1. Power distribution

2. Interconnect properties
Not all metal layers have the same properties:
Hard to fabricate small-pitch metal on higher layers.
Match the uses of each layer to its performance and power properties.

3. Levels of interconnect6X
global 2X 1X
local

4. Resistance vs. size Increasing width struggles scaling in resistance.
Constant scaling increases resistance quadratically.
nX layers are larger, can support fewer wires per square centimeter.
Use higher layers for global power and signals.

5. Wire design Long global signals usually require repeaters.
The transistors are on the silicon layer---must use vias to go all the way down and back up.
Thermal gradients can exist horizontally and to some extent vertically.

6. Power distribution
Must size wires to be able to handle current—requires designing topology of VDD/VSS networks.
Want to keep power network in metal—requires designing planar wiring.
Power distribution problems:
IR drops from steady state current.
L di/dt drops from transient current.

7. Power Distribution Network
Ohmic drops that degrade the signal level are especially important in the power distribution network where current levels can easily reach amperes.
Such IR drops
affect reliability
impact the performance as even a small drop in VDD can cause a significant increase in delay

8. Design the techniques for power distribution networks to Reduce the maximum distance between the supply pins and the circuit supply connections by adopting a structured layout of the power distribution network
route power and ground vertically (or horizontally) inter-digitized on the same layer bringing power in from two sides of the die
use two metal layers for power distribution bringing power in from four sides of the die
use two solid metal planes for distribution of VDD and GND
Size the power network appropriately

9. Interdigitated power and ground lines
VDD
VSS

10. Power tree design
Each branch must be able to supply required current to all of its subsidiary branches:
Trees are interdigitated to supply both sides of power supply.

11. Planar power/ground routing theorem
Draw a dividing line through each cell such that all VDD terminals are on one side and all VSS terminals on the other.
If floorplan places all cells with VDD on same side, there exists a routing for both VDD and VSS which does not require them to cross.
VSS
cell
VDD
VSS
VDD

12. Planar routing theorem example
cut line
no cut line B
VSS
VDD
no connection
VDD C
VSS A
VDD
VSS
VDD
VSS
VDD
VSS

13. Power supply noise
Variations in power supply voltage manifest themselves as noise into the logic gates.
Power supply wiring resistance creates voltage variations with current surges.
Voltage drops on power lines depend on dynamic behavior of circuit.

14. Tackling power supply noise
Must measure current required by each block at varying times.
May need to redesign power/ground network to reduce resistance at high current loads.
Worst case, may have to move some activity to another clock cycle to reduce peak current.

15. Power distribution grids
Upper layers carry global power to subsystems.
Lower layers distribute to smaller blocks.
Physical design:
Within a layer, interdigitate VDD/VSS.
Between layers, put power lines orthogonally.

16. Decoupling capacitors

17. Clock distribution Goals:
deliver clock to all memory elements with acceptable skew;
deliver clock edges with acceptable sharpness.
Clocking network design is one of the greatest challenges in the design of a large chip.

18. Clock delay varies with position

19. H-tree f

20. Clock distribution tree
Clocks are generally distributed via wiring trees.
Want to use low-resistance interconnect to minimize delay.
Use multiple drivers to distribute driver requirements—use optimal sizing principles to design buffers.
Clock lines can create significant crosstalk.

21. Clock distribution tree example

22. Floorplanning tips
Develop a wiring plan. Think about how layers will be used to distribute important wires.
Sweep small components into larger blocks. A floorplan with a single NAND gate in the middle will be hard to work with.
Design wiring that looks simple. If it looks complicated, it is complicated.

23. Floorplanning tips, cont’d.
Design planar wiring. Planarity is the essence of simplicity. It isn’t always possible, but do it where feasible (and where it doesn’t introduce unacceptable delay).
Draw separate wiring plans for power and clocking. These are important design tasks which should be tackled early.

24. Cross talk
Unwanted coupling with adjacent signal wires injects noise into a signal depending on the transient values of the other signals routed in the neighborhood

25. Power optimization Glitches cause unnecessary power consumption.
Logic network design helps control power consumption:
minimizing capacitance;
eliminating unnecessary glitches.

