纳米互连中的电迁移:在冗余网格网络中确定可靠性边际,使用可扩展的物理统计混合范式
1IMEC, Kapeldreef 75, B-3001 Leuven, Belgium.
Micromachines
|August 29, 2024
概括
本研究介绍了一种混合模型,将基于物理的电迁移建模和统计数据结合起来,以评估网格网络中纳米互连的可靠性. 它显示,与传统方法相反,网络冗余性大大提高了电迁移电流极限.
科学领域:
- 电气工程 电气工程
- 材料科学 材料科学 材料科学
- 半导体设备物理 半导体设备物理
背景情况:
- 电迁移 (EM) 是纳米互连中一个关键的可靠性问题,特别是在复杂的网格网络中.
- 传统的EM极限评估方法往往忽视了网络冗余的有益影响,可能导致低估.
- 在电力输送网络 (PDN) 中准确评估EM对于确保长期设备完整性至关重要.
研究的目的:
- 开发和介绍一种混合建模方法,整合基于物理的电迁移建模 (PEM) 和统计方法.
- 评估网格网络中纳米互连的电迁移电流极限和时间到故障 (TTF) 分布.
- 量化网络冗余和电压域 (Vdd与Vss) 对EM可靠性的影响.
主要方法:
- 一个混合建模框架,将基于物理的电迁移建模 (PEM) 与统计分析相结合.
- 与标准的P&R (Place and Route) 工具和实践的兼容性,用于实际应用.
- 数字模拟分析EM电流极限,TTF分布和PDN单元细胞中的应力因子.
主要成果:
- 传统方法低估了高达80%的EM电流极限,因为忽视了冗余性.
- 对于 PDN 单元单元的 TTF 分布遵循一个 lognormal 分布,与单个互连相比,显著减少了 lognormal sigma (σlogn).
- 负电压 (Vss) 网格比正电压 (Vdd) 网格更容易受到电磁波的影响,显示出更高的空隙点和拉力应力.
结论:
- 开发的混合模型准确地捕捉了网络冗余对EM电流极限的积极影响.
- 与Vdd电网相比,Vss电网对电迁移引起的故障更容易受到伤害.
- 这项研究为EM合规评估提供了务实增强,提高了预测网格网络中纳米互连可靠性的准确性.
相关概念视频
01:10Gauss's Law: Problem-Solving
Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...
01:16Electrostatic Boundary Conditions
Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
01:28Magnetostatic Boundary Conditions
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
01:25Multimachine Stability
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
01:21Boundary Conditions: Lossless Lines
Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...