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Sep 25

Mechanical Stresses Estimation in Silicon and Glass Bonded at Elevated Temperature

During electrostatic bonding, also known as anodic bonding, silicon is bonded to glass by applying an external voltage and simultaneous heating to temperatures of 200...450 °C. While cooling to working temperature after bonding happened pieces are mutually deformed. Due to linear thermal expansion coefficients mismatch of anodically bonded glass and silicon samples an internal stress state is generated. Such stresses are called thermal mismatch stresses. The aim of this paper is a determination of technological and design solutions to achieve minimal thermal mismatch stresses in resulting bond. The nonlinear dependence of linear thermal expansion coefficients of bonded samples' materials on temperature makes it difficult to minimize thermal mismatch stresses by chosing materials with close average thermal expansion coefficients in particular temperature range. To assess means of lowering thermal mismatch stress in this paper two different ways to describe assembly are used: two thin bonded layers and multilayered composite material. Based on properties of two brands of glass (LK5, Borofloat 33) and silicon used with described mathematical models thermal mismatch stresses at temperature T_w in samples bonded at several different temperatures T_b are evaluated. Bonded silicon surface stress dependence of glass to silicon wafer thickness ratio is evaluated. Based on such evaluations one can say that by varying thickness of glass bonded to silicon one can obtain zero thermal mismatch stress at a particular depth of material or obtain stress of some defined value at this depth. Models of assembly description used in this paper can be used to optimize anodic bonding process parameters. Such usage aimed to minimize thermal mismatch stresses at device working temperatures is presented in this paper.

  • 1 authors
·
Feb 6, 2018

Calculation and selection of silicon to glass anodic bonding modes based on the criterion of minimum residual stress

The goal of this work is a scientifically justified choice of efficient technological parameters of anodic bonding of silicon to glass, ensuring a minimum level of residual stresses. The relevance of this dissertation is determined by the continuous efforts to reduce the negative effects of the joint use of dissimilar materials in electronic devices. Theoretical and practical results: the temperature dependence of the true values of the coefficient of thermal expansion of popular glass brands in the temperature range from minus 100 °C to 500 °C were obtained; the ratio of thicknesses of silicon and glass that minimizes residual stress on the silicon surface was calculated; the technique of minimizing the residual stresses in silicon anodically bonded to glass was developed. Results of this research are applicable to MEMS devices design and simulations. The first chapter provides the analysis of the current state of research in the field of anodic bonding technology application. The second chapter is devoted to the experimental study of temperature dependence of the linear thermal expansion coefficient of the glass. Thermomechanical properties and composition of the following glass brands: LK5, Schott Borofloat 33, Corning 7740, Hoya SD-2 were measured. The third chapter describes the existing models of estimating the residual stresses in the silicon-glass bonds. Two models based on a theory of strength of materials and the classical lamination theory with an additional temperature dependence of coefficients of thermal expansion are proposed for further use. Residual stresses in silicon-glass bonds are estimated with these models and data from the preceding chapter. The fourth chapter describes the experiments carried out to confirm claims from the previous chapters. The proposed technique of minimizing residual stresses is described as steps for a device designer.

  • 1 authors
·
Apr 22, 2018

An error indicator-based adaptive reduced order model for nonlinear structural mechanics -- application to high-pressure turbine blades

The industrial application motivating this work is the fatigue computation of aircraft engines' high-pressure turbine blades. The material model involves nonlinear elastoviscoplastic behavior laws, for which the parameters depend on the temperature. For this application, the temperature loading is not accurately known and can reach values relatively close to the creep temperature: important nonlinear effects occur and the solution strongly depends on the used thermal loading. We consider a nonlinear reduced order model able to compute, in the exploitation phase, the behavior of the blade for a new temperature field loading. The sensitivity of the solution to the temperature makes {the classical unenriched proper orthogonal decomposition method} fail. In this work, we propose a new error indicator, quantifying the error made by the reduced order model in computational complexity independent of the size of the high-fidelity reference model. In our framework, when the {error indicator} becomes larger than a given tolerance, the reduced order model is updated using one time step solution of the high-fidelity reference model. The approach is illustrated on a series of academic test cases and applied on a setting of industrial complexity involving 5 million degrees of freedom, where the whole procedure is computed in parallel with distributed memory.

