Metallicity of CNT/ GNR Metallicity of CNT/ GNR Periodic boundary condition quantizes the allowed k values π ⋅ = ⋅ 2 i C k If slices hit the apex of cone � zero gap Otherwise � Band gap Graphene bandstructure π ⋅ = ⋅ i w k Similarly, GNR also has boundary condition Armchair Zigzag Chiral CNT metallic n or m = 3 i n - m =3 i GNR N =3 i -1 metallic - Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Metallic Condition Metallic Condition Reciprocal space C r : reciprocal vector of T T r : reciprocal vector of T K : Dirac point of Brillouin zone C: the chiral vector C r : Quantized due to circumferential (circumference) boundary condition uuur + 2 n m T: the translational = XK C vector r 3 Hence, the condition for metallicity is (2n+m)= 3 i , or equivalently ( n-m )=3 i Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Band Structure of CNTs with Band Structure of CNTs with Different Chirality Different Chirality (n, m)= (9, 0) (n, m)= (13, 0) (n, m)= (7, 7) D= 0.7 nm D= 1 nm D= 0.95 nm 10 10 5 5 Energy (eV) Energy (eV) 0 0 -5 -5 -10 -10 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 K K Zero gap, metallic Zero gap, metallic Semiconducting Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Bandgap of CNT vs Diameter Bandgap of CNT vs Diameter � Bandgap Bandgap scales with scales with � diameter of the diameter of the nanotube due to nanotube due to confinement confinement ~ 0.8eV/D 0.8eV/D ~ � Additional small gaps Additional small gaps � due to curvature of due to curvature of the CNTs CNTs the � Large diameter (>5 Large diameter (>5 � nm ) MWCNTs will ) MWCNTs will nm have a vanishing gap have a vanishing gap @ 300K @ 300K Kane et al., PRL , 1997 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Band Structure and Density of States Band Structure and Density of States (DOS) for Small Diameter (SWCNT) (DOS) for Small Diameter (SWCNT) � DOS of SWCNT is very small DOS of SWCNT is very small F. Kreupl, et al., AMC , 2005 � � Doping has almost no influence on its DOS Doping has almost no influence on its DOS � Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Band Structure and DOS for Large Band Structure and DOS for Large Diameter (MWCNT) Diameter (MWCNT) F. Kreupl, et al., AMC , 2005 � DOS of MWCNT is larger DOS of MWCNT is larger � � Doping can shift Fermi energy and DOS easily Doping can shift Fermi energy and DOS easily � Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Conducting Channel of CNTs Conducting Channel of CNTs 10 � For SWCNT = 4 For SWCNT = 4 � – L – Lattice degeneracy (x2) attice degeneracy (x2) 5 – S Spin degeneracy (x2) pin degeneracy (x2) – 0 � F For MWCNT (depends on diameter) or MWCNT (depends on diameter) � -5 ∑ = N f shell i -10 subbands -1 -0.5 0 0.5 1 1 K ∑ = − + exp( E E k T ) 1 (n, m)= (7, 7) subbands i F B SWCNT, D= 0.95 nm Can be approximated by: ≈ + > N D aD b D nm ( ) , 3 shell A. Naeemi, et al., IEEE EDL , 2006 a=0.0612 nm -1 , b=0.425 Almost Linear with the diameters. Almost Linear with the diameters. ∑ ∑ = = ⋅ + N N a D b tot i i shells shells Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Electron Mean Free Path ( λ ) of CNTs Electron Mean Free Path ( λ ) of CNTs Dependence of diameter Dependence of diameter � � – Metallic shells Metallic shells – πψ 2 3 λ = ⋅ D σ + σ 2 2 J. Jiang, et al., Phys. Rev. B , 2001 2 9 ε ψ – Semiconducting shells Semiconducting shells – v λ = ⋅ F D X. Zhou, et al., Phys. Rev. Lett. , 2005 α T Hence, λ is proportional to the diameter. λ~1 ~1μ μ m Based on measurements, λ Based on measurements, m for D=1nm CNT for D=1nm CNT � � J. Y. Park et al., NanoLetter, 2004. We can set λ ≈ 1000 D Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Band Structure of GNRs Band Structure of GNRs C. Xu et al., TED , 2009 E (eV) E (eV) N = 44 0.12 eV N = 45 w = 11 nm w = 11 nm 3 ka 3 ka Metallic ac-GNR Semiconducting ac-GNR N = 3 m − 1 � Metallic N = 26 N = 3 m , 3 m + 1 � Semiconducting E 2 E (eV) E 1 E 0 − E 1 − E 2 Always Metallic w = 11 nm Small variation of N � Negligible change in band structure ka zz-GNR Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Thermal Transport Thermal Transport κ = π κ 2 2 B T /3 h Quantized thermal conductance Quantized thermal conductance � � 0 At room temperature At room temperature � � κ κ ~ 4 – Electron contribution Electron contribution – el 0 (4 conduction modes, bandgap bandgap ~ ~ eV eV) ) (4 conduction modes, – Phonon: A large number of modes ( Phonon: A large number of modes (bandgap bandgap ~ ~ meV meV ) ) – ka/ π F. Kreupl, et al., AMC , 2005 H. Li et al., TED , 2009 T. Yamamoto, PRL , 2004 Phonon dominates thermal transport! Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Basic Properties of Cu, CNT and GNR Basic Properties of Cu, CNT and GNR Graphene or Cu SWCNT MWCNT GNR >1x10 9 >1x10 9 >1x10 9 >1x10 9 >1x10 8 >1x10 8 Max current density 10 7 Wei, et al., Novoselov, et al., , et al., Radosavljevic, et al., , et al., Wei, et al., Novoselov Radosavljevic (A/cm 2 ) Appl. Phys. Let., 2001 Appl. Phys. Let., 2001 Science, 2001 Science, 2001 Phys. Rev. B , 2001 , 2001 Phys. Rev. B 1356 3800 (graphite) Melting point (K) Tensile strength 22.2 ± 2.2 0.22 11-63 (GPa) 1.75- -5.8 5.8 1.75 3.0 3.0 ~3.0- ~3.0 -5.0 5.0 Thermal conductivity 0.385 Kim, et al., Balandin, et al., , et al., Hone, et al., Kim, et al., Balandin Hone, et al., ( × 10 3 W/m-K) Phys. Rev. Let. , 2001 Phys. Rev. Let. , 2001 Nano Let. , 2008 Nano Let. , 2008 Phys. Rev. B , 1999 Phys. Rev. B , 1999 Temp. Coefficient of <1.1 -1.37 -1.47 4 Resistance (10 -3 Kane, et al., Kane, et al., Kwano et al., Kwano et al., Shao et al., Shao et al., Europhys. . Lett Lett., ., 1998 1998 Nano Lett Lett. . , 2007 , 2007 Appl. Phys. . Phys. Lett Lett. . , 2008 , 2008 Europhys Nano Appl /K) >1,000 25,000 ~1,000 >1,000 25,000 ~1,000 Mean free path (nm) 40 McEuen, et al., McEuen , et al., Li, et al., Li, et al., Bolotin Bolotin, et al., , et al., @ room temp. Trans. Nano Trans. Nano ., 2002 ., 2002 Phys. Rev. Let. , 2005 Phys. Rev. Let. , 2005 Phys. Rev. Let. , 2008 Phys. Rev. Let. , 2008 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Outline Outline Part I : Part I : � Limitations of Copper Interconnects Limitations of Copper Interconnects � � Carbon Carbon Nanomaterials Nanomaterials: Basics : Basics � � Circuit Elements of CNT/ GNR