bow-tie diodes on bases of selectively doped semiconductor structures are successfully used in the detection and imaging of electromagnetic radiation in millimeter and submillimeter wavelength ranges. Although the signal formation mechanism in these high-frequency diodes is said to be based on charge-carrier heating in a semiconductor in a strong electric field, the nature of the electrical signal across the bow-tie diodes is not yet properly identified. In this research paper, we present a comprehensive study of a series of various planar bow-tie diodes, starting with a simple asymmetrically shaped submicrometer-thick n-GaAs layer and finishing with bow-tie diodes based on selectively doped GaAs/AlGaAs structures of different electrical conductivity. The planar bow-tie diodes were fabricated on two different types of high-resistivity substrates: bulky semi-insulating GaAs substrate and elastic dielectric polyimide film of micrometer thickness. The microwave diodes were investigated using DC and high-frequency probe stations, which allowed us to examine a sufficient number of diodes and collect a large amount of data to perform a statistical analysis of the electrical parameters of these diodes. The use of probe stations made it possible to analyze the properties of the bow-tie diodes and clarify the nature of the detected voltage in the dark and under white-light illumination. The investigation revealed that the properties of various bow-tie diodes are largely determined by the energy states residing in semiconductor bulk, surface, and interfaces. It is most likely that these energy states are responsible for the slow relaxation processes observed in the studied bow-tie diodes. Full article

The rising demand for increased integration and higher power outputs poses a hidden risk to the long-term reliable operation of third-generation semiconductors. Thus, the power cycling test (PCT) is widely regarded as the utmost critical test for assessing the packaging reliability of power devices. In this work, low-thermal-resistance packaging design structures of SiC devices are introduced, encompassing planar packaging with dual heat dissipation, press-pack packaging, three-dimensional (3D) packaging, and hybrid packaging. PCT methods and their control strategies are summarized and discussed. Direct-current PCT is the focus of this review. The failure mechanisms of SiC devices under PCT are pointed out. The electrical and temperature-sensitive parameters adopted to monitor the aging of SiC devices are organized. The existing international standards for PCT are evaluated. Due to the lack of authoritative statements for SiC devices, it is difficult to achieve comparison research results without consistent preconditions. Furthermore, the lifetimes of the various packaging designs of the tested SiC devices under PCTs are statistically analyzed. Additionally, problems related to parameter monitoring and test equipment are also summarized. This review explores the broader landscape by delving into the current challenges and main trends in PCTs for SiC devices. Full article

The space- and temperature-dependent electron distribution $n(\mathbf{r},T)$ determines optoelectronic properties of disordered semiconductors. It is a challenging task to get access to $n(\mathbf{r},T)$ in random potentials, while avoiding the time-consuming numerical solution of the Schrödinger equation. We present several numerical techniques targeted to fulfill this task. For a degenerate system with Fermi statistics, a numerical approach based on a matrix inversion and one based on a system of linear equations are developed. For a non-degenerate system with Boltzmann statistics, a numerical technique based on a universal low-pass filter and one based on random wave functions are introduced. The high accuracy of the approximate calculations are checked by comparison with the exact quantum-mechanical solutions. Full article

The surgical robots currently used in cardiac surgery are equipped with a remote center of motion (RCM) mechanism that enables the required spherical workspace. The dynamics model of the surgical robot’s RCM mechanism presented in this work includes a direct current (DC) motor, an optimal proportional–integral–derivative (PID) controller, and a LuGre friction model that takes into account the Stribeck effect and surface deformation. A finite element method (FEM) analysis of transients was carried out using the energy hypothesis of von Mises with an optimal input signal from the mechatronic system with a PID controller obtained using the Runge–Kutta differentiation method in the Dormand–Prince ordinary differential equations variant (ODE45). Five criteria were adopted for the objective function: the safety factor related to the stress function in the time-varying strength problem, the first natural frequency related to stiffness and the resonance phenomenon, the buckling coefficient in the statics problem related to stability, the static factor of safety, and the displacement of the operating tip. The force inputs to the dynamics model were derived from in vitro force measurements on cardiovascular tissue using a force sensor. The normality of the statistical distribution of the experimental data was confirmed using the Kolmogorov–Smirnov statistical test. The problem of multi-criteria optimization was solved using the non-sorter genetic algorithm (NSGA-II), the finite element method, and the von Mises distortion energy hypothesis. Velocity input signals for the transient dynamics model were obtained from a second in vitro experiment on cardiovascular tissue using the minimally robotic invasive surgery (MIRS) technique. An experienced cardiac surgeon conducted the experiment in a modern method using the Robin Heart Vision surgical robot, and a system of four complementary metal–oxide–semiconductor (CMOS) optical sensors and ariel performance analysis system (APAS-XP 2002) software were used to obtain the endoscopic tool trajectory signal. The trajectory signal was accurate to ±2 [mm] in relation to the adopted standard, and it was smoothed using the Savitzky–Golay (SG) polynomial smoothing, whose parameters were optimally selected using the Durbin–Watson (DW) statistical test. Full article

