1. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Topics n Wire and via structures. n Wire parasitics. n Transistor parasitics.

2. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Wires and vias p-tub poly n+ metal 1 metal 3 metal 2 vias

3. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Metal migration n Current-carrying capacity of metal wire depends on cross-section. Height is fixed, so width determines current limit. n Metal migration: when current is too high, electron flow pushes around metal grains. Higher resistance increases metal migration, leading to destruction of wire.

4. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Metal migration problems and solutions n Marginal wires will fail after a small operating period—infant mortality. n Normal wires must be sized to accommodate maximum current flow: I max = 1.5 mA/  m of metal width. n Mainly applies to V DD /V SS lines.

5. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Diffusion wire capacitance n Capacitances formed by p-n junctions: n+ (N D ) depletion region substrate (N A ) bottomwall capacitance sidewall capacitances

6. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Depletion region capacitance n Zero-bias depletion capacitance: –C j0 =  si /x d. n Depletion region width: –x d0 = sqrt[(1/N A + 1/N D )2  si V bi /q]. n Junction capacitance is function of voltage across junction: –C j (V r ) = C j0 /sqrt(1 + V r /V bi )

7. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Poly/metal wire capacitance n Two components: –parallel plate; –fringe. plate fringe

8. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Metal coupling capacitances n Can couple to adjacent wires on same layer, wires on above/below layers: metal 2 metal 1

9. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Example: parasitic capacitance measurement n n-diffusion: bottomwall=2 fF, sidewall=2 fF. n metal: plate=0.15 fF, fringe=0.72 fF. 3  m 0.75  m 1  m 1.5  m 2.5  m

10. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Wire resistance n Resistance of any size square is constant:

11. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Mean-time-to-failure n MTF for metal wires = time required for 50% of wires to fail. n 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. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Skin effect n At low frequencies, most of copper conductor’s cross section carries current. n As frequency increases, current moves to skin of conductor. –Back EMF induces counter-current in body of conductor. n Skin effect most important at gigahertz frequencies.

13. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Skin effect, cont’d n Isolated conductor: n Conductor and ground: Low frequency High frequency Low frequency High frequency

14. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Skin depth n Skin depth is depth at which conductor’s current is reduced to 1/3 = 37% of surface value: –  = 1/sqrt(  f  ) –f = signal frequency –  = magnetic permeability –  = wire conducitvity

15. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Effect on resistance n Low frequency resistance of wire: –R dc = 1/  wt n High frequency resistance with skin effect: –R hf = 1/2  (w + t) n Resistance per unit length: –R ac = sqrt(R dc 2 +  R hf  2  Typically  = 1.2.

16. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Transistor gate parasitics n Gate-source/drain overlap capacitance: gate sourcedrain overlap

17. Modern VLSI Design 3e: Chapter 2 Copyright  1998, 2002 Prentice Hall PTR Transistor source/drain parasitics n Source/drain have significant capacitance, resistance. n Measured same way as for wires. n Source/drain R, C may be included in Spice model rather than as separate parasitics.