Transcript Chip Interconnect Design: Reliability Advisor

Blech Effect
in Interconnects:
Applications and Design Guidelines
Ali Abbasinasab
Malgorzata Marek-Sadowska
Overview

Introduction

Material Migration: Multiphysics
 Blech
Effect

CAD Model: New Mortality Criterion

Conclusions
2
Number of metal levels
Current Status
ITRS 2014-2020 (Reliability Challenge)

TCAD / Multiphysics Simulations
Devices, Interconnects and Packaging (nanoscale process)


Chemical, thermal, mechanical and electrical properties of new
materials: capping (MnSiO, CuAl , CuTi….), liners (Co, Ru) and
thickness, air-gap, low-k ILD

Technology, dual-damascene
Jmax (MA/cm2) – int wire ( 105C)
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Total wire length (m/cm2)
(6 levels)
CAD

Accurate Compact Models

Chip level assessment
20,000
15,000
10,000
5,000
0
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
Introduction
3
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
Trends in Interconnect Design
17
15
13
11
9
7
5
3
1
Material Migration
Introduction

Material-migration
Material transportation caused by the gradual movement of the atoms in conductor


Electromigration

Stressmigration

Thermomigration
Criticality: Technologies and Applications

Process, Manufacturing, 3D Integration, Packaging

Power and Signal/Clock Lines

Long-Term/Constantly-In-Use Chips: Automotive, Servers and Routers
4
Material Migration: Multiphysics
5
Material concentration change (vacancy transport) described by continuity equation:
𝜕𝐶𝑣
𝜕𝑡
𝐷𝐶𝑣
∗
𝑒𝑍
𝑗𝜌
𝑘𝑇
𝐷𝐶𝑣 𝑄 ∗
 Thermo-migration : 𝐽𝑡𝑚 = −
𝛻T
𝑘𝑇 𝑇
𝐷𝐶𝑣
 Stress-migration : 𝐽𝑠𝑚 = −
𝑓Ω𝛻σ
𝑘𝑇


+ 𝛻. 𝐽 = G
Electro-migration : 𝐽𝑒𝑚 = −
Diffusion-migration : 𝐽𝑚𝑚 = 𝛻𝐶𝑣
𝐶𝑣 ∗
𝐶𝑣
𝐶𝑣 𝑄∗
𝐽 = −𝐷( 𝑒𝑍 𝑗𝜌 +
𝑓Ω𝛻σ + 𝛻𝐶𝑣 +
𝛻T)
𝑘𝑇
𝑘𝑇
𝑘𝑇 𝑇
𝐺=
𝑸∗
𝑓Ω𝜎
𝐶𝑣0 𝑒 𝑘𝑇
𝐶𝑣 − 𝐶𝑒𝑞
𝐶𝑣 −
=−
𝜏𝑠
𝜏𝑠
𝒇Ω𝝈
𝑪𝒗𝟎 𝒆 𝒌𝑻
𝝏𝑪𝒗
𝑪𝒗
𝑪𝒗
𝑪𝒗
𝑪𝒗 −
= −𝜵. −𝑫( 𝒆𝒁∗ 𝒋𝝆 +
𝒇Ω𝜵𝝈 + 𝛁𝑪𝒗 +
𝛁𝐓) −
𝝏𝒕
𝒌𝑻
𝒌𝑻
𝒌𝑻 𝑻
𝝉𝒔
CAD models
What matters to a Designer or a CAD Engineer?

Geometry and Topology


Electrical


Conductivity and Current Density (𝐽 𝑎𝑛𝑑 𝜌)
Thermal


L, W, T and Interconnects Configuration
Joule Heating (Thermal Expansion Coefficient)
Chemical/Physical

Material (Activation energy, Young’s modulus, Diffusion…)
6
Blech Effect
Material Migration: Multiphysics
𝒊𝒎𝒎𝒐𝒓𝒕𝒂𝒍 𝒘𝒉𝒆𝒏:
𝜟𝝈𝒎𝒂𝒙
𝒋𝑳 < 𝒋𝑳 𝒄𝒓𝒊𝒕𝒊𝒄𝒂𝒍 =
𝒆𝒁∗ 𝝆
Competition between two main forces
cathode
𝐽𝑒𝑚 ≈ 𝐽𝑠𝑚 ≫ 𝐽𝑡𝑚 ≫ 𝐽𝑚𝑚
anode
Critical Tensile Stress
If stress required
for void
nucleation is
not reached at
cathode end in
steady state,
no void will
nucleate
𝑱𝒄𝒐𝒎𝒑𝒆𝒕𝒊𝒕𝒊𝒐𝒏
𝑫𝑪𝒗
=−
𝒆𝒁∗ 𝒋𝝆 + 𝒇Ω𝛁𝛔
𝒌𝑻
Hydrostatic Stress Distribution
In steady state,
back-stress
force balances
electron wind
force
7
Blech Effect
Hydrostatic Stress
JL
Current density
Material Migration: Multiphysics
jLBlech is valid for a simple single bounded wire
𝒋 𝟐
𝒋
𝒋
𝑳
𝑳
𝑳 𝟐
Critical Stress
(0.5J)L
Critical Stress
JL
Critical Stress
J(0.5L)
8
Motivation and Problem Description
CAD Model: new Mortality Criterion