Circuit Elements of CNT/ GNR � � Fabrication and Integration of CNT/GNR Fabrication and Integration of CNT/GNR � Interconnect Interconnect Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT/ GNR Resistances: R Q , R C and CNT/ GNR Resistances: R Q , R C and R S R S R Q R Q : : Intrinsic quantum contact resistance Intrinsic quantum contact resistance - - even for very even for very � � h = short lengths with no scattering and perfect contacts short lengths with no scattering and perfect contacts 2 N e 2 (lowest possible R ( lowest possible R— —hence need CNT hence need CNT- -bundles or multi bundles or multi- - layer GNRs GNRs) ) layer N = number of conducting channels R C : Imperfect parasitic contact resistance ( Imperfect parasitic contact resistance (can be can be R C : � � Ω ) high… high …up to 100 K up to 100 K Ω ) h L R S : length dependent scattering resistance = R S : length dependent scattering resistance � � N e λ 2 2 (for Length >> MFP = ( for Length >> MFP = λ λ ) ) Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT/ GNR Conductance Model CNT/ GNR Conductance Model Linear response Landauer formula ∂ 2 ⎛ ⎞ 2 q f ∫ = τ − G ( ) E 0 dE ⎜ ⎟ n n ∂ h ⎝ E ⎠ G n : Conductance of the n th conduction channel f 0 ( E ) : Fermi-Dirac distribution function τ n ( E ) : Transmission coefficient If all channels are identical, it can be simplified as: 2 2 q M : Total number of conducting channel = ⋅ ⋅ τ G M n h τ : Effective transmission coefficient ( ) − ∑ 1 ⎡ ⎤ = + − M 1 exp E E k T Can be calculated from bandstructure ⎣ ⎦ n F B n τ = 1, if it is ballistic, otherwise… H. Li et al., TED , vol. 56, no. 9. 2009 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT/ GNR Conductance Model CNT/ GNR Conductance Model ( contd. ) ( contd. ) − 1 ⎡ ⎤ L τ = + ( ) E 1 ⎢ ⎥ n λ ⎣ ⎦ CNT λ CNT : Mean free path (MFP) of CNT − 1 ⎡ ⎤ ⎛ ⎞ 1 1 τ = + + ( E ) 1 L ⎢ ⎥ ⎜ ⎟ n λ θ θ cos w cot ⎝ ⎠ ⎣ ⎦ D λ D : Mean free path corresponding to non-edge scattering mechanisms C. Xu et al., TED , 2009 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Comparison of Resistivity Comparison of Resistivity 100 -cm] 10 Resistivity [ Cu: W=14nm, =8.19 Cu: W=22nm, =6.01 Cu: W=32nm, =4.83 A 1 ρ = + ( R R ) Q S L 1 10 100 1000 Length [ m] H. Li et al., TED, 2008 � Area of MWCNT is much larger than that of SWCNT • short length: MWCNTs have larger resistivity than SWCNTs � However, MWCNTs have longer MFP than SWCNTs • long length: R s is much smaller for MWCNTs, so that resistivity of MWCNT becomes comparable to SWCNT Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Resistance Comparison Resistance Comparison H. Li et al., TED , vol. 56, no. 9. 2009 Dielectric w m] Dielectric m] w Graphene Intercalation Resistance per micron [ Resistance per micron [ Layers Layers Mono-layer GNRs Multi-layer GNRs Mono-layer GNRs Intercalation doped multi-layer GNRs Dielectric 0.815 nm w 0.335 nm Ideal case SWCNT and DWCNT have similar resistance Ideal case SWCNT and DWCNT have similar resistance Multi-layer GNRs � � Stage 1 Stage 2 Stage 3 For GNR, intercalation doping and high specularity For GNR, intercalation doping and high specularity are needed are needed Graphene Layers Neutral multi-layer GNRs � � Intercalation Layers (AsF 5 ) C. Xu et al., TED , vol. 56, no. 8, 2009 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT/ GNR Capacitance: C Q and C E CNT/ GNR Capacitance: C Q and C E Adding electron raises up the E F { } ∫ δ = − − − + δ Q e dE D E ( ) f E ( E ) f E [ ( E e V )] F F 2 ( ) = δ e D E V δ 2 Q 2 e ≈ μ = = 97 aF / m C Q δ V hv F δ 2 1 1 1 Q δ 2 δ 2 Q Q = + = = + Δ = Δ + Δ E E E ES F 2 C 2 C 2 C C C C E Q E Q Electrostatic Capacitance, C E 2 πε = C CNT For single CNT: μ ~ aF / m E ⎛ ⎞ 4 y ⎜ ⎟ ln ⎝ d ⎠ For other structures, it will depend on the geometry and may need numerical calculation. Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT Bundle Structure for CNT Bundle Structure for Estimating C E Estimating C E GND2 CNT h=t Bundle gnd gnd t left right aF/um s=w s=w w w h=t GND1 Inner CNTs are effectively screened from the surrounding interconnect geometry N. Srivastava et al., TNT , 2009 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT Bundle Electrostatic CNT Bundle Electrostatic Capacitance Capacitance 28 nm 14 nm 36 nm 18 nm 44 nm 22 nm N. Srivastava et al., TNT , 2009 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT/ GNR I nductance: L K and L M CNT/ GNR I nductance: L K and L M Current I E E Small density of states cause large total kinetic energy: e δ V 1 h = × × 2 Δ I E 2 2 2 e v F ≈ μ L 16 nH / m K k k Scaling by conducting channel number N Magnetic inductance, L M SWCNT has 4 channels, hence: d For single CNT: ≈ μ L 4 nH / m KSWCNT y μ ⎛ ⎞ 4 y μ L K is 3 orders larger than L M ! ~ pH / m = L CNT ln ⎜ ⎟ M 2 π ⎝ d ⎠ Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Existence of L k Existence of L k High- High -Frequency (20GHz) Frequency (20GHz) � � S- -parameter parameter S measurements for both measurements for both individual SWCNT and individual SWCNT and μ m SWCNT bundle (L=2 μ SWCNT bundle (L=2 m ) ) Shows L K Shows L K of SWCNT is of of SWCNT is of � � order of nH nH/ / μ which order of m, which μ m, agrees with theoretical agrees with theoretical analysis analysis The inductance of CNT The inductance of CNT � � bundle scales with the bundle scales with the number of CNTs CNTs number of Plombon et al., Appl. Phys. Let., 2007 In order to analyze inductive effects in CNT interconnects, we need accurate inductance (including kinetic and magnetic) model for CNT bundles… Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Outline Outline Part I : Part I : � Limitations of Copper Interconnects Limitations of Copper Interconnects � � Carbon Nanotubes: Basics Carbon Nanotubes: Basics � � Circuit Elements of CNT/GNR Circuit Elements of CNT/GNR � � Fabrication and I ntegration of CNT/ GNR Fabrication and I ntegration of CNT/ GNR � I nterconnects I nterconnects Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT I nterconnect Fabrication CNT I nterconnect Fabrication [Kreupl et. al., (Infineon) IEDM , 2004] [Sato et. al., (Fujitsu) IITC , 2006] [Awano et al., (Fujitsu) 2006] [Choi et. al., (Samsung) Nano Conf. , 2006] [Nihei et. al., (Fujitsu) IITC , 2007] Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT I nterconnect (via) Fabrication CNT I nterconnect (via) Fabrication Catalytic CVD Growth nature does it for you….all you need is 3 ingredients 1. Catalyst nanocluster: Fe, Ni or Co + a reducing gas 2. Carbon containing compound (gas): CH4, C2H2, CH3CH2OH…. 