Impedance-Based Static Analysis for Interconnect Reliability
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Solution Overview
Problem
Deep sub-micron integrated circuit designs face challenges with interconnect and transistor reliability due to increasing current densities and temperature, leading to failures from electromigration, time-dependent dielectric breakdown, hot carrier injection, and bias temperature instability, which are difficult to accurately analyze using existing methods.
Innovation Solution
An impedance-based static analysis method that models current steering among multiple parallel charge/discharge paths using decision diagrams to account for switching constraints, computes power dissipation, and performs statistical reliability analysis based on thermal maps.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If circuit simulation is used to accurately solve DC and RMS currents in each interconnect segment, then reliability analysis accuracy is improved, but computational complexity and time increase significantly
Solution Approach 1:
The circuit is divided into segments based on switching constraints and parallel paths. Decision diagrams segment the current paths into discrete charge and discharge paths, allowing accurate analysis of each segment without requiring full-circuit simulation. This segmentation enables focused computation on critical paths while ignoring irrelevant portions.
Solution Approach 2:
The method performs partial simulation by focusing only on the necessary current paths identified through decision diagrams. Rather than simulating all possible current paths exhaustively, the approach identifies and analyzes only the dominant charge and discharge paths that contribute most to reliability concerns, achieving sufficient accuracy with reduced computation.
2Productivity
If filtering is applied to exclude nets driving small capacitance loads, then computational load is reduced, but thermal gradient-induced failures in adjacent nets are missed
Solution Approach 1:
The method applies different analysis depths to different regions of the circuit based on local characteristics. Nets with switching constraints and parallel paths receive detailed local analysis through decision diagrams, while other regions are handled more coarsely. This localized quality adjustment ensures critical areas are thoroughly analyzed without unnecessarily processing entire circuits.
Solution Approach 2:
The decision diagram construction performs preliminary identification of critical current paths and switching constraints before the actual reliability analysis. By pre-processing the circuit to identify which nets and paths require detailed attention, the method prepares a focused analysis plan that prevents both over-filtering and unnecessary computation.
3Device complexity
If static linear analysis is used to make the problem tractable, then computational feasibility is improved, but accuracy may be compromised
Solution Approach 1:
The method transforms the analysis parameters by representing currents and voltages in terms of path-based variables rather than node-based variables. The decision diagram framework changes the parameter space to focus on path currents, enabling static linear analysis to achieve better accuracy by working in a more appropriate parameter domain for the specific reliability analysis goals.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Accurately models current paths and densities, computes power dissipation, and enhances reliability analysis for interconnects and transistors, improving the mean time to failure and reducing chip-level failures by accounting for thermal gradients and switching constraints.
Implementation Method 1
An impedance-based static analysis method to performing interconnect and transistor reliability analysis for deep sub-micron integrated circuit designs is set forth. The method accurately models current steering amongst multiple parallel charge/discharge paths
Implementation Method 2
In addition, Joule heating can reduce mean time to failure (MTTF) of interconnects and transistors, and can place constraints on the root mean squared (RMS) current density that an interconnect line or a transistor can support
Implementation Method 3
In deep sub-micron designs, however, the ever increasing component density can cause thermal gradients to induce failures in unsuspecting nets adjacent to high current nets
Data Source
AI summary
A system and method for providing a statistical budgeting approach to modeling reliability effects such as interconnect electromigration (EM), transistor time-dependant dielectric breakdown (TDDB), hot-carrier injection effects (HCI) and bias temperature instability (BTI) is disclosed. A static analysis flow captures the effects of design topology, switching constraints, interactions between signal nets and supply rails as well as thermal gradients due to interconnect and transistor self as well as mutual heating, and was used to verify successive iterations of deep sub-micron integrated circuit designs.