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