  • 2 authors
·
Apr 19, 2019

Conditional Normalizing Flow for Gas-Surface Scattering from Thermal to Hypersonic Velocities

Accurate aerodynamic modeling of satellites in very low Earth orbit (VLEO) requires gas-surface interaction (GSI) models that capture the full velocity spectrum from thermal to orbital speeds. Atmospheric particles initially strike spacecraft surfaces at hypersonic velocities of 6 000 - 10 000 m/s. Due to surface roughness and complex geometries, especially within air-breathing electric propulsion (ABEP) intake systems, multiple collisions occur, progressively reducing the particle velocities. A recent machine learning framework for deriving scattering kernels from molecular dynamics (MD) simulations has shown promise, but remains limited to high-velocity single impacts and possibly violates fundamental equilibrium principles such as detailed balance. This work extends this machine learning based scattering kernel to cover the complete velocity range using conditional normalizing flows trained with physics-informed constraints, enabling accurate modeling of multi-bounce scenarios in realistic VLEO applications. We train a conditional Real-valued Non-Volume Preserving (cRealNVP) model on expanded molecular dynamics simulations covering velocities from thermal to hypersonic speeds, incorporating a detailed balance loss term. The resulting model demonstrates improved accuracy compared to previous approaches even in the original high-velocity regime, while successfully capturing thermal-velocity scattering. Quantitative assessment shows that thermalization is approximated within acceptable tolerances. This framework provides essential capabilities for accurate ABEP intake optimization and VLEO mission planning while offering a general methodology applicable to broader rarefied gas dynamics problems requiring thermodynamic consistency.

  • 6 authors
·
Jul 2

New RVE concept in thermoelasticity of periodic composites subjected to compact support loading

This paper introduces an advanced Computational Analytical Micromechanics (CAM) framework for linear thermoelastic composites (CMs) with periodic microstructures. The approach is based on an exact new Additive General Integral Equation (AGIE), formulated for compactly supported loading conditions, such as body forces and localized thermal effects (for example laser heating). In addition, new general integral equations (GIEs) are established for arbitrary mechanical and thermal loading. A unified iterative scheme is developed for solving the static AGIEs, where the compact support of loading serves as a new fundamental training parameter. At the core of the methodology lies a generalized Representative Volume Element (RVE) concept that extends Hill classical definition of the RVE. Unlike conventional RVEs, this generalized RVE is not fixed geometrically but emerges naturally from the characteristic scale of localized loading, thereby reducing the analysis of an infinite periodic medium to a finite, data-driven domain. This formulation automatically filters out nonrepresentative subsets of effective parameters while eliminating boundary effects, edge artifacts, and finite-size sample dependencies. Furthermore, the AGIE-based CAM framework integrates seamlessly with machine learning (ML) and neural network (NN) architectures, supporting the development of accurate, physics-informed surrogate nonlocal operators.

  • 1 authors
·
Dec 21, 2025

Development of different methods and their efficiencies for the estimation of diffusion coefficients following the diffusion couple technique

The interdiffusion coefficients are estimated either following the Wagner's method expressed with respect to the composition (mol or atomic fraction) normalized variable after considering the molar volume variation or the den Broeder's method expressed with respect to the concentration (composition divided by the molar volume) normalized variable. On the other hand, the relations for estimation of the intrinsic diffusion coefficients of components as established by van Loo and integrated diffusion coefficients in a phase with narrow homogeneity range as established by Wagner are currently available with respect to the composition normalized variable only. In this study, we have first derived the relation proposed by den Broeder following the line of treatment proposed by Wagner. Further, the relations for estimation of the intrinsic diffusion coefficients of the components and integrated interdiffusion coefficient are established with respect to the concentration normalized variable, which were not available earlier. The veracity of these methods is examined based on the estimation of data in Ni-Pd, Ni-Al and Cu-Sn systems. Our analysis indicates that both the approaches are logically correct and there is small difference in the estimated data in these systems although a higher difference could be found in other systems. The integrated interdiffusion coefficients with respect to the concentration (or concentration normalized variable) can only be estimated considering the ideal molar volume variation. This might be drawback in certain practical systems.

