EM-sensitive components on
semiconductor chips
• Modern RF circuits often feature on-chip
inductors required by circuit design
– Operating frequencies are high enough to
make this feasible
• Increasing circuit complexity also creates
other inductive components
– Long transmission (bus) lines; signal/clock
distribution networks…
Motivation for modeling
• Investigating parasitic effects
– Vulnerability to external EM interference
– Potential to create on-chip interference
• Radiation
• Substrate current
• System-on-a-chip RF circuits require onchip inductors with high L, small area and
high Q
– Automated design and speedy evaluation of
geometrical tradeoffs.
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…
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
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)
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.
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
Calculate  from the magnetic
vector potential and I from the Lm ,ij 
current distribution; the mutual
inductance between two
current segments is then
 1
4 ai
Lij 
 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)
Inductor modeling---Design issues
• Variations in layout:
– 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
AMIS 0.5 μm; 3 Metal layers
5
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
AMIS 0.5 μm; 3 Metal layers
4
Structures on chip 1:
1. Planar inductor on pin-diode
2. Stacked inductor on psubstrate
3. Planar inductor on p-plus
4. De-embedding structure:
Thru
1
2
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 (Y21 )
 Y21
2
Inductors--- Test Chip, measurements
Inductors--- Test Chip, measurements
Inductors--- Test Chip, measurements
Inductors--- Test Chip, measurements
Inductors--- Test Chip, measurements
Inductors--- Test Chip, measurements
Inductors--- Test Chip, measurements
Inductors--- Test Chip, measurements