Transcript Radio-Frequency Effects in Integrated Circuits

Radio-Frequency Effects in
Integrated 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
freq > 1GHz
Chip density > tens of millions of transistors
RLC delay due to interconnects become significant
Metal – SiO2 – Si – Ground Plane
Distributed Circuit Model
R
In
te
rc
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nn
ec
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L
C
Insulator
Semiconductor Substrate
Metal Plate
G
On-Chip Inductors
Analog RF Circuits:
• Low Noise Amplifiers
• Mixers
• Voltage-Controlled Oscillators
Experimental
EM Simulator
Port 1
Metal
Via
Port 2
Numerical Modeling
Insulator
Insulator
Semiconductor Substrate
Empirical Equations
Metal Ground Plane
Electromagnetic Coupling
q
M
et
al
M
et
al
• Bus Lines
• Interconnects
p
Insulator
EM Simulator
Numerical Modeling
Empirical Equations
Substrate
Metal Plate
What is Inductance?
• Energy Definition: Magnetic Energy Storage
1
 1



Wm  Re    H  B dv   LII *
  4
4 V 
• Flux Definition: Magnetic Flux Leakage

L
I
• Circuit Definition: Induced Voltage by AC Current
V L
dI
dt
Inductance Classification
Inductance
Self
Internal
Mutual
External
Internal Self-Inductance
Ri
Li
Z i  Ri  jLi
J  E
Internal Impedance:
 E  
Ez 0
Z i  / m  
I
 H  J 
Maxwell’s Equation:
 
 E 
 E    E  
t 
t 
B
t
2
Skin Effect:

2

D
t
External Self-Inductance
 H  J

I
Average Flux:
 E  
B
t
Loop Inductance
 
Le 
1
da

a a

I
Mutual Inductance
  H ij  J j
Magnetic Vector Potential:
B   A
Ij
Ii
d li
Rij
i
Lm ,ij 
  Eij  
 1
4 ai
 Bij
t
ci
 
cj
J j d li  d l j
Rij
a i bi a j b j
 J da
j
dl j
j
aj
j
dai da j
In
te
rc
o
nn
ec
t
What is L for an Interconnect
Insulator
Semiconductor Substrate
Metal Plate
Internal + External
Interconnect Internal Impedance
y
Current Distribution:
f=1GHz
f=5GHz
f=10GHz
1.2
0
z
W
2
x
1
0.8
|Jz /Jz0|
W

2
0.6
1D approximation:
0.4


 2 Ex  j   2  Ex
0.2
-2
-1.5
-1
-0.5
0
x, m
Zi 
k
 kW 
2 tan 

 2 
0.5
1
1.5
2
Complex Image Theory
I
 
Perfect
Ground Plane
2
2 
 
 h  
  w   
Leff 
ln 1  32  1  1  
 
4 
w
8
h
  

  


I
Signal Current
hox
hsub
Insulator
D

Substrate
Metal Plate
Image Current
 1  j hsub 
D  2hox  1  j    tanh 

    
Leff  L 
R
j
Interconnect External Impedance
100
13
Na=1015cm-3
Na=1016cm-3
90
Na=1017cm-3
80
External Self-Resistance, /cm
External Self-Inductance, nH/cm
12.5
12
11.5
11
70
60
50
40
30
20
10.5
10
15
-3
Na=10 cm
Na=10 16cm-3
Na=10 17cm-3
1
2
3
10
0
4
5
6
7
Frequency, GHz
Quasi-TEM
I
I
8
9
10
1
2
3
4
5
6
7
8
9
10
Frequency, GHz
I
I
Slow Mode
Coupled Interconnects
q
al
Lm , pq 
M
et
M
et
al
p

x p1 
2
Wp
x p1 
 1
4 W p
Wp
y p2
x q1 
y p1
x q1 
 
2
Wq
2
Wq

yq 2
x
y q1
2
J q xq 
 xq    y p  yq   hpq
2
p

Wq

Insulator
Lm , pq 
Substrate
 1
4 W p

x p1 
x p1 
Wp
2
Wp
yp2
xq 1 
y p1
xq 1 
 
2
Wq
2
Wq

2
x
2
J q x q 
 x q    y p  y q   h pq
2
p

Wq

2
Wq
2
dx p dy p dxq dyq
J q xq dxq
2
Wq
yq 2
y q1
2
2
2
dx p dy p dx q dy q
J q x q dx q
2
Metal Plate
p
ẑ
ŷ
q
J xq 
y p2
Virtual Ground Plane
yq 2
h pq
y p1
hqq '
yq1

