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Interpretation of Current Density Specifications of TSMC0.18um

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pancho_hideboo

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In document of TSMC 0.18um CMOS, I can see the following description about Current Density Specification.
It's nominal AlCu thickness instead of genuine total thickness.
Jrms is root-mean-square current density through a metal line.
The numbers given below are for <10degC Joule heating.

Jrms <= 8 mA/um(= 2e6 A/cm^2) for M1
Jrms <= 4 mA/um(= 1e6 A/cm^2) for M2 to M5
Jrms <= 8 mA/um(= 1e6 A/cm^2) for M6

I can not understand what this description mean.

Can you teach me what this description mean physically ?
 

Joule heating means heating by the electrical power P converted in the metal line resistance R: P = I2*R in watts = joules per second.

The actual heating in degrees ΔT is determined by the thermal resistance Rth to the environment and the specific thermal resistivity of the environmental layer(s), respectively the reference temperature of the substrate material, if the thermal resistance Rth of the isolating layers (SiO2, Si3N4) is the limiting factor, i.e. the specific thermal resistivity of the substrate material is sufficient high, as is the case with silicon.

ΔT = P * Rth
 

More importantly since conductor temperature !=
chip or package or oven temperature, and the
conductor temperature is a prime exponential
accelerating factor in the back-figuring of the
allowable current density at rated temp from
stress temp, they insist to constrain the heating
of metal in order for the numbers to be sound.

I have suffered at the hands of an in-house
technology group who allowed EM test stress of
1E7 A/cm2 in Met2 (but 1E6 in the rest) and paid
no attention to the self heating (neither mentioned,
calculated or measured). Just assumed oven temp
and did the math. So I had to live with a sub-1E5
A/cm2 current density rule (sweet, for power
management). And of course nobody wanted to
pay for the retest or admit their screw-up.

2E6 A/cm2 seems awfully aggressive for DC, 1E6
is normal-ish for AC (truly reversing, balanced).
 

ΔT = P * Rth
Thanks for answering.

So does 10degC in the following mean ΔT ?
Code:
[b][color=red]It's nominal AlCu thickness instead of genuine total thickness.[/color][/b]
Jrms is root-mean-square current density through a metal line.
The numbers given below are [b][color=red]for <10degC Joule heating[/color][/b].

What does "It's nominal AlCu thickness instead of genuine total thickness." mean ?

In document of TSMC 0.18um CMOS, I can see the following description about EM(Electro Migration) Specification.
Code:
Jmax is maximum DC current allowed per um of metal line width.
The number is based on 0.1% point of measurement data at 20% resistance increase after 10 years continuous operation at 110degC.
Jmax <= 1 mA/um for M1 to M5


Jav is AVERAGE current density through a metal line.
The numbers given below are for 10% resistance increase after 10-year continuous operation at 110degC.
Jav <= 1 mA/um(= 2.5e5 A/cm^2) for M1 to M5 (0.4um thickness)

If I don't care about ΔT, can I conclude these limitations regarding Jmax and Jav are critical than Jrms ?
 

For reliability "guarantees" to apply, none of the Jxyz
limits shall be violated. Each applies to a specific type
of electrical stress (DC=Jmax, unidirectional pulsed =
timer-averaged Javg, symmetric reversing AC-only is
Jrms. The case of AC-riding-on-DC is a judgment call
I suppose as now there is a reversible and irreversible
component to material migration, summed.

Re thickness, you are unlikely to know, care or find out
what the true thickness is (or was in the foundational
experiment behind all the rules derivations) and so
everyone just gets to pretend that nominal is the case
at hand, regardless. Unless you want to go get SEM
photos (at the worst case step, which you get to
find and indicate for the sample sectioning) and then
repeat the reliability analysis with the new numbers
(a fool's errand since the original sample metal layer
thicknesses are likely to be either never known or
simply not worth digging up and providing, so your
relation between material in hand and material in
rules, can never be known beyond process tolerance
slop).

I'd forget about delta-T until you get close to a rule
violation and need a shave.
 

So does 10degC in the following mean ΔT ?
Yes, right.

What does "It's nominal AlCu thickness instead of genuine total thickness." mean ?

I'd think with "nominal AlCu thickness" the metal layers' thickness stated as nominal in the process (qualification) report/description is meant. "Genuine total thickness" presumably is the real thickness, which may differ from the nominal thickness due to process variations.
 

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