3. Energy (Temperature): 400-1400 0 C Substrate –catalyst interaction is also very important…. Courtesy: F. Kreupl, Infineon Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Fabrication Techniques & Challenges-I Fabrication Techniques & Challenges-I Long throat catalytic deposition (via PVD) in high � aspect ratio trenches Duesberg et al., Nanoletters, 2003 nanotube Via definition Nanotube Long throat lift-off Via etch by resist growth catalyst deposition Challenges: i) sidewall deposition causes sidewall CNT growth---via filled but no electrical contact to the bottom! ii) catalyst thickness and nucleation depends strongly on surface condition after etch, results are irreproducible…. Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Fabrication Techniques & Challenges-I I Fabrication Techniques & Challenges-I I [Graham et. al., Diamond and Related Materials , 2004, � Buried catalyst layer Buried catalyst layer � Liebau et al., AIP P ., Kirchberg, 2004] � Etching of via stops on top of 1 Etching of via stops on top of 1- -3 nm thick catalyst layer 3 nm thick catalyst layer � Nanotube Via etch stop Resist strip Via definition growth on catalyst by resist Challenges: i) etch stop on thin catalyst layer is critical ii) Wafer/chip scale homogeneity not yet demonstrated Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Diameter-Controlled Nanoparticles Diameter-Controlled Nanoparticles Size distribution, Diameter: ~ 4 nm, δ : ~ 25% CMP: to cut-off the cap and make contact with inner shells… S. Sato et al., IITC , 2006 M. Nihei et. al., IITC , 2007 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Alternative Process: Bottom up Alternative Process: Bottom up � Overcomes the need for etching high aspect ratio Overcomes the need for etching high aspect ratio vias vias needed needed � in future technologies in future technologies � Can reliably grow MWCNT bundles Can reliably grow MWCNT bundles Li et. al., APL , 2003 � PECVD Metal Catalyst Deposition Patterning Top Metal Layer TEOS CVD CMP Deposition Challenges: i) quality of CNTs is low and so is electrical conductivity ii) tilt for small diameter tubes is also considerable---subsequent litho step is difficult Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Process I mprovements Process I mprovements � Densification Densification � Z. Liu et. al., IITC , 2007] Increases the density of CNT bundle by 5~25 times. (a) Before and (b) after densification. � Increase fraction of metallic Increase fraction of metallic NTs NTs � Applying an electrical field makes metallic CNT and semiconducting CNTs to have different movements. Hence, increase the fraction of metallic… Krupke et. al., Science, 2003; Peng, J. Appl. Phys. 2006 However, this method is difficult to combine with CNT interconnect fabrication… and even when they increase the fraction of metallic, the density of CNT is quite low… Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Low Temperature CNT Growth Low Temperature CNT Growth 400 o C 365 o C 450 o C Growth temperature down to 365 0 C - the lowest reported for interconnect application. However, the lower the growth temperature, the worse it gets for CNT quality… A. Kawabata et. al., IITC , 2008 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT Wafer CNT Wafer Y. Hayamizuet. al., Nature Nanotech. , 2008 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
I ntegration with Low-K Dielectric I ntegration with Low-K Dielectric CNT Single Kelvin via CNT Single Kelvin via 0 C grown at 400 0 C grown at 400 A. Kawabata et. al., IITC , 2008 CNT via is robust under current high- -density density CNT via is robust under current high stress over long time… ….. .. stress over long time Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT I nterconnect I ntegration I ssues CNT I nterconnect I ntegration I ssues H. Li et al., TED , vol. 56, no. 9. 2009 Process Advantages vis- -à à- -vis Copper vis Copper Process Advantages vis � � – Diffusivity into Si/dielectric is not a problem Diffusivity into Si/dielectric is not a problem--- ---no need for barrier no need for barrier – – Bottom Bottom- -up growth processes can eliminate the need for etching high up growth processes can eliminate the need for etching high – aspect ratio vias vias aspect ratio – No No “ “dishing dishing” ” type effect type effect… …. . – Key Issues: Key Issues: � � – Difficult to grow dense high – Difficult to grow dense high- -metallic fraction metallic fraction SWCNT SWCNT bundles bundles – Most interconnect processes so far employ – Most interconnect processes so far employ MWCNTs MWCNTs which have which have been easier to grow-- --recently it has become possible to recently it has become possible to grow grow been easier to grow bundles of SWCNTs also by adding water or oxygen to increase also by adding water or oxygen to increase bundles of SWCNTs activity (to 84%) of the growth catalyst [Futaba et al., activity (to 84%) of the growth catalyst [Futaba et al., J. Phys. Chem. B J. Phys. Chem. B , 2006] , 2006] – High temperatures – High temperatures involved in CNT growth involved in CNT growth— —recently grown at 365 recently grown at 365 C (Fujitsu), but need better quality. 0 C (Fujitsu), but need better quality. – Metal Metal- -CNT CNT contact resistance contact resistance – – Control over growth mode – Control over growth mode (substrate (substrate- -catalyst interaction) catalyst interaction) Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Graphene Fabrication Methods and Graphene Fabrication Methods and I mplication for I nterconnect Application I mplication for I nterconnect Application 1. Chemical vapor deposition G. Aichmayr, IEEE Symp. VLSI Tech. 2007 -- Not single crystal; low electrical conductivity 2. Thermal decomposition of single crystal SiC C. Berger, Science , 2006 -- Requires high processing temperature 3. Mechanical exfoliated from graphite, and deposited onto an insulating substrate J. C. Meyer, Nature , 2007 -- Uncontrollable for massive fabrication 4. Segregation, transferring and removing substrate Q. Yu, APL , 2008 -- Seems OK, will be explained in the next slide Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
