Design and Implementation of VLSI Systems (EN0160) Lecture 14: Interconnects

1. Design and Implementation of VLSI Systems (EN0160) Lecture 14: Interconnects Prof. Sherief Reda Division of Engineering, Brown University Spring 2007 [sources: Weste/Addison Wesley – Rabaey/Pearson]

2. Wires (interconnects) are as important as transistors Speed Power Noise Alternating layers run orthogonally Transistors + Wires = Circuits

3. Interconnects have resistance, capacitance (and inductance) Interconnects increase circuit delay: The wire capacitance adds loading to each gate Long wires have significant resistance that further contribute to the delay Interconnects increase dynamic power: Because of the wire capacitance How interconnects contribute to delay and power?

4. Pitch = w + s Aspect ratio: AR = t/w Old processes had AR << 1 Modern processes have AR  2 Pack in many skinny wires Wire geometry

5. ρ = resistivity (W*m) R = sheet resistance (Ω/)  is a dimensionless unit(!) 1. Wire Resistance

6. Until 180 nm generation, most wires were aluminum Modern processes often use copper Cu atoms diffuse into silicon and damage FETs Must be surrounded by a diffusion barrier How does the kind of metal impact resistivity?

7. Contacts and vias also have 2-20 Ω Use many contacts for lower R Many small contacts for current crowding around periphery Contact and via resistance

8. Wire has capacitance per unit length To neighbors To layers above and below Ctotal = Ctop + Cbot + 2Cadj 2. Wire capacitance

9. Parallel plate equation: C = eA/d Wires are not parallel plates, but obey trends Increasing area (W, t) increases capacitance Increasing distance (s, h) decreases capacitance Dielectric constant e = ke0 e0 = 8.85 x 10-14 F/cm k = 3.9 for SiO2 Processes are starting to use low-k dielectrics k  3 (or less) as dielectrics use air pockets Factors impacting the capacitance

10. Typical wires have ~ 0.2 fF/mm Compare to 2 fF/mm for gate capacitance) Polysilicon has lower C but high R Use sparingly for very short wires between gates M2 capacitance data

11. Wires are a distributed system Approximate with lumped element models 3-segment p-model is accurate to 3% in simulation L-model needs 100 segments for same accuracy! Use single segment p-model for Elmore delay Given R and C, how to calculate interconnect delay?

12. Interconnect delay: the lumped case Vm Vout 0V Upper bound on delays in RC trees [Pileggi’97]

13. Interconnect delay: ideal analysis tpd~0.38RC

14. Interconnect delay: distributed Elmore delay r = resistance per unit length c = capacitance per unit length lumped overestimates delay (ideally, modeling using diffusion equation; covered in class)

15. Delay calculations Assuming ideal wires: Realistic wire modeling:

16. AMI 0.6 mm process has 3 metal layers Modern processes use 6-10+ metal layers Example: Intel 180 nm process M1: thin, narrow (< 3l) High density cells M2-M4: thicker For longer wires M5-M6: thickest For VDD, GND, clk Layer stack Why do you think different metal layers have different widths/thickness?