H
R
L
Study of On-Chip Coplanar
Transmission Lines Over the Lossy
Silicon Substrate
R.Gordin, D.Goren, M.Zelikson
IBM
Research and Development Labs in Haifa
Coplanar T-line cross sections
Lossless
oxide dielectric
Lossless
oxide dielectric
H
R G
L
S
G
Lossy silicon substrate
G
S1
S2
G
Lossy silicon substrate
Main modeling issues vs. micro-strip T-lines
ƒ
ƒ
ƒ
ƒ
How to meet closed environment requirements?
Should the frequency dependent capacitance be modeled?
Should the substrate losses be modeled?
Should the current in the substrate be considered?
‹ Transverse current
‹ Longitudinal (return) current
Test cage with Coplanar T-lines
H
R
L
Example: single coplanar Tline, M2/sub, l~=4360um
S-parameters for a coplanar line from the test site –
measurements setup
ƒ 2 independent measurement sessions have been performed in IBM
H and IBM Burlington on different units of the same test chip
Haifa
R
ƒ IBM
Burlington: Agilent 8517 40GHz 2-port Vector Network
L
Analyzer, used for single T-lines measurements
ƒ IBM Haifa: Agilent 8720ES 20GHz Vector Network Analyzer with
an ATN-4112A 4-port unit, used for both single and coupled T-lines
measurements
ƒ Balanced (GSG & GSGSG) coplanar probes have been used in both
cases
ƒ The Y-parameter subtraction de-embedding has been performed for
bottom shielded on-chip pads and other on-chip parasitics besides the
T-lines, using on-chip reference de-embedding structures
Measurements vs. HFSS computations –
some potential sources of results discrepancy
ƒ Measurements
H‹ Different measurement equipment
R‹ Technology parameters scatter: much stronger in silicon-based
technologies, compared to GaAs technologies
L
‹ Within-dye and dye-to-dye variation: wire thickness, pitch, and
dielectric thickness vary from 10 to 20%, the substrate resistivity from 1 to 2 Ohm*cm
ƒ HFSS computations
‹ Modeling inaccuracy
‹ Numerical method inaccuracy
ƒ Both
‹ Intrinsic inaccuracy at low frequencies
In order to understand wideband behavior of on-chip coplanar T-lines
over the lossy substrate, the data achieved by all available methods
should be combined
S-parameters for a coplanar T-line from the test site –
measurements vs. HFSS computations
-1.0
0
-2.0
-5
H
R
L
-10
Phase S11 (deg)
Mod S11 (dB)
-3.0
-4.0
-5.0
-6.0
-15
-20
-25
-30
-7.0
-35
-8.0
-40
0
HFSS
5
10
Frequency (GHz)
Haifa meas.
15
20
0
Burlington meas.
5
HFSS
-15
10
Frequency (GHz)
Haifa meas.
15
20
Burlington meas.
250
200
150
Phase S21 (deg)
Mod S21 (dB)
-20
-25
-30
100
50
0
-50
-100
-35
-150
-40
-200
0
5
10
15
20
0
Frequency (GHz)
HFSS
Haifa meas.
Burlington meas.
HFSS
5
10
Frequency (GHz)
Haifa meas.
15
20
Burlington meas.
Reasonably good agreement among computations and measurements
Z
Substrate resistivity impact analysis
based on the HFSS modeling
A half of a T-line
cross-section
to the right of the
symmetry axis Z
H
RA half of a signal
Side shield
L
Lossless oxide dielectric
Y
Lossy silicon substrate
Using T-line cross-section symmetry
ƒ Reduces computation domain
ƒ Produces desired solution modes
ƒ Ensures mesh symmetry
Single T-line, M2/sub, w = s = ws = 0.6um,
Computed E and H magnitude on the symmetry plane and at
a cross-section at freq = 50GHz
H
R
L
ρsub=1 Ohm*cm
Closed environment requirements are met by
proper choice of the cross-section geometry