9
jL is solely used in industry-standard P/G and signal integrity solutions and tools.
Existing EM analysis solutions are not accurate for complex wire structures
Thus they need designers’ time-consuming manual adjustments

QUESTION: Are j and L the only information needed for capturing EM failure precisely?

We reveal the weakness of jL-based methods by motivating examples

j and L are weaker predictors for more complicated interconnect structures

j and L don’t include atomic flux, geometry and material properties correctly
Past Works
CAD Model: new Mortality Criterion

Other advanced models:

𝑗𝐿 [Riege TED‘98]:
Find the longest anode-cathode path with respect to jL


Does not capture interconnect interaction accurately.

Not applicable to complex structures
Via Vector [Park RPS’10]:
Calculate the atomic flux divergence at via nodes

Does not offer a compact model or a systematic analysis

Lack of explanation for experimental observations
10
Motivation and Problem Description
CAD Model: new Mortality Criterion
Same longest anode-cathode path, yet different hydrostatic stress distribution
11
Motivation and Problem Description
12
CAD Model: new Mortality Criterion
𝒋
Hydrostatic Stress
𝒋
𝟎
𝝈𝒎𝒂𝒙 = 𝟓𝟎𝟎𝑴𝑷𝒂
JL
Current density
jLBlech can be used only for single bounded wire (due to adjacent wire segment interaction)
JL
𝒋
𝒋
𝝈𝒎𝒂𝒙 = 𝟔𝟎𝟎𝑴𝑷𝒂
𝝈𝒎𝒂𝒙 = 𝟑𝟎𝟎𝑴𝑷𝒂
JL
JL
JL
Motivation and Problem Description
CAD Model: new Mortality Criterion
What is missing in previous models?

Electrical




Atomic flux divergence
Geometry (studied only for single bounded wire & other extensions are inaccurate)