GNR I nterconnect Fabrication… GNR I nterconnect Fabrication… Graphene Segregate Nickel Substrate Nickel Substrate Desired substrate Silicone film Transfer to desired Graphene Silicone film substrate Graphene Nickel Substrate Nickel Substrate Nickel Substrate Graphene Graphene Remove Nickel Silicone film Silicone film Desired substrate Desired substrate Pattern & Pattern Graphene GNR make via Silicone film GNR wire Silicone film contacts Desired Substrate Desired Substrate Implication from Q. Yu, APL , 2008 C. Xu et al., TED , 2009 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Hybrid Graphene/ CNT Hybrid Graphene/ CNT I nterconnects I nterconnects Vertical via is based on CNTs Vertical via is based on CNTs and horizontal wire is based and horizontal wire is based CNTs CNTs � � http://www.fujitsu.com/global/news/pr/archives/month/2008/20080303-01.html Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Part I : References (1) Part I : References (1) Limitations of Cu Limitations of Cu Journal of Applied Physics, Vol. 97, No. 2, 023706 Journal of Applied Physics, Vol. 97, No. 2, 023706- -1 1 – – 023706 023706- -7, 2005 7, 2005 � � W. W. Steinhogl Steinhogl, G. Schindler, G. , G. Schindler, G. Steinlesberger Steinlesberger, M. , M. Traving Traving and M. and M. Engelhardt Engelhardt, , “ “Comprehensive Study of the Resistivity Comprehensive Study of the Resistivity of Copper Wires With Lateral Dimensions of 100 nm and Smaller” of Copper Wires With Lateral Dimensions of 100 nm and Smaller ”. . IEEE Trans. Electron Device, vol. 52, no. 12, pp. 2710- -2719, 2719, IEEE Trans. Electron Device, vol. 52, no. 12, pp. 2710 � � S. S. Im Im, N. , N. Srivastava Srivastava, K. , K. Banerjee Banerjee and K. E. Goodson, and K. E. Goodson, “ “Scaling Analysis of Multilevel Interconnect Temperatures for Scaling Analysis of Multilevel Interconnect Temperatures for High Performance ICs.” ” High Performance ICs. Proceedings Intl. VLSI Multilevel Interconnect Conference, 2004, pp. 393 pp. 393- -398. 398. Proceedings Intl. VLSI Multilevel Interconnect Conference, 2004, � � N. Srivastava Srivastava and K. and K. Banerjee Banerjee, , “ “A Comparative Scaling Analysis of Metallic and Carbon Nanotube I A Comparative Scaling Analysis of Metallic and Carbon Nanotube Interconnections for nterconnections for N. Nanometer Scale VLSI Technologies” ”. . Nanometer Scale VLSI Technologies TMS Journal of Materials, vol. 56, no. 10, pp. 30 TMS Journal of Materials, vol. 56, no. 10, pp. 30- -31, 2004. 31, 2004. � � N. Srivastava Srivastava and K. and K. Banerjee Banerjee, , “ “Interconnect challenges for Interconnect challenges for nanoscale nanoscale electronic circuits, electronic circuits,” ” N. CNT/ GNR Basics CNT/ GNR Basics IEEE Trans. Electron Devices, vol. 56, no. 9, September, 2009 IEEE Trans. Electron Devices, vol. 56, no. 9, September, 2009 � � H. Li, C. H. Li, C. Xu Xu, N. , N. Srivastav Srivastav, K. , K. Banerjee Banerjee, , “ “Carbon Carbon Nanomaterials Nanomaterials for Next Generation Interconnects and Passives: for Next Generation Interconnects and Passives: Physics, Status and Prospects” ”. . Physics, Status and Prospects IEEE Trans. Electron Devices, vol. 56, no. 8, pp. 1567 IEEE Trans. Electron Devices, vol. 56, no. 8, pp. 1567- -1578 Aug 2009. 1578 Aug 2009. � � C. C. Xu Xu, H. Li, and K. , H. Li, and K. Banerjee Banerjee, , “ “Modeling, Analysis and Design of Graphene Modeling, Analysis and Design of Graphene Nano Nano- -Ribbon Interconnects Ribbon Interconnects” ” IEEE Trans. Nanotechnology, vol. 8, no. 4, pp. 542- -559, July, 2009. 559, July, 2009. IEEE Trans. Nanotechnology, vol. 8, no. 4, pp. 542 � � N. N. Srivastav Srivastav, H. Li, F. , H. Li, F. Kreupl Kreupl, and K. , and K. Banerjee Banerjee, , “ “On the Applicability of Single On the Applicability of Single- -Walled Carbon Nanotubes as VLSI Walled Carbon Nanotubes as VLSI Interconnects” ” Interconnects Imperial College Press, 1998. London, U. K. Imperial College Press, 1998. London, U. K. � � R. Saito, G. Dresselhaus Dresselhaus, and M. S , and M. S Dresselhuas Dresselhuas, Physical Properties of Carbon Nanotubes. , Physical Properties of Carbon Nanotubes. R. Saito, G. Proceedings of the IEEE, Vol. 91, pp. 1772 Proceedings of the IEEE, Vol. 91, pp. 1772- -1784, 2003. 1784, 2003. � � P. Avouris Avouris, et al., , et al., “ “Carbon Nanotube Electronics. Carbon Nanotube Electronics.” ” P. IEEE Trans. Nanotechnology, vol. 1, no. 1, pp. 78 IEEE Trans. Nanotechnology, vol. 1, no. 1, pp. 78- -85, 2002. 85, 2002. � � P. L. McEuen McEuen, M. S. Fuhrer, and H. K. Park, , M. S. Fuhrer, and H. K. Park, “ “Single Single- -walled carbon nanotube electronics walled carbon nanotube electronics” ”. . P. L. Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
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Part I : References (3) Part I : References (3) Proc. of Intl. Interconnect Conf. 2008, pp. 237- -240 240 Proc. of Intl. Interconnect Conf. 2008, pp. 237 � � A. Kawabata, S. Sato, T. Nozue A. Kawabata, S. Sato, T. Nozue, T. , T. Hyakushima Hyakushima, M. , M. Norimatsu Norimatsu, M. , M. Mishima Mishima, T. Murakami, D. Kondo, K. Asano, , T. Murakami, D. Kondo, K. Asano, M. Ohfuti Ohfuti, H. , H. Kawarada Kawarada, T. Sakai, M. Nihei, and Y. , T. Sakai, M. Nihei, and Y. Awano Awano, , “ “Robustness of CNT via interconnect fabricated by Robustness of CNT via interconnect fabricated by M. low temperature process over a high low temperature process over a high- -density current density current” ”. . Appl. Phys. Appl . Phys. Lett Lett., vol. 93, no. 11, pp. 113103, Nov. 2008 ., vol. 93, no. 11, pp. 113103, Nov. 2008 � � Q. Yu, J. Q. Yu, J. Lian Lian, S. , S. Siriponglert Siriponglert, H. Li, Y. P. Chen, and S. , H. Li, Y. P. Chen, and S.