An Introduction to Electromigration-Aware Physical Design Jens Lienig Dresden University of Technology Dresden, Germany
Contents 1 Introduction 2 Electromigration Issues 3 Electromigration-Dependent Design Parameters 4 Physical Design Methodologies Addressing Electromigration • Current-Driven Routing • Current-Density Verification • Current-Driven Decompaction 5 Summary J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 2
Contents 1 Introduction 2 Electromigration Issues 3 Electromigration-Dependent Design Parameters 4 Physical Design Methodologies Addressing Electromigration • Current-Driven Routing • Current-Density Verification • Current-Driven Decompaction 5 Summary J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 3
Introduction: Electromigration Electromigration (EM): Electromigration is the forced movement of metal ions due to an electric field F total = F direct + F wind Direct action of Force on metal ions resulting from << electric field on momentum transfer from the metal ions conduction electrons Anode Cathode Al + Al - - + - E - - Note: For simplicity, the term “electron wind force” often refers to the net effect of these two electrical forces J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 4
Introduction: Electromigration => Metal atoms (ions) travel toward the positive end of the conductor while vacancies move toward the negative end Effects of electromigration in metal interconnects: • Depletion of atoms (Voids): Voids → Slow reduction of connectivity → Interconnect failure • Deposition of atoms (Hillocks, Whisker): → Short cuts Hillocks J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 5
http://ap.polyu.edu.hk/apavclo/public/gallery.htm J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 6
http://www.usenix.org/events/sec01/full_papers/gutmann/gutmann_html J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 7
http://www.usenix.org/events/sec01/full_papers/gutmann/gutmann_html J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 8
Common Failure Mechanisms in Integrated Circuits A) Line Depletion Ta/TaN Liner Layer Metal2 Cu e SiN, NSiC Cap Layer Metal1 Cu Void Low κ Dielectric B) Via Depletion Ta/TaN Liner Layer Metal2 Cu SiN, NSiC Cap Layer Metal1 Cu e Void Low κ Dielectric J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 9
e www.lamel.bo.cnr.it/research/ elettronica/em/rel_res.htm e e J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 10
Electromigration and Current Density Black‘s Equation [1]: Mean time to failure of a single wire due to electromigration Cross-section-area- Activation energy dependent constant for electromigration A E = ⋅ a MTTF n exp ⋅ k T J Temperature Current density Scaling factor Boltzmann constant (usually set to 2) -> Current density is the major parameter in addressing electromigration during physical design J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 11
Why is Electromigration Becoming a Problem? I J = A J J ref 1 I I ref A A ref 1996 (ref) 2006 J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 12
Why is Electromigration Becoming a Problem? (cont‘d.) Industry Example (Robert Bosch GmbH): Maximum tolerable current in minimum line width interconnect (Metal1, Al) due to technology scaling Reduction 1996 - 2006: 95 % 1 Imax(Time) / Imax (1996) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1996 2000 2001 2002 2003 2004 2005 2006 J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 13
Why is Electromigration Becoming a Problem? (cont‘d.) Industry Example (Robert Bosch GmbH): # Nets Critical nets: Nets with currents near or above maximum tolerable current value # Nets(ref) 100 -> “Manual consideration” of electromigration problem no longer feasible 10 Uncritical nets 1 Critical nets 1996 (ref) 2006 J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 14
Maximum Tolerable Current Densities • Conventional metal wires (house wiring, etc.) ≈ 19,100 A/cm 2 Al ≈ 30,400 A/cm 2 Cu … reaching melting temperature due to Joule heating Melting temperature limits maximum current densities • Thin film interconnect on integrated circuits can sustain current densities up to 10 10 A/cm 2 before reaching melting temperature, however, at ≈ Al 200,000 A/cm 2 (J max (Cu) ≈ 5* J max (Al) ) ≈ 1,000,000 A/cm 2 Cu … it reaches its maximum value due to the occurance of electromigration Electromigration limits maximum current densities J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 15
Contents 1 Introduction 2 Electromigration Issues 3 Electromigration-Dependent Design Parameters 4 Physical Design Methodologies Addressing Electromigration • Current-Driven Routing • Current-Density Verification • Current-Driven Decompaction 5 Summary J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 16
History of Electromigration Research • 1861 Discovery of electromigration by M. Gerardin • 1950s First systematic studies of electromigration by W. Seith and H. Wever (Correlation between the direction of the current flow and the material transport) • 1960s Electromigration is recognized as one of the main reasons for IC failure • 1967 J. R. Black: Relationship between MTTF (mean time to failure) and current density and temperature (Blacks law [1]) • 1975 I. A. Blech: Discovery of „immortal wires“ by considering the product of current density and wire length (Blech length [2]) J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 17
Migration in Solid State Materials Migration in Solid State Materials Stress Migration Electromigration Thermomigration due to due to due to mechanical stress electric field thermal gradient Electrolytic electromigration Solid state electromigration J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 18
Diffusion Processes and Activation Energies E A Grain : homogeneous Grain boundary : Triple Point lattice of metal atoms shift in the orientation of the lattice J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 19
Diffusion Processes and Activation Energies E A - Al Al Grain Boundary Diffusion Triple Point E A_GRAIN = 0.7 eV (Al) E A_GRAIN = 1.2 eV (Cu) Grain Bulk Diffusion Al Al Al Al Al E A_BULK = 1.2 eV (Al) Al Al Al Al Al E A_BULK = 2.3 eV (Cu) Al Surface Diffusion E A_SURF . = 0.8 eV (Al) Aluminum: Copper: E A_SURF . = 0.8 eV (Cu) Grain Boundary Diffusion Surface Diffusion + Surface Diffusion J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 20
Special Effects (1): Bamboo Wires I = constant Diffusion MTTF [h] T = constant – + w Grain Boundary w < ∅ Grains w = ∅ Grains (Bamboo Wires) Wire Width w [ µ m] w MTTF_min J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 21
Special Effects (2): Immortal Wires F N2 F N4 F N1 F N3 F N5 Electromigration (EM) Stress Migration (SM) – + Al+Al+ Al+ Al+ Al+ Al+ F N2 F N4 F N1 F N3 F N5 – Al+ Al+ Al+ Al+ + Al+ Al+ Al+ F N2 F N4 F N1 F N3 F N5 Equilibrium between EM and SM if l segment < “Blech length” – + Al+ Al+ Al+ Al+ Al+ Al+ J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 22
Maximum Current Density With Regard to Temperature Black‘s Equation [1]: Mean time to failure of a single wire due to electromigration Cross-section-area- Activation energy dependent constant A E = ⋅ a MTTF n exp ⋅ k T J Temperature Current density Scaling factor Boltzmann constant (usually set to 2) J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 23
Maximum Current Density With Regard to Temperature Jmax(T) compared to Jmax(Tref = 25 C) [Black1969] 100 Jmax(T) / Jmax(T = 25 C) 10 1 -40 0 25 60 80 100 125 150 175 0,1 Consumer Electronics 0,01 Automotive Electronics Temperature T [Celsius] MTTF(T) = MTTF(T Ref ) Example: A temperature rise of 100 K in an Al metallization reduces the permissible current density by about 90 %. J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 24
Contents 1 Introduction 2 Electromigration Issues 3 Electromigration-Dependent Design Parameters 4 Physical Design Methodologies Addressing Electromigration • Current-Driven Routing • Current-Density Verification • Current-Driven Decompaction 5 Summary J. Lienig: An Introduction to Electromigration-Aware Physical Design, ISPD 2006, pp. 39-46 25
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