Electromigration Reliability Budgeting for Metal Paths
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Solution Overview
Problem
Existing circuit design approaches treat all metal paths equally for electromigration reliability, leading to inefficiencies in current density allocation and potential overdesign, as they do not account for varying current waveforms and specific contributions of each path to electromigration degradation.
Innovation Solution
The solution involves determining a parameter value representing the magnitude of excess current flowing in each metal path, allowing for unequal apportionment of electromigration reliability contributions, with higher current densities permitted in paths that predominantly carry large average currents while ensuring overall reliability, using duty cycle and root mean squared current calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If equal reliability budget is allocated to all metal paths, then electromigration reliability is uniformly maintained, but implementation area increases due to overdesign in low-current paths
Solution Approach 1:
The patent applies local quality by allocating electromigration reliability budget differently across metal paths based on their individual characteristics. Paths carrying larger average currents receive higher reliability budgets, while paths with smaller currents receive lower budgets. This is achieved by computing a reliability budget for each metal path proportional to its average current magnitude, allowing optimal wire sizing tailored to local current conditions rather than applying a uniform safety margin to all paths.
Solution Approach 2:
The patent changes the reliability budget parameter from a uniform value to a variable value that depends on the average current through each metal path. By making the reliability budget proportional to the average current magnitude, the system optimizes the trade-off between reliability and area. This parameter change enables high-current paths to have larger reliability margins while low-current paths use smaller margins, reducing overall implementation area.
2Area of stationary object
If higher current densities are permitted in high-current metal paths, then implementation area is reduced, but electromigration degradation risk increases
Solution Approach 1:
The patent changes the current density parameter from a uniform limit to a variable limit that scales with the average current through each metal path. By permitting higher current densities in paths with larger average currents (while maintaining the proportionality constraint), the system reduces implementation area without excessively compromising reliability. The key insight is that the reliability budget also scales proportionally, maintaining an acceptable reliability level.
Solution Approach 2:
The patent introduces dynamics by making both the reliability budget and permitted current density adaptive to the actual current conditions of each metal path. Rather than static uniform limits, the system dynamically adjusts the reliability margin and current density allowance based on the average current magnitude, enabling optimized area utilization while maintaining reliability proportionality.
3Reliability
If uniform current density limits are applied to all metal paths, then electromigration reliability is simplified to ensure, but design optimality is lost due to ignoring current waveform variations
Solution Approach 1:
The patent applies local quality by computing and applying different reliability budgets and current density limits for each metal path based on its specific average current characteristics. This localized approach replaces the simplified uniform limit with path-specific optimized parameters, improving design optimality while systematically ensuring electromigration reliability through the proportionality constraint.
Solution Approach 2:
The patent changes the design parameters from static uniform values to dynamic path-specific values that reflect actual current conditions. By computing reliability budgets and current density limits proportional to each path's average current, the system achieves both design optimality (through customized parameters) and reliability assurance (through the proportionality relationship).
Data Source
AI summary
Apportioning unequally contributions of different metal paths of a circuit to electromigration (EM) reliability. In an embodiment, a corresponding parameter value representing a magnitude of excess current flowing in a single direction in each metal path is determined. A desired reliability measure for electromigration (EM) is apportioned among the metal paths based on computed parameter values for the corresponding metal path. A reliability analysis for the circuit is performed based on the apportioning. In an embodiment, metal paths which predominantly carry currents with an average value less than a threshold are excluded from being considered as contributors to EM degradation.