Transcript Frequency-Dependent Interconnect Modeling

On-chip Inductors: Design and Modeling
UMD Semiconductor Simulation Lab
March 2005
Passive components on
semiconductor chips

Modern RF circuits may feature on-chip inductors
required by circuit design


Increasing circuit complexity also creates or
requires other inductive components



Operating frequencies are high enough to make this
feasible
Long transmission (bus) lines; signal/clock distribution
networks…
Transformers
System-on-a-chip RF circuits require on-chip
inductors with high L, small area and high Q
Issues in modeling

Semiconductor substrates are conductive
unable to treat system as
metal/dielectric/ground plane


New processes feature higher doping, higher
conductivity
Device circuits underneath metal structures
display variable doping

Non-uniform substrate: n+ and p+ active
regions, n-wells, p-wells, lightly doped chip
substrate…
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)
Inductor modeling---theory
Modeling Approach: Divide a spiral inductor into segments and treat
each current segment separately.
 V1   L11
V   L
 2    m,21
  
  
VN   Lm, N 1
Lm,12
L22
Lm, N 2
Lm,1N   I 
Lm,1N   I 
s 
  
  
LNN   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
Resistance &
Internal Self Inductance


Z
Calculate the internal current distribution in the
cross-section
Treat the current as “response to surface field” to
find impedance
E0
 J  ds
 R( )  iLint,self ( )
cond .
Resistance rises: Effective area of
current reduced at high freq
Inductance falls: ω is rising, and
imaginary current is falling
External self-inductance
Lext ,self


I
 
   B  ds
;
External self inductance
of a single segment
Weisshaar et.al. showed in 2002 that an image current with a complex distance can be
defined for the metal-oxide-lossy substrate system.
Signal Current
hox
hsub
Insulator
D

Substrate
 1  j  hsub 
heff  hox  1  j     tanh 



  

Metal Plate
Effective virtual ground plane distance
from the signal current
Image Current
Return current depth
Mutual inductance
Mutual inductance: The magnetic flux created
by the current on one loop linking to the area
of other loop
Lij 
Calculate  from the magnetic
 1
vector potential and I from the
current distribution; the mutual
4 ai
L

inductance between two
m ,ij
current segments is then
 ij
Ij
ci
   
ai
bi
aj
J j d li  d l j
dai da j
Rij
cj
bj
J
j
da j
aj
p
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.
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)
On-Chip Inductor Modeling
Multilayer inductor
Inductor modeling---Design
issues
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Variations in layout:
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Metal layer
Length
Number of turns
Metal trace width
Metal trace spacing
Substrate doping
Shape
…
Some Results
Substrate Doping Variation
Overall, 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.
Inductors--- Test Chips
Designed for RF-probe station
measurements
Manufactured through MOSIS
4
5
AMIS 0.5 μm; 3 Metal layers
Structures on chip 1:
1
2
3
1. Planar inductor on
grounded poly
2. Planar inductor on n-well
3. Planar inductor on psubstrate
4. Planar inductor on n-plus
5. De-embedding structure:
Open
Inductors--- Test Chips
Designed for RF-probe station
measurements
Manufactured through MOSIS
3
4
AMIS 0.5 μm; 3 Metal layers
Structures on chip 1:
1
1. Planar inductor on pin-diode
2. Stacked inductor on psubstrate
3. Planar inductor on p-plus
4. De-embedding structure:
2
Thru
De-embedding
Open
Thru
DUT_full
De-embedding
DUT_full: SDF ZDF, YDF
Open: SOZO, YO
Thru: STZT, YT
----DUT----
-----Ref. frame after Open is taken out-------
--------Measured reference frame for DUT_full------------
De-embedding
DUT_full: SDF ZDF, YDF
Open: SOZO, YO
Thru: STZT, YT
YDF-O=YDF-YO
 ZDF-O
YT-O=YT-YO
ZT-O
ZDUT=ZDF-O-ZT-O
YDUT, SDUT
L( ) 
imag (1/ Y11 )

Quick interpretation guide
Inductors--- Test Chip, measurements
Inductors--- Test Chip, measurements
Inductors--- Test Chips
AMIS 0.5 μm; 3 Metal layers
Structures:
4
3
1. Planar inductor on psubstrate, metal 3
2. Planar inductor p-substrate,
metal 1
3. Coil inductor type 2
4. Coil inductor type 1
5. De-embedding structures:
Open and through
5
2
1
Inductors--- Test Chips
AMIS 0.5 μm; 3 Metal layers
Structures:
3
4
2
5
1
1. Planar inductor on pn diode,
metal 1
2. Planar inductor pn junction,
metal 3
3. Coil inductor type 3
4. Stacked inductor
5. Staggered-stacked inductor
Inductors--- Test Chip, measurements
Inductors--- Test Chip, measurements
Inductors--- Test Chip, measurements
Transformers--- Test Chips
AMIS 0.5 μm; 3 Metal layers
Structures:
4
5
6
3
2
1
1. Transformer: Metal2:Metal3
2. Transformer: interwound
spirals
3. Transformer: Metal2: Metal 3
and Metal 1
4. Transformer: spiral-withinspiral
5. Transformer: coil-within-coil
6. De-embedding structure:
short