IR Drop

 
Derivations

Horizontal power straps are half the width (or twice the pitch) of vertical ones; metal resistivities are different; core power consumption is 2W with 32 core Vdd and 32 core Vss pads.

Step 1: Calculate Ipad and Vcore:

Ipad = 
Pnom
Vdd × Npad
2⁄(1.2×32) = 0.052A
Vcore = 
Vddmin(1−2× Ipad ×(Rpkg+Rbond+Rpad))
  Vdd  
1.14×(1−2×0.052×(0.025+0.025+0.1)⁄1.2
1.125V

Step 2: Calculate the reference power supply conductance G:

G = 
7
r2
 
7 ⁄ (4 × 0.07) =  25 mhos

Step 3 is to set out the values of kan, kwn, kcn and mn for each metal layer, and use these to calculate the value of L.

metal layer 1 2 3 4 5 6
 kan  50% 100%  50% 100%  50% 200%
power metal allocated coefficient
 kwn  80%  80%  80%  80%  80%  80%
power metal used coefficient
 kcn  78%¹ 100% 100% 100% 100% 350%²
conductivity coefficient
 mn   0%   0%   0%   0%   0%   0%
core area blocked
¹78%=.07/.09; ²350%=.07/.02

Normally we can't calculate L directly because its value depends on p which we don't know. But in this case with m1‑6=0 we can

L =  kw1kc1(1-ps)(1-m1(1-ka2p)(1-ka3p))+
  kw2kc2(1-m2(1-ka2p)(1-ka3p))+
  kw3kc3(1-m3(1-ka2p)(1-ka3p))+
  kw4kc4(1-m4(1-ka2p)(1-ka3p))+
  kw5kc5(1-m5(1-ka2p)(1-ka3p))+
  kw6kc6(1-m6(1-ka2p)(1-ka3p))
( 0.24 + 0.8 + 0.4 + 0.8 + 0.4 + 5.6 )
8.24

Step 4: Calculate the power strap allocation percentage p:

p = 
{ Vddmin×Pnom kc1×ps } ×  1 
(VcoreVminVdd2×G L
{ 1.14×2 −0.78×0.22 } × 1
(1.125−1.08)×1.22×25 8.24
(1.403−0.173)×0.121 = 14.92%

As shown on the right, a spreadsheet can be used to iterate to the answer.

If the designer sets the power strap pitch, then the supply allocation for each metal layer n is pitch×kan×p⁄2 and the supply width is pitch×kwn×p⁄2. An example is shown in the spreadsheet on the right where we have chosen a vertical power strap pitch of 250µm.

Step 5: Calculate the new core size. If the initial core size estimate without power straps is x, then with power straps the core size becomes x

x′ =   x  =   x  =   x  = x+12.70%
  (((1−ka2p)(1−ka3p))   √(0.8508×0.9254)   0.8873  

The value 12.7% is called the IR Drop Adder.

This represents a more "normal" power busing scenario (but not necessarily a better one), where vertical power straps are preferred over horizontal ones. The extra use of metal-6 for power straps makes sense (a) because it is a long way from the transistors and so the impact on routing density should be less; and (b) because it is a thick metal layer with better conductivity.

Note the value of L=8.24 of which 5.6 comes from metal-6.

Design Attribute Value
Pnom core power consumption 2W
ps fraction of metal-1 in the standard cells used for power supplies 22% (for vsclib)
r1 resistivity of metal layer 1 in ohms per square 0.09Ω per sq.
r2-5 resistivity of metal layers 2-5 in ohms per square 0.07Ω per sq.
r6 resistivity of metal layer 6 in ohms per square 0.02Ω per sq.
ka1,3,5
user defined   
ratio of
metal layers 1,3,5 allocated to power
metal-2 allocated to power
50%
ka4
user defined   
ratio of
metal layer 4 allocated to power
metal-2 allocated to power
100%
ka6
user defined   
ratio of
metal layer 6 allocated to power
metal-2 allocated to power
200%
mn percentage of metal layer n blocked to power straps 0%
Vdd the nominal supply voltage 1.2V
Vddmin the minimum supply voltage, 5% less than nominal 1.14V
Vmin the desired voltage at the centre of the die, 10% less than the nominal 1.08V
Npad number of core Vdd or core Vss power pads 32
Rpkg the resistance of the package leadframe 25mΩ
Rbond the resistance of the bond wire 25mΩ
Rpad the resistance of the bond pad 100mΩ

kcn = 
r2
rn

spreadsheet example