- -S. Pei, S. Pei, “ “Graphene segregated on Ni surfaces and Graphene segregated on Ni surfaces and transferred to insulators transferred to insulators” ” Science Express Reports, 10.1126/science.1171245, May 2009 Science Express Reports, 10.1126/science.1171245, May 2009 � � X. Li, W. Cai X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. , J. An, S. Kim, J. Nah, D. Yang, R. Piner Piner, A. , A. Velamakanni Velamakanni, I. Jung, E. , I. Jung, E. Tutuc Tutuc, S. K. , S. K. Banerjee Banerjee, L. , L. Colombo, R. S. Ruoff Ruoff, , “ “Large Large- -Area Synthesis of High Area Synthesis of High- -Quality and Uniform Graphene Films on Copper Foils Quality and Uniform Graphene Films on Copper Foils” ” Colombo, R. S. Appl. Phys. . Phys. Lett Lett., vol. 89, pp. 143106, 2006 ., vol. 89, pp. 143106, 2006 Appl � � J. Hass, R. Feng Feng, T. Li, X. Li, Z. , T. Li, X. Li, Z. Zong Zong, W. A. de , W. A. de Heer Heer, P. N. First, E. H. , P. N. First, E. H. Conrada Conrada, C. A. Jeffrey, C. Berger, , C. A. Jeffrey, C. Berger, J. Hass, R. "Highly ordered graphene for two dimensional electronics," "Highly ordered graphene for two dimensional electronics," CNT Process Achievement and I mprovement CNT Process Achievement and I mprovement Science, vol. 301, no. 5631, pp. 344 Science, vol. 301, no. 5631, pp. 344- -347, 2003. 347, 2003. � � R. R. Krupke Krupke, F. , F. Hennrich Hennrich, H. v. , H. v. Lohneysen Lohneysen, M. M. , M. M. Kappes Kappes, , “ “Separation of metallic from semiconducting single Separation of metallic from semiconducting single- - walled carbon nanotubes,” ” walled carbon nanotubes, Physical Review Letters, vol. 95, 086601, 2005 Physical Review Letters, vol. 95, 086601, 2005 � � H. J. Li, W. G. Lu, J. J. Li, X. D. Bai Bai, and C. Z. , and C. Z. Gu Gu, , “ “Multichannel ballistic transport in multiwall carbon Multichannel ballistic transport in multiwall carbon H. J. Li, W. G. Lu, J. J. Li, X. D. nanotubes nanotubes” ”. . IEICE Trans. Electron., vol. E89- -C, pp. 1499 C, pp. 1499- -1503, Nov. 2006 1503, Nov. 2006 IEICE Trans. Electron., vol. E89 � � Y. Awano Y. Awano, , “ “Carbon nanotube technologies for LSI via interconnects Carbon nanotube technologies for LSI via interconnects” ” Proc. of Intl. Interconnect Conf. 2007, pp. 201- -203 203 Proc. of Intl. Interconnect Conf. 2007, pp. 201 � � Z. Liu. N. Bajwa Bajwa, L. , L. Ci Ci, S. H. Lee, S. , S. H. Lee, S. Kar Kar, P. M. , P. M. Ajayan Ajayan, and J. Q. Lu, , and J. Q. Lu, “ “Densification of Carbon Nanotube Densification of Carbon Nanotube Z. Liu. N. Bundles for Interconnect Application Bundles for Interconnect Application” ”. . Nature Nanotechnology, vol. 3, pp. 289- -295, May 2008 295, May 2008 Nature Nanotechnology, vol. 3, pp. 289 � � Y. Y. Hayamizu Hayamizu, T. Yamada, K. Mizuno, R. C. Davis, D. N. Futaba, M. , T. Yamada, K. Mizuno, R. C. Davis, D. N. Futaba, M. Yumura Yumura, and K. , and K. Hata Hata, , “ “Integrated three Integrated three- - dimensional microelectromechanical microelectromechanical devices from devices from processable processable carbon nanotube wafers, carbon nanotube wafers,” ” dimensional Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Part I I Part I I Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Outline Outline Part I : Part I : � Limitations of Copper Interconnects Limitations of Copper Interconnects � � Carbon Carbon Nanomaterials Nanomaterials: Basics : Basics � � Circuit Elements of CNT/GNR Circuit Elements of CNT/GNR � � Fabrication and Integration of CNT/GNR Interconnects Fabrication and Integration of CNT/GNR Interconnects � Part I I : Part I I : � Performance Evaluation of CNT/ GNR Performance Evaluation of CNT/ GNR � I nterconnects I nterconnects � Electro Electro- -thermal Analysis of CNT thermal Analysis of CNT Vias Vias � � High High- -Frequency Analysis of CNT Interconnects Frequency Analysis of CNT Interconnects � � Passives and Other Applications Passives and Other Applications � Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Equivalent Circuit Equivalent Circuit SWCNT and GNR H. Li et al., TED , vol. 56, no. 9, 2009 MWCNT (including DWCNT) H. Li et al., TED , 2008 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Delay Comparison: Local Delay Comparison: Local I nterconnects I nterconnects H. Li et al., TED , vol. 56, no. 9, 2009 Delay Ratio w.r.t Cu Delay Ratio w.r.t Cu W=14 nm H = 28 nm Ideal SWCNT and DWCNT are similar Ideal SWCNT and DWCNT are similar � � MWCNT has better performance due to smaller capacitance MWCNT has better performance due to smaller capacitance � � For GNR, intercalation doping and high specularity specularity are needed are needed For GNR, intercalation doping and high � � – Some Mono Some Mono- -layer could have low delay due to much smaller capacitance layer could have low delay due to much smaller capacitance – Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Delay Comparison: I ntermediate and Delay Comparison: I ntermediate and Global Global 1.4 1.2 1.0 Intermediate Global 0.8 0.6 0.4 100 1000 Length of Interconnect [ m] 14 nm technology node H. Li et al., TED , vol. 56, no. 9, 2009 Almost all CNTs CNTs could outperform Cu could outperform Cu Almost all � � For GNR, intercalation doping and high specularity specularity are needed are needed For GNR, intercalation doping and high � � Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Outline Outline Part I I : Part I I : � Performance Evaluation of CNT/GNR Interconnects Performance Evaluation of CNT/GNR Interconnects � � Electro Electro- -thermal Analysis of CNT thermal Analysis of CNT Vias Vias � � High High- -Frequency Analysis of CNT Interconnects Frequency Analysis of CNT Interconnects � � Passives and Other Applications Passives and Other Applications � Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Expectation vs. Reality of CNT Vias Expectation vs. Reality of CNT Vias Expectation Reality � Ideally, ballistic transport � High thermal conductivity � Interface effect • Isolated SWCNT >2000 W/mk (L=2.76 μ m) � Short length C. Yu et al., Nano Letter, 2005 • Isolated MWCNT >3000 W/mk � Bundle density (L=2.5 μ m, D=14 nm) P. Kim et al., PRL, 2001 � Reliability is a more important concern in CNT via � Need accurate electro-thermal analysis Provide guidelines to fabrication community Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Electrically Ballistic CNT Vias Electrically Ballistic CNT Vias H. Li et al., IEDM, 2007 � For SWCNT: λ >300 nm even in worst case ( D = 0.4 nm @ 110 o C). � For MWCNT: λ will be longer than SWCNT due to large Global diameter. Local � From ITRS, height of vias will always be smaller than λ . It’s safe to assume that CNT vias are electrically ballistic conductors Resistance of ballistic CNT Resistance of ballistic CNT � � R = Q < λ R length N : Number of conducting channels , N Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT Via: Resistance CNT Via: Resistance H. Li et al., IEDM, 2007 CNT via can always be assumed to be electrically ballistic... � With perfect contact, only 800 Via Resistance [ Ω ] smallest SWCNTs have 600 comparable resistance to Cu 400 � With non-zero R mc , SWCNT resistance will be even larger than 200 Cu 500 450 20 15 400 10 350 5 Diameter [nm] 300 MWCNT via SWCNT via R MWCNT Via > R SWCNT Via > R Cu Via (<100 Ω ) ( ~10 Ω ) Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
