Radio-Frequency Effects inIntegrated Circuits
Yun Bai
Directed by Professor Neil Goldsman
Abstract
• Tendency of IC evolvement: faster speed and higher chip density.
• Inductance of on-chip interconnects draws more attention in terms of signal transmission and circuit design.
• Skin effects and semiconductor substrate losses are considered.
• Electromagnetic coupling happens between on-chip components and affects circuit performance.
Thesis Outline
I. Introduction to Inductance
II. Characterization of On-Chip Interconnects
III. Characterization of On-Chip Inductors
IV. High-Speed On-Chip Digital Signal Transmission
V. Electromagnetic Coupling Effects
Transmission Line Theory
L R
C G
Distributed Circuit Model
Semiconductor Substrate
Inter
conn
ect
Insulator
Metal Plate
Metal – SiO2 – Si – Ground Plane
freq > 1GHzChip density > tens of millions of transistors
RLC delay due to interconnects become significant
On-Chip Inductors
Insulator
Insulator
Semiconductor Substrate
Port 1
Port 2
Metal
Via
Metal Ground Plane
Analog RF Circuits:• Low Noise Amplifiers• Mixers• Voltage-Controlled Oscillators
Experimental
EM Simulator
Numerical Modeling
Empirical Equations
Electromagnetic Coupling
Substrate
Insulator
Meta
l
Meta
l
qp
Metal Plate
• Bus Lines• Interconnects
EM Simulator
Numerical Modeling
Empirical Equations
What is Inductance?
• Energy Definition: Magnetic Energy Storage
• Flux Definition: Magnetic Flux Leakage
• Circuit Definition: Induced Voltage by AC Current
*
4
1
4
1Re LIIdvBHW
V
m
IL
dt
dILV
Inductance Classification
Inductance
Self Mutual
Internal External
Internal Self-Inductance
t
BE
EJ
t
DJH
Skin Effect:
iR iL
iii LjRZ
I
EmZ z
i0/
t
EE
tE 2
Maxwell’s Equation:
Internal Impedance:
2
External Self-Inductance
JH
t
BE
I
a
daa
1
ILe
Average Flux:
Loop Inductance
Mutual Inductance
jij JH
t
BE ij
ij
jI
iI
j
i
i
i j
j
j
a
jj
a
c
b a
c
b jiij
jij
iijm
daJ
dadaR
ldldJ
aL
1
4,
AB
Magnetic Vector Potential:
ijR
ild
jld
i
j
What is L for an Interconnect
Semiconductor Substrate
Inter
conn
ect
Insulator
Metal Plate
Internal + External
Interconnect Internal Impedance
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0.2
0.4
0.6
0.8
1
1.2
x, m
|Jz/J
z0|
f=1GHzf=5GHzf=10GHz
2tan2
kWk
Zi
1D approximation:
Current Distribution:
x
y
z
0
2
W
2
W
xx EjE 22
Complex Image Theory
I
I
PerfectGround Plane
22
811321ln
4 h
w
w
hLeff
subox
hjjhD
1tanh12
jR
LLeff
D
Insulatoroxh
Metal Plate
subh Substrate
Signal Current
Image Current
Interconnect External Impedance
1 2 3 4 5 6 7 8 9 1010
10.5
11
11.5
12
12.5
13
Frequency, GHz
Ext
erna
l Sel
f-In
duct
ance
, nH
/cm
Na=1015
cm-3
Na=1016cm-3
Na=1017cm-3
I
I
I
I
1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
60
70
80
90
100
Frequency, GHz
Ext
erna
l Sel
f-R
esis
tanc
e,
/cm
Na=1015cm-3
Na=1016cm-3
Na=1017cm-3
