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 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 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. L kk =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. L kl =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 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 ; 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 External self inductance of a single segment

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 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 Multilayer inductor

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 AMIS 0.5 μm; 3 Metal layers Structures on chip 1: 1.Planar inductor on grounded poly 2.Planar inductor on n-well 3.Planar inductor on p- substrate 4.Planar inductor on n-plus 5.De-embedding structure: Open

Inductors--- 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 pin-diode 2.Stacked inductor on p- substrate 3.Planar inductor on p-plus 4.De-embedding structure: Thru

De-embedding Open ThruDUT_full

De-embedding DUT_full: S DF  Z DF, Y DF Open: S O  Z O, Y O Thru: S T  Z T, Y T  Measured reference frame for DUT_full   -----Ref. frame after Open is taken out   ----DUT---- 

De-embedding DUT_full: S DF  Z DF, Y DF Open: S O  Z O, Y O Thru: S T  Z T, Y T Y DF-O =Y DF -Y O Y T-O =Y T -Y O  Z DF-O  Z T-O Z DUT =Z DF-O -Z T-O  Y DUT, S DUT

Quick interpretation guide

Inductors--- Test Chip, measurements

Inductors--- Test Chips AMIS 0.5 μm; 3 Metal layers Structures: 1.Planar inductor on p- substrate, 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

Inductors--- Test Chips AMIS 0.5 μm; 3 Metal layers Structures: 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

Transformers--- Test Chips AMIS 0.5 μm; 3 Metal layers Structures: 1.Transformer: Metal2:Metal3 2.Transformer: interwound spirals 3.Transformer: Metal2: Metal 3 and Metal 1 4.Transformer: spiral-within- spiral 5.Transformer: coil-within-coil 6.De-embedding structure: short