1. Topics
Wire and via structures.
Wire parasitics.

2. Wires and vias
metal 3
metal 2
vias
metal 1
poly
poly
p-tub n+ n+

3. Metal migration
Current-carrying capacity of metal wire depends on cross-section. Height is fixed, so width determines current limit.
Metal migration: when current is too high, electron flow pushes around metal grains. Higher resistance increases metal migration, leading to destruction of wire.

4. Metal migration problems and solutions
Marginal wires will fail after a small operating period—infant mortality.
Normal wires must be sized to accomodate maximum current flow:
Imax = 1.5 mA/m of metal width.
Mainly applies to VDD/VSS lines.

5. Diffusion wire capacitance
Capacitances formed by p-n junctions:
sidewall
capacitances
depletion region
n+ (ND)
bottomwall
capacitance
substrate (NA)

6. Depletion region capacitance
Zero-bias depletion capacitance:
Cj0 = si/xd.
Depletion region width:
xd0 = sqrt[(1/NA + 1/ND)2siVbi/q].
Junction capacitance is function of voltage across junction:
Cj(Vr) = Cj0/sqrt(1 + Vr/Vbi)

7. Poly/metal wire capacitance
Two components:
parallel plate;
fringe.
fringe
plate

8. Metal coupling capacitances
Can couple to adjacent wires on same layer, wires on above/below layers:
metal 2
metal 1
metal 1

9. Wire resistance
Resistance of any size square is constant:

10. Metal mean-time-to-failure
MTF for metal wires = time required for 50% of wires to fail.
Depends on current density:
proportional to j-n e Q/kT
j is current density
n is constant between 1 and 3
Q is diffusion activation energy

11. Skin effect
At low frequencies, most of copper conductor’s cross section carries current.
As frequency increases, current moves to skin of conductor.
Back EMF induces counter-current in body of conductor.
Skin effect most important at gigahertz frequencies.

12. Skin effect, cont’d Isolated conductor: Conductor and ground:
Low frequency
Low frequency
High frequency
High frequency

13. Skin depth
Skin depth is depth at which conductor’s current is reduced to 1/3 = 37% of surface value:
d = 1/sqrt(p f m s)
f = signal frequency
m = magnetic permeability
s = wire conductivity

14. Effect on resistance Low frequency resistance of wire:
Rdc = 1/ s wt
High frequency resistance with skin effect:
Rhf = 1/2 s d (w + t)
Resistance per unit length:
Rac = sqrt(Rdc 2 + k Rhf 2)
Typically k = 1.2.

15. Wire capacitance and resistance
Capacitance to ground (aF/mm)
Coupling capacitance (aF/mm)
Resistance/ length (W/mm)
Metal 3 18 9
0.2
Metal 2 47 24
0.3
Metal 1 76 36

16. Gate delay vs. wire delay
Minimum-size inverter delay: 2.9 ps
Length of wire with equal delay---assume wire with capacitance equal to inverter input capacitance = 0.12 fF.
Metal 3 length is 6.7 mm.
About 75 times width of minimum-size transistor.