Wp x p Wp
2
2
W x W
 q q q
2
2
x̂
 J xq 
q' (image)
Mutual Impedance
100
9.5
Na=1019cm-3
9
90
8.5
80
Mutual Inductance, nH/cm
Mutual Inductance, nH/cm
8
7.5
7
6.5
6
5.5
Na=10 19cm-3
Na=10 18cm-3
Na=10 17cm-3
Na=10 16cm-3
5
4.5
4
1
2
3
Na=1018cm-3
Na=1017cm-3
Na=1016cm-3
70
60
50
40
30
20
10
4
5
6
7
8
9
10
0
Frequency, GHz
1
2
3
4
5
6
Frequency, GHz
p
ẑ
ŷ
q
J xq 
y p2
Virtual Ground Plane
yq 2
h pq
y p1
hqq '
yq1

Wp x p Wp
2
2

Wq xq Wq
2
2
x̂
 J xq 
q' (image)
7
8
9
10
On-Chip Inductors
Segment 4N
Metal
Insulator
Insulator
Segment 1
Port 2
Segment 2
Segment i
Via
Segment (4N-1)
Port 1
Semiconductor Substrate
Metal Ground Plane
 L11
 L
m , 21
L
 

 Lm , 4 N 1
Lm ,12
L22

Lm , 4 N  2
 Lm ,1 4 N 
 Lm , 2  4 N 

 

