On-chip inductance and coupling
description
Transcript of On-chip inductance and coupling
![Page 1: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/1.jpg)
On-chip inductance and coupling
Zeynep Dilli, Neil Goldsman
Thanks to Todd Firestone and John Rodgers for providing the laboratory equipment and expertise for measurements.
![Page 2: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/2.jpg)
EM-sensitive components on semiconductor chips
Modern RF circuits often feature on-chip inductors required by circuit designOperating frequencies are high enough to
make this feasibleIncreasing circuit complexity also creates
other inductive componentsLong transmission (bus) lines; signal/clock
distribution networks…
![Page 3: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/3.jpg)
Motivation for modeling
Investigating parasitic effectsVulnerability to external EM interferencePotential to create on-chip interference
RadiationSubstrate current
System-on-a-chip RF circuits require on-chip inductors with high L, small area and high QAutomated design and speedy evaluation of
geometrical tradeoffs.
![Page 4: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/4.jpg)
Issues in modeling
Semiconductor substrates are conductive unable to treat system as metal/dielectric/ground planeNew processes feature higher doping, higher
conductivityDevice circuits underneath metal structures
display variable dopingNon-uniform substrate: n+ and p+ active
regions, n-wells, p-wells, lightly doped chip substrate…
![Page 5: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/5.jpg)
Inductor modeling---theory
Modeling Approach: Divide a spiral inductor into segments and treat each current segment separately.
11 ,12 ,11
,21 22 ,12
, 1 , 2
m m N
m m N
m N m N NNN
L L LV I
L L LV Is
L L LV I
Lkk=self-inductance (external+internal) of segment k Sources: Frequency-dependent current distribution within the segment and the magnetic flux linkage to the loop formed by the segment and its return current. Lkl=mutual inductance between segments k and l Sources: Magnetic flux linkage of the current in the first segment to the loop formed by the second segment and its return current.Lossy substrate effect: The return current has an effective distance into the substrate; this is frequency-dependent and can be modeled as a complex distance to account for the losses.
Other frequency dependency: Skin effect in the metal; current crowding in the metal
![Page 6: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/6.jpg)
Internal self-inductance
Frequency-dependent current distribution creates an internal self-impedance
JjJ 22
)()( int,
.
0 self
cond
LRdsJ
EZ
Solve Helmholtz Eqn. for current distribution:
Obtain resistance and inductance from J:
![Page 7: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/7.jpg)
Internal self-inductance
Physical current in cylindrical conductor, f=5GHz
J
center r edge
![Page 8: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/8.jpg)
External self-inductance
Flux of magnetic field linked to surface between interconnect and its return current
IL selfext
,
;
sdB
Need to define the return current path to determine the flux linkage area. If the frequency is low enough or substrate has low conductivity, the physical ground plane below the substrate is used for this purpose.
But silicon substrates are not dielectric: With higher doping levels in modernprocess technologies to optimize the active devices on chips, the substrate conductivities rise.
And our operating frequencies of interest are high.
![Page 9: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/9.jpg)
Skin depth of semiconductor substrate
Within our frequency range the skin depth will fall below our substrate thickness
(around 5 GHz for p-type sub.,around 2 GHz for n-well, lower for active regions)
![Page 10: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/10.jpg)
External self-inductance
;
Weisshaar et.al. showed in 2002 that an image current with a complex distance can be defined for the metal-oxide-lossy substrate system.
11 tanh sub
eff ox
j hh h j
D
Insulatoroxh
Metal Plate
subh Substrate
Signal Current
Image Current
Effective virtual ground plane distancefrom the signal current
![Page 11: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/11.jpg)
Return current depth
![Page 12: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/12.jpg)
Mutual inductance
,
14
i j
i i j j
j
c c j i ji ja b a b
i ijm ij
j j
a
J dl dlda da
a RL
J da
������������� �
Mutual inductance: The magnetic flux created by the current on one loop linking to the area of other loop
ijij
j
LI
Calculate from the magnetic vector potential and I from the current distribution; the mutual inductance between two current segments is then
Frequency dependency: The signal current of a current segment and its image current both induce voltages on the “target” current segment; the distribution of the image current varies with frequency on a semiconductor substrate.
xpx
qx
2pW
2
pW
2qW
2
qW
qxJ
qxJ
'qqh
yz
Virtual Ground Plane
qp
'q (image)
1py
2py
1qy
2qy
pqh
![Page 13: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/13.jpg)
Inductor modeling---Design issues
Variations in layout:Metal layerLengthNumber of turnsMetal trace widthMetal trace spacingSubstrate dopingShape…
![Page 14: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/14.jpg)
Some ResultsLength Variation
Increasing the length of the inductor increases inductance, but leads to a decline in Q due to increasing serial resistance as well, this effect worsening at higher frequencies as skin effect increases the resistance faster than linearly with length.
![Page 15: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/15.jpg)
Some ResultsNumber of Turns VariationAn inductor with the same length but with more turns has higher inductance, but the resistance does not rise quite so high so the detrimental effect to Q is less: Increasing the number of turns is a better way to increase inductance.
![Page 16: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/16.jpg)
Some ResultsTrace Spacing VariationNarrower spacing yields a higher inductance, but will probably increase capacitive coupling between turns.
![Page 17: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/17.jpg)
Some ResultsSubstrate Doping VariationOverall, higher doping reduces inductance (closer return current, smaller loops) and makes it more freq-dependent (low enough doping pushes all current to bottom). Relationship between resistance and doping is not straightforward, since conductivity of substrate affects return current distribution, composition, and its frequency dependence all at the same time and these effects interact.
![Page 18: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/18.jpg)
Inductors--- Test Chip
Designed for RF-probe station measurements
Manufacturedthrough MOSIS
AMIS 0.5 μm3 Metal layers
![Page 19: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/19.jpg)
Inductors--- Test Chip
Planar inductoron substrate
Planar inductoron grounded poly
Planar inductor on n-well
Transformer
Stacked inductoron substrate
RF probe tip
![Page 20: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/20.jpg)
Inductors--- Test Chip, measurements
Cascade probes used with Hewlett-Packard Network AnalysisMeasured: S22
0 2222 0
0 22
1
1L
LL
Z Z SS Z Z
Z Z S
![Page 21: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/21.jpg)
Inductors--- Test Chip, measurements
![Page 22: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/22.jpg)
Inductors--- Test Chip, measurements
![Page 23: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/23.jpg)
EM Coupling Test Chip 2
For RF-probestation measurements
Manufacturedthrough MOSIS
AMIS 0.5 μm3 Metal layers
![Page 24: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/24.jpg)
EM Coupling Test Chip 2
Planar inductor
NMOS 1
NMOS 2
N-wells
inverter
NMOS 3
![Page 25: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/25.jpg)
On-Chip EM Coupling
• Coupling between On-chip Inductors
Left: Results from literature and circuit model for coupled on-chip inductorsRight: Our test structure for measuring coupling between inductors on different metal layers
![Page 26: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/26.jpg)
On-Chip EM Coupling: Inductor to inductor
![Page 27: On-chip inductance and coupling](https://reader036.fdocuments.in/reader036/viewer/2022081515/5681528c550346895dc0af9e/html5/thumbnails/27.jpg)
On-Chip EM Coupling: N-well to n-well
P-Type Silicon Substrate
N Well N Well
Oxide
Metal Contact
Port 1 Port 2
m8.28 m8.28m45.102
Need substrate current analysis….