Topics

1. Topics • Wire and via structures. • Wire parasitics. • Transistor 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. Example: parasitic capacitance measurement • n-diffusion: bottomwall=2 fF, sidewall=2 fF. • metal: plate=0.15 fF, fringe=0.72 fF. 1.5 m 3 m 0.75 m 2.5 m 1 m

10. Wire resistance • Resistance of any size square is constant:

11. 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

12. 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.

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

14. 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 conducitvity

15. 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(Rdc2 + k Rhf2) • Typically k = 1.2.

16. Transistor gate parasitics • Gate-source/drain overlap capacitance: gate source drain overlap

17. Transistor source/drain parasitics • Source/drain have significant capacitance, resistance. • Measured same way as for wires. • Source/drain R, C may be included in Spice model rather than as separate parasitics.