Quasi-TEM
Slow Mode
Coupled Interconnects
Substrate
Insulator
Meta
l
Meta
l
qp
Metal Plate
xpx qx
2pW
2pW
2qW
2qW
qxJ
qxJ
'qqh
yz
Virtual Ground Plane
qp
'q (image)
1py
2py
1qy
2qy
pqh
2
2
2
2
2
2222
,
1
1
2
1
1
1
2
11
4 q
q
pp
pp
p
p
q
q
W
W qqq
Wx
Wx
y
y
Wx
Wx
y
y qqpp
pqqpqp
ppqm
dxxJ
dydxdydxhyyxx
xJ
WL
2
2
2
2
2
2222
,
1
1
2
1
1
1
2
1
1
4 q
q
pp
pp
p
p
q
q
W
W qqq
Wx
Wx
y
y
Wx
Wx
y
y qqpp
pqqpqp
ppqm
dxxJ
dydxdydxhyyxx
xJ
WL
Mutual Impedance
1 2 3 4 5 6 7 8 9 104
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
Frequency, GHz
Mut
ual I
nduc
tanc
e, n
H/c
m
Na=1019cm-3
Na=1018
cm-3
Na=1017cm-3
Na=1016cm-3
1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
60
70
80
90
100
Frequency, GHz
Mut
ual I
nduc
tanc
e, n
H/c
m
Na=1019cm-3
Na=1018cm-3
Na=1017cm-3
Na=1016cm-3
xpx qx
2pW
2pW
2qW
2qW
qxJ
qxJ
'qqh
yz
Virtual Ground Plane
qp
'q (image)
1py
2py
1qy
2qy
pqh
On-Chip Inductors
Insulator
Insulator
Semiconductor Substrate
Port 1
Port 2
Metal
Via
Metal Ground Plane
NNNmNm
Nmm
Nmm
LLL
LLL
LLL
L
4424,14,
42,2221,
41,12,11
Seg
men
t 1
Segment 2
Segment 4N
Seg
men
t (4N
-1)
Segm
ent i
Inductor Inductance
1 2 3 4 5 6 7 8 9 101
2
3
4
5
6
7
8
Frequency, GHz
Indu
ctan
ce, n
H
Total Length = 3000mTotal Length = 2000mTotal Length = 1000m
1 2 3 4 5 6 7 8 9 10
5.8
6
6.2
6.4
6.6
6.8
Frequency, GHz
Indu
ctan
ce, n
H
N=3N=4N=5
1 2 3 4 5 6 7 8 9 105.7
5.8
5.9
6
6.1
6.2
6.3
6.4
6.5
Frequency, GHz
Indu
ctan
ce, n
H
S=2mS=4mS=6m
1 2 3 4 5 6 7 8 9 104.6
4.8
5
5.2
5.4
5.6
5.8
6
6.2
6.4
6.6
Frequency, GHz
Indu
ctan
ce, n
H
Na=1016
cm-3
Na=1017
cm-3
Na=1018
cm-3
Na=1019
cm-3
NL
S Na
Inductor Resistance
1 2 3 4 5 6 7 8 9 100
5
10
15
20
25
Frequency, GHz
Res
ista
nce,
Total Length = 3000mTotal Length = 2000mTotal Length = 1000m
1 2 3 4 5 6 7 8 9 100
5
10
15
20
25
Frequency, GHz
Res
ista
nce,
nH
N=3N=4N=5
1 2 3 4 5 6 7 8 9 100
5
10
15
20
25
Frequency, GHz
Res
ista
nce,
S=2mS=4mS=6m
1 2 3 4 5 6 7 8 9 10-10
0
10
20
30
40
50
60
70
80
Frequency, GHz
Res
ista
nce,
Na=1016
cm-3
Na=1017
cm-3
Na=1018
cm-3
Na=1019
cm-3
L
S
N
Na
Multi-Layer Spiral
Port 1
Port 2
• Higher Inductance
• Less Chip Area
• Higher Q Factor
On-Chip Digital Transmission
V10 VoVs V0 V1 V2 V3 V4 V5 V6 V7 V8 V9
MOSFET_PMOSMOSFET3
Width=30 umLength=0.24 umModel=PMOS
V_DCSRC3Vdc=2.5 V
MOSFET_NMOSMOSFET4
Width=10 umLength=0.24 umModel=NMOS
VtPulseSRC4
Period=100 psecWidth=50 psecFall=10 psecRise=10 psecEdge=linearDelay=1 psecVhigh=0 VVlow=2.5 V
t
I_ProbeI_dd
V_DCSRC1Vdc=2.5 V
BSIM3_ModelPMOS
BSIM3_ModelNMOS
TranTran1
MaxTimeStep=1 psecStopTime=1000.0 psec
TRANSIENT
S2PSNP10File="tl_4u_x_1mm.s2p"
21
Ref
S2PSNP9File="tl_4u_x_1mm.s2p"
21
Ref
S2PSNP8File="tl_4u_x_1mm.s2p"
21
Ref
S2PSNP7File="tl_4u_x_1mm.s2p"
21
Ref
S2PSNP6File="tl_4u_x_1mm.s2p"
21
Ref
S2PSNP5File="tl_4u_x_1mm.s2p"
21
Ref
