Study of Floating Fill Impact on Interconnect Capacitance

Andrew B. Kahng Kambiz Samadi Puneet Sharma

CSE and ECE DepartmentsUniversity of California, San Diego

Outline

• Introduction

• Foundations

• Study of Capacitance Impact of Fill– Proposed Guidelines

• Validation of Guidelines

• Conclusions

Introduction

• Why fill is needed?• Planarity after chemical-mechanical polishing (CMP)

depends on pattern• Metal fill reduces pattern density variation• Stringent planarity requirements fill mandatory now

• Impact on capacitance• Grounded fill

• Increases capacitance larger delay• Shields neighboring interconnects reduced xtalk

• Floating fill• Increases coupling capacitance significantly

more xtalk signal integrity & delay• Increases total capacitance larger delay

Motivation• Floating-fill extraction is complex

• Floating-fill capability recently added to full-chip extractors• In past large buffer distance design-rule used

• Reduces coupling impact• Density constraints cannot be met reduce buffer distance

inaccuracy in capacitance estimation

• We systematically analyze capacitance impact of fill config. parameters (e.g., fill size, fill location, interconnect width, etc.)

• Propose guidelines for floating fill insertion to reduce capacitance impact

• Grounded fill used despite disadvantages (e.g., higher delay impact, routing needed)

• Designers use floating fill extremely conservatively Better understanding of capacitance impact needed

Assumptions & Terminology• Same-layer analysis

– Fill affects coupling of all interconnects in proximity

– We study effect on coupling capacitance of same-layer interconnects simplifies analysis

• Terminology– Fill and coupling interconnects are on Layer M (layer of interest)– ia and ib are interconnects of interest with coupling Cab

– We study increase in coupling ΔCab due to fill insertion– Dimensions measured in tracks (=0.3µ)

– Usability not compromised because:1. Coupling with same-layer neighbor large

– Validation: multiple configs with different densities on different layers considered2. Fill insertion between two same-layer interconnects, increases coupling

significantly– Validation: fill inserted everywhere

Large fraction of coupling impact captured by same-layer analysis• Synopsys Raphael, 3D field solver, used in all experiments

Outline

• Introduction

• Foundations

• Study of Capacitance Impact of Fill– Proposed Guidelines

• Validation of Guidelines

• Conclusions

Foundation 1

• Experimental Setup• Two interconnects on Layer M separated by three

tracks• Fill inserted on Layer M between two interconnects• M+1/M-1 density is set to 33%• 20% , 33% , 100% metal density for Layer M+2/M-2

tried

For ΔCab analysis, Layers M-2 and M+2 may be assumed as groundplanes

Foundation 2

• Experimental Setup• Two interconnects on Layer M separated by three

tracks• M+1 & M-1 density is set to 33%• M+2 & M-2 assumed groundplanes• Fill features inserted on Layer M at different locations

ΔCab is affected by fill geometries in the region REab only.

Outline

• Introduction

• Foundations

• Study of Capacitance Impact of Fill– Proposed Guidelines

• Validation of Guidelines

• Conclusions

Fill Size• Fill length (along the interconnects)

• Linear increase in ΔCab with Y-intercept

Guideline: Increase fill length instead of width

• Fill width• Increases super-linearly

• Using parallel-plate capacitor analogy, 1/w relation expected• Settings:

• Interconnect separation = 3 tracks• Layers M-1/M+1 have 33% density• 2 track width, 1 track length

Interconnect Spacing• ΔCab decreases super-linearly with spacing• For larger spacings (>10 tracks), coupling with

M-1 and M+1 wires more significant• Settings:

• Fill size = 2 tracks x 2 tracks• Layers M-1/M+1 have 33% density

Guideline: Insert fill where wire spacing is large

Fill Location• Y-axis translation

• Cab unaffected until fill close to an interconnect ending

Guideline: Center fill horizontally between interconnects

• X-axis translation • ΔCab increases ~linearly• Capacitance between fill & closer

interconnect increases dramatically• Settings:

• Wire spacing = 8 tracks• Fill size = 2 tracks wide, 4 long• Layers M-1/M+1 have 33% density

Edge Effects• Study two cases: (1) two interconnects horizontally

aligned, and (2) not horizontally aligned• With Y-axis translation of fill, edge effects observed

• When fill no longer in Rab, ΔCab dramatically decreases

• Settings:• Layers M-1/M+1 have 33% density• Interconnect width = 2 tracks• Fill size = 4 tracks long, 2 wide

Guideline: Insert fill in low-impact region (= outside Rab)

Rab

Interconnect Width

• Change width of one interconnect•Interconnect-fill spacing and

interconnect spacing constant• ΔCab increases rapidly, but saturates at ~ 4

tracks

Guideline: Insert fill next to thinner interconnects

Multiple Columns• Vertically aligned fill geometries are said to be

in a fill column • Change number of fill columns in fill pattern

•Fill area is kept constant • ΔCab reduces with number of fill columns

•Cf. Tran. Electron Devices ’98 (MIT)•Cf. VMIC-2004 invited paper (UCSD / UCLA)

Guideline: Increase number of fill columns

Multiple Rows• Horizontally aligned fill geometries are said to be

in a fill row• Change number of fill rows in fill pattern

• Fill area is kept constant • ΔCab increases with number of fill rows• As spacing between two fill rows decreases, the

ΔCab decreases

Guideline: Decrease number of fill rows and inter-row spacing

Outline

• Introduction

• Background & Terminology

• Study of Capacitance Impact of Fill– Proposed Guidelines

• Validation of Guidelines

• Conclusions

Application of Guidelines

Regular Staggered With guidelines

Guidelines applied1. Edge effects2. Maximize columns3. Minimize rows4. Centralize fill

ΔΔC = 6

4%

C = 6

4%

ΔΔC = 6

2%

C = 6

2%

ΔΔC = 1

6%

C = 1

6%

• Apply guidelines on 3 interconnect configurations• Reasonable design rules assumed• Configuration 1

Guidelines on Configuration 2

ΔΔC = 4

1%

C = 4

1%

ΔΔC = 4

1%

C = 4

1%

ΔΔC = 3

0%

C = 3

0%

Guidelines applied1. Wire width2. Minimize rows

Guidelines on Configuration 3

ΔΔC = 2

7%

C = 2

7%

ΔΔC = 2

7%

C = 2

7%

ΔΔC = 1

1%

C = 1

1%

Guidelines applied1. High-impact region2. Edge effects3. Wire spacing4. Minimize rows5. Centralize fill

Conclusions• Coupling with same-layer neighboring wires

significant and same-layer fill insertion increases it dramatically

• Systematically analyzed the impact of floating fill configurations on coupling of same-layer interconnects

• Propose guidelines for floating fill insertion to reduce coupling increase

• Ongoing work:– 3D extensions: Impact on coupling of different-layer

interconnects

– Timing- and SI-driven fill insertion methodology