????

1
?????? ?? ?????? ??????

• ???? ???? ???
• ?????????? ??-????

2
????? ?????? - Crosstalk
???? ?????
V1(t)
R1
-
C1
C12
VsU(t)
R2
V2(t)
C2
3
???? ?????? ?????? ???? ?????
1. 2. 3. 4.
4
???? ?- CROSSTALK ????
V1(t)
V2,max
V2(t)
tmax
5
??????
1. ???? ???? ??????? ?- CROSSTALK ?? ????
???????? ??? 2. ?- CROSSTALK ???? ???? C/C12 3.
???? ???? C/C12 ??? ???? ?????? ??????? ????????
???????? ???? ??? ??? ???? ????? 4. ???? ???? 1
C/C12 ???? ?????? ??? 0.19. 5.
6
???? ??????
7
?? ?????? ?? ?????
8
????? ????? ????? ??????
9
????? ??????
10
????? ( ??? ???? ?? 5 ????) - ???? ???

• ???? ???? ????? ????? ? 1.67 ????
• ???? ??? T ???? ??? ???? ?????.
• ?? ?? ???? ????? ?2/3 ???? ????? ??? ????.

11
????? ( ????)
12
?? ??????
13
????? ????? ???????? ?????
14
????? ???????
15
?? ?????? RLC
Ldx Rdx
Cdx
z
16
?? ?????? RLC (????)
17
????
18
????? ????? ????
19
???? ??????
20
???? RLC ?????
Lt
Rt
Ct
?????? ?? ????
21
???????? ???????? ?? ?? ?????? RLC
22
??????? ???????? ???? ???? ????
23
???? CMOS ???? ?? ??????
VDD
VDD
PMOS
Vin(t)
0
Vout(t)
tf
NMOS
KpmCox, ap is in the range of 1 to 2. We
assume that the PMOS is in saturation and
neglects the NMOS. VTP is the threshold voltage
of the PMOS
24
?????

• KpmCox, ap is in the range of 1 to 2.
• We assume that the PMOS is in saturation and
  neglects the NMOS.
• VTP is the threshold voltage of the PMOS
• 0 lt t lt 2T0
• T0 is the time it takes for the signal to
  travel the distance equal to the length of theline

25
?? ???? ???? tgtT0 ?
???? ????? ???? ??????? ???? ??? ??? ???? (?????
?????? ??????? ???) ????? ????? ????? ???? tT0
. ???? ????? ????? ????? ?????? ???? ???? ??????
?- ????? ??????????? ??? ???? ??? ???? ?????
???? ??? ??? -1 ????? ????? ???? ??? 1 ????
?????? ?????? ????? ???? ?????
26
????? ??????? ???
Vout
RC approximation
RLC transmission line
t
27
??? ?? ?????? ??????? ?
???? ? ??? ?????? ???? ????? ????? ??? ?????
?????
???? ? ???? ????? ??? ??? ??? ?????? ?????
??? ????? ??? ????? ?????? ????? ???
28
??? ????? ?? ?????? ?
????? ?? ??????? ????? ???????? ??? ???? ????.
Length
L ????
Transition time, tr
29
On- chip Inductance Modeling and RLC Extraction
of VLSI Interconnects for Circuit Simulation
Xiaoning Qi, G. Wang, Z. Yu, R. Dutton Stanford
University T. Young Synopsys Inc. N. Chang HP
Labs, Palo Alto
30
Outline Background and motivation 3D geometry
modeling and inductance extraction using field
solvers Analytical formulae for
inductance estimation Applications in circuit
simulation Summary
31
Background and Motivation

• Long wires exhibit transmission line
• effects with faster transistor rise/ fall time.
• Inductance component becomes
• comparable to resistance component.
• Signal ringing and inductive cross talk are
• observed. Ground bounce becomes
• worse.

32
3D Geometry Modeling for Field Solver
33
Path Searching in 3D Geometry Modeling
34
Extracted 3D Geometry
35
????? ??????? ????? , L
36
????? ??????? ????? ?? ????? ?- SKIN EFFECT
37
?????? ?????
38
6 ????????? ?????? ???? ?? ?????
39
????? ????? M ????? 3
40
????? ?????? M - ???? 4
41
?????? ????? ?? ?? ?? ???
42
?????? ??? ?????? ??????? ?????? ???-???? ?????
43
???????? ?? ????? ??????
44
????? ???? ??? ??????? - RINGING
45
?????? ??? ?? ???? ??????
46
Summary

• Accurate automatic 3D geometry
• generation
• Analytical formulae for self and mutual
• inductance estimation
• Impact of on- chip inductance on signal
• integrity and power/ ground noise

47
????? ???? ?? ???
Sharad Kapur, kapur_at_research.bell-labs.com Jinsong
Zhao, zhaojs_at_cse.ucsc.edu
L
R
?????????
SiO2
???????
48
(No Transcript)
49
????? ????? ???????
Bendik Kleveland, Xiaoning Qi, Liam Madden 1 ,
Robert W. Dutton, and S. Simon Wong Center for
Integrated Systems, Stanford University,
Stanford, CA 94305, USA 1 MIPS Technologies Inc.,
Mountain View, CA 94043, USA
50
???? ??? ??????
51
???? ????? ????????? ??- LAYOUT
52
???? L ????? ??? ?????
53
???? ??????? ????? ???
54
???? ??????? ????
55
???? ?????? ??????? ???? ????
56
???????? - ?? RC
57
???????? - ?? RLC
58
????? ???? ?????? ????? ?????? (?)
59
????? ???? ?????? ????? ?????? (?)
60
????? ????? ??????? ?????
61
???? ?????? ?????
62
???? ?? ???? ???? ???? ??????? ?????????
63
?????? ?- SHIELD ?? ???????

• The shield of CLK A is well connected to the
  power grid.
• The shield of CLK B is only connected at one
  end
• The shield of CLK C is left floating to mimic
  neighboring tristate buses.

64
??????? ?? ????? ???? ?????
65
?????

• ?????? ????? ???? ???????, ????? ???? ????
• ?????? ????? ????? ???? ?? ?????? ???? ?? ?????
  ?? ?????
• ??? ?????? ?? ????? ???????.
• ???????? ?????? ?? ??????? ?????? ??????? ???
  ??????.