Exploring 3D Power Distribution Network Physics

Xiang Hu1, Peng Du2, and Chung-Kuan Cheng2

1ECE Dept., 2CSE Dept., University of California, San Diego

10/25/2011

Page 2

Outline

Introduction

3D power distribution network (PDN) model

– Circuit model

– Current model

3D PDN analysis flow

Experimental results

– On-chip Current Distribution

– Resonance phenomena

Noise reduction techniques

– Larger decap around TSVs

– Reduce Tier to tier impedance

Conclusions

Page 3

Introduction

Power delivery issues in 3D ICs

– More tiers => More current

– Same footprint on package

– TSVs and µbumps between tiers

Coarse power grid models

– Missed detailed metal layer information

– Current source models

Detailed 3D PDN analysis

– Frequency domain: resonance behavior

– Time domain: worst-case noise

Page 4

3D PDN Circuit and Current Models

Circuit Model

–Lump model: Two-port model for chip between tiers

–Fine grid model: all metal layers: m1+

Current Model

–Power law

–Phase in f domain

Page 5

3D PDN Distributed Model[1]

Power grid

– Structure: M1, M3, M6, RDL

– Each layer extracted in Q3D

T2T: TSV+μbump

– Modeled as an RLC element

Package: C4 bump based RLC model

[1] X. Hu et al., “Exploring the Rogue Wave Phenomenon in 3D Power Distribution Networks,” IEEE 19th Conf. on Electrical Performance of Electronic Packaging and Systems, Oct. 2010, pp. 57–60.

Page 6

Frequency-Domain Current Stimulus Model

Noise depends on the current model

Rents rule power law:

– P: power consumption

– A: area

– k: constant number

– γ: exponent of the power law

Current configurations

– γ =0: single current load

– 0< γ <1: taper-shaped current distribution

– γ =1: uniform current distribution

– In f domain, we can tune the phase

P kA

Page 7

3D PDN Analysis Flow

Page 8

Experiment Base Setup

– Two-tier PDN

– TSV setup: 3x4 TSVs connected to M1 and AP on both side

– 5nF/mm2 decap on T1; 50nF/mm2 decap on T2

– 2x2 C4 on T1 AP

• Per bump inductance: 210pH

• Per bump resistance: 18.7mΩ

M1 M3 M6 AP TSV

T1 T2

Pitch (um)

Width (um)

Pitch (um)

Width (um)

Pitch (um)

Width (um)

Pitch (um)

Width (um)

Pitch (um)

Width (um)

X step

Y step

2.5 0.2 8.5 0.25 30 4 400 30 8.5 3 20 40

Page 9

Current Model: Input on T1

Two-tier PDN + VRM, board, and package

– Decap: 5nF/mm2@T1; 50nF/mm2@T2

– Current: T1; distr.(γ=0, 0.5, 1)

Probe

– A: T1 TSVs

– B: T1 between TSVs

– C: T2

Observation

– Smaller γ => larger noise

– Resonance at non-TSVs, but not at TSVs

104

106

108

1010

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

Frequency (Hz)

Vo

ltag

e (

V)

=0, Output A=0, Output B=0, Output C=0.05, Output A=0.05, Output B=0.05, Output C=1, Output A=1, Output B=1, Output C

VRM-brd brd-pkg T1-T2

Page 10

Current Model: Noise Map w/ Input on T1 (@1GHz)

T1

T20

2040

6080

100120

140

0

10

20

30

40

50

600

0.5

1

1.5

2

2.5

3

M3 directionM1 direction

Vol

tage

(V

)

020

4060

80100

120140

0

10

20

30

40

50

600

0.2

0.4

0.6

0.8

1

1.2

1.4

M3 directionM1 direction

Vol

tage

(V

)

020

4060

80100

120140

0

10

20

30

40

50

600

0.05

0.1

0.15

0.2

0.25

M3 directionM1 direction

Vol

tage

(V

)

020

4060

80100

120140

0

10

20

30

40

50

600.0165

0.017

0.0175

0.018

0.0185

0.019

0.0195

0.02

0.0205

0.021

M3 directionM1 direction

Vol

tage

(V

)

020

4060

80100

120140

0

10

20

30

40

50

600.0165

0.017

0.0175

0.018

0.0185

0.019

0.0195

0.02

0.0205

0.021

M3 directionM1 direction

Vol

tage

(V

)

020

4060

80100

120140

0

10

20

30

40

50

600.0165

0.017

0.0175

0.018

0.0185

0.019

0.0195

0.02

0.0205

0.021

M3 directionM1 direction

Vol

tage

(V

)