S2PSNP4File="tl_4u_x_1mm.s2p"
21
Ref
S2PSNP3File="tl_4u_x_1mm.s2p"
21
Ref
S2PSNP2File="tl_4u_x_1mm.s2p"
21
Ref
S2PSNP1File="tl_4u_x_1mm.s2p"
21
Ref
MOSFET_PMOSMOSFET2
Width=150 umLength=0.24 umModel=PMOS
MOSFET_NMOSMOSFET1
Width=50 umLength=0.24 umModel=NMOS
Semiconductor Substrate
Inter
conn
ect
Insulator
Metal Plate
Each Box: 1 mm
Intrinsic Interver Delay
0.00.51.0
1.52.0
2.5
-0.5
3.0
Vs,
V
20 40 60 80 100 120 140 160 1800 200
0
2
-2
4
time, psec
Vo,
V
rising/falling < 10 ps
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.250.00 2.50
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
0.00
2.50
Vin
Vout
Inverter Transfer Characteristics
Vs = 1.26 V
Signal Attenuation, Delay, Dispersion
1
2
0
3
Vs,
V
012
-1
3
V0,
V
012
-1
3
V1,
V
0.00.51.01.5
-0.5
2.0
V2,
V
0.00.51.0
-0.5
1.5
V3,
V
0.00.51.0
-0.5
1.5
V4,
V
0.00.51.0
-0.5
1.5
V5,
V
0.00.51.0
-0.5
1.5
V6,
V
0.00.51.0
-0.5
1.5
V7,
V
0.00.51.0
-0.5
1.5
V8,
V
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.0 1.0
1.82.02.22.42.6
1.6
2.8
time, nsec
Vo,
V
0.5
0.0
1.0
Vs1, V
-0.5
0.0
0.5
-1.0
1.0
Vs3, V
-0.5
0.0
0.5
-1.0
1.0
Vs5, V
-0.5
0.0
0.5
-1.0
1.0
Vs7, V
100 200 300 4000 500
-0.5
0.0
0.5
-1.0
1.0
time, psec
Vs9, V
200
400
600
0
800
Vo1, m
V
-200
0
200
400
-400
600
Vo3, m
V
-200
0
200
-400
400
Vo5, m
V
-200
0
200
-400
400
Vo7, m
V
100 200 300 4000 500
-200
0
200
-400
400
time, psec
Vo9, m
V
Critical Length: 8 mm
1 GHz : 220 ps9 GHz : 150 ps
CLv
1
Electromagnetic Coupling
SMA SMA
Device1
Device2
Bond Padwith ESD
Bond Padwith ESD
P+ Guard Ring
Die: P-Type Substrate
Inte
rcon
nect
Inte
rcon
nect
Pin(Leadless)
Pin(Leadless)
Bond Wire Bond Wire
LCC-28 IC Package
Trace Trace
Print Circuit Board
Instruments
Cable Cable
Scattering Parameters
1V
1V
2V
3V
NV
2V
3V
NV
NNNNN
N
N
N V
V
V
SSS
SSS
SSS
V
V
V
2
1
21
22221
11211
2
1
S11: Insertion Loss at Port 1 when Port 2 is matched
S21: Forward Gain from Port 1 to Port 2 when Port 2 is matched
N-Wells
P-Type Silicon Substrate
N Well N Well
Oxide
Metal Contact
Port 1 Port 2
m8.28 m8.28m45.102
2 3 4 5 6 7 8 9 10-30
-28
-26
-24
-22
-20
-18
-16
Frequency, GHz
|S21
|, dB
Measured DataFitted Curve
Transformer
Port 1
Port 2
Metal 3
Metal 2
2 3 4 5 6 7 8 9 10-35
-30
-25
-20
-15
-10
Frequency, GHz
|S21
|, dB
Measured DataFitted Curve
subC subCsubR subR
oxC oxC
2L 2R
2sC
Port 1
12,oxC0L 0R
1sC
Port 1
12,mL12,oxC
Spiral and Transistor
Port 1
Port 2
n+ n+
P-Type Silicon Substrate
2 3 4 5 6 7 8 9 10-55
-50
-45
-40
-35
-30
-25
-20
-15
Frequency, GHz
|S21
|, dB
Measured Data (N=1)Measured Data (N=5)Fitted Curve (N=1)Fitted Curve (N=5)
mW 300
D SG
mW 60
G
D
S
Digital Switching NoisePort 1 Port 2
n+ n+
P-Type Silicon Substrate
n+ n+ p+ p+n
GNDVDD
Acknowledgement
• Professor Neil Goldsman
• Our Group: Zeynep, Xi, Akin, Bo, …
• Committee: Professor Peckerar and Orloff