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Next we move to resistance

This is the model of the wire resistance

And we know this is the length of the wire.

This is the direction of the current

And this is the thickness of the wire.

This is the width of the wire

So according to the resistance,

how to calculate resistance, that one equals

The ρover H times the length over width. Right?

And you know this the length, the width, the thickness,

theρhere stands for resistivity of commonly used conductors

For example the silver, the copper, the gold,

the aluminum and tungsten

And normally we use the copper and aluminum as the wires.

So you can see the resistivity of the copper and aluminum.

This is, this one is much bigger than that of this one

And according to this expression you can find out

Because the p over H times L over W. So this one

For example this is width, this is length.

This one if we scale this one,

scale the width and length by the same factor

Therefore this one has the same resistance as this one

Right? Because the length over width of

this one is equal to the length over width of this one. Right?

Therefore because normally the resistivity of

the conductor is constant and also the thickness

of the wire in the same process is constant

Therefore, we can define the ρ over H as this one.

This is called R square

R square, unit is Ω per square.

Therefore the resistance of

wire equals R square times L over W

Right? So with this one

we can calculate the resistance of the wire

And here I just mentioned that the copper has a resistance

which is the substantially lower than that of the aluminum

However the copper has

The disadvantage that it is very easy for copper to diffuse into the silicon

So that's a big issue.

So how could we solve that?

As for as I know,

in about twenty years ago, about 1998, the IBM company

Invented a process called dual damascene process.

The dual damascene process is that coating the copper

with a buffer material called Titanium nitride,

Titanium nitride

And the etch or trench,

I mean the etch or trench in the insulator.

Then fill the copper,

I mean coated by the buffer material Titanium nitride into the trench

OK? And that will prevent the diffusion of the copper into the silicon

Therefore the coexistence of the device will not degrade

So this is in contrast with the traditional process

The traditional process is that it deposit the metal onto insulator

Then etch, remove, remove the redundant one by etching.

So this is different from that one.

This is called IBM dual damascene process

OK?After that the copper is widely

used to interconnect different components

This is the sheet resistance of different material

For example this one,

the n-well region p-well region, n-plus,

p-plus region and this one n-plus p-plus polysilicon

And aluminum,

so you can see the aluminum is,

the R square is much much smaller than that of the others

And also how could we reduce the resistance of the polysilicon?

So we normally use the approach called silicide.

So silicide is a compound material formed

using silicon and a refractory metal.

This creates a highly conductive material

that can withstand high-temperature process steps without melting

so you can see here is a silicide.

this is polysilicon.

this is SiO2.

So by using this one we can heavily reduce

their resistance of the ploysilicon

So conductivity of this one is 8 to 10 times better than polysilicon

This foil tells us, you can find out

when the n-plus p-plus diffusion is with the silicide

you can see the resistance R square is much smaller

than that of this one.

The same is true here that this one,

The polysilicon with silicide

is much smaller than that of this one.

How could we deal with resistance?

We can use selective technology scaling.

You can scale down the width and length of the wire

and keep the thickness of the wire constant

And we can use more interconnect layers,

reduce average wire-length

And we can use better interconnect

materials such as copper and silicides.