In recent decades, wireless sensor networks (WSNs) have become a popular ambient sensing and model-based solution for various applications. WSNs are now achievable due to the developments of micro electro mechanical and semiconductors logic circuits with rising computational power and wireless communication technology. The most difficult issues concerning WSNs are related to their energy consumption. Since communication typically requires a significant amount of energy, there are some techniques/ways to reduce energy consumption during the operation of the sensor’s communication systems. The topology control technique is one such effective method for reducing WSNs’ energy usage. A cluster head (CH) is usually selected using a topology control technique known as clustering to control the entire network. A single factor is inadequate for CH selection. Additionally, with the traditional clustering method, each round exhibits a new batch of head nodes. As a result, when using conventional techniques, nodes decay faster and require more energy. Furthermore, the inceptive energy of nodes, the range between sensor nodes and base stations, the size of data packets, voltage and transmission energy measurements, and other factors linked to sensor nodes are also completely unexpected due to irregular or hazardous natural circumstances. Here, unpredictability represented by Triangular Fuzzy Numbers (TFNs). The associated parameters of nodes were converted into crisp ones via the defuzzification of fuzzy numbers. The fuzzy number has been defuzzified using the well-known signed distance approach. Here, we have employed a multi-criteria decision-making (MCDM) approach to choosing the CHs depending on a bunch of characteristics of each node (i) residual energy, (ii) the number of neighbors, (iii) distance from the sink, (iv) average distance of cluster node, (v) distance ratio, and (vi) reliability. This study used the entropy-weighted Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) approach to select the CH in WSNs. For experiments, we have used the NSG2.1 simulator, and based on six characteristics comprising residual energy, number of neighbor nodes, distance from the sink or base station (BS), average distance of cluster nodes, distance ratio, and reliability, optimal CHs have been selected. Finally, experimental results have been presented and compared graphically with the existing literature. A statistical hypothesis test has also been conducted to verify the results that have been provided. Full article

Using the quasi-classical kinetic theory of dielectric relaxation, in addition to existing methods, fundamental mathematical expressions are built, which make it possible to more strictly consider the effects of the main charge carriers’ (protons’) tunneling on the numerical values of the molecular parameters (activation energy, equilibrium concentration) of protons in HBC. The formulas for calculating the statistically averaged non-stationary quantum transparency of a parabolic potential barrier for protons have been modernized by more stringent consideration of the effects of corrections caused by an external electric field. For the model of a double-symmetric potential well, a generalized nonlinear solution of the quasi-classical kinetic equation of dielectric relaxation in HBC was built. The phenomenological Bucci-Rive formula for thermally stimulated depolarization current density (TSDC) was first investigated, taking into account quantum transparency, for the case of a parabolic potential barrier. The choice of the parabolic shape of the potential barrier allowed, at a theoretical level, for the mathematical model of relaxation polarization to be brought closer to the conditions of the real spatial structure of the crystal potential field, in comparison with the rectangular potential barrier model. It has been found that quantum effects due to proton tunnel transitions significantly affect the mechanism of thermally stimulated depolarization currents in HBC, over a wide temperature range (50–550 K) and external field parameters (0.1–1 MV/m). Generalized solutions of the nonlinear kinetic equation, recorded considering the effects of field parameters on proton tunnel transitions, made it possible to significantly approximate the theoretical values of activation energies, equilibrium concentrations of protons and amplitudes of the theoretical maxima of the current density of thermally stimulated depolarization, according to their experimental values in the field of low-temperature (50–100 K) and high-temperature (350–550 K) maxima of TSDC density in HBC. For the first time, precision measurements of TSDC temperature spectra were carried out for chalcanthite crystals. The effects of alloying impurities concentrations and crystal calcination temperatures on the parameters of experimental maxima in the TSDC spectrum of chalcanthite were established. A physical mechanism of the quantum tunnel motion of protons in HBC with a complex crystal structure (crystalline hydrates, layered silicates, ferroelectric HBC (KDP, DKDP)) is described. The patterns found in this article indicate a fairly high degree of applied scientific significance for the obtained theoretical results, allowing for the further development of electrophysics and optoelectronics of heterogeneous structures (MIS, MSM) based on proton semiconductors and dielectrics (PSD) and their composites. Full article

