scholarly journals An Anisotropic Equivalent Thermal Model for Shield Differential Through-Silicon Vias

Micromachines ◽  
2021 ◽  
Vol 12 (10) ◽  
pp. 1223
Author(s):  
Guangbao Shan ◽  
Guoliang Li ◽  
Dongdong Chen ◽  
Zifeng Yang ◽  
Di Li ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Finite Element Method ◽  
Thermal Model ◽  
Maximum Temperature ◽  
The Finite Element Method ◽  
Equivalent Thermal Conductivity ◽  
Thermal Distribution ◽  
Mathematical Expressions ◽  
Proposed Model ◽  
Silicon Vias

An accurate equivalent thermal model is proposed to calculate the equivalent thermal conductivity (ETC) of shield differential through-silicon via (SDTSV). The mathematical expressions of ETC in both horizontal and vertical directions are deduced by considering the anisotropy of SDTSV. The accuracy of the proposed model is verified by the finite element method (FEM), and the average errors of temperature along the X-axis, Y-axis, diagonal line, and vertical directions are 1.37%, 3.42%, 1.76%, and 0.40%, respectively. Compared with COMSOL, the proposed model greatly improves the computational efficiency. Moreover, the effects of different parameters on the thermal distribution of SDTSV are also investigated. The thermal conductivity is decreased with the increase in thickness of SiO2. With the increase in pitch, the maximum temperature of SDTSV increases very slowly when β = 0°, and decreases very slowly when β = 90°. The proposed model can be used to accurately and quickly describe the thermal distribution of SDTSV, which has a great prospect in the design of 3D IC.

Thermal Analysis on Symmetric Rectangular Stackable Supercapacitors

2015 ◽  
Vol 1092-1093 ◽  
pp. 539-542 ◽  
Author(s):  
Mei Na Zheng ◽  
Yan Song Li ◽  
Jun Liu
Keyword(s):  
Finite Element Method ◽  
Thermal Management ◽  
Thermal Model ◽  
Management Systems ◽  
Maximum Temperature ◽  
Discharge Process ◽  
The Finite Element Method ◽  
Applied Current ◽  
Cooling Systems ◽  
Simulation Results

In this paper, thermal model of the symmetric rectangular stackable supercapacitors are established. By using the finite element method, the temperature distribution of the supercapacitor is simulated. Then the supercapacitor's thermal behavior under the ambient temperature, but with different current density is analyzed. The simulation results show that the maximum temperature during the discharge process occurs in the center of the supercapacitor. The maximum temperature is associated with the applied current, and the higher the applied current is, the higher the maximum temperature is. It's necessary to control the maximum temperature within the allowable values, by establishing reasonable thermal management systems and cooling systems.

The Effect of Curvature and Torsion on the Temperature Distribution in a Helix

1985 ◽  
Vol 52 (3) ◽  
pp. 529-532 ◽  
Author(s):  
D. D. Sayers ◽  
M. C. Potter
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Partial Differential Equation ◽  
Temperature Distribution ◽  
Strong Dependence ◽  
Maximum Temperature ◽  
Nonuniform Heating ◽  
The Finite Element Method ◽  
Curvature Parameter ◽  
Curvature And Torsion

Traditional analysis treats the helix as a straight wire with the effects of nonuniform heating, torsion, and large curvature ignored. Using a helical coordinate system the governing partial differential equation including these effects is derived. The equation is then solved numerically using the finite element method. The results indicate a strong dependence of the temperature on the torsion parameter when the curvature parameter is significant. As the curvature parameter increases, the temperature distribution becomes skew-symmetric and the maximum temperature in the helix increases. Nonuniform heating influences the temperature distribution independent of the curvature and torsion.

scholarly journals Integrating the Finite Element Method with a Data-Driven Approach for Dam Displacement Prediction

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Chenfei Shao ◽  
Chongshi Gu ◽  
Zhenzhu Meng ◽  
Yating Hu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Modulus ◽  
Random Coefficient ◽  
Arch Dam ◽  
Data Driven ◽  
The Finite Element Method ◽  
Random Coefficient Model ◽  
Proposed Model ◽  
Element Method