I mpact of Via Resistance on I mpact of Via Resistance on I nterconnect Delay I nterconnect Delay H. Li et al., IEDM , 2007 5 Local 32 nm Global 4 22 nm 14 nm 3 2 1 0 0 10 20 30 40 50 R CNT /R Cu Local interconnect (M1) Global interconnect (buffered) � Local via resistance has slight � Global via resistance could impact on interconnect have larger impact on performance (electrical latency) performance � If CNT resistance can be within an order of magnitude of Cu via resistance, the delay penalty is small…. Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Thermal Transport in CNT Vias: I s I t Thermal Transport in CNT Vias: I s I t Ballistic? Ballistic? � Phonon mean free path ( Phonon mean free path ( L L o ) o ) � � L=2.76 μ m , D=1 nm (SWCNT), T= 100-300 K, ballistic L o >2.76 μ m C. Yu et al., Nano Letter, 2005 � L=2.5 μ m , D=14 nm (MWCNT), T= 10-300 K, estimated L o ~500 nm P. Kim, et al., PRL , 2001 CNT vias (<300 nm) can be regarded as thermal ballistic � Ballistic thermal conductance model of CNT Ballistic thermal conductance model of CNT � ∂ dq f ∑ ∫ = h ω τ ω G q v q q ( ) ( ) ( , ) J. Wang and J. Wang, APL , 2006 th n n n n π ∂ T 2 > n v N. Mingo et al., PRL , 2005 , 0 n ω (q) : phonon dispersion, f( ω ,T) is Bose-Einstein distribution function Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Thermal Conductivity of CNT Thermal Conductivity of CNT H. Li et al., IEDM , 2007 Thermal conductivity ( K CNT ) as a function of D, T and L � K CNT increases with temperature � Smaller diameter SWCNT has higher K CNT � For long length, K CNT >> K Cu � For short length (via case), K CNT ~ K Cu Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Electro-thermal Simulations Electro-thermal Simulations H. Li et al., IEDM , 2007 Cu: T max occurs at M2 SWCNT ( D = 0.47nm ): Perfect contact T max occurs at M2, ~ T max of Cu MWCNT ( D =5 nm ): Perfect contact T max >> T max of Cu - Contact is the bottleneck - Large Joule heating due to large electrical contact resistance Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
I mpact of I ncreasing Via Height I mpact of I ncreasing Via Height H. Li et al., IEDM , 2007 Advantage of ballistic CNT: K CNT Via and R CNT Via remains the same for tall vias � T max of Cu via increases with height Max. Temperature [K] � T max of SWCNT via almost remains constant � Even with imperfect contact, SWCNT could be better than Cu for tall vias � MWCNT via is worse than Cu even at 300nm height Dense and small diameter SWCNT vias with good electrical and thermal contact are needed…..and would be better as tall vias Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Outline Outline Part I I : Part I I : � Performance Evaluation of CNT/GNR Interconnects Performance Evaluation of CNT/GNR Interconnects � � Electro Electro- -thermal Analysis of CNT thermal Analysis of CNT Vias Vias � � High High- -Frequency Analysis of CNT I nterconnects Frequency Analysis of CNT I nterconnects � � Passives and Other Applications Passives and Other Applications � Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
High-Frequency Effects in Cu High-Frequency Effects in Cu Skin effect Skin depth: 1 δ = πμσ f Krauter et al., DAC, 1998 Proximity effect Z = R + j ω L � Current distribution is no Current distribution is no � Resistance increases due Resistance increases due � � longer uniform longer uniform to skin & proximity to skin & proximity effects effects What will happen in CNT interconnects? Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Magnetic I nductance of I ndividual CNT Magnetic I nductance of I ndividual CNT � Using Geometric Mean Distance (GMD) to calculate inductance. � GMD is valid if we assume current in each CNT to be uniform. � Self Self- -inductance inductance H. Li et al., TED , vol. 56, no. 10, 2009 � μ ⎡ ⎤ 2 L AMD self = ⋅ − + 0 L L ln 1 ⎢ ⎥ CNT π 2 ⎣ GMD L ⎦ = − ξ ln GMD ln D ln out ζ = − γ − γ + γ γ = 2 4 ln 0.1( a b c d ), D / D in out = = = = a 2.51, b 0.31, c 3.81, d 1.61 2 D ≈ AMD out Arithmetic Mean Distance π � Mutual inductance Mutual inductance � ⎡ ⎤ ⎛ ⎞ μ 2 2 L L S S = ⋅ ⋅ ⎢ ⎜ + + ⎟ − + + ⎥ L 0 L ln 1 1 ⎜ ⎟ m π 2 2 2 S S L L ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ S Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
I mpedance of CNT Bundle I mpedance of CNT Bundle H. Li et al., TED , vol. 56, no. 10, 2009 � Impedance matrix Impedance matrix � ⎡ ⎤ ω ω 1 21 n 1 Z j L j L L CNT m m ⎢ ⎥ ω 21 2 ω n 2 j L Z j L L ⎢ ⎥ [ ] = ⎢ Z m CNT m ⎥ matrix M M O M ⎢ ⎥ ω ω n 1 n 2 n ⎢ j L j L Z ⎥ L ⎣ ⎦ m m CNT = ω + + i Self kinetic i Z j ( L L ) R CNT CNTi CNTi CNT = + λ = Ω i SWCNT R , R (1 L / ), R 6.5 K CNT Q Q ∑ = = + λ λ = i MWCNT R , 1/ 1/ R , R R (1 L / ) / N , 1000 D CNT shell shell Q shell shell [ ] [ ][ ] = ⇒ = + ω V Z I Effective Z R j L matri x bundle tot to t � Each self-impedance (Z i CNT ) includes R, L self , and L K � Effective value of total inductance and total resistance of CNT bundle can be calculated Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Understanding of Current Redistribution Understanding of Current Redistribution Impedance of each filament Impedance of each filament Z = Z + Z Self mutual 3D metal: no L K 3D metal: no L 1 � � K – low frequency, R ( Z self ) dominates, Z 1 ~Z 2 – high frequency, j ω L becomes important 2 1 2 � Z 1 > Z 2 � nonuniform current � skin effect Z > Z Mutual Mutual CNT: has large L K CNT: has large L � � K Z = R + j ω L + j ω L Self self K 1 L K > > L Mutual ， Z >> Z Self Mutual Z 1 ~ Z 2 � 2 Negligible skin effect Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