26. Glitching example
Gate network:

27. Glitching example behavior
NOR gate produces 0 output at beginning and end:
beginning: bottom input is 1;
end: NAND output is 1;
Difference in delay between application of primary inputs and generation of new NAND output causes glitch.

28. Adder chain glitching
bad
good

29. Explanation
Unbalanced chain has signals arriving at different times at each adder.
A glitch downstream propagates all the way upstream.
Balanced tree introduces multiple glitches simultaneously, reducing total glitch activity.

30. Signal probabilities
Glitching behavior can be characterized by signal probabilities.
Transition probabilities can be computed from signal probabilities if clock cycles are assumed to be independent.
Some primary inputs may have non-standard signal probabilities— control signal may be activated only occasionally.

31. Delay-independent probabilities
Compute output probabilities of primitive functions:
PNOT = 1 - Pin
POR = 1 -  Pi)
PAND = Pi
Can compute output probabilities of re convergent fanout-free networks by traversing tree.

32. Factorization techniques
In example, a has high transition probability, b and c low probabilities.
Reduce number of logic levels through which high-probability signals must travel in order to reduce propagation of glitches.

33. Wires and vias

34. Wires and vias Wire and via structures. Wire parasitics.
Transistor parasitics.
Fabrication theory and practice.

35. Wires and vias
metal 3
metal 2
vias
metal 1
poly
poly
p-tub n+ n+

36. Metal interconnect Many layers of metal interconnect are possible.
12 layers of metal are common.
Lower layers have smaller features, higher layers have larger features.
Can’t directly go from a layer to any other layer.

38. Copper interconnect Much better electrical characteristics.
Copper is poisonous to semiconductors---must be isolated from silicon.
Bottom layer of interconnect is aluminum.

39. Metal migration
Current-carrying capacity of metal wire depends on cross-section.
Height is fixed, so width determines current limit.
Metal migration: when current is too high, electron flow pushes around metal grains.
Higher resistance increases metal migration, leading to destruction of wire.

40. Metal migration problems and solutions
Marginal wires will fail after a small operating period.
Normal wires must be sized to accommodate maximum current flow:
Imax = 1.5 mA/m of metal width.
Mainly applies to VDD/VSS lines.

41. wiring capacitance
The wiring capacitance depends upon the length and width of the connecting wires and is a function of the fan-out from the driving gate and the number of fan-out gates.
Wiring capacitance is growing in importance with the scaling of technology.

42. Dealing with Capacitance
EE141
Dealing with Capacitance
Low capacitance (low-k) dielectrics (insulators) such as polymide or even air instead of SiO2
family of materials that are low-k dielectrics
must also be suitable thermally and mechanically and
compatible with (copper) interconnect
Copper interconnect allows wires to be thinner without increasing their resistance, thereby decreasing interwire capacitance
SOI (silicon on insulator) to reduce junction capacitance

43. Diffusion wire capacitance
Capacitances formed by p-n junctions:
sidewall
capacitances
depletion region
n+ (ND)
bottomwall
capacitance
substrate (NA)

44. Depletion region capacitance
Zero-bias depletion capacitance:
Cj0 = si/xd.
Depletion region width:
xd0 = sqrt[(1/NA + 1/ND)2siVbi/q].
Junction capacitance is function of voltage across junction:
Cj(Vr) = Cj0/sqrt(1 + Vr/Vbi)

45. Poly/metal wire capacitance
Two components:
parallel plate;
fringe.
fringe
plate

46. Fringe capacitance is the capacitance due to the stray electric fields at the edges of a capacitor.
Think of the parallel plate capacitor, where the electric field lines in the center are straight.
The edges of the plates have fringing fields.
The capacitance due to the field at the edges is the fringe capacitance.
In the case of interconnect capacitance, the metal lines on the chip will cross over each other and form parallel plate capacitors, with edges.

