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CAD for VLSI Design - II
Lecture 6
V. Kamakoti and Shankar Balachandran
Overview of this Lecture
• CMOS Transistor Theory
– Delay Issues (Cont’d)
• Types and effects of Capacitances on delay
Parasitic Capacitance
• Switching speeds of MOS systems strongly depend on
the parasitic capacitances associated with MOSFETs
and interconnections
• Total Cload on the output of a CMOS gate is the sum of:
– Gate capacitance (Cg)
– Junction capacitance due to the source and drain
regions and their surroundings (Csb and Cdb)
– Interconnect (or routing) capacitance (Cw)
• Gate oxide capacitance per unit area,
ε ε
= 0 ox
ox
ox
C
t
MOSFET Capacitances
xd xd
xd
Gate Capacitance
• Gate capacitance, Cg = Cox WL
• Total gate capacitance Cg can be
decomposed in two elements:
1. Overlap capacitance: due to the topological
structure of the MOSFET.
2. Gate-to-Channel capacitance: due to the
interaction between gate voltage and channel
charge.
Gate Overlap Capacitance
• In reality , actual channel length, Leff < drawn length, L
(mask length), due to the extension of the source and
drain regions somewhat below the oxide by an amount
xd, called the lateral diffusion, i.e., Leff = L – 2.xd
• xd gives rise to overlap capacitance which is linear and
has a fixed value.
Co is overlap capacitance per unit transistor width
(fF/μm)
= = =gso gdo ox d oC C C x W C W
Gate-to-Channel Capacitance
• It has thee components: Cgs, Cgd and Cgb
Average Gate Capacitance
Region Cgb Cgs Cgd Cg
Cutoff CoxWL
eff
0 0
CoxWLeff/2
0
CoxWLeff+2CoW
Linear 0 CoxWLeff/2 CoxWLeff+2CoW
Saturation (2/3)CoxWLe
ff
(2/3)CoxWLeff+2C
oW
Area and Side-wall Capacitance
• Area Capacitance (Carea) due to the bottom-plate
junction formed by the source (drain) region with doping
ND and substrate with doping NA (bottom area 5).
• Side-wall (perimeter) Capacitance (Csw) formed by
junctions 2, 3, and 4. These are surrounded by the p+
channel-stop implant with doping level NA+ which is
usually larger than that of the substrate larger
capacitance per unit area.
= ,area j s jC C WL Cwhere is junction capacitanceperunitarea
( )
( )
where is junction side-wall capacitanceperunit
length
= + ⋅
′=
2
,
sw jsw s
j sw
jsw jsw j
C C W L
C
C C x
MOSFET Capacitance Model
=
= +
=
+
+
+
GS
GS gs gso
GD
GD g
g
gdo
bg
d
C C
C
C C
C C
C C C
Wire (Routing) Capacitance
( )
ε ε πε
≈ +
≈ +
⋅ 2
log
pp
o o
fri
x
nge
o
w
x
C
wl
h
CC
h
t
Parallel-plate and Fringing
Capacitance
Total Cap.
w/t
w
t
h
t/h=1
t/h=0.5
Cpp
Modern Interconnect
• Inter-layer capacitance increases with decreasing feature
sizes.
• Multi-layer capacitive interactions result in unwanted
coupling among neighboring signals cross talk
Impact of Inter-layer
Capacitance
Capacitances for a 0.25μm Process
Capacitance
Area Cap
(fF/μm2)
Perim. Cap
(fF/μm)
Poly - substrate 0.088
0.041
0.015
n+ diff - substrate 1.660 0.399
n+ overlap cap. -- 0.562
p+ overlap cap. -- 0.630
Cox 5.951
Metal1 - poly 0.017 0.041
1.832
0.038
0.054
Metal1 - substrate 0.047
Metal2 - substrate 0.027
p+ diff - substrate 0.323
Metal2 – metal1 0.054
0.25μm Interconnect Hierarchy
• Optimize interconnect structure at
each layer.
– for local wires, density and low
C are important – use dense
and thin wiring grid
– for global wires in order to
reduce delays, use fat, widely
spaced wires.
• Improve wire delays by using
better material (Cu) and low-K
dielectrics for insulators.
Intracell
Intercell
Intermodule
Global
Electrical Wire Models
• Ideal Wire - it is simply a line with no attached
parameters or parasitics it has no impact on electrical
behavior.
• Lumped Model – simplified model simple and fast
computation, e.g., lumped C, lumped RC or lumped
RLC
• Distributed Model - Parasitics of a wire are distributed
along its length and are not lumped into a single
position, distributed C, distributed RC, or distributed
RLC
Clumped = lwire.cwire
Elmore Delay Formula
• For an n stage RC chain, the first order time constant is
given by,
• If Ri = Rj and Ci = Cj for all i and j , (1≤ i, j ≤ n) then,
( ) ( )
n i
n i j
i j
n nC R C R R C R
C R
R R
= =
τ
= + + + + + + +
= ∑ ∑
1 1 2 1 2 1 2
1 1
... ...
( )+
τ =
1
2
n
n n
RC
Distributed RC Model for a Wire
Using Elmore delay formula we can determine the dominant time constant
of the wire, i.e., it is a first-order approximation.
