VLSI systems #9
Speed, space and power trade-offs.
P.J. Drongowski

******************
Power calculations
******************

Power distribution.

  * Power and ground must be distributed on metal.
  * The metal path are usually enmeshed:
        ---------------------
        |      |      |     |
            |      |     |
        ---------------------
    because the paths cannot cross.
  * Fundamental limit on current per unit cross section of metal.
  * Metal migration.
    + Poorly understood.
    + If density threshold is exceeded, metal atoms physically
      move in the direction of the current.
    + Current is higher through constrictions in metal.
    + Eventually, a constriction will blow like a fuse!
  * For aluminum, maximum current density is about 2-3 mA/sq-micron.
    Conservative designers use a density of 1 mA/sq-micron.
  * For a minimum width metal wire of 3 lambda, lambda = 2 microns,
    and wire depth of 1, the current should be limited to:
      3 lambda * 2 microns/lambda * 1 micron * 1 mA/sq-micron = 6 mA

Subsystem power estimation.

  * Draw an inverter with W/L   = 1/4 and W/L   = 1/1.
                             pu              pd
  * Calculate the channel resistance from Vdd to ground, assuming
    that the input is ON.
      R = (4 + 1) * 10^4 ohms = 5 * 10^4 ohms
  * Let Vdd = +5V, then the current through the channel is:
               5V
      I = ------------- = 0.1 mA
          5 * 10^4 ohms
  * Therefore, a 3 lambda metal wire can power 60 inverters of
    this size.
  * 3 lambda power lines are only good for small subsystems.

*************
Trading S/S/P
*************

  * Delay, transistor size and power consumption can all be
    traded against each other.

       W/L   W/L        W/L   W/L        W/L   W/L  
          pu    pd         pu    pd         pu    pd
       ---------------------------------------------
       1/4   1/1        1/2   2/1        1/1   4/1
       ---------------------------------------------
Delay   15/>60 ns        11/49 ns         9/16 ns
Current  0.1 mA           0.2 mA           0.4 mA

    Rise and fall times are time required to go to minimum low
    and maximum high.

               5V
    I     = -------- = 0.1 mA
     long   5 * 10^4

                5V
    I     = ---------- = 0.2 mA
     wide   2.5 * 10^4

                5V
    I    = ----------- = 0.4 mA
     mid   1.25 * 10^4

-> Compute current and power (I * V) requirements for
   10,000 and 100,000 gate systems.

-> Describe the S/S/P optimization dilemma.
   * Need to drive long wire -> Make transistors bigger.
   * Change in layout makes wire shorter/longer -> Adjust transistor sizes.
   * Change makes power to big -> Make delays longer.
   * Etc.

Why does nMOS consume a lot of power?

Describe CMOS and switching time/power relationship.

Copyright (c) 1984 Paul J. Drongowski