47. Metal coupling capacitances
Can couple to adjacent wires on same layer, wires on above/below layers:
metal 2
metal 1
metal 1

48. Example: parasitic capacitance measurement
n-diffusion: bottomwall=2 fF, sidewall=2 fF.
metal: plate=0.15 fF, fringe=0.72 fF.
1.5 m
3 m
0.75 m
2.5 m
1 m

49. Wire resistance
Resistance of any size square is constant:

50. Wire Spacing Comparisons
Intel P858
Al, 0.18m
Intel P856.5
Al, 0.25m
IBM CMOS-8S
CU, 0.18m
 M1
 M6
 M7
 M2
 M3
 M4
 M5
 M6
 M5
 M5
 M4
 M4
 M3
From the Intel generations, its clear that the wires get closer together, but the vertical dimensions do not shrink proportionally, which increases capacitance.
In contrast, IBM’s copper interconnect has much thinner layers – thus less capacitance – even though the wire resistance (including cladding) is similar to that of the P858 technology
 M3
 M2
 M2
 M1
 M1
Scale: 2,160 nm
From MPR, 2000

51. Skin effect
At low frequencies, most of copper conductor’s cross section carries current.
As frequency increases, current moves to skin of conductor.
Back EMF induces counter-current in body of conductor.
Skin effect most important at gigahertz frequencies.

52. The skin effect causes the effective resistance of the conductor to increase at higher frequencies where the skin depth is smaller, thus reducing the effective cross-section of the conductor.

53. Skin effect, cont’d Isolated conductor: Conductor and ground:
Low frequency
Low frequency
High frequency
High frequency

54. Skin depth
Skin depth is depth at which conductor’s current is reduced to 1/3 = 37% of surface value:
d = 1/sqrt(p f m s)
f = signal frequency
m = magnetic permeability
s = wire conducitvity

55. Effect on resistance Low frequency resistance of wire:
Rdc = 1/ s wt
High frequency resistance with skin effect:
Rhf = 1/2 s d (w + t)
Resistance per unit length:
Rac = sqrt(Rdc 2 + k Rhf 2)
Typically k = 1.2.

56. Transistor gate parasitics
Gate-source/drain overlap capacitance:
gate
source
drain
overlap

57. Transistor source/drain parasitics
Source/drain have significant capacitance, resistance.
Measured same way as for wires.

58. source/drain overlap capacitances.
During fabrication, the dopants in the source/drain regions diffuse in all directions, including under the gate as shown in Figure.
The source/drain overlap region tends to be a larger fraction of the channel area in deep submicron devices.
The overlap region is independent of the transistor length, so it is usually given in units of Farads per unit gate width.
Then the total source overlap capacitance for a transistor would be

59. The substrates underneath the transistors must be connected to a power supply: the p-tub (which contains n-type transistors) to VSS and the n-tub to VDD. These connections are made by special vias called tub ties.

60. Parasitic: silicon-controlled rectifier

61. The parasitic bipolar transistors and resistors create a parasitic silicon-controlled rectifier, or SCR.
The SCR has two modes of operation.
When both bipolar transistors are off, the SCR conducts essentially no current between its two terminals.
As the voltage across the SCR is raised, it may eventually turn on and conducts a great deal of current with very little voltage drop.

62. The SCR formed by the n- and p-tubs, when turned on, forms a high-current, low-voltage connection between VDD and VSS.
Its effect is to short together the power supply terminals.
When the SCR is on, the current flowing through it floods the tubs and prevents the transistors from operating properly.
In some cases, the chip can be restored to normal operation by disconnecting and then reconnecting the power supply; in other cases the high currents cause permanent damage to the chip.

63. Manufacturing problems
Photoresist shrinkage, tearing.
Variations in material deposition.
Variations in temperature.
Variations in oxide thickness.
Impurities.
Variations between lots.
Variations across a wafer.

64. Transistor problems Varaiations in threshold voltage:
oxide thickness;
ion implanatation;
poly variations.
Changes in source/drain diffusion overlap.
Variations in substrate.