T-lines with the same dimensions
and different substrate properties:
γ, Zvi for Rosub=1 Ohm*cm, 13.5 Ohm*cm
H
Single T-line
R
L M2/sub
w=s=ws=0.6um
Freq, GHz
1
50
γ
Zvi
Re,
Np/m
Im,
rad/m
Re,
Ohm
Im,
Ohm
3.27E+1
3.25E+1
4.37E+02
4.30E+02
9.70E+01
9.67E+01
2.71E+03
2.70E+03
116.7
116.7
65.3
66.5
-39.20
-39.08
-10.26
-10.36
The substrate losses are seen, but are relatively small
for this specific case
Single coplanar Tline, M1/sub
th = 0.29, h = 0.325, w = s = ws = 6um
H
Z
R
L
A half of the T-line
cross-section
to the right of the
symmetry axis Z
Y
Two different substrates:
ƒρsub=13.5 Ohm*cm
ƒρsub=1 Ohm*cm
Single T-line, M1/sub, w = s = ws = 6um
E vector at a cross-section
at freq = 50GHz
H
R
L
ρsub=13.5 Ohm*cm
H
R
L
Single T-line, M1/sub, w = s = ws = 6um
E magnitude on the symmetry plane and at a cross-section
at freq = 50GHz
ρsub=13.5 Ohm*cm
Single T-line, M1/sub, w = s = ws = 6um
H vector at a cross-section
at freq = 50GHz
H
R
L
ρsub=13.5 Ohm*cm
Single T-line, M1/sub, w = s = ws = 6um
Jvol magnitude on the symmetry plane and at a cross-section
at freq = 50GHz
H
R
L
ρsub=13.5 Ohm*cm
H
R
L
Single T-line, M1/sub, w = s = ws = 6um
Jvol magnitude on surface of the substrate
at freq = 50GHz
Isub/Isignal~1%
ρsub=13.5 Ohm*cm
Single T-line, M1/sub, w = s = ws = 6um
Jvol vector on surface of the substrate
at freq = 50GHz
H
R
L
Z
Y
X
ρsub=13.5 Ohm*cm
Single T-line, M1/sub, w = s = ws = 6um
Jvol vector on surface of the substrate
at freq = 50GHz
H
R
L
Z
X
Y
ρsub=13.5 Ohm*cm
Note: Jvol is almost purely transverse
Single T-line, M1/sub, w = s = ws = 6um
Jvol magnitude on the symmetry plane and at a cross-section
at freq = 50GHz
H
R
L
ρsub=1 Ohm*cm
Single T-line, M1/sub, w = s = ws = 6um
Jvol magnitude on surface of the substrate at freq = 50GHz
H
R
L
Isub/Iwire~4%
ρsub=1 Ohm*cm
Single T-line, M1/sub, w = s = ws = 6um
Jvol distribution within the signal wire cross-section
at freq = 50GHz
H
R
L
ρsub=1 Ohm*cm
Strong proximity effect at 50GHz
Single T-line, M1/sub, w = s = ws = 6um
Jvol distribution within the signal wire cross-section
at freq = 150GHz
H
R
L
ρsub=1 Ohm*cm
Both proximity and skin-effect at 150GHz
Single T-line, M1/sub, w = s = ws = 6um
Re(γ) (attenuation const.) for ρsub=1 Ohm*cm, 13.5 Ohm*cm
3000
400
H
2500
R
L
2000
300
1500
Relaxation freq
200
1000
Relaxation freq
500
0
0
50
100
150
100
200
50
0
10
20
Relaxation freq ~= 1/(2περsub)
30
40
50
Single T-line, M1/sub, w = s = ws = 6um, l = 100um
Im(γ) (propagation const.) for Rosub=1 Ohm*cm, 13.5 Ohm*cm
12000
H
R
10000
L
3000
8000
2000
6000
1000
4000
2000
0
0
0
50
100
150
200
0
10
20
30
40
50
Single T-line, M1/sub, w = s = ws = 6um
L(f), R(f), C(f),G(f) for ρsub=1 Ohm*cm, 13.5 Ohm*cm
2.5E+04
1.05E-06
1.00E-06
H
R
L
9.00E-07
Resistance (Ohm)
Inductance (H/m)
9.50E-07
8.50E-07
8.00E-07
7.50E-07
7.00E-07
6.50E-07
2.0E+04
1.5E+04
1.0E+04
6.00E-07
5.50E-07
0
10
20
30
40
5.0E+03
50
0
10
Frequency (GHz)
Ro=13.5 Ohm*cm
20
30
40
50
Frequency (GHz)
Ro=1 Ohm*cm
Ro=13.5 Ohm*cm
6.0E-10
Ro=1 Ohm*cm
6.0E+01
5.5E-10
5.0E+01
4.0E+01
4.5E-10
G (1/Ohm)
Capacitance (F/m)
5.0E-10
4.0E-10
3.5E-10
3.0E+01
2.0E+01
3.0E-10
2.5E-10
1.0E+01
2.0E-10
0.0E+00
1.5E-10
0
10
20
30
40
Frequency (GHz)
Ro=13.5 Ohm*cm
Ro=1 Ohm*cm
50
0
10
20
30
40
Frequency (GHz)
Ro=13.5 Ohm*cm
Ro=1 Ohm*cm
50