on-chip inductors: design and modeling umd semiconductor simulation lab march 2005

On-chip Inductors: Design and ModelingOn-chip Inductors: Design and Modeling

UMD Semiconductor Simulation LabMarch 2005

Passive components on Passive components on semiconductor chipssemiconductor chips

Modern RF circuits may feature on-chip inductors required by circuit design Operating frequencies are high enough to make this

feasible

Increasing circuit complexity also creates or requires other inductive components 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 modelingIssues in modeling

Semiconductor substrates are conductive unable to treat system as metal/dielectric/ground plane New processes feature higher doping, higher

conductivityDevice 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 Skin depth of semiconductor substratesubstrate

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---theoryInductor 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

Resistance & Resistance & Internal Self Inductance Internal Self Inductance

Calculate the internal current distribution in the cross-section

Treat the current as “response to surface field” to find impedance

)()( int,

.

0 self

cond

LiRdsJ

EZ

Resistance rises: Effective area of current reduced at high freqInductance falls: ω is rising, and imaginary current is falling

External self-inductanceExternal 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

IL selfext

,

sdB

External self inductanceof a single segment

Return current depthReturn current depth

Mutual inductanceMutual 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

2pW

2qW

2qW

qxJ

qxJ

'qqh

yz

Virtual Ground Plane

qp

'q (image)

1py

2py

1qy

2qy

pqh

On-Chip Inductor ModelingOn-Chip Inductor Modeling

Multilayer inductor

Inductor modeling---Design Inductor modeling---Design issuesissues

Variations in layout: Metal layer Length Number of turns Metal trace width Metal trace spacing Substrate doping Shape …

Some ResultsSome Results

Substrate 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.

Inductors--- Test ChipsInductors--- Test Chips

Designed for RF-probe station measurements

Manufactured through MOSIS

AMIS 0.5 μm; 3 Metal layers

Structures on chip 1:

1. Planar inductor on grounded poly

2. Planar inductor on n-well3. Planar inductor on p-

substrate4. Planar inductor on n-plus5. De-embedding structure:

Open

1 2 3

4 5


Designed for RF-probe station measurements

Manufactured through MOSIS


Structures on chip 1:

1. Planar inductor on pin-diode 2. Stacked inductor on p-

substrate3. Planar inductor on p-plus4. De-embedding structure:

Thru1 2

3 4

De-embeddingDe-embedding

Open Thru DUT_full


DUT_full: SDF ZDF, YDF

Open: SOZO, YO

Thru: STZT, YT

--------Measured reference frame for DUT_full-----------------Ref. frame after Open is taken out-------

----DUT----


DUT_full: SDF ZDF, YDF

Open: SOZO, YO

Thru: STZT, YT

YDF-O=YDF-YO YT-O=YT-YO

ZDF-O ZT-O

ZDUT=ZDF-O-ZT-O

YDUT, SDUT

11(1/ )( )

imag YL

Quick interpretation guideQuick interpretation guide

Inductors--- Test Chip, measurements Inductors--- Test Chip, measurements


123

4 5


Structures:

1. Planar inductor on p-substrate, metal 3

2. Planar inductor p-substrate, metal 1

3. Coil inductor type 24. Coil inductor type 15. De-embedding structures:

Open and through



Structures:

1. Planar inductor on pn diode, metal 1

2. Planar inductor pn junction, metal 3

3. Coil inductor type 34. Stacked inductor5. Staggered-stacked inductor

12

3 4 5

Inductors--- Test Chip, measurements Inductors--- Test Chip, measurements

Transformers--- Test ChipsTransformers--- Test Chips


Structures:

1. Transformer: Metal2:Metal32. Transformer: interwound

spirals3. Transformer: Metal2: Metal 3

and Metal 14. Transformer: spiral-within-

spiral5. Transformer: coil-within-coil6. De-embedding structure:

short

123

4 5 6

on-chip inductors: design and modeling umd semiconductor simulation lab march 2005

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