65. Wiring problems
Diffusion: changes in doping -> variations in resistance, capacitance.
Poly, metal: variations in height, width -> variations in resistance, capacitance.
Shorts and opens:

66. Oxide problems Variations in height.
Lack of planarity -> step coverage.
metal 2
metal 2
metal 1

67. Via problems Via may not be cut all the way through.
Undersize via has too much resistance.
Via may be too large and create short.

68. Routing

69. Routing – Complete the interconnections between modules.
Factors like critical path, clock skew, wire spacing, etc., are considered.
Divided in to global routing and detailed routing v
Feedthrough
Type 1 standard cel1
Type 2 standard cell

70. Construct a decision graph Gd
Labels of some of the inner angles of G can be immediately determined 3 2 1 2 3 1
a plane graph G

71. Construct a decision graph Gd3 2 1 2 3 1 2 2
a plane graph G

72. Construct a decision graph Gd3 2 1 3 2 3 1 3 2 2 2 2 2 3 1 3 3 2
a plane graph G

73. Construct a decision graph Gd3 2 1 2 3 1 2 2 1 1
a plane graph G

74. Construct a decision graph Gd3 2 1 2 3 1 2 2 1 1
a plane graph G

75. Construct a decision graph Gd3 2 1 2 3 1 1 1 2 2 1 1
a plane graph G

76. Construct a decision graph Gd3 2 1 2 3 1 1 1 2 2 1 1
a plane graph G

77. Construct a decision graph Gd3 2 1 2 3 2 1 2 1 1 2 2 1 1 1
a plane graph G

78. Construct a decision graph Gd3 2 1 2 3 1 2 1 2 1 1 1 2 2 1 1
a plane graph G

79. Construct a decision graph Gd3 2 1 2 3 1 1 2 1 2 1 1 1 1 2 2 1 1 1 1 1
a plane graph G

80. Construct a decision graph Gd
outer vertex of degree 3 3 2 1 2 3 1 1 2 1 2 1 1 1 1 2 2 1 1
a plane graph G

81. Construct a decision graph Gd3 2 1 2 3 1 1 2 1 2 1 1 1 1 1 2 2 1 1
a plane graph G

82. Construct a decision graph Gd3 2 1 2 3 1 1 2 1 2 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1
a plane graph G

83. Construct a decision graph Gd3 2 1 2 3 1 1 2 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
a plane graph G

84. Construct a decision graph Gd3 2 1 2 3 1 1 2 1 2 1
a plane graph G

85. Construct a decision graph Gd3 2 1 2 3 1 1 2 1 2 1 2
a plane graph G

86. Construct a decision graph Gd3 2 1 2 3 1 1 2 1 2 1 1 2 2
a plane graph G

87. Inner Rectangular Drawings of Plane Graphs ーＡｐｐｌｉｃａｔｉｏｎ　ｏｆ　Ｇｒａｐｈ　Ｄｒａｗｉｎｇ　ｔｏ　ＶＬＳＩ　Ｌａｙｏｕｔ－

88. Routing Connect the various standard cells using wires Input: Output:
Cell locations, netlist
Output:
Geometric layout of each net connecting various standard cells
Two-step process
Global routing
Detailed routing
The routing stage connects the various standard cells of our system using wires. The routing algorithms use cell locations and netlist as the input and generate a geometric layout of each net that connects the various standard cells. The routing process is a two step process – global routing and detailed routing.

89. Global routing
In global routing, connections are completed between proper blocks of the circuit disregarding exact geometric details of each wire and pin.
For each wire GR finds a lists of channels which are to be used as a passageways for that wire. In other words, GR specifies different regions in the routing space through which a wire should be routed.

90. Detailed routing
DR completes point-to-point connections between pins on the blocks.
GR is converted into exact routing by specifying geometric information such as location and spacing of wires and their layer assignments.
It includes channel and switchbox routing.