Chemical mechanical planarization (CMP) is a wafer-surface-polishing planarization technique based on a wet procedure that combines chemical and mechanical forces to fully flatten materials for semiconductors to be mounted on the wafer surface. The achievement of devices of a small nano-size with few defects and good wafer yields is essential in enabling IC chip manufacturers to enhance their profits and become more competitive. The CMP process is applied to produce many IC generations of nanometer node, or those of even narrower line widths, for a better performance and manufacturing feasibility. Slurry is a necessary supply for CMP. The most critical component in slurry is an abrasive particle which affects the removal rates, uniformity, defects, and removal selectivity for the materials on the wafer surface. The polishing abrasive is the source of mechanical force. Conventional CMP abrasives consist of colloidal silica, fume silica or other inorganic polishing particles in the slurries. We were the first to systematically study nanoparticles of the polymer type applied in CMP, and to compare traditional inorganic and polymer nanoparticles in terms of polishing performance. In particular, the polymer nanoparticle size, shape, solid content dosing ratio, and molecular types were examined. The polishing performance was measured for the polishing removal rates, total defect counts, and uniformity. We found that the polymer nanoparticles significantly improved the total defect counts and uniformity, although the removal rates were lower than the rates obtained using inorganic nanoparticles. However, the lower removal rates of the polymer nanoparticles are acceptable due to the thinner film materials used for smaller IC device nodes, which may be below 10 nm. We also found that the physical properties of polymer nanoparticles, in terms of their size, shape, and different types of copolymer molecules, cause differences in the polishing performance. Meanwhile, we used statistical analysis software to analyze the data on the polishing removal rates and defect counts. This method helps to determine the most suitable polymer nanoparticle for use as a slurry abrasive, and improves the reliability trends for defect counts. Full article

Nowadays, Predictive Maintenance is a mandatory tool to reduce the cost of production in the semiconductor industry. This paper considers as a case study a critical part of the electrochemical deposition system, namely, the four Pins that hold a wafer inside a chamber. The aim of the study is to replace the schedule of replacement of Pins presently based on fixed timing (Preventive Maintenance) with a Hardware/Software system that monitors the conditions of the Pins and signals possible conditions of failure (Predictive Maintenance). The system is composed of optical sensors endowed with an image processing methodology. The prototype built for this study includes one optical camera that simultaneously takes images of the four Pins on a roughly daily basis. Image processing includes a pre-processing phase where images taken by the camera at different times are coregistered and equalized to reduce variations in time due to movements of the system and to different lighting conditions. Then, some indicators are introduced based on statistical arguments that detect outlier conditions of each Pin. Such indicators are pixel-wise to identify small artifacts. Finally, criteria are indicated to distinguish artifacts due to normal operations in the chamber from issues prone to a failure of the Pin. An application (PINapp) with a user friendly interface has been developed that guides industry experts in monitoring the system and alerting in case of potential issues. The system has been validated on a plant at STMicroelctronics in Catania (Italy). The study allowed for understanding the mechanism that gives rise to the rupture of the Pins and to increase the time of replacement of the Pins by a factor at least 2, thus reducing downtime. Full article