1. EE 587 SoC Design & Test Partha Pande School of EECS Washington State University pande@eecs.wsu.edu

2. SoC Physical Design Issues Wire Inductance

3. Wire Inductance Wide wires in clock distribution & upper level metal layers These wires have low resistance Exhibit significant inductive effects New materials with low-resistance interconnect

4. Inductance Complete interconnect model should include inductance With increasing frequency and a decrease in resistance due to wide wires and the use of copper, inductance will begin to influence clocks/busses: Z = R + j  L Inductance, by definition, is for a loop not a wire  inductance of a wire in an IC requires knowledge of return path(s)  inductance extraction for a whole chip is virtually impossible... R L C V=Ldi dt V +- i

5. Evolution of Interconnect Model

6. Transmission Line Model Follow Board Notes

7. Inductance Effects Lumped RLC line R L C Treat RC problem as a resistive divider: V O = Z o V in ZtZt Z o ZtZt = 1 sC 1 sC + (R + sL) = 1 s 2 LC + sRC + 1 VOVO V in Poles are P 1,2 =  n  sqrt(    = n2n2 s 2 + s2  n +  n 2  n = 1/sqrt(LC)  =RC/2sqrt(LC) = damping factor  > 1 we have two real poles (RC effects)  < 1 we have two complex poles (RLC effects) +-+-

8. Inductance Effects Follow board notes

9. Other Inductance Effects For most gates R on is in the order of K  so typically R >> j  L  response is dominant by RC delay for most signals Only the large drivers have a small enough R on to allow the inductance to control the dynamic response  clocks  busses For clocks, self-inductance term can dominate the response (especially if shielding is used) For busses, mutual inductance term dominates and creates noise events that could cause malfunction For power supplies, inductance can also be a problem due to the Ldi/dt drop (in addition to the IR drop) as supplies scale down

10. Capacitive and Inductive Noise For most wires, j  L < (Rwire+Rdrive) for the frequency and R of interest. So, for delay, L is not a big issue currently. But  L can be  20 - 30% of R so noise may be seen on adjacent line (mutual coupling) Return path current + - - + Dangerous scenario is a combination of localized capacitive coupling noise and long range mutual inductive coupling noise Double noise events

11. Gate Driving an RLC Transmission Line

12. Propagation Delay R t =Rl, L t =Ll, C t =Cl, C T =C L /C t

13. Propagation Delay (Cont’d) 50% propagation delay where ζ and w n are the damping factor and natural frequency of the circuit Function of both the interconnect and gate impedance

14. Propagation Delay (Cont’d) If the ratio of the total resistance of the line to the lossless characteristic impedance increases, inductive effects can be neglected If the ratio of the driver resistance to the lossless characteristic impedance increases, inductive effects can be neglected If the ratio between the time required to charge the load capacitance through the gate and wire resistance to the time of fight increase then inductive effects can be neglected

15. Effect of inductance on Signal Delay

16. Dependence of Delay on Interconnection Length If the gate parasitic impedances (C L and R tr ) are neglected then the propagation delay can be expressed as For the limiting case where L →0, the above equation reduces to For the limiting case R ->0, the delay is given by

17. Repeater Insertion revisited Lower repeater size and less number of repeaters The amount of inductance effects present in an RLC line depends on the ratio between the RC and the LC time constants of the line As Inductance effect increases the LC time constant dominates the RC time constant and the delay of the line changes from a quadratic to a linear dependence on the line length. Optimum number of repeaters for the minimum propagation delay decreases

18. Inductance & Power Dissipation The dynamic power is given as Increasing inductance effects results in fewer number of repeaters as well as smaller repeater size Significantly reduces total capacitance Faster rise time results in lower short-circuit power

19. Inductance Extraction Inductance can only be defined for a closed current loop The inductance of the loop is proportional to the area of the loop At low frequency resistive impedance dominates Current uses as many returns as possible to have parallel resistances Situation is different at higher frequencies

20. Mutual Inductance Causes extra noise and delay effects

21. Inductive Noise in a bus Physically, a wide bus with all the lines switching in the same direction behaves as one wide line Hence, the effective inductance of a line that is part of a bus is far larger than the self-inductance of that line LC time constant of the line becomes much larger

22. L di/dt effects on the Power Supply

23. Antenna Effects As each metal layer is placed on the chip during fabrication, charge builds up on the metal layers due to CMP 1, etc. If too much charge accumulates on gate of MOS transistor, it could damage the oxide and short the gate to the bulk terminal Higher levels of metal accumulate more charge so they are more troublesome (i.e., metal 5 is worse than metal 1) Need to discharge metal lines during processing sequence to avoid transistor damage (becomes a design/layout issue) + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + This transistor could be damaged Metal 1 Poly Metal 2 Antenna Ratio = Area wire Area gate 1. CMP is chemical mechanical polishing which is used to planarize each layer before the next layer is placed on the wafer.

24. Preventing Antenna Effects A number of different approaches for antenna repairs: Diode Insertion - Make sure all metal lines are connected to diffusion somewhere to discharge the metal lines during fabrication n+ + + + + + + + + + + + + + + + + + + + + + + + + + + + Antenna diode p -diodes costs area - need to optimize number and location - causes problems for design verification tool

25. Preventing Antenna Effects Note that there are always diodes connecting to source/drain regions of all transistors and charge on each layer is drained before next layer is added…so why are we worried? Gate input of next device may not be connected to a diode until it’s too late…charge accumulation on metal exceeds threshold Should put antenna diode here. Keep area of upper layer metals small near next transistor

26. Preventing Antenna Effects Second approach is to add buffers to interconnect to break up long wire routes and provide more gate area for antenna ratio Third approach is to use metal jumpers to from one layer of metal to another Metal 1/polish vias (charge removed) Metal2/polish + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++++++ + + + + + + + + + + + +

27. Class Presentation The first class presentation assignment will be posted soon. One of you has to present the basic concepts discussed in the paper to the class Presentation time ~20 minutes After the presentation everybody has to participate in the discussion