γ=0 γ=0.05 γ=1

Page 11

Current Model: Input on T2

Two-tier PDN + VRM, board, and package

– Decap: 5nF/mm2@T1; 50nF/mm2@T2

– Current: T2; distr.(γ=0, 0.5, 1)

Probe

– A: T1 TSV location

– B: T1 non-TSV location

– C: T2

Observation

– Smaller γ => larger noise

104

106

108

1010

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

Frequency (Hz)

Vo

ltag

e (

V)

=0, Output A=0, Output B=0, Output C=0.05, Output A=0.05, Output B=0.05, Output C=1, Output A=1, Output B=1, Output C

Page 12

Current Model: Noise Map w/ Input @T2 (1GHz)

0

50

100

150

0

20

40

600.01

0.015

0.02

0.025

0.03

M3 direction

M1 direction

Vo

ltag

e (

V)

0

50

100

150

0

20

40

600.01

0.015

0.02

0.025

0.03

M3 directionM1 direction

Vo

ltag

e (

V)

0

50

100

150

0

20

40

600.0175

0.018

0.0185

0.019

0.0195

0.02

0.0205

0.021

M3 directionM1 direction

Vo

ltag

e (

V)

0

50

100

150

0

20

40

600

2

4

6

8

M3 directionM1 direction

Vo

ltag

e (

V)

0

50

100

150

0

20

40

600

0.5

1

1.5

2

2.5

3

M3 directionM1 direction

Vo

ltag

e (

V)

0

50

100

150

0

20

40

600.019

0.0195

0.02

0.0205

0.021

0.0215

M3 directionM1 direction

Vo

ltag

e (

V)

T1

T2

γ=0 γ=0.05 γ=1

Page 13

Resonance Phenomena

Decap: 5nF/mm2 @T1; 50nF/mm2 @T2

Current: T1 or T2, unif. (γ=1)

Observation: resonance vary with decap configurations

Global mid-freq resonance peak @ non-TSV locations.From lumped model:

1

1

2mid

p d

fL C

No resonance peak @ TSV locations

No mid-freq resonance peak due to “Rm1”

Probe: T1Current: T1

Probe: T2Current: T2

Page 14

Decap: Larger Decap Around TSVs

Decap: 50nF/mm2@T1; 5nF/mm2@T2

– Case 1: uniform distribution @T1

– Case 2: half of decap at TSVs @T1

Observation: Case 2 is better

Probe: T1 between TSVsCurrent: T1 unif.

Probe: T2Current: T2, unif

Probe: T2Current: T1 unif

105

106

107

108

109

1010

1011

0

0.05

0.1

0.15

0.2

0.25

Frequency (Hz)

Vo

ltag

e (

V)

Case 1Case 2

105

106

107

108

109

1010

1011

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Frequency (Hz)

Vo

ltag

e (

V)

Case 1Case 2

105

106

107

108

109

1010

1011

0

0.05

0.1

0.15

0.2

0.25

Frequency (Hz)

Vo

ltag

e (

V)

Case 1Case 2

Page 15

Tier to Tier Impedance: Number of TSVs

Setup Case 1 Case 2 Case 3

TSV X step (M1 segments) 40 20 15

TSV Y step (M3 segments) 100 40 18

# TSV 4 12 32

TSV Setup

Page 16

105

106

107

108

109

1010

1011

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

X: 3.162e+008Y: 0.1077

Frequency (Hz)

Vo

ltag

e (

V)

X: 7.943e+008Y: 0.5745

Case 1, Output ACase 1, Output BCase 1 Output CCase 2, Output ACase 2, Output BCase 2 Output CCase 3, Output ACase 3, Output BCase 3 Output C

Tier to Tier Impedance: Number of TSVs

TSV(Xpitch,Ypitch)

– Case 1: (40, 100)

– Case 2: (20, 40)

– Case 3: (15, 18)

Current: T1, unif. (γ=1)

Probes

– A: T1 TSV

– B: T1 between TSVs

– C: T2

Observation

– noise drops as #TSV increases

– resonance f drops as #TSV increases

1 2

1237.7

2 ( )mid

p d d

f MHzL C C

As T2T impedance becomes smaller,resonance frequency is determined by both Cd1 and Cd2

Resonant f determined by Cd1

1

1788.2

2mid

p d

f MHzL C

Page 17

Conclusion

On-chip power network model

Current distribution model

– Power law current distribution model reflects the current-area relation

Decap: Various on-chip resonances

Techniques of reducing 3D PDN noise

– Larger decap around TSV area

– Small tier to tier impedance

Page 18

Thank You!Q & A