  • 2 authors
·
Jul 23, 2018

TeX-1500: A Paired Real-World LWIR Hyperspectral Dataset and Benchmark for Temperature-Emissivity-Texture Decomposition

Temperature-emissivity-texture (TeX) decomposition seeks to recover object heat state, material spectral response, and visible-like geometric texture from long-wave infrared hyperspectral imaging (LWIR HSI). Existing TeX pipelines are mainly scene-specific inverse solvers, and the lack of paired LWIR HSI-TeX supervision has limited learning-based decomposition. To address this gap, we introduce TeX-1500, a large-scale paired LWIR HSI-TeX dataset and benchmark for supervised HSI-to-TeX decomposition. TeX-1500 contains 1,522 calibrated real-scene pairs from DARPA Invisible Headlights (DARPA IH) pushbroom imagery and our FTIR acquisitions, covering five locations, four seasons, diverse acquisition times, heterogeneous wavelength layouts, and two sensor families. Each sample stores a calibrated valid-band radiance cube, calibrated wavelength positions, and aligned temperature, emissivity, and texture supervision constructed through a consistent restoration and TeX-construction protocol. We further provide TeX-UNet, a simple wavelength-aware baseline that maps calibrated HSI bands and wavelength positions to TeX fields. Experiments on the held-out DARPA IH pushbroom scenes and zero-/few-shot transfer to FTIR scenes show that TeX-1500 provides usable paired supervision and a measurable benchmark for data-driven physical-property-centered thermal perception.

  • 6 authors
·
Jun 1

Understanding Linear Probing then Fine-tuning Language Models from NTK Perspective

The two-stage fine-tuning (FT) method, linear probing (LP) then fine-tuning (LP-FT), outperforms linear probing and FT alone. This holds true for both in-distribution (ID) and out-of-distribution (OOD) data. One key reason for its success is the preservation of pre-trained features, achieved by obtaining a near-optimal linear head during LP. However, despite the widespread use of large language models, there has been limited exploration of more complex architectures such as Transformers. In this paper, we analyze the training dynamics of LP-FT for classification tasks on the basis of the neural tangent kernel (NTK) theory. Our analysis decomposes the NTK matrix into two components. This decomposition highlights the importance of the linear head norm alongside the prediction accuracy at the start of the FT stage. We also observe a significant increase in the linear head norm during LP, which stems from training with the cross-entropy (CE) loss. This increase in the linear head norm effectively reduces changes in learned features. Furthermore, we find that this increased norm can adversely affect model calibration, which can be corrected using temperature scaling. Additionally, we extend our analysis with the NTK to the low-rank adaptation (LoRA) method and validate its effectiveness. Our experiments using a Transformer-based model on multiple natural language processing datasets confirm our theoretical analysis. Our study demonstrates the effectiveness of LP-FT for fine-tuning language models. Code is available at https://github.com/tom4649/lp-ft_ntk.

  • 2 authors
·
Oct 21, 2024

Additive general integral equations in thermoelastic micromechanics of composites

This work presents an enhanced Computational Analytical Micromechanics (CAM) framework for the analysis of linear thermoelastic composite materials (CMs) with random microstructure. The proposed approach is grounded in an exact Additive General Integral Equation (AGIE), specifically formulated for compactly supported loading, including both body forces and localized thermal changes (such as those from laser heating). New general integral equations (GIEs) for arbitrary mechanical and thermal loading are proposed. A unified iterative solution strategy is developed for the static AGIE, applicable to CMs with both perfectly and imperfectly bonded interfaces, where the compact support of loading is introduced as a new fundamental training parameter. Central to this methodology is a generalized Representative Volume Element (RVE) concept, which extends Hill classical definition. The resulting RVE is not predefined geometrically, but rather emerges from the characteristic scale of the localized loading, effectively reducing the analysis of an infinite, randomly heterogeneous medium to a finite, data-driven domain. This generalized RVE approach enables automatic exclusion of unrepresentative subsets of effective parameters, while inherently eliminating boundary effects, edge artifacts, and finite size limitations. Moreover, the AGIE-based CAM framework is naturally compatible with machine learning (ML) and neural network (NN) architectures, facilitating the construction of accurate and physically informed surrogate nonlocal operators.

  • 1 authors
·
Dec 21, 2025