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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 Operating frequencies are high enough to make this feasible

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On chip inductors design and modeling

On-chip Inductors: Design and Modeling

UMD Semiconductor Simulation Lab

March 2005


Passive components on semiconductor chips
Passive components on semiconductor 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 modeling
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
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
Inductor modeling---theory

Modeling Approach:Divide a spiral inductor into segments and treat each current segment separately.

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
Resistance & Internal Self Inductance

  • Calculate the internal current distribution in the cross-section

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

Resistance rises: Effective area of current reduced at high freq

Inductance falls:ω is rising, and imaginary current is falling


External self inductance
External self-inductance

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.

Effective virtual ground plane distance

from the signal current



Mutual inductance
Mutual inductance

Mutual inductance: The magnetic flux created by the current on one loop linking to the area of other loop

Calculate Y 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.


On chip inductor modeling
On-Chip Inductor Modeling

Multilayer inductor


Inductor modeling design issues
Inductor modeling---Design issues

  • Variations in layout:

    • Metal layer

    • Length

    • Number of turns

    • Metal trace width

    • Metal trace spacing

    • Substrate doping

    • Shape


Some results
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
Inductors--- Test Chips

  • Designed for RF-probe station measurements

  • Manufactured through MOSIS

  • AMIS 0.5 μm; 3 Metal layers

  • Structures on chip 1:

  • Planar inductor on grounded poly

  • Planar inductor on n-well

  • Planar inductor on p-substrate

  • Planar inductor on n-plus

  • De-embedding structure: Open

4

5

1

2

3


Inductors test chips1
Inductors--- Test Chips

  • Designed for RF-probe station measurements

  • Manufactured through MOSIS

  • AMIS 0.5 μm; 3 Metal layers

  • Structures on chip 1:

  • Planar inductor on pin-diode

  • Stacked inductor on p-substrate

  • Planar inductor on p-plus

  • De-embedding structure: Thru

3

4

2

1


De embedding
De-embedding

Open Thru DUT_full


De embedding1
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 embedding2
De-embedding

DUT_full: SDF ZDF, YDF

Open: SOZO, YO

Thru: STZT, YT

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

 ZDF-O ZT-O

ZDUT=ZDF-O-ZT-O

YDUT, SDUT





Inductors test chips2
Inductors--- Test Chips

  • AMIS 0.5 μm; 3 Metal layers

  • Structures:

  • Planar inductor on p-substrate, metal 3

  • Planar inductor p-substrate, metal 1

  • Coil inductor type 2

  • Coil inductor type 1

  • De-embedding structures: Open and through

4

5

3

2

1


Inductors test chips3
Inductors--- Test Chips

  • AMIS 0.5 μm; 3 Metal layers

  • Structures:

  • Planar inductor on pn diode, metal 1

  • Planar inductor pn junction, metal 3

  • Coil inductor type 3

  • Stacked inductor

  • Staggered-stacked inductor

3

4

5

2

1





Transformers test chips
Transformers--- Test Chips

  • AMIS 0.5 μm; 3 Metal layers

  • Structures:

  • Transformer: Metal2:Metal3

  • Transformer: interwound spirals

  • Transformer: Metal2: Metal 3 and Metal 1

  • Transformer: spiral-within-spiral

  • Transformer: coil-within-coil

  • De-embedding structure: short

4

5

6

3

2

1


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