91. Global routing vs detailed routing*
So what is the difference between global routing and detailed routing. Suppose the chip is is North America and some travelers in California need advice on how to drive from Stanford (near San Francisco) to Caltech (near Los Angeles). The floorplanner has decided that California is on the left (west) side of the ASIC and the placement tool has put Stanford in Northern California and Caltech in Southern California. Floorplanning and placement have defined the roads and freeways. There are two ways to go: the coastal route (using Highway 101) or the inland route (using Interstate I5, which is usually faster). The global router specifies the coastal route because the travelers are not in a hurry and I5 is congested (the global router knows this because it has already routed onto I5 many other travelers that are in a hurry today). Next, the detailed router looks at a map and gives indications from Stanford onto Highway 101 south through San Jose, Monterey, and Santa Barbara to Los Angeles and then off the freeway to Caltech in Pasadena. So in case of a chip, global routing generates a loose route for each net and list of routing regions are assigned, while detailed routing does the geometric layout for each net within the assigned routing regions. As you can see from this example, global routing determined the approximate routes between the various modules of the system, while detailed routing generated the geometric layout of each net.
* Sung Kyu Lim

92. Net Ordering in Area Routing
Effect of net ordering on routability A´ B´
Optimal routing of net B A B A´ B´
Nets A and B can be routed only with detours A B A´ B´
Optimal routing of net A A B
© 2011 Springer Verlag

93. Net Ordering in Area Routing
Effect of net ordering on total wirelength A A´ B B´
Routing net A first
Routing net B first A A´ B B´
© 2011 Springer Verlag

94. Line probe routing
Heuristic(experience based) method for finding a short route.
Works with arbitrary combination of obstacles.
Does not explore all possible paths—not optimal.

95. Line probe example
line 1 A A
line 2

96. Maze algorithm
find the shortest path for a single wire between a set of points, if any path exists.
Maze runner is a connection routing method that represents the entire routing space as a grid.
Parts of this grid are blocked by components, specialised areas, or already present wiring.
The grid size corresponds to the wiring pitch of the area.
The goal is to find a chain of grid cells that go from point A to point B.

97.  Initialisation
Select start point, mark with 0 - i := 0
REPEAT - Mark all unlabeled neighbors of points marked with i with i+1 - i := i+1 UNTIL ((target reached) or (no points can be marked))
go to the target point REPEAT - go to next node that has a lower mark than the actual node - add this node to path UNTIL (start point reached)
Block the path for future wirings - Delete all marks

98. Maze Search Expansion (2) Backtracing Expansion (1) S T 1 2 T 1 2 3 S
© 2011 Springer Verlag

99. Maze Search S T

101. Maze routing Mainly for single-layer routing Strengths Weakness
Finds a connection between two terminals if it exists
Weakness
Large memory required as dense layout
Slow
Application – global routing, detailed routing
This particular algorithm is specifically for single-layer routing. The obvious strength of this technique is that it finds a connection between two terminal if it exists. However, it requires large amount of memory as you need to store the information about various grid points that are located at a particular distance from the source and also this technique is very slow. This routing technique can be easily applied for global routing and detailed routing.

102. Routing algorithms Global routing Detailed routing Maze routing
Cong/Prea’s algorithm
Spanning tree algorithm
Steiner tree algorithm
Detailed routing
2-L Channel routing: Basic left-edge algorithm
Y-K algorithm
Various other routing algorithms have been proposed. Various algorithms have shown improvement over the maze routing technique in terms of time, memory requirements and routing solutions. Some of the popular algorithms include Spanning tree algorithm, Steiner tree based routing, Channel routing etc.

103. Specialized routing
Once we have routed the signal interconnects, next we route the clocks and power lines. We talked about clock routing last week. The idea is to minimize the clock skew and the delay along the clock routing path. In case of power routing, we need to have low resistance metal lines to ensure adequate current.

104. Power routing
Power can be distributed on a chip in various ways. You can use two stacked layer of metals – one for Vdd and one for Gnd. This is a good option for low-cost and low power designs. You can used a power grid where vertical and horizontal power bars are interconnected. Typically the upper layers of the metal stack are used for routing power. Here typically 2-3 signal lines are used to separate the power lines. Also the power lines have larger widths compared to the signal lines. You could also use dedicated Vdd and Gnd planes, but it is very expensive. Intel uses the power grid while AMD uses dedicated power and ground planes

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