Both numerical simulations and data-driven methods have been applied in dam’s displacement modeling. For monitored displacement data-driven methods, the physical mechanism and structural correlations were rarely discussed. In order to take the spatial and temporal correlations among all monitoring points into account, we took the first step toward integrating the finite element method into a data-driven model. As the data-driven method, we selected the random coefficient model, which can make each explanatory variable coefficient of all monitoring points following one or several normal distributions. In this way, explanatory variables are constrained. Another contribution of the proposed model is that the actual elastic modulus at each monitoring point can be back-calculated. Moreover, with a Lagrange polynomial interpolation, we can obtain the distribution field of elastic modulus, rather than gaining one value for the whole dam in previous studies. The proposed model was validated by a case study of the concrete arch dam in Jinping-I hydropower station. It has a better prediction precision than the random coefficient model without the finite element method.

scholarly journals Simulation of a Contact Pseudo-Environment in Calculating Thermal Resistance

2021 ◽  
Vol 346 ◽  
pp. 03049
Author(s):  
Alexander Denisenko ◽  
Roman Grishin ◽  
Liubov Podkruglyak
Keyword(s):  
Thermal Conductivity ◽  
Finite Element Method ◽  
Numerical Modeling ◽  
Thermal Resistance ◽  
Contact Zone ◽  
Metal Cutting ◽  
The Finite Element Method ◽  
Contact Thermal Resistance ◽  
Temperature Criterion ◽  
The Ideal

The use of the temperature criterion in the design of metal-cutting machines, determined on the basis of models that take into account the contact thermal resistances, is an objective necessity. These models should take into account to the maximum extent the actual conditions of contact of parts in the design under consideration, determined by the deviations of the mating surfaces from the ideal shape. The article presents the results of numerical modeling based on the finite element method of the formation of the contact thermal resistance and the evaluation of the influence of the parameters of the intermediate layer (pseudo-environment) that occurs in the contact zone of surfaces with macro-deviations on the passage of the heat flow. The obtained results allowed us to identify the most significant of the considered parameters. It is established that when modeling a pseudo-environment, it is necessary to take into account the coefficient of its thermal conductivity, the size, location and integrity of the actual contact zone.

A Novel Compact Method for Thermal Modeling of On-Chip Interconnects Based on the Finite Element Method

2003 ◽  
Author(s):  
Siva P. Gurrum ◽  
Yogendra K. Joshi ◽  
William P. King ◽  
Koneru Ramakrishna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thermal Modeling ◽  
Computational Cost ◽  
Compact Model ◽  
Maximum Temperature ◽  
The Finite Element Method ◽  
Detailed Model ◽  
Modeling Methodology ◽  
Element Method

Prediction of the temperature field generated with Joule heating in multilayer interconnect stacks is of critical importance for the design and reliability of future microelectronics. Interconnect failure due to electromigration is strongly dependent on its temperature. Simple models fail to capture thermal interaction between layers and within the layer. Detailed simulations on the other hand, take tremendous time and require large storage. This paper describes a threedimensional compact thermal modeling methodology that captures thermal interactions at a lower computational cost and storage requirements. The method is applicable for arbitrary geometries of interconnects due to the use of the finite element method. Case studies with three interconnects placed on a single level at a pitch of 1.0 μm generating different heat rates are reported. The compact model predicts a temperature rise of 4.11 °C at a current density of 10 MA/cm2 for 6.0 μm long interconnects of 0.18 μm width and an aspect ratio of 2. The error in maximum temperature is about 5% when compared with detailed simulations. The compact model for the current cases consists of 219 nodes whereas the detailed model has 99,000 nodes where temperature is computed.

scholarly journals THERMAL DRILLING OPTIMIZATION IN MULTI HOLE PLATES

2021 ◽  
Vol 13 (2) ◽  
pp. 45-54
Author(s):  
Jan Kosmol ◽  
Keyword(s):  
Finite Element Method ◽  
Heat Exchangers ◽  
Thermal Deformation ◽  
Maximum Temperature ◽  
Drilling Machine ◽  
The Finite Element Method ◽  
Thermal Deformations ◽  
Drilling Optimization ◽  
Thermal Drilling ◽  
Axis Of Symmetry

The article presents the results of simulation of thermal deformations by the finite element method for round multi-hole plates used in heat exchangers. The heat generated when drilling holes causes thermal deformation of these objects, which contributes to errors in the location of the holes. Obtained results of simulation were compared for different drilling strategies (the studies considered 24 different strategies). It was found that the maximum drilling temperatures according to different strategies may differ by up to 100%. Similar conclusions can be drawn for thermal deformations. The general conclusion that results from the conducted research indicates the need to choose a strategy that ensures the symmetry of the drilled holes in relation to the axis of symmetry of the object. Then, both thermal deformation and maximum temperature are the smallest. The thus identified thermal deformations can form the basis for the correction of the coordinates of the holes on a CNC multi-spindle drilling machine.

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