 L4 N  4 N 
Inductor Inductance
N=3
N=4
N=5
8
Total Length = 3000 m
Total Length = 2000 m
Total Length = 1000 m
7
6.8
6.6
5
N
4
Inductance, nH
L
Inductance, nH
6
3
6.4
6.2
6
2
5.8
1
1
2
3
4
5
6
7
8
9
1
10
2
3
4
7
8
9
10
7
8
9
10
6.4
6.2
6.4
6
6.2
Na
6.1
Inductance, nH
6.3
Inductance, nH
6
6.6
S=2m
S=4m
S=6m
6.5
S
5
Frequency, GHz
Frequency, GHz
5.8
5.6
5.4
6
5.2
5.9
5.8
5.7
Na=10 16cm-3
Na=10 17cm-3
Na=10 18cm-3
Na=10 19cm-3
5
4.8
4.6
1
2
3
4
5
6
Frequency, GHz
7
8
9
10
1
2
3
4
5
6
Frequency, GHz
Inductor Resistance
25
25
Total Length = 3000 m
Total Length = 2000 m
Total Length = 1000 m
N=3
N=4
N=5
20
15
N
10
Resistance, nH
L
Resistance, 
20
10
5
5
0
15
0
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
7
8
9
10
Frequency, GHz
Frequency, GHz
80
25
S=2 m
S=4 m
S=6 m
Na=1016cm-3
Na=1017cm-3
Na=1018cm-3
Na=1019cm-3
70
20
60
Na
10
Resistance, 
S
Resistance, 
50
15
40
30
20
10
5
0
0
1
2
3
4
5
6
Frequency, GHz
7
8
9
10
-10
1
2
3
4
5
6
Frequency, GHz
Multi-Layer Spiral
Port 1
• Higher Inductance
• Less Chip Area
• Higher Q Factor
Port 2
ec
t
On-Chip Digital Transmission
nn
te
rc
o
Vout
Insulator
4
Vo, V
Inverter Transfer Characteristics
2.50
2.25
In
Vs, V
Intrinsic Interver Delay
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
2
Semiconductor Substrate
0
0.25
0.00
-2
0
20
40
60
80
100
120
140
160
180
200
Metal Plate
time, psec
rising/falling < 10 ps
Each Box: 1 mm
2.00
1.75
1.50
1.25
1.00
0.75
0.50
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50
Vin
Vs = 1.26 V
Signal Attenuation, Delay, Dispersion
1.0
V4, V
1.5
1.0
0.5
0.0
-0.5
V5, V
1.5
1.0
0.5
0.0
-0.5
V6, V
1.5
1.0
0.5
0.0
-0.5
V7, V
1.5
1.0
0.5
0.0
-0.5
1.5
1.0
0.5
0.0
-0.5
1.5
1.0
0.5
0.0
-0.5
Vo1, mV
600
400
200
0
1.0
600
0.5
400
Vo3, mV
0.0
0.0
-0.5
200
0
-200
-400
1.0
400
0.5
200
Vo5, mV
-1.0
0.0
-0.5
0
-200
-1.0
-400
1.0
400
0.5
200
Vo7, mV
Vs3, V
Vs5, V
Vs7, V
2.0
1.5
1.0
0.5
0.0
-0.5
Vs9, V
V0, V
V1, V
V2, V
3
2
1
0
-1
V8, V
V3, V
3
2
1
0
-1
0.5
0.0
-0.5
0
-200
-1.0
-400
1.0
400
0.5
200
Vo9, mV
1
0
Vo, V
800
2
Vs1, V
Vs, V
3
0.0
-0.5
-1.0
0
-200
-400
0
100
200
300
400
500
0
100
200
time, psec
v
2.8
2.6
2.4
2.2
2.0
1.8
1.6
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
time, nsec
Critical Length: 8 mm
0.9
1.0
300
time, psec
1
L C  
1 GHz : 220 ps
9 GHz : 150 ps
400
500
P+ Guard Ring
Device
1
Device
2
Interconnect
Bond Pad
with ESD
Interconnect
Electromagnetic Coupling
Bond Pad
with ESD
Die: P-Type Substrate
Bond Wire
Bond Wire
Pin
(Leadless)
LCC-28 IC Package
Trace
SMA
Pin
(Leadless)
Trace
SMA
Print Circuit Board
Cable
Cable
Instruments
Scattering Parameters
V2
V3
V3
V2
V1
V1   S11
  
V2    S 21
    
  
VN   S N 1
S12
S 22

SN 2
 S1N  V1 
 
 S 2 N  V2 
    
 
 S NN  VN 
V1
VN
VN
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
Metal Contact
Port 1
Port 2
Oxide
N Well
N Well
P-Type Silicon Substrate
102.45m
-18
28.8m
-20
|S21|, dB
28.8m
-16
-22
-24
-26
-28
Measured Data
Fitted Curve
-30
2
3
4
5
6
Frequency, GHz
7
8
9
10
Transformer
Metal 3
Port 1
-10
Metal 2
Port 2
-15
-20
|S21|, dB
C s1
Port 1
C ox ,12
L0
Lm ,12
R0
C ox ,12
-25
Port 1
R2
L2
-30
Cs2
Cox
Cox
Measured Data
Fitted Curve
C sub
Rsub
Rsub
C sub
-35
2
3
4
5
6
Frequency, GHz
7
8
9
10
Spiral and Transistor
Port 2
Port 1
-15
n+
n+
-20
P-Type Silicon Substrate
-25
D
G
S
D
G
|S21|, dB
-30
-35
-40
W  300m
W  60m
-45
Measured Data (N=1)
Measured Data (N=5)
Fitted Curve (N=1)
Fitted Curve (N=5)
-50
S
-55
2
3
4
5
6
Frequency, GHz
7
8
9
10
Digital Switching Noise
Port 1
D
GN
n+
n+
Port 2
D
VD
p+
p+
n
P-Type Silicon Substrate
n+
n+
Acknowledgement
• Professor Neil Goldsman
• Our Group: Zeynep, Xi, Akin, Bo, …
• Committee: Professor Peckerar and Orloff