Length, Width, Thickness Effect

Angle Effect: Current crowding

Via cut surface, thickness and perpendicularity
Layout Topology

Multi-branch structure and remote connections

Passive segments: dummy vias and reservoirs
Damascene Materials

Interface Thickness: Barrier and Capping

Grain boundaries configuration

Interface Properties: Stiffness (Young’s Modulus)
Can be compacted into a diffusion coefficient
13
New Compact Model
14
CAD Model: new Mortality Criterion
𝒄 𝒅𝑽 = 𝑵𝟎
𝒏𝒆𝒕
Δ𝑐𝑑𝑉 =
𝑠𝑒𝑔𝑚𝑒𝑛𝑡
𝜟𝒄 𝒅𝑽 = 𝟎
𝒏𝒆𝒕
𝜎𝑎𝑛𝑜𝑑𝑒
𝑍 ∗ eρ
𝜎𝑎𝑛𝑜𝑑𝑒
Δ𝜎
𝜎𝑎𝑛𝑜𝑑𝑒 + 𝜎𝑎𝑛𝑜𝑑𝑒
𝑐0
− 𝑐0
𝑗𝐿 𝑉 = 𝑐0
− 𝑐0
𝑉=
𝑉
𝐵
2BΩ
𝐵
2𝐵
2𝐵
Δ𝑐 𝑑𝑉 =
𝑛𝑒𝑡
∴
𝒔𝒆𝒈𝒎𝒆𝒏𝒕𝒔 𝒌
Δ𝑐 𝑑𝑉 =
𝑠𝑒𝑔𝑚𝑒𝑛𝑡𝑠 𝑠𝑒𝑔𝑚𝑒𝑛𝑡
𝝈𝒌−𝒂𝒏𝒐𝒅𝒆 + 𝝈𝒌−𝒄𝒂𝒕𝒉𝒐𝒅𝒆
𝑽𝒌 = 𝟎 ∎
𝟐𝑩𝒌
𝑐 = 𝑐0 exp −
𝜎
𝜎
≈ 𝑐0 (1 −
𝐵
𝐵
New Compact Model
a
CAD Model: new Mortality Criterion
a'
Δ𝑐 𝑑𝑉 = 0
2
net I
Sbc =
Sab
d'
b'
b
𝑠𝑒𝑔𝑚𝑒𝑛𝑡𝑠 𝑠𝑒𝑔𝑚𝑒𝑛𝑡
15
2
c
net II
c'
σb + σc
Lbc
2
σa + σb
=|
Lab |
2
|𝑆𝑎𝑏 | = |𝑆𝑏𝑐 |
Atom Accumulation = Atom Depletion
𝒔𝒆𝒈𝒎𝒆𝒏𝒕𝒔 𝒌
𝝈𝒂𝒌 + 𝝈𝒄𝒌
(
) × 𝑳𝒌 = 𝟎
𝟐
New Compact Model
a
CAD Model: new Mortality Criterion
a'
Δ𝑐 𝑑𝑉 = 0
2
net I
Sb′c′ =
Sa′b′ = Sd′b′ =
d'
b'
b
𝑠𝑒𝑔𝑚𝑒𝑛𝑡𝑠 𝑠𝑒𝑔𝑚𝑒𝑛𝑡
16
2
c
net II
c'
σb′ + σc′
Lb′c′
2
σa′ + σb′
La′b′
2
|𝑆𝑎′ 𝑏′ | + |𝑆𝑑′ 𝑏′ | = |𝑆𝑏′ 𝑐 ′ |
Atom Accumulation = Atom Depletion
𝒔𝒆𝒈𝒎𝒆𝒏𝒕𝒔 𝒌
𝝈𝒂𝒌 + 𝝈𝒄𝒌
(
) × 𝑳𝒌 = 𝟎
𝟐
New Compact Model: HOWTO
CAD Model: new Mortality Criterion
𝑵𝒆𝒘 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏 𝒎𝒖𝒍𝒕𝒊 − 𝒔𝒆𝒈𝒎𝒆𝒏𝒕 :
(𝝈𝒂 𝒌 + 𝝈𝒄 𝒌 ) × 𝑳𝒌 = 𝟎
𝒔𝒆𝒈𝒎𝒆𝒏𝒕𝒔 𝒌
𝑩𝒍𝒆𝒄𝒉 𝑪𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏 (𝒔𝒊𝒏𝒈𝒍𝒆 − 𝒔𝒆𝒈𝒎𝒆𝒏𝒕):
𝝈
−
𝝈
𝒂
𝒄𝒌
𝒌
∗
−𝟏
𝒆𝒁 𝝆𝛀 =
(𝒋𝑳)𝒌
17
New Compact Model
19
Improved Blech Effect
Complex Net
c2
c2'
c3
c1
a2
b1
c3'
c1'
a2 '
b1 '
a1
a1
a3
a4
net I
c4
a4 '
a3 '
c4'
net II
𝑍∗e < 0
New Compact Model
20
CAD Model: new Mortality Criterion
Current Flows in Different Directions Also Impact Each Other
net I
Critical Stress
net II
Simulation Parameters T=459K, J=40MA/cm2 , Critical Stress =120MPa
New Compact Model
CAD Model: new Mortality Criterion
21
Segments with No Current Also Impact Active Segments
no current
Critical Stress
net I
net II
worse
no current
net III
better
New Compact Model (passive elements)
22
CAD Model: new Mortality Criterion
Proposed Compact Model Holds True For Passive Elements
active segment (
sink (
𝜎𝑎 =
𝐿 + 2𝐿𝑟
𝑗𝐿
2(Ls + L + Lr )
reservoir (
𝜎𝑐 = −
The critical current density for interconnect void nucleation in
a wire connected to a passive reservoir and a sink is
𝑗𝑒𝑥𝑡𝑒𝑛𝑠𝑖𝑜𝑛−𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 =
L s + L + Lr
𝑗
𝐿 + 2𝐿𝑠 𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙
𝐿 + 2𝐿𝑠
𝑗𝐿
2(Ls + L + Lr )
Material Effects on Lifetime
23
CAD Model: new Mortality Criterion
via with no current
net II
net I
low diffusivity
region
B1~140Gpa
𝒔𝒆𝒈𝒎𝒆𝒏𝒕𝒔 𝒌
𝝈𝒌−𝒂𝒏𝒐𝒅𝒆 + 𝝈𝒌−𝒄𝒂𝒕𝒉𝒐𝒅𝒆
𝑽𝒌 = 𝟎
𝟐𝑩𝒌
B1~140Gpa
Bm
Steady state
analysis does
not capture
temporal
effects of
microstructure
and material
properties
Applications Explored
24
New Mortality Criterion

EM-resilient Design Guideline:

Partial widening

Decreasing width –if helps!

Round L shape connection(avoid current crowding)

Passive Extention

EM-tolerant configuration

Routing through alternative paths and layers!

Multiple vias, Dummy Vias
c2
c2'
c3
c1
via with no current
net II
net I
a2
b1
c3'
c1'
a2 '
b1 '
a1
a1
a3
a4
net I
c4
a4 '
a3 '
net II
c4'
Conclusions

DONEs:


New compact model that captures

Physical and Electrical Impact

Explains wire segments interactions
TODOs:

EM-Resilient Design Guidelines

Can be readily developed based on the proposed model
25