Questions and Answers
Thank You

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CAD for VLSI Design - II Lecture on CMOS Transistor Theory and Parasitic Capacitances

  • 1. CAD for VLSI Design - II Lecture 6 V. Kamakoti and Shankar Balachandran
  • 2. Overview of this Lecture • CMOS Transistor Theory – Delay Issues (Cont’d) • Types and effects of Capacitances on delay
  • 3. Parasitic Capacitance • Switching speeds of MOS systems strongly depend on the parasitic capacitances associated with MOSFETs and interconnections • Total Cload on the output of a CMOS gate is the sum of: – Gate capacitance (Cg) – Junction capacitance due to the source and drain regions and their surroundings (Csb and Cdb) – Interconnect (or routing) capacitance (Cw) • Gate oxide capacitance per unit area, ε ε = 0 ox ox ox C t
  • 5. Gate Capacitance • Gate capacitance, Cg = Cox WL • Total gate capacitance Cg can be decomposed in two elements: 1. Overlap capacitance: due to the topological structure of the MOSFET. 2. Gate-to-Channel capacitance: due to the interaction between gate voltage and channel charge.
  • 6. Gate Overlap Capacitance • In reality , actual channel length, Leff < drawn length, L (mask length), due to the extension of the source and drain regions somewhat below the oxide by an amount xd, called the lateral diffusion, i.e., Leff = L – 2.xd • xd gives rise to overlap capacitance which is linear and has a fixed value. Co is overlap capacitance per unit transistor width (fF/μm) = = =gso gdo ox d oC C C x W C W
  • 7. Gate-to-Channel Capacitance • It has thee components: Cgs, Cgd and Cgb
  • 8. Average Gate Capacitance Region Cgb Cgs Cgd Cg Cutoff CoxWL eff 0 0 CoxWLeff/2 0 CoxWLeff+2CoW Linear 0 CoxWLeff/2 CoxWLeff+2CoW Saturation (2/3)CoxWLe ff (2/3)CoxWLeff+2C oW
  • 9. Area and Side-wall Capacitance • Area Capacitance (Carea) due to the bottom-plate junction formed by the source (drain) region with doping ND and substrate with doping NA (bottom area 5). • Side-wall (perimeter) Capacitance (Csw) formed by junctions 2, 3, and 4. These are surrounded by the p+ channel-stop implant with doping level NA+ which is usually larger than that of the substrate larger capacitance per unit area. = ,area j s jC C WL Cwhere is junction capacitanceperunitarea ( ) ( ) where is junction side-wall capacitanceperunit length = + ⋅ ′= 2 , sw jsw s j sw jsw jsw j C C W L C C C x
  • 10. MOSFET Capacitance Model = = + = + + + GS GS gs gso GD GD g g gdo bg d C C C C C C C C C C
  • 11. Wire (Routing) Capacitance ( ) ε ε πε ≈ + ≈ + ⋅ 2 log pp o o fri x nge o w x C wl h CC h t
  • 12. Parallel-plate and Fringing Capacitance Total Cap. w/t w t h t/h=1 t/h=0.5 Cpp
  • 13. Modern Interconnect • Inter-layer capacitance increases with decreasing feature sizes. • Multi-layer capacitive interactions result in unwanted coupling among neighboring signals cross talk
  • 15. Capacitances for a 0.25μm Process Capacitance Area Cap (fF/μm2) Perim. Cap (fF/μm) Poly - substrate 0.088 0.041 0.015 n+ diff - substrate 1.660 0.399 n+ overlap cap. -- 0.562 p+ overlap cap. -- 0.630 Cox 5.951 Metal1 - poly 0.017 0.041 1.832 0.038 0.054 Metal1 - substrate 0.047 Metal2 - substrate 0.027 p+ diff - substrate 0.323 Metal2 – metal1 0.054
  • 16. 0.25μm Interconnect Hierarchy • Optimize interconnect structure at each layer. – for local wires, density and low C are important – use dense and thin wiring grid – for global wires in order to reduce delays, use fat, widely spaced wires. • Improve wire delays by using better material (Cu) and low-K dielectrics for insulators. Intracell Intercell Intermodule Global
  • 17. Electrical Wire Models • Ideal Wire - it is simply a line with no attached parameters or parasitics it has no impact on electrical behavior. • Lumped Model – simplified model simple and fast computation, e.g., lumped C, lumped RC or lumped RLC • Distributed Model - Parasitics of a wire are distributed along its length and are not lumped into a single position, distributed C, distributed RC, or distributed RLC Clumped = lwire.cwire
  • 18. Elmore Delay Formula • For an n stage RC chain, the first order time constant is given by, • If Ri = Rj and Ci = Cj for all i and j , (1≤ i, j ≤ n) then, ( ) ( ) n i n i j i j n nC R C R R C R C R R R = = τ = + + + + + + + = ∑ ∑ 1 1 2 1 2 1 2 1 1 ... ... ( )+ τ = 1 2 n n n RC
  • 19. Distributed RC Model for a Wire Using Elmore delay formula we can determine the dominant time constant of the wire, i.e., it is a first-order approximation.