High-Frequency I mpedance of CNT High-Frequency I mpedance of CNT 0.68 30 Cu wire SWCNT D=1nm, Fm=1 25 MWCNT D=20nm 0.66 Inductance [nH] MWCNT D=40nm Resistance [ Ω ] MWCNT D=40nm 20 Length = 500 μ m MWCNT D=20nm Width=2 μ m, Height=1 μ m SWCNT D=1nm Fm=1 0.64 15 Cu wire Equivalent d.c. Equivalent d.c. Conductivity Model Conductivity Model 10 0.62 Length = 500 μ m 5 Width=2 μ m, Height=1 μ m 0.60 1 10 100 1000 1 10 100 1000 Frequency [GHz] Frequency [GHz] H. Li et al., TED , vol. 56, no. 10, 2009 SWCNT: resistance/inductance saturate at high frequencies � MWCNT: resistance/inductance negligible shift � Reduced skin effect in CNT interconnect! � Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
High-Frequency Behavior of CNT High-Frequency Behavior of CNT Bundle—From Maxwell’s Equations Bundle—From Maxwell’s Equations H. Li et al., TED , vol. 56, no. 10, 2009 u r u r 2 E ∇ = ωμσ j E 2 ⎡ ⎤ δ = ⋅ ωτ 2 + ⋅ ωτ 2 + − ωτ [( ) 1] ( ) 1 ⎣ ⎦ ωμσ 0 ω τ ~1 Skin Depth [ m] CNT: skin depth saturates after � certain frequencies Saturation depends on the � momentum relaxation time MWCNT has largest skin depth � and lowest saturation frequency ω τ <<1 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Outline Outline Part I I : Part I I : � Performance Evaluation of CNT/GNR Interconnects Performance Evaluation of CNT/GNR Interconnects � � Electro Electro- -thermal Analysis of CNT thermal Analysis of CNT Vias Vias � � High High- -Frequency Analysis of CNT Interconnects Frequency Analysis of CNT Interconnects � � Passives and Other Applications Passives and Other Applications � – CNT Based Inductors and Capacitors CNT Based Inductors and Capacitors – – CNT Off CNT Off- -chip Applications chip Applications – – CNT NEMS CNT NEMS – – CNT ESD applications – CNT ESD applications – System System- -level Applications level Applications – Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
H. Li et al., TED , vol. 56, no. 10, 2009 CNT Based I nductor CNT Based I nductor S � Metal contact at each corner Metal contact at each corner � Metal D out Contact � Take advantage of high Take advantage of high- - CNT � W Bundle frequency properties of CNT frequency properties of CNT bundle bundle Ls & Rs: Using previous method � – Ls: including kinetic and magnetic inductance – Rs: includes R Q, R S , and R mc Since the CNT bundle cross-sectino is � very large ( μ m order), C Q is very large and can be neglected I I C S , C ox and C C sub is using distributed C S , C ox and sub is using distributed � � capacitance model capacitance model L L eddy eddy and R and R eddy eddy are captured by complex are captured by complex � � image theory image theory Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
I mpact of Kinetic I nductance on Q-factor I mpact of Kinetic I nductance on Q-factor H. Li et al., TED , vol. 56, no. 10, 2009 � Consider upper Consider upper- -bound of Q factor bound of Q factor ω ω L L tot /R tot /R � – – Has two component in CNT Has two component in CNT ω ω L = = + = + tot Q ( L L ) Q Q upbound m k mag kinetic R R Q factor due to L K Traditional Q factor 0.07 ω L × L L N / K _ Bundle 0.06 = = ω k Q Q factor due to L K kinetic ⎛ ⎞ L R 10GHz + 0.05 R 1 N Bundle ⎜ ⎟ 50GHz Q λ ⎝ ⎠ 0.04 100GHz λ ⋅ L L 1 0.03 = ω < ω ⋅ k k ⎛ ⎞ R 1 1 R + 0.02 Q Q ⎜ ⎟ λ ⎝ L ⎠ 0.01 λ =1 μ m, L k =4nH/ μ m, R Q =6.5K Ω 0 0 1 2 3 4 10 10 10 10 10 Q kinetic < 0.062 at 100 GHz Kinetic inductance itself has very little impact on Q… Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Role of Kinetic I nductance Role of Kinetic I nductance � Although, L Although, L K itself has marginal impact on Q factor… … K itself has marginal impact on Q factor � – L – L K K increases the total inductance increases the total inductance – More importantly, L More importantly, L K reduces skin & proximity effects – K reduces skin & proximity effects at high frequency in CNT interconnects at high frequency in CNT interconnects – Prevents decrease of total inductance with frequency Prevents decrease of total inductance with frequency – – Prevents increase of resistance with frequency Prevents increase of resistance with frequency – � Very promising for high Very promising for high- -frequency interconnect frequency interconnect � application application – Inductor design: potential low loss, high – Inductor design: potential low loss, high- -Q Q… … Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Q Factor Comparison Q Factor Comparison H. Li et al., TED , vol. 56, no. 10, 2009 D out =200 μ m, N=4, 70 142% ρ sub = 10 Ω -cm W=10 μ m, H=2 μ m, S=1 μ m 60 Cu SWCNT Fm=1/3 50 SWCNT Fm=1 Quality Factor -cm] MWCNT D=10nm 40 MWCNT D=20nm Resistivity [ MWCNT D=40nm 30 20 10 0 0.1 1 10 (a) Frequency [GHz] CNT can give better performance than Cu CNT can give better performance than Cu � � – MWCNT can obtain 2.4 times higher Q factor than that of Cu MWCNT can obtain 2.4 times higher Q factor than that of Cu – – Even for higher resistivity case (D=10 nm), still have higher Q Even for higher resistivity case (D=10 nm), still have higher Q – – I ndicating reduced skin effect has significant impact – I ndicating reduced skin effect has significant impact Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Q Factor Comparison (Ultra High-Frequency) Q Factor Comparison (Ultra High-Frequency) H. Li et al., TED , vol. 56, no. 9, 2009 60GHz 231% ρ sub = 10 Ω -cm 100 Cu SWCNT Fm=1/3 80 SWCNT Fm=1 Quality Factor MWCNT D=10nm MWCNT D=20nm 60 MWCNT D=40nm 40 20 0 1 10 100 Frequency [GHz] Advantage of CNT is enhanced for ultra Advantage of CNT is enhanced for ultra- -high high- -frequency frequency � � applications applications Maximum Q factor enhancement is 3.3 times! Maximum Q factor enhancement is 3.3 times! � � Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT Based Capacitor CNT Based Capacitor Expectation of CNT capacitor: Expectation of CNT capacitor: � High density due to small form factor of High density due to small form factor of CNTs CNTs � � High aspect ratio, especially for DRAM applications High aspect ratio, especially for DRAM applications � � Lower electrode resistance Lower electrode resistance � � Higher Q factor Higher Q factor � � Higher switching speed Higher switching speed � Important concern: Important concern: � Lower leakage current Lower leakage current � Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Fabricated MWCNT Based Capacitor Fabricated MWCNT Based Capacitor 6.5fF/ μ m 2 10 μ m 1e -8 A/cm 2 (ITRS 2014) J. E. Jang, et.al., ESSDERC, 2005 Diameter: 70nm Height of MWCNT: 3.5um Can not match the ITRS requirement at 2014, Insulator thickness: 65nm need more efforts… Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT Based Capacitors CNT Based Capacitors H. Li et al., TED , vol. 56, no. 9, 2009 Take advantage of bottom up approach to achieve high aspect ratio… 210 nm 20 nm 480 nm 20 nm (a) Circular Electrostatic capacitance Total effective capacitance Height = 1 μ m density (fF/ μ m 2 ) density (including C Q , fF/ μ m 2 ) Circular 31.76 30.65 Square 39.48 38.39 (Dense, d = 0.34 nm) Square 30.25 28.99 (Sparse, d = 20 nm) Much larger than ITRS requirement for 2014: 7 fF/ μ m 2 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT Off-chip Applications CNT Off-chip Applications Some Concerns and Requirements Some Concerns and Requirements � Form factor: Form factor: � – Number of I/O pads – Number of I/O pads – Area of pads – Area of pads – Smaller form factor is required – Smaller form factor is required � Low parasitics: Low parasitics: � – Lower inductance Lower inductance – – Lower noise Lower noise – � Good thermal properties Good thermal properties � – Heat dissipation Heat dissipation – � High predictability High predictability � – Easier to model and design Easier to model and design – � High reliability High reliability � – Electromigration Electromigration – – Thermal/Mechanical Thermal/Mechanical – Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Example 1: Flip-chip Bumps Example 1: Flip-chip Bumps T. Iwai et al., IEDM., 2005 (Fujitsu) 12 μ m MWCNT, D~10 nm Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Example 2: TI M for Packaging Example 2: TI M for Packaging K. Zhang et al., ICEPT., 2006 (HKUST) MWCNT, D= 20-30 nm Length ~ 50 μ m Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Example 3: Chip Cooling Example 3: Chip Cooling K. Kordas et al., APL, 2007 (RPI ) CNT Heat Spreader, 1*1 mm MWCNT, Length~1.2 mm, D= 10-90 nm N 2 gas flow Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT Transfer Tech. CNT Transfer Tech. L. Zhu et al., Nano Lett ., 2006; L. Zhu et al., MRSSP , 2007 High temperature CVD High temperature CVD � � growth (@ 775 growth (@ 775 o o C C) ) Open Open- -ended ended CNTs CNTs � � Low temperature Low temperature � � bonding (@ 270 o o C C) ) bonding (@ 270 Substrate is Cu Substrate is Cu � � CNTs break along the axis rather than at the CNT-solder interface Open-ended CNTs Closed-ended CNTs Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT Vias in 3D-I C Applications CNT Vias in 3D-I C Applications CNT through- -wafer via wafer via CNT through � High aspect ratio (>10) High aspect ratio (>10) � μ m � Long length (>100 Long length (>100 μ ) m ) � Process steps: Process steps: Through holes in the top wafer Through holes in the top wafer ① ① Bonding layer is deposited onto Bonding layer is deposited onto ② ② top wafer top wafer Catalyst film is deposited onto the Catalyst film is deposited onto the ③ ③ bottom layer bottom layer Two wafers are bonded together Two wafers are bonded together ④ ④ Grow CNT via thermal CVD Grow CNT via thermal CVD ⑤ ⑤ T. Xu et al., APL ., 2007 Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT NEMS…. CNT NEMS…. CNT-based Relay H. Dadgour et al., IEDM, 2008 Lee, et al. Appl. Phys. 2003 CNT NEMS can operate in GHz GHz range due to very small mass range due to very small mass CNT NEMS can operate in � � Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
ESD Metal Current Density ESD Metal Current Density C. Duvvury, IEDM ., 2008 Failure current decreases with scaling Failure current decreases with scaling � � High current carrying capability material will be preferred High current carrying capability material will be preferred � � Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Using CNT to Enhance Charge Using CNT to Enhance Charge Dissipation Dissipation � The rate of charge dissipation is governed by The rate of charge dissipation is governed by � τ = = ρε ρε τ , resistivity of material ρ , resistivity of material – – ρ ε , permittivity of material , permittivity of material – ε – � Applications in Polymer filling Applications in Polymer filling � – By filling MWCNT, it will By filling MWCNT, it will – ρ is small since MWCNT has good conductance is small since MWCNT has good conductance � ρ � ε is small since the filling fraction could be small due to its h is small since the filling fraction could be small due to its high aspect ratio igh aspect ratio � ε � – Desirable for fast charge dissipation Desirable for fast charge dissipation – � One of the largest bulk application of One of the largest bulk application of CNTs CNTs today today � – Company: Company: Hyperison Hyperison Catalysis International Catalysis International – Hyperion Catalysis (www.fibrils.com) Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
ESD Protection Using MWCNTs in ESD Protection Using MWCNTs in Polymer Polymer Hyperion Catalysis (www.fibrils.com) Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
CNT I nterconnects: System-Level CNT I nterconnects: System-Level Applications ? Applications ? CNT I nterconnect Enhanced: CNT I nterconnect Enhanced: � Memory (Cache) design Memory (Cache) design � � FPGA design FPGA design � � Network Network- -on on- -chip design chip design � � Multi Multi- -core processor design core processor design � Note: it is important to use the correct physical and compact models for CNT/GNR, depending on the application…. Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
Summary Summary 1.4 20 Cu wire SWCNT D=1nm, Fm=1 1.2 Lower MWCNT D=20nm d-GNR ( p =0.41) Lower d-GNR ( p =1) MWCNT D=40nm Negligible Resistance [ Ω ] latency latency 1.0 Length = 500 μ m SWCNT ( Fm =1) skin Width=2 μ m, Height=1 μ m 10 for long for long SWCNT ( Fm =1/3) 0.8 8 effects DWCNT (D=1.5nm) wires wires 6 MWCNT (D=14nm) 0.6 4 0.4 2 100 1000 1 10 100 1000 Length of Interconnect [ m] Frequency [GHz] S Metal D out Contact CNT W Bundle Off-Chip and Through-Silicon Vias Promising for passive devices Promising for passive devices Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA
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