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Electromigration is the movement of atoms based on the flow of current through a material. If the current density is high enough, the heat dissipated within the material will repeatedly break atoms from the structure and move them. This will create both ‘vacancies’ and ‘deposits’. The vacancies can grow and eventually break circuit connections resulting in open-circuits, while the deposits can grow and eventually close circuit connections resulting in short-circuit.
Uniform electromigration within metallization lines, if it could be maintained, would not be damaging. In steady-state, no damage should be observed other than at the beginning and end of the metallization line. This is because along the metallization line the number of atoms arriving in a given local volume is equal to the number of atoms leaving the volume.
Damage to the metallization lines is caused by divergences in atomic flux. When the amounts of matter leaving and entering a given volume are unequal, the associated accumulation or loss of material results in damage. This results in two types of inequalities:
The existing solution to avoid electromigration is to ensure that wires with potential large current densities have proper widths to hold them. Due to chemical-mechanical polishing (CMP) effects which reduces the thickness of wires, a thinner wire may be able to hold a larger current density than a wider one. So there could be more than one ranges of EM compliant widths for a wire that has a large current density. Current density tables are typically used to calculate EM compliant widths.
In a design, net routing always needs to meet various constraints, such as EM and resistance constraints. An automatic methodology of checking EM and resistance constraints is needed to improve their designer productivity. With such capability, users then can check their routing results at any stage of the routing flow and make adjustments accordingly to achieve EM and resistance constraints compliance.
The EM constraint tells us how much current a connection object can sustain continuously to achieve a predefined mean time to failure (MTTF). There are 4 types of EM constraints for the 4 kinds of equivalent currents below:
To do an EM constraint check for a net, designers define the equivalent current of this type for each analog or digital cell pin, according to which the EM/R checking engine calculates the equivalent current of this type for each connection object of the net and then performs the following checks:
Factors affecting electromigration:
Black’s Equation: MTTF= CJ-ne(Ea/kT) where
? C= a constant based on metal line properties;
? J = the current density;
? n = integer constant from 1 to 2
? T = temperature in deg K;
? k = the Boltzmann constant; and
? Ea = Activation Energy
If the frequency is less than a critical value f0 = ?(MTFdc), the interconnect will follow a DC electromigration behavior. System fails even before the onset of reverse current. A gradual improvement in MTF happens as frequency is increased above f0. This is due to increased effectiveness of damage healing during reverse period.
At the beginning of positive and negative pulses, atoms and vacancies start to migrate along grain boundaries and interfaces. This migration can recover with opposing stress. A shorter stress period means a relatively small displacement of atoms and vacancies, which is easy to be healed.
Within a very high frequency range, the damage healing process can overcome all defects which are brought during the other half period. However, an interconnect is never immortal. It can fail because of temperature gradients only. In this case Joule Heating sets the lifetime based on RMS current density. Waveform of a stress also has an impact on failure rates. For example, local melting will happen and cause failures for very large peak current densities even if the RMS current density is not very high.
草榴社区 offers electromigration analysis solutions for both digital and custom design environments: