The Influence of Skin Effect on Via-Vicinity-Interfaces Current Density of Cu Interconnects

2012 ◽  
Vol 548 ◽  
pp. 551-554
Author(s):  
Ming Yao ◽  
Xu Liang Zhang
Keyword(s):  
Current Density ◽  
Skin Effect ◽  
Ground Plane ◽  
Three Dimensional ◽  
Current Density Distribution ◽  
Copper Interconnects ◽  
Current Crowding ◽  
Cu Interconnects ◽  
Surface Areas ◽  
Cu Interconnect

This paper presents a research on skin effect’s influence on the current density distribution of Cu/barrier layer and Cu/cap layer interfaces of copper interconnects’ via vicinities. A two-level Cu-interconnect structure in different positional relationships with the ground plane is discussed. Through the three-dimensional (3D) finite element simulation of the interconnect structure, the variations of current density on three important surface areas are obtained when skin effect is significant, showing that the current density in the three surface areas near the via has been strongly influenced by current crowding and skin effect. So in many cases the influence of skin effect on via top and via bottom failures of Cu interconnects under high frequencies can not be ignored.

Enhanced method for pulse skin effect calculation of cylindrical conductors

2020 ◽  
Vol 39 (3) ◽  
pp. 623-635
Author(s):  
Nebojsa B. Raicevic ◽  
Slavoljub R. Aleksic ◽  
Ilona Iatcheva ◽  
Marinko Barukcic
Keyword(s):  
Electromagnetic Field ◽  
Density Distribution ◽  
Cross Section ◽  
Current Density ◽  
Skin Effect ◽  
Current Density Distribution ◽  
Accurate Solution ◽  
Lightning Strike ◽  
Content Type ◽  
Cylindrical Conductors

Purpose This paper aims to present a new approach to the numerical solution of skin effect integral equations in cylindrical conductors. An approximate, but very simple and accurate method for calculating the current density distribution, skin-effect resistance and inductance, in pulse regime of cylindrical conductor, having a circular or rectangular cross-section, is considered. The differential evolution method is applied for minimization of error functional. Because of its application in the practice, the lightning impulse is observed. Direct and inverse fast Fourier transform is applied. Design/methodology/approach This method contributes to increasing of correctness and much faster convergence. As the electromagnetic field components depend on the current density derivation, the proposed method gives a very accurate solution not only for current density distribution and resistance but also for field components and for internal inductance coefficients. Distribution of current and electromagnetic field in bus-bars can be successfully determined if the proximity effect is included together with the skin effect in calculations. Findings The study shows the strong influence of direct lightning strikes on the distribution of electrical current in cables used in lightning protection systems. The current impulse causes an increase in the current density at all points of the cross-section of the conductor, and in particular the skin effect on the external periphery. Based on the data calculated by using the proposed method, it is possible to calculate the minimum dimensions of the conductors to prevent system failures. Research limitations/implications There are a number of approximations of lightning strike impulse in the literature. This is a limiting factor that affects the reliability and agreement between measured data with calculated values. Originality/value In contrast with other methods, the current density function is approximated by finite functional series, which automatically satisfy wave equation and existing boundary conditions. It is necessary to minimize the functional. This approach leads to a very accurate solution, even in the case when only two terms in current approximation are adopted.

Three-Dimensional Current Density Distribution Simulations for a Resistive Patterned Wafer

2004 ◽  
Vol 151 (9) ◽  
pp. D78 ◽  
Author(s):  
M. Purcar ◽  
B. Van den Bossche ◽  
L. Bortels ◽  
J. Deconinck ◽  
G. Nelissen
Keyword(s):  
Density Distribution ◽  
Current Density ◽  
Three Dimensional ◽  
Current Density Distribution

scholarly journals INFLUENCE OF SKIN EFFECT ON THE CALCULATION OF BUSBAR SYSTEMS HAVING RECTANGULAR CROSS SECTION

2021 ◽  
Vol 20 (1) ◽  
pp. 057
Author(s):  
Nebojša Raičević ◽  
Ana Vučković ◽  
Mirjana Perić ◽  
Slavoljub Aleksić
Keyword(s):  
Electromagnetic Field ◽  
Cross Section ◽  
Current Density ◽  
Proximity Effect ◽  
Skin Effect ◽  
Rectangular Cross Section ◽  
Error Function ◽  
Current Density Distribution ◽  
Accurate Solution ◽  
Flow Through

One method for the calculation of current density distribution in a finite number of long parallel conductors, having rectangular cross section, is proposed in this paper. Numerical results aim to highlight the importance of the skin effect, which can be combined with the proximity effect. The method of superposition of these two effects was applied to the calculation of the electromagnetic field in electric power busbars systems. It has been shown that the skin effect has a much greater impact, especially when the conductors are thin and strong electric currents flow through them, so special attention is paid to its calculation. For numerical solution the integral equations are used. The function of current density is approximated by the finite functional series. This way leads to a very accurate solution with only two terms. Differential evolution method is applied for minimization of error function. To demonstrate the application of the proposed approach, numerical values for busbars are presented and compared with values obtained by using the finite elements method.

Transient Multi-Field FEA Model for Predicting Current Density Distribution When Deforming Sheet Metal Under a Direct Current

2008 ◽  
Author(s):  
John T. Roth ◽  
Amir Khalilollahi ◽  
Daniel J. Jageman
Keyword(s):  
Temperature Distribution ◽  
Density Distribution ◽  
Sheet Metal ◽  
Current Density ◽  
Three Dimensional ◽  
Current Density Distribution ◽  
Electrode Placement ◽  
Dome Height ◽  
Current Electrode ◽  
Fea Model

Previous investigations have been performed that involve developing new ways in which to deform a material while minimizing the energy required to do so. More recent research involves applying an electric current to the workpiece to achieve superplasticity. However, those investigations only utilized uniaxial workpieces and lack the ability to be used for more common geometries. The research presented herein, however, the effect is investigated under three-dimensional conditions so that the results could be projected to more realistic sheet metal geometries. A working finite element analysis (FEA) model has been developed to analyze these more complicated three-dimensional flow fields and will be presented as a part of this research. The model was used to solve for the temperature and current density distributions across the workpiece. The results from the FEA model are compared to results obtained from experimental tests. In the experimental setup, the two dome heights were separately tested under the same conditions that the FEA model simulated, however, only a temperature distribution was obtained here. The comparison of the FEA results and the experimental results related the temperature distribution to the current density distribution across the workpiece. From here, the individual effects of certain parameters on the distributions were found. The parameters included: duration of current, amount of current, electrode placement, and dome height geometry. The results showed that the current density distribution can be manipulated by varying the above parameters. This capability can be used to delay tearing/necking of a sheet metal workpiece under deformation.

The MLT distribution and detailed structure of ring current:  MMS observations

2021 ◽  
Author(s):  
Xin Tan ◽  
Malcolm Dunlop ◽  
Xiangcheng Dong ◽  
Yanyan Yang ◽  
Christopher Russell
Keyword(s):  
Current Density ◽  
Large Scale ◽  
Ring Current ◽  
Current System ◽  
Radial Profile ◽  
Three Dimensional ◽  
Current Density Distribution ◽  
Magnetic Storms ◽  
In Situ Data

<p>The ring current is an important part of the large-scale magnetosphere-ionosphere current system; mainly concentrated in the equatorial plane, between 2-7 R<sub>E</sub>, and strongly ordered between ± 30 ° latitude. The morphology of ring current directly affects the geomagnetic field at low to middle latitudes. Rapid changes in ring current densities can occur during magnetic storms/sub-storms. Traditionally, the Dst index is used to characterize the intensity of magnetic storms and to reflect the variation of ring current intensity, but this index does not reflect the MLT distribution of ring current. In fact, the ring current has significant variations with MLT, depending on geomagnetic activity, due to the influence of multiple factors; such as, the partial ring current, region 1/region 2 field-aligned currents, the magnetopause current and sub-storm cycle (magnetotail current). The form of the ring current has been inferred from the three-dimensional distribution of ion differential fluxes from neutral atom imaging; however, this technique can not directly obtain the current density distribution (as can be obtained using multi-spacecraft in situ data). Previous in situ estimates of current density have used: Cluster, THEMIS and other spacecraft groups to study the distribution of the ring current for limited ranges of either radial profile, or MLT and MLAT variations. Here, we report on an extension to these studies using FGM data from MMS obtained during the period September 1, 2015 to December 31, 2016, when the MMS orbit and configuration provided good coverage. We employ the curlometer method to calculate the current density, statistically, to analysis the MLT distribution according to different geomagnetic conditions. Our results show the clear asymmetry of the ring current and its different characteristics under